Contents

 

Introduction

 

1. Theory

Refinement

EXAFS theory

Muffin-tin potential

Exchange

Phaseshift Calculation

Disorder

Mean square variation in path length

Calculation of atomic correlations

Polarisation dependence

Amplitudes

Statistical Terms

 

2. Program Guide

Command Syntax

Abbreviations

Command List

Command Documentation

Parameters and Options

Reading in spectra

Defining the structural model

Defining atom types

Defining the Symmetry

Multiple Clusters

Mixed Sites

Phaseshifts - introduction

Calculating Potentials

Muffin-tin Radii and related Parameters

Calculating Phaseshifts

Calculating the Theory

Refinement

Plotting the Spectra

Output files

Disorder

Multiple Oxidation States

Multiple Spectra

Multiple Scattering

Units

Constrained Refinement

Rules and Cell Parameters

Restrained Refinement

Metallo-proteins

Single Crystals and Surfaces

Whole-spectrum fitting

Startup files

Bond Valence Sums

 

3. Examples

Copper Foil

Whole Sectrum Refinement ofCopper Foil

Gallium Antimonide

Cu-Zn Superoxide dismutase

Tetrakis imidazole Copper(II) Nitrate

Surface parameters

Fe tris(DMPP

 

4. Parameters

Terminology

Parameter Definitions

1. Cell parameters

2. Shell parameters

3. Unit parameters

4. Phaseshift parameters

5. Site parameters

6. Spectrum parameters

7. Theory parameters

8. Control parameters

9. Fourier Transform parameters

10. Surface parameters

11. XANES parameters

12. Restrained refinement parameters

13. Bond parameters

Parameter usage

1. The crystallographic cell parameters

2. Shell parameters

3. Unit parameters

4. Phaseshift parameters

5. Site parameters

6a. Spectrum parameters - beam polarisation parameters

7a. Theory parameters - multiple scattering parameters

7b. Theory parameters - energy parameters

7c. Theory parameters - whole-spectrum parameters

8. Control parameters

9. Fourier transform parameters

10a. Surface parameters - surface displacement parameters

10b. Surface parameters - the surface relaxation parameter SURREL

11. XANES parameters

12. Restrained refinement parameters

 

5. Command Reference

ALIAS

ANGLE

CALC

CCHANGE

CHANGE

COMPARE

CONFIG

COPLOT

DEBYE

DISPLAY

DRAW

END

EXPAND

EXTRACT

FFILTER

FIT

FTSET

GENERATE

GSET

HELP

IDEALISE

INFO

INQUIRE

LIST

MAP

PLANE

PLOT

PRINT

READ

RECOVER

REFINE

ROTATE

RULE

SAVE

SET

SITE

SORT

SPARE

STATS

STRUCTURE

SYMMETRY

TABLE

TIME

UNDO

XADD

XANES

 

6. Tables

 

Glossary

 

Bibliography

 

Index

 



 

Introduction


EXCURVE was written in 1982 as an alternative to the programs available at the time. It attempted to provide an integrated environment for the analysis of EXAFS spectra while providing a platform for the newly developed fast spherical wave method, later published by Gurman, Binsted and Ross (1984). The current version is based on this method for single scattering, but uses the method of Lee and Pendry (1975) for the exact polarisation dependent theory. Multiple scattering has options to use the methods of Lee and Pendry (1975), Gurman, Binsted and Ross (1986), and Rehr and Albers (1990). It allows fitting of both background-subtracted, and normalised total absorbance spectra. In the latter case the program calculates the atomic contribution of the spectrum. This is referred to as whole-spectrum fitting.


The purpose of the program is to find a structural model of a material which agrees with the available XAFS spectra.


In order to evaluate a structure, a model must first be defined in terms of one or more clusters of atoms, weighted according to the average composition of the material. Clusters may represent different atomic sites in a single phase, or multiple phases. A full description of each cluster requires :


1. the radial or cartesian coordinates of scattering atoms about each absorbing atom for which spectra are available

2. a pair distribution function for each symmetrically unique excited-atom/scattering atom pair

3. the point group of each cluster


The parameters used to define the model may be refined until optimum agreement with the XAFS data is obtained.


Refinement may use additional data to that given by XAFS spectra, for example distance and angle restraints using bond distances obtained by other techniques.


For crystalline solids, cluster information may readily be obtained from a crystallographic model. In this instance, the point symmetry of each site is defined and therefore all the distances and angles within the structure. A full multiple scattering calculation may then be performed.


For amorphous solids, only the partial radial distribution functions for pairs of atoms are defined, and the calculation is in general limited to single scattering.


In other instances, a model of the solid may include certain bond angles, or the presence of well-defined groups, which permit a limited treatment of multiple scattering. Such an approach is typical of metallo-proteins.


The manual is organised into a Theory section, a Program Guide, an Examples section, and Reference sections on parameters and commands, terminated by Tables. The program guide is largely a sequential guide, terminated by discussion of topics which might initially only be used optionally. Most of the background knowledge required is included in the theory section, but a basic knowledge of quantum mechanics is assumed, as is a knowledge of Unix or DOS commands, which can be used within the program to supplement the built-in commands. The reference sections contain definitions of the parameters and commands needed to analyse data, with information essential to their use but with a minimum of background material. References quoted in the text, together with others that might be useful, are given in the bibliography.


Acknowledgements.


We are grateful to the University of Washington, WA, and especially to Prof. J.Rehr for permission to use code derived from FEFF in calculating the Hedin-Lundqvist excited state exchange and correlation potential.


The refinement routine VA05A is used under licence from UKAEA, Harwell Laboratory.



1. Theory


This section discusses the calculation of the theoretical spectra, the way in which differences between theory and experiment are minimised, and the criteria used to define the best-fitting parameters.


Refinement


Refinement involves minimising the quantity given by:

( 1)



The weightings wexafs etc. determine the relative significance of the EXAFS, distance, and angle contributions. The sum wexafs + wdistances + wangles must equal one.


Often, only the XAFS contribution is used. The other two terms are restraints, used in special circumstances where a model includes well characterised groups of atoms.


The EXAFS contribution is given by:

( 2)



χexp(k) and χth(k) are experimental and theoretical XAFS:

( 3)



Here k is the magnitude of the photoelectron wavevector.


The distance and angle contributions to the refinement are:


( 4)




                            with:

( 5)



                            and:


( 6)



                            with:


( 7)




Where rref and rmodel refer to refined and model distances respectively, and where βref and βmodel refer to refined and model angles.



Calculation of the EXAFS theory


Analysis of XAFS spectra is greatly simplified by the fact that in a single particle approximation, provided coupling between final states is ignored, the atomic contribution (μ0) and the scattering contribution (χ) to the total absorption (μ) may be separated, as in:


( 8)



where the sum is over all allowed final states lm and the atomic contribution to the cross section, μ0lm (E) is given in the dipole approximation by the Golden rule expression:


( 9)



Here e is the electric vector of the photon, r the position with respect to the atomic nucleus and D(E) the energy density of final states. D(E) depends on the way the wavefunctions are normalised and is usually 1 for Rydberg states below the ionisation threshold and proportional to k, the magnitude of the photo-electron wave vector for a free electron.


Unless otherwise stated, Hartree atomic units (h=e=m=1) are used to avoid unnecessary constants, hence the unit of μ is here the square of the Bohr radius.


Many-body effects may be included approximately within this basic formalism, for example by including additional terms for two-electron transitions, and by using effective one-electron potentials calculated for an embedded atom with a complex energy to account for inelastic losses to represent the true many body potential.


It is normal to separate the oscillatory part of the experimental spectrum, χ, from the atomic contribution by means of a background subtraction, in which the atomic background is approximated by polynomial or spline functions. Here it is assumed that this has been done, and it is only necessary to calculate the oscillatory part. This is not the case with XANES or whole-spectrum fitting.


For an amorphous or polycrystalline sample, the oscillatory part of the spectrum due to a transition to a specific final state l is:


(10)



The final exponential factor is a phase term due to the outward and inward passage of the photoelectron through the central atom potential. It is described in terms of the atomic phaseshift δl, which is described later. The m sum is over all allowed quantum numbers -l ≥ m ≥ l.


Z is expanded as a scattering series:


(11)



Z1 includes a sum over all atoms, excluding the central atom, Z2 a sum over all pairs of atoms i ≠ j, etc.


For single scattering from an atom at (r,Ω):


(12)



Simple algebra leads to the well known expression of Gurman, Binsted and Ross:


(13)




The l sums are strongly restricted by the rules on coupling of angular momentum: (l1+l2+l) even, l2≤l1l, l1≥l2-l. This results in just two terms for a K-edge, 3 for an L3, etc. The 3J coefficient above is that of Brink and Satchler (1968), also given by Zare (1988).


The equation above refers to atoms in fixed positions r. Disorder is expressed as a pair distribution function g(r) describing the motion of a scattering atom relative to the central atom. In the case of static disorder, g(r) may also describe the distribution of an atom in a disordered site, again relative to the excited atom:

(14)




Where Z0 is calculated neglecting all thermal or static disorder.


Traditionally this has been approximated by:


(15)



Here, even if Z is calculated exactly using a spherical wave theory, disorder is treated in a plane wave approximation, which ignores terms due to spherical-wave effects (see Rennert, 1992/3). This approximation gives rise to the familiar exponential Debye-Waller factor. This expression also ignores anharmonic contributions, that is the cumulant expansion of g(r) involves no terms of higher order than two. In this event, g(r) is a Gaussian characterised by σ:


(16)



Also ignored here are terms arising from motion of the atoms in the plane normal to the interatomic bond. The inclusion of these would give rise to multi-dimensional distribution function g(r). The treatment of disorder is discussed at greater length below.


For the single-scattering, polarisation independent expression above [13], all the structural information is included in the Hankel functions h(kr). Similarly all the information on the scattering atoms is contained within the T matrix, whose l'th element is given by:


(17)




Here it is assumed that T is diagonal, that is, that the scattering potential is spherically symmetric. The atomic scattering phaseshifts which define Tl have already been encountered in the description of the central atom phase. The scattering phaseshift, δl, for each partial wave of angular momentum l contains all the information that is needed to completely describe the scattering properties of an atom.


Muffin-tin potential


Before discussing the calculation of the phaseshifts it is necessary to introduce a model for the atomic potentials in a solid.

In a free atom, the electron density near the nucleus is associated with tightly bound, relatively localised orbitals. Valence orbitals are less localised, and there is finite electron density well beyond what would normally be considered the atomic radius. An example is shown in figure 1 (top). This is the radial charge density, 4/3πr3ρ, calculated for Cu, using a relativistic Hartree-Fock program. This was used to generate the charge-density tables for the program. The program calculates potentials and charge densities self-consistently in the one-electron approximation, in which the complex many-body interactions between electrons are approximated by an effective one-electron potential. A potential is the best way of representing the force on an electron due to its electro-static interaction with the nucleus and other electrons. The potential also includes the quantum effects of exchange and correlation, which lower the potential further relative to a purely electrostatic model. The one electron potential can be used to calculate the Schrödinger wave functions ( or their relativistic equivalents, the Dirac wave functions) either for an electron in the atom, or a photo-electron passing through it.

It is not necessary to tabulate both the charge-densities and the potentials - the effective one-electron potential can be recovered from the charge density using Poisson's equation:


(18)



In XAFS however, what is usually required, is a potential for a solid or molecule rather than a free atom. The muffin-tin approximation is a simple model of a solid. The solid is defined as an array of touching spheres, using a regular lattice, such as FCC, BCC. Inside the spheres the potential is atom-like (though with spherical symmetry). Between the spheres (26% of the crystal volume for FCC), the potential is a constant value, obtained from averaging the potential in this region. The justification for this model is that the potential due to overlapping those of individual atoms, is lowered, and flattened relative to the free atom in this region. The Muffin-tin potential is further lowered relative to the free-atom potential by a term for the exchange and correlation energy of the photoelectron. An example is shown in figure 1 (bottom). This is for FCC Cu, looking along the (110) direction of the crystal. The solid lines are the overlapped free atom potentials. The dotted line is the muffin-tin potential for the solid, including the ground-state exchange contribution. An excited state exchange contribution (a +ve correction which raises the potential), is added later. It depends on the energy of the

photoelectron.

exfig1.gifFigure 1: Atomic Charge Density (above) and Muffin-tin potential (below) for Cu.

Ground state Exchange and Correlation potential


  The correct treatment of exchange is controversial. Indeed, in view of the simplicity of the model that is used, and the wide range of compounds to which the method is applied, it is unlikely that a single equation will give the best results in all cases. The program has two options for the ground state exchange term, and two for the energy dependent excited state term. Evaluating the four resulting options can provide weeks of amusement. For ground state, the two schemes are the X-α and the von-Bart and Hedin terms. These are both functions of the local electron density ρ(r). The X-α formula, in Rydberg atomic units is (Clarke, 1984):


(19)



where α normally takes a value of 2/3 and with α=1 is equivalent to the Slater free electron formula.


The von Barth and Hedin (1972) formula is:


(20)




The appropriate term is used both in the Hartree-Fock calculations used to derive the atomic charge-densities and in the photo-electron exchange and correlation. There is no consistent preference for either of the two approaches, either in terms of quality of fit or agreement with crystallographic results. Where a significant difference occurs, it is usually due to a small energy shift in a resonance where one of the phaseshifts goes through π/2. In applying the Mattheis method to compounds other than the metals or van der Waals solids for which it was designed it might be expected that some flexibility needs to be introduced to ensure alignment of these features.


Phaseshift Calculation


Within the muffin-tin model, the electrons outside the spheres can easily be described as complex spherical Bessel functions, with the photoelectron described as a sum over many partial waves of given angular momentum when it is necessary to describe it with reference to a point other than the centre of the excited atom. It is never actually necessary to know what happens inside the spheres. It is only necessary to know 1. the phase-change when passing in and out of the central atom and 2. how an electron is scattered by the sphere.


Quantum scattering is totally unlike classical scattering. An electron is scattered whenever there is a change in potential. In the constant potential region there is no scattering. At the muffin-tin boundary, where there is a small, and rather unrealistic step, and within the sphere, there is a scattered and transmitted wave, the intensity of each of which varies continuously. In practice, most of the scattering occurs where the potential varies most strongly, which is near the nucleus. All that is required to describe scattering completely is the phaseshift evaluated at the muffin-tin boundary. This is given by δl in:


(21)




where the β are forms of complex spherical Bessel function, and the L are logarithmic derivatives of the Schrödinger (or Dirac) wave function given by:


(22)



Evaluation of L involves an integration of the potential, out to the muffin-tin radius, using the boundary conditions that φ must not be singular at the origin, and must match the photoelectron wave (spherical Bessel function) at the sphere radius. The program optionally allows for scalar relativistic terms, i.e. ignoring those involving spin-orbit coupling. If necessary, the wave-function itself, and the dipole transition rate between a core state and φ may be evaluated so the atomic contribution to XAFS can be included.


Because the excited state contribution to the potential includes the effect of inelastic losses, due to core-hole lifetimes and electron inelastic scattering, the wave-function, the phaseshift and the scattered wave intensity given by exp(2iδl) are all complex, the imaginary part of δl being derived from the imaginary potential.


Disorder


Thermal and static disorder have a significant effect on both XRD and EXAFS spectra, yet in neither technique is disorder treated exactly. The approximations used might be expected to give rise not only to incompatible values for the disorder parameters but also systematic errors in distances. This means that distances and disorder parameters may not be comparable between the two techniques. The treatment of disorder attempts to minimise these problems, using methods outlined in Binsted, Pack, Weller and Evans (1997).


Information on disorder in solids is often derived from structure determinations by X-ray or neutron diffraction.

For X-ray and coherent neutron methods it is usual that the thermal disorder associated with each atom is represented in the harmonic approximation by a mean square displacement <u2(r)>, with components <u2x>, <u2y>, <u2z>. In the case of powder diffraction, or low resolution single crystal refinements, it is further assumed that motion is isotropic and can be represented by an isotropic thermal factor given by:


(23)




An exact treatment of disorder in both techniques requires a configurational average over all possible atomic positions. For EXAFS each path can be treated individually, giving rise to an integral over the three coordinates of each atom in the path:


(24)



If many-body correlations are ignored these integrals are of the form:


(25)



Where the g are pair distribution functions for each leg of the scattering path for each coordinate (x,y,z).


For single scattering only, if isotropic motion of each atom is assumed, equation (25) reduces to a single integral over the mean interatomic separation rm, as assumed in (14). Due to the effect of motion in three dimensions, rm differs from the equilibrium separation between atoms r0 by rm = r0+σ2/2r0 where σ2, the mean square separation in interatomic positions, is assumed small in comparison with r0. This makes the assumption that correlation is isotropic, although this is unlikely to be the case. Indeed, normal to the bond, motion is as likely to be anti-correlated as correlated. This integral can be evaluated numerically, avoiding further approximations, or else solved assuming the asymptotic form of the Hankel functions, h(kr) = 1/(kr) eikr. An approximate solution in one dimension has been given by Tranquada and Ingalls (1983), which, separating the r-dependent terms in the expression for χ(k) is:


(26)



where:

(27)



 

Previously only the Debye-Waller factor e-2σ2k2 , neglecting the phase term, has been used. In EXCURVE there are two options, one to perform the integral numerically, and one to use a plane-wave Debye-Waller factor but including the phase term. Using the numerical integral automatically includes spherical wave effects. Failure to include the phase term produces a small but significant apparent shortening in EXAFS distances in most cases. When disorder is large, as in inert gas solids, neglecting this term will give significant errors, such as the apparent thermal contraction noted by a number of authors ( see for example Beattie et. al. (1990)). If the term due to three dimensional motion is included, the overall distance correction will be smaller than that of Tranquada and Ingalls (1983). An option to include this term is present in the program. but due to lack of theoretical or experimental evidence for the model of 3D correlation, and the fact that it does not seem to improve agreement with crystallographic results, its use is not recommended at present.

 

The Debye-Waller term can be generalised to e-1/2σp2k2 where σp is the mean square variation in path-length. The same expression then describes the amplitude term for multiple scattering paths in addition to single scattering. Numerical results indicate that the phase terms are less significant for most MS paths than for single scattering, and for simplicity are neglected. The effects of disorder on bond angles can be represented by calculating the mean bond angle at each atom. This differs significantly from the equilibrium value only for angles close to 1800 when disorder will always result in smaller values. MS is particularly sensitive to changes in angles for these values hence the effects can be important and are included in the calculations.


Third and fourth order cumulant terms can now be used in the program both in the direct integrals and when using the plane-wave Debye Waller terms. If thermal expansion can be adequately represented by an isotropic coefficient of linear expansion, then only the linear expansion coefficient, α, need be entered in order to calculate the third cumulants for all the shells. This is done using an anharmonic oscillator model (see Edwards et.al.,1997). The third cumulant terms appear to make a noticeable contribution to the spectrum and their use in phases such as Cu where the model is good ( at least for shells 1,4 etc.) is being evaluated. It is not recommended that higher cumulants are refined - they are so strongly correlated with other variables (eg C3 with EF+R1) that almost any solution will appear successful.


An additional model of disorder, using a truncated exponential convoluted with a gaussian, is also included in the program. This is appropriate for certain systems of high disorder, such as in melts and ionic solids, where the series of cumulants fails to converge.


Mean square variation in path length


The mean square variation in path length can be expressed in terms of the atomic mean square displacements <ua2>, <ub2> etc. for each atom and the correlations between pairs of atoms Cab. Here anharmonic or anisotropic effects introduced by correlation and many-body correlations are ignored, although they may be important in many cases, and our intention is to include them in future versions of the program.


The expression for the mean square variation in path length takes into account the fact that the photoelectron velocity is fast in comparison with thermal motion. If an atom is included in n legs of the scattering path, the contribution it makes to σp is n times of an atom at a 'loose end'. For σp2 the contribution is n2 times. This is an important factor leading to a reduction in the contribution of triple scattering paths involving only two or three atoms, such as paths 0-a-0-a-0 or 0-a-b-a-0 ( 0 is the central atom ). For single scattering this generates the traditional term:


(28)




 

where the mean square relative displacement σab2 is:


(29)



The general result for σp2 is:


(30)



The effective correlations Ce are dependent on all the angles in the path. This can be appreciated by taking a long linear chain of atoms. The correlation effecting an atom at one end is that with the atom at the other end, not any of the atoms in between. If the chain departs from linearity, the intervening atoms will all make some contribution. No accurate solution to this problem has been obtained; it is assumed that all the correlations contribute with a relative weight determined by the same cos2(α/2) dependence as in equation 30. Ce is therefore given by:


(31)




The equation only applies where there is a unique angle at each atom. Complex paths with many non-parallel legs involving the same atom are treated differently using further approximations..


Calculation of atomic correlations.


In order to obtain meaningful Debye-Waller factors it would be desirable to use just a single isotropic thermal parameter for each crystallographic site. In order to derive EXAFS Debye-Waller factors however, it is necessary to calculate the correlations between them as defined by equation (31) . The best way to do this is by means of a common theory which will generate both the atomic mean square displacements, <u2> and the correlations Cab. This can be done using Debye theory. A widely used expression for a monatomic cubic solid is given by Beni and Platzmann, 1976. The results of applying this to copper are given below. This expression has been generalised for binary metal oxides, but agreement with experiment in this case requires ad hoc expressions for the mass dependence which are still being investigated.


In many cases, for example where strongly covalent bonding occurs, Debye theory would not be expected to work. In such cases there is the option of using a single set of atomic displacements, and specifying the important correlations. Further correlations, which are principally a function of interatomic distance, are interpolated, and assumed to tend to zero for outer shells. A variant of this option which is also available is to define the correlations in terms of three refinable polynomial coefficients. This option ensures a realistic model of disorder for both methods, and reduces the number of free parameters when compared to the third method available, which is to refine XRD and EXAFS thermal parameters independently. In the latter case, because only the mean square displacements relative to the central atom are available, it is necessary to approximate σp2 for multiple scattering by:


(32)



Where the sum is over all unique atoms, and σ20a is the mean square relative displacement between atom a and the central atom (except the case that a is itself the central atom when σ102 is used).





Polarisation dependence


Polarisation dependence enters into the calculation, because in a dipole interaction, the momentum-vector of the emitted electron lies parallel to that of the electric field vector e of the photon. In an isolated atom, the matrix element is zero for transitions to orbitals with an angular momentum vector parallel to e. In a solid, scattering of the final state must be considered. The matrix element is then given by:


(33)



with the final state:


(34)



where |lm> is the unmodified final state wavefunction


Substituting this in the expression for XAFS, without the angle-averaging, only the radial part of the matrix element now cancels top and bottom, leaving:


(35)




In general M is an i by j matrix where, for a specific transition, i is the number of allowed m values for the initial state, and j the number of m values for the final state.


In the case of a K-edge (i=1, j=3) the direction vector M = (A, -B, -A*) is given by:


(36)




Where (θ,φ) is the beam direction and ϖ the azimuthal angle of the e vector, in the notation of Gurman (1988).


In the small atom and plane wave approximations to the scattering matrix Z, the scattered components normal to a particular leg of the scattering path actually go to zero. In this instance the expression above simplifies greatly and goes to:


(37)




where delta is the angle between e and the leg of the scattering path. This approximation is in fact extremely good in the EXAFS region, but becomes very poor very near the edge, where the difference between the different polarisation directions is reduced. The program offers the exact polarisation dependent calculation as an option, at very considerable computational expense.



Amplitudes


The above discussion ignores two factors which govern the EXAFS amplitudes. From equation (10) onwards it was assumed that there is one scattering atom per excited atom, with either a fixed distance, or small variations in distance governed by a pair distribution function g(r). In practice, in order to perform the sum over all atoms, it is necessary to define many shells of atoms, each with an occupation number N representing the average coordination of the excited atoms. The sum over all atoms can then be expressed as the sum:


(38)



 

Where the sum is over all shells k with occupation number N and pdf g(rk). The factor A is the other missing term. In the program it is represented by the parameter AFAC. In other codes it is sometimes called S02. It represents the average proportion of excitations which contribute to EXAFS. That is, it provides a measure of events such two-electron transitions where the energy difference between the photon and the photoelectron is so large that the they are not seen in the spectrum. If the effect of such events are not included in the excited state contribution to the potential, then typically A should be .7 to .9, depending on the edge in question. For a Hedin-Lundqvist potential, however, multi-channel events are included, although only approximately, and only above the plasmon threshold. Although in principal A should be 1 with the HL theory, it may be necessary to use slightly lower or higher values to compensate for errors in the theory. In particular, if the edge region is fitted, a lower value may be required. Adjusting both A and the effective core-hole lifetime to obtain a good fit to a model compound, although theoretically unsound, is often the only possible procedure.



Statistical Terms


The EXAFS R-factor is defined as:


(39)



and gives a meaningful indication of the quality of fit to the EXAFS data in k-space.

A value of around 20% would normally be considered a reasonable fit, with values of 10% or less being difficult to obtain on unfiltered data.


An absolute index of goodness of fit, which takes account of the degree of overdeterminacy in the system is given by the reduced chi2 function. For EXAFS this is (Lytle et al., (1989)):

(40)



where Nind is the number of independent data points and p the number of parameters. Nind is normally less than the number of data points N , and in the case that the data from kmin to kmax is Fourier filtered using a window rmin to rmax it is given by:


(41)



rmin and rmax should indicate the range in r-space actually fitted, not just that where structure is apparent.The variable p should include all parameters refined at any time, not just those included in the last refinement. In the program, Nindis calculated automatically, but may be overridden if the automatic value is inappropriate. p must always be entered by the user. Both these parameters should be quoted and justified along with chi2 if changes in chi2 are to be used as evidence for a fit. The absolute value of chi2 is not meaningful, unless actual experimental statistical errors σi have been read-in, and used to weight the spectra.






 



2. Program Guide


The program is started by typing EXCURVE from a Unix/Linux or DOS command prompt, or using the desktop icon provided. Generally a number of versions are provided, with different dimension limits, which involve trade-offs between, for example, the number of allowed data points, and the number of stored multiple-scattering (MS) paths (which allow rapid refinement of MS Debye-Waller factors, and experimentation with filter conditions).


Command Syntax


The program operates using a series of commands:


                command keyword option


for example:


                SET RELCOR ON


There are also a number of special characters, which will be described before the commands are introduced.


                %


Indicates that control is to pass from the keyboard to a command file. For example:


                %abc


Will execute the commands in file abc before returning to the terminal. The normal way of starting the program is to execute a startup file in this way. The startup file may contain filenames, options and command aliases that are invariably used in connection with a particular compound. Command files may also be used for frequently used command sequences or lists of variables, as with Word-Perfect or assembly language 'macros'.


                !



Is a comment line, usually only used within command files. The only action the program will take is to write the line in question in the logfile and at the terminal.


                ^


Accesses UNIX/Linux sh, or DOS commands - (there is no way of accessing commands unique to csh or other Unix shells, or aliases defined in csh .files). For example:


                ^rm -r ~/*


Will remove the whole of the current users filestore.


                ?


Gives a menu. At the command prompt ( ENTER COMMAND: ), it gives a list of commands. Following a command it gives a list of keywords, and in some cases options. For example:


                REFINE ?


Gives a list of keywords for the REFINE command.


                ;


Has the same effect as a carriage return key. It may be used in order to enter several commands on one line, or at the end of a line, so as to accept a default value and avoid a prompt. e.g.:


                C X1 .1;C X2 0


to change two x-coordinates to .1 and 0 respectively


                PR 1120;


to output EXAFS spectra, using the default filename


                =


Is used as an escape character. It can be used almost anywhere to terminate a command, or skip to the next part of a command. It must be followed by a carrommand. <esc> may also be used, but must again be followed be a carriagew return.



                INFO SPACE;=


will terminate a listing of space group symbols after the first page


Abbreviations

 


Each command can be executed using the minimum unambiguous string that will define the command. Some commands also have specific abbreviations which can be used in place of the minimum string. Keyword abbreviations are treated differently. The first entry in the list of keywords will be used (usually but not always alphabetical). Thus R P will match READ PARAMETERS and READ PHASE, but READ PARAMETERS will be used as it comes first. The names of parameters, such as AFAC, may not be abbreviated. Character options may usually be abbreviated to one letter.


 

Command List


                Command Abbreviations   Function



                ALIAS AL allows you to define your own abbreviations for commands or sets of commands


                ANGLE AN display an angle defined by three atoms


                CALC CA used to calculate atomic potentials and phaseshifts


                CCHANGE CC allows parameters to be changed using constraints


                CHANGE CH C used to change the values of structural and theoretical variables.


                COMPARE COM CM compares another experimental file with the current experiment and theory.


                CONFIG CON configures fonts and other hardware features


                COPLOT COP CP displays fourier transforms at the same time as the theory and experiment.


                DEBYE DE calculates the shell Debye-Waller factors using Debye theory.


                DISPLAY DI shows a table of interatomic distances and angles.


                DRAW DR produces a three dimensional display of clusters, units or paths.


                END END terminates the program.


                EXCLUDE EXC exclude regions of the spectrum from least squares fitting or statistical analysis.


                EXPAND EXP generate a cluster with C1 symmetry from higher symmetry (produce single-atom shells).


                EXTRACT EXT generate a file containing a sub-set of multiple scattering paths. Also used to view information on multiple scattering paths.


                FFILTER FF allows back-transformation of part of the fourier transform so that shell contributions can be isolated.


                FIT FI updates the theory and displays fitting statistics.


                FTSET FT selects options which control the calculation of fourier transforms.


                GENERATE GE produces a new cluster using an atom in an existing cluster as the centre


                GSET GS selects options which control the appearance of graphs.


                IDEALISE ID convert amino acids to ideal geometry


                INFO INF give tables of information used by the program


                INQUIRE INQ displays information about the current state of the program control parameters.


                LIST L lists current values of variables, and of SET, GSET and FTSET options.

                MAP M draws a contour plot of the variation of fit-index with parameter values.


                PLANE PLA 3-D geometry associated with planes of atoms.


                PLOT P displays experiment and theory, Fourier transforms, phaseshifts etc.


                PRINT PR generates files of spectra and/or parameters and variables.


                READ R reads in files of experimental data, phaseshifts and parameters.


                RECOVER REC restore parameter values, e.g. from previous session.


                REFINE REF used for the refining variables to produce the best fit.


                ROTATE RO rotate cluster or units


                RULE RU defines algebraic rules which constrain parameters


                SAVE SA saves current parameters, errors and statistics for recall, especially in conjunction with table.


                SET S allows modification of parameters which control major program options.


                SITE SI define mixed-atom sites


                SORT SO puts shells in order of distance


                SPARE SPA compresses collections of symmetry related MS spectra


                STATS STA controls the Joyner statistical tests.


                STRUCTURE STR generates shell coordinates for simple structure types.


                SYMMETRY SY calculates atomic positions from shell variables given the point symmetry.


                TABLE TA displays comparative tables of parameters, errors, and statistics.


                TIME TI displays current time of day, CPU usage and elapsed time.


                UNDO U remove the effect of the last CHANGE or ROTATE


                XADD XAD allows contributions from batch calculations to be added to the theory.


                XANES XAN calculates and displays XANES by matrix inversion method.



A full list of commands can be obtained by typing ? at the command prompt.


Command Documentation



A full description of each command is given in the command reference section of the manual, chapter 5. All the keywords and options are described there. Here only sufficient information is given to start analyzing data. A thorough knowledge of the theory section is assumed. Menu options for each command can be obtained by typing command_name ?.This document is available in Word Perfect, MSWord and html versions.


Parameters and Options


Theory calculation, refinement and restraints are governed by a large number of parameters. These are listed and described in the PARAMETERS section of the documentation. Parameters are changed using the command CHANGE and displayed using the command LIST. Program control is by means of innumerable options: these are randomly distributed amongst the commands SET, GSET, and FTSET. The keywords and options associated with these commands are fully described in the command reference section.


Reading in spectra


The command READ is used to read in one or more EXAFS spectra, structural parameters or scattering phaseshifts.



EXAFS spectra can be read using:


                READ EXPERIMENT n


where n (1, 2, 3 etc.) is incremented for each experiment read.


Background-subtracted data given in terms of eV above the edge position. For whole-spectrum analysis, however, absorbance as a function of absolute photon energy may be used. The variable E0 is then used to define the edge position (E0 must be 0 if the energy is relative to the edge). With Unix/Linux, make sure that the data is in Unix format - terminated only by a carriage return character. Most Linux commands now accept both Unix and DOS formats, making it difficult to determine what the format is. For the Windows version only, it is possible to browse files, be entering *.* at the command prompt, or *.suf to restrict the search to a particular file suffix. If your data is in k_space use the command READ KEX instead. E0 is then the difference between the edge position and the origin of the wave vector (Ez in k^2=2.(E+Ez)). It is essential that this is correct. For background programs which write only absorbance versus k, Ez is often but not necessarily 0.


The program will prompt for information [default values are given in brackets - type return to accept them]:


                Point frequency ? [1]


1 to read every point, 2 for alternate points etc. this option is useful in speeding up the early stage of analysis or reading files where the number of points exceeds the program dimension limits.


                Column combination ?                 [12]


For EXAFS spectra - determines the location of the energy (ev) and absorbance columns in the file. e.g.


79 if energy (ev) is in column 7 and absorbance in column 9.



                Edge ? [CU K]


defines the central atom type and the initial state. The reply should be an element symbol + a label for the core electron excited, as two words .e.g.





CU K, RB L3, W L1



                Sequence-number in                 polarisation set [0]


is set to 1, 2, 3 etc. for polarisation dependent spectra differing only in their orientation (otherwise 0). Members of a polarisation set must use a common edge position.


                Number of clusters for                 this experiment [1]


is used to relate the atomic clusters defined by the parameter table to the various spectra. It is 1 or more unless the spectrum shares clusters with the previous spectrum.


More information on using READ is given in the Command Documentation section (chapter 5), and under fitting multiple spectra in this chapter.


Having read in the data, it is useful to check it. This can be done using PLOT EXAFS. Neither the theory nor fitting statistics will make sense at this stage, because no structural model has been defined, and no atomic phaseshifts are available. The EXAFS plot may not show much structure because it is dominated by data below the edge. In this case either decrease the range used by changing EMIN:


                C EMIN 10


Or use a k^n weighting:


                S W K3


If something is wrong it might be helpful to check the correct filename was entered:


                LIST FILES


If the problem is unresolved, check how many points were read, what energy range was used, etc. using:


                INQUIRE


If the energy range is too short or too long, the spectrum may have been read using the wrong column combination, the number of data points may have exceeded the current dimension limit or E0 may be wrong (it should normally be zero).

The dimension limits may be inspected using:


                LIST DIMENSION


If the high energy end of the spectrum does not appear, it may be necessary to change EMAX, e.g. to any high number.


                C EMAX 9999



Defining the structural model


A model for the structure should now be defined. This may be done in a number of ways:


1. Read a program parameter file.


                READ PAR


Once created, a parameter file can be edited, but it is tedious to create it from scratch.


If parameters are available in Brookhaven protein database format, or .car files are available from the Cerius Explorer modelling program, these may be read using R PAR B or R PAR C. See the READ command documentation for more details.


2. For high symmetry structures, such as those with NaCl structure, use the command STRUCTURE to generate the shells.


                C ATOM[1,3] CA;C ATOM2 O;C T1 O;C T2 CA

                C NS 7;C R1 2.405;STR NACL


Sets up 7 shells for the Ca edge of CaO - only the Debye-Waller terms A[1-7], the edge position EF and various multiple scattering parameters (see below) need then be changed in order to fit the spectrum.


3. Enter the data by hand.


Although not essential, it is best to define all the atoms that are to be used before defining the structure. One or more central or excited atoms are required (ATOM1 is always the central atom of the first cluster). Each scattering atom should also be defined (a scattering atom for the same element as the central atom is normally required, as excited and scattering atom phaseshifts are calculated slightly differently). For a copper protein, the atoms required might be as follows:


                C ATOM1 CU;C ATOM2 C;C ATOM3 N;C ATOM4 O;C ATOM5 CU


ATOM variables are described more fully below.


To set up the structure 'manually', first define the number of shells:


                C NS 4


Then define the characteristics of each atomic shell.

 

                C S1


You will be prompted for the following (there are no defaults in EXCURVE at present, the values in brackets are typical preset values)



                N1           [4]            Shell occupation number (must be the multiplicity generated by the point group if the symmetry                                                 is to be defined).

                T1            [2]            Element to be used for EXAFS phaseshifts. If phaseshifts have been read, or ATOM parameters                                                 have been defined, use an element symbol. Otherwise, use unique numbers > 1 for each element.

                R1           [2.4]         Shell radius in angstroms.

                A1           [0.005]     2 x 2nd cumulant (Gaussian term in DW factor) - 2σ22

                B1           [0]            10 x 3rd cumulant (Skewness of DW factor) - Å3

                C1           [0]            100 x 4th cumulant (Kurtosis of DW factor) - Å4

                D1           [0]            Truncated exponential term - Å

                UN1         [0]            Unit number (for group-fitting, group MS)

                ANG1      [0]            angle 0-n-1, where n is the shell nearest the centre or the pivotal atom of a unit. Usually undefined for shell 1, which is itself normally the nearest shell to the centre. ANG is 0 for shells not associated with units (see below and in the parameters section, chapter 4).

                TH1         [0]            spherical polar coordinate θ (0 to 1800)

                PHI1        [0]            spherical polar coordinate φ (0 to 360)

                X1           [0]            Cartesian coordinate X

                Y1           [0]            Cartesian coordinate Y

                Z1            [0]            Cartesian coordinate Z


Normally only the first few parameters are entered. After sufficient information has been entered, "=" will terminate the command ("=" is often used for such a purpose in many commands). If the spherical polar coordinates R, TH and PHI are used, the cartesian coordinates X, Y and Z are not generally used. Changing any one of the polar coordinates will update all the cartesian coordinates and vice-versa.


This should be repeated for each of the atomic positions. Once the positions are defined, the defaults are the existing values. Normally, however, CHANGE Sn will not be used again - it is usually easier to change the individual parameters:


                C X4 .7395


                C T1 HG


CHANGE S may also be used to duplicate shells for editing:


                C S2 1


Will copy shell 1 to shell 2.


An element symbol may be used for Tn both here and when the C Sn format above is used, only once the ATOM variables have been defined.


Once a set of parameters have been entered it is wise to save them immediately:


                PRINT PAR


The program will issue a prompt for a filename, of the form expara1.dat. If the file already existed, the a1 suffix will be incremented to generate a unique name. If you wish to use another filename it can be entered. You will be asked to confirm whether an existing file should be overwritten.


Parameters can be listed using


                LIST


Typical output looks like this:


 LMAX = 25.000 DLMAX= 6.000 TLMAX= 5.000 WP = 0.100 NS = 4.000

 EF = -7.159 VPI = 0.000 AFAC = 0.914 EMIN = 20.000 EMAX =1519.880

 EF1 = -7.159 VPI1 = 0.000 AFAC1= 0.914 EMIN1= -20.000 EMAX1=1519.880

 Shell 0 N0 = 1.000 T0 = 1(CU) R0 = 0.000 A0 = 0.000 B0 = 0.000-1 0

 Shell 1 N1 = 12.000 T1 = 2(CU) R1 = 2.556 A1 = 0.008 B1 = 0.000 1 0

 Shell 2 N2 = 6.000 T2 = 2(CU) R2 = 3.615 A2 = 0.011 B2 = 0.000 1 0

 Shell 3 N3 = 24.000 T3 = 2(CU) R3 = 4.427 A3 = 0.016 B3 = 0.000 1 0

 Shell 4 N4 = 12.000 T4 = 2(CU) R4 = 5.112 A4 = 0.011 B4 = 0.000 1 0


Individual parameters are described in the parameters section, chapter 4. The two sets starting EF... are significant for multi-spectrum fitting. If only one spectrum has been read, only the first set need be used. The second set is still displayed however, because they will effect the result if they have previously been changed. The final two columns in the table of shell parameters are the cluster number (-ve for a central atom), and the unit number. UNITS, for use with molecular compounds such as enzymes, are not often needed and are described later. If the table is very long, the first part may be displayed using, say, LIST 10 (the default keyword SHELLS is still assumed).


When changing parameters, values may be defined in terms of other parameters or arithmetic expressions


                C N1 4/3


is more accurate than C N1 1.3333


Similarly, for two shells at x and 2x


                C R2 R1*2


is better than entering a specific value, as if R1 has been refined, it will be stored with 6 or 7 decimal places.


The program has to judge whether two numbers are equivalent in some situations, and therefore it is better to be unambiguous.


Defining atom types


The most difficult aspect of parameter definition involves the atom type T1 etc. T1 takes a numeric value which is associated with a particular scattering phaseshift. Normally the cross-reference is defined by atom parameters.


For example:


                C ATOM1 CU

                C ATOM2 O

                C ATOM3 C

                C ATOM4 CU


defines the atoms required for Cu(CO)3. ATOM1 is always the excited central atom of the first or only cluster. ATOM4 is defined because Cu is present as a scattering atom in addition to an excited atom.


If T1=2, T2=3 and T3=4, the first 3 shells are O, C and Cu respectively. Once the atom parameters are defined, it is usually possible to forget about the numbers, and use element symbols for the atom types:

 

                C T1 O etc.


If phaseshifts are calculated, they will be calculated in the correct order. If phaseshifts are read-in, it is however the users responsibility to ensure the correct correlation between phaseshifts and ATOM or T parameters (there is as yet no automatic checking in most situations).


To check that the order is correct type:


                L PHASE (which will display all the atom variables, among other things)


and

                L FILES (which will give any phaseshift files that have been read)


The situation is more complicated if multiple edges are being fitted. If the core-hole lifetimes of all the edges are similar, a single set of scattering phaseshifts may suffice. In most cases however, a separate set of scattering phaseshifts is required for each spectrum. It is then essential to ensure that T variables refer to phaseshifts not only of the correct atomic number, but also to the correct central atom type.


Defining the Symmetry


The symmetry is defined using the command SYMMETRY which sets the point-group of each cluster in the material (often there is just one cluster)


A list of point group symbols (Schönflies notation) is given by:


                INFO POINT


The list of available symbols is followed by a longer list including the equivalent international symbols and the multiplicities associated with general and special positions.


A few symbols differ from normal - C0v instead of C∞v etc.. Cx and Cy are settings of Ci where the principal axis is x or y rather than z as in Ci (it is possible to transform the coordinates using ROT variables, but it is often useful to retain coordinates in a familiar orientation). The use of Cx and Cy has been superseded by new code allowing multiple settings.


                SYM                        will request a point group

 

                SYM c4h                 for examples, will assign c4h to the first cluster


The occupation numbers and solid angles must be consistent with the point group operator. Often several shells with the same radial distance must be defined if atoms are not symmetrically related (i.e, the shell has a higher symmetry than the cluster as a whole). This is most obvious with cubic lattices, where shells of 36 atoms must clearly be composed of at least two shells, one with 12 and one with 24 atoms. Sometimes one of several possible orientations must be selected. If the shell variables do not correspond to a standard orientation, the program will attempt to find an appropriate alternative setting. If the setting number is other than zero, the coordinates used for MS calculations, for the command DRAW, etc. will differ from those in the table of shell parameters. The actual values used are displayed by SYMMETRY Normally the setting is defined automatically, but it is possible to override this using for example:


                SYM c4h:1


For setting 1. The standard setting is 0.


If STRUCTURE is used to define the shells initially, the point group will be defined at the same time (for example, Oh for NaCl structures). Note that a subsequent use of structure will overwrite the existing coordinates, while symmetry will never change the shell parameters.


Multiple Clusters


In the case above, it is assumed that there is one phase and one crystallographic site containing the excited atom. In practice, there may be many phases and many sites containing the excited atom, either with full occupancy, or as a component of a mixed site.


For each site containing one of the excited atoms, a radial cluster must be generated. Each cluster consists of an excited atom and a number of shells. If only single scattering is being used, multiple clusters can be represented by adjusting the shell occupation numbers, remembering to include a factor relating to the multiplicity of the sites containing a central atom. For multiple scattering calculations this approach will not work, as occupancies must be integer, scattering between clusters must be excluded and each shell must consist only of atoms replicated by the point symmetry of the cluster in question. The clusters in this case must be identified by a cluster number, using the shell parameters CLUSn. CLUS parameters are the same for each atom in the cluster. The cluster number is 1 for the first or only cluster. Excited atoms are signified by a negative value. Thus by default, CLUS0 is -1, CLUS[1-NS] is 1. The second cluster will have an excited atom with, say, CLUS5 = -2. Shells are normally arranged in blocks, in order of cluster, thus successive excited atoms, with cluster numbers -2, -3 etc. will mark the start of a new cluster. The occupation numbers of the excited atom shells must reflect the site multiplicity, and determine the relative significance of each cluster (they should of course always add up to 1). Thus N0 is normally set to 1, but with two clusters, with the same frequency in the crystal, each with the same excited atom type, its value should be .5. The situation becomes particularly complicated when the excited atoms occur in mixed sites. See the section on multiple spectra for an example of a parameter table for multiple clusters.



Mixed Sites


Mixed sites enable the program to calculate the spectrum when either the excited atom or a scattering atom has partial occupancy of a site. This includes the calculation of multiple scattering contributions associated with such sites. As the occupation numbers for sites must be exactly that determined by the point group symmetry, mixed sites also provide a means of calculating the effect of site vacancies. Mixed sites must be used if full multiple scattering calculations are to be performed for disordered systems.


Mixed sites are defined using the command SITE. It is used to define a pseudo-element symbol. For example the symbol QA may represent Cu.33Zn.67. These symbols are assigned -ve 'atomic numbers', starting at -1. The symbol, or its 'atomic number' may be used wherever a normal element or Z-value is used within the program. To set up the example above


                SITE QA


Will give rise to the prompt


                 Enter element and percentage for component A


                CU 1/3


                Enter element and percentage for component B:


                ZN 2/3


                Enter element and percentage for component C:


                =              (no more components)


To check site definitions type


                SITE


The site command will have defined three variables. Assuming this was the first use of the command, it will have defined PERCA1 (=.33333), PERCB1 (=.66667), and PERCC1 (=0.). The composition of the site may be changed by altering these variables. The variables may also be refined. If PERCAn is refined, then PERCBn will be adjusted so the sum PERCA+PERCB+PERC is constant, unless PERCB is also refined. This provides a mechanism for maintaining the stoichiometry of the site.


In order to refine site vacancies, it is necessary to refine PERCB ( or PERCC for 3 component sites) rather than PERCA, which should be set to 0.


In order to use mixed sites in calculations, it is first necessary to define an ATOM type, as in


                C ATOM7 QA


Atom type 7 may be then be used to define the shell variables (e.g. for shell 4).


                C T4 7     or             C T4 QA (once ATOM7 has been defined)


 

Phaseshifts - introduction


If phaseshifts for each central atom and each scattering atom are available, they may be read in using


                READ PHASE


The order must correspond to that of the ATOM variables (if defined) and consistent with the atom types Tn defined in the parameter table (as yet there is no checking in most situations).

If no phaseshift files are available, they must be calculated. Phaseshifts should be calculated for:


 All the central atoms required for the XAFS experimental files that have been read in.


 All the scattering atoms Tn referred to in the list of shell parameters.


The first step in a phaseshift calculation is to calculate embedded atom potentials.


Before this is done, all the required ATOM parameters must be defined. For CuO:


                C ATOM1 CU*

                C ATOM2 O

                C ATOM3 CU


Calculating Potentials



The first stage is to set the method of calculating the ground state exchange energy of the excited photoelectron, as described in the theory section. For this example we use:


                SET GROUND VON_BARTH


If the alternative X_ALPHA option is selected, the potentials are dependent on the parameters ALFn (see the theory section on muffin-tin potentials, chapter 2). The potentials are calculated using:


                CALC POT


There is a prompt for the level of output:


                G (graphics), T (terminal output), M (charge densities) or C (continue without output) [C]:

 

M is used only in order to generate charge densities for other programs. The other options are self explanatory.


The next prompt requests the neighbouring atom type - phaseshifts are calculated individually using a different cluster for each. There can be at most two atom types per cluster. Prompts are of the type:


                Atom: 1 (GA). Enter neighbouring atom [3 (O)]


If there are several scattering atoms with the same atomic number, a number should be entered. Otherwise, a chemical symbol may be used.


If there are several different neighbours, it is often best to choose the lightest. Atomic potentials can be significantly affected by the choice of neighbouring atom. If you are unsure of the neighbour, and do not wish to bias attempts to discover its nature, use monatomic clusters (but where the neighbour is a ground state not an excited atom).


The next prompt will occur for excited atoms only - the menu available will depend on the edge, for a K-edge it is as follows:

 

                Select Code For Exited Atom                                                [1]:

 

                 No Correction                                                                         (0)

                 1S Core Hole (K-edge - relaxed approximation)                 (1)

                 1S Core Hole (K-edge - Z+1 approximation)                        (-1)


A positive number will select atomic potentials calculated self-consistently in the presence of a core-hole (relaxed approximation). A negative number will use the 'Z+1 approximation' of von Barth (sudden approximation). In general, the fully relaxed case should be preferable at low energies. The best option at high energies is debateable.


The program will then attempt to calculate the potentials. If the graphics option has been selected, the charge density and potential functions will be plotted. If the terminal output option is selected, tables of charge densities and potentials will be displayed. In all cases the charge density is integrated over the Wigner-Seitz sphere to give the apparent number of electrons in the atom. This is compared to the atomic number Z.


The program will also display values of V0, RHO0 and FE0 when the calculation is finished. V0 is the Muffin-tin zero, the energy of the flat region in figure 1. This is the effective energy-origin of the theory in EXAFS. It is some way below the edge, which is itself below the vacuum zero level. Ideally, the calculated FE0 will correspond to the Fermi energy, which should equal the difference between the experimental edge and the vacuum zero (a negative number). It is unlikely to do so however except for metals with free-electron-like conduction bands. RHO0 is the interstitial charge density.


If several phaseshifts are calculated, the values of V0, RHO0, FE0 will differ for each two-atom cluster. This contradicts the muffin-tin model which depends on a common interstitial potential in the crystal. If the differences are large, the theory calculations for different shells of atoms may be out of phase with one another, effecting the result. Ideally calculations should be performed to give consistent values, although there may be instances of partial ionicity where inconsistent values give the best result, due to their mimicking the effects of charge transfer.


It is, however, possible to calculate all the potentials so as to give a common value of V0, RHO0 or FE0. It is also possible to refine these variables. The option SET COMMON V, for example, will ensure that all potentials are calculated to a common value of V0. (Do not type S CONST V0 - V0 is a parameter, which will be evaluated, so the command may be interpreted as S CONST -7 etc.). The muffin-tin radii will be adjusted to give the required value. This method is to be preferred to using a cluster consisting of many atom types. This could cause steps in the potential at the muffin-tin radius, resulting in spurious effects associated with the strong scattering from potential steps.


If whole-spectrum fitting is being used, i.e. if ATOMABS is set to ON, then a second set of excited atom potentials labelled 'ATOM0' will be generated. These are identical to the normal excited atom potentials, except that the excited state term, generated when the phaseshifts are calculated, will be entirely real. They will be used to generate the atomic transition rates. Real potentials are required because the trick of generating an imaginary potential to account for inelastic process in scattering, does not work in the calculation of dipole matrix elements. Among other problems, it results in loss of charge conservation.


Muffin-tin Radii and related Parameters


The potential calculations make use of a table of values for muffin-tin radii (the radius of the touching spheres used in modelling the potential in the solid). They also use parameters describing ionicity, exchange and Madelung corrections. The muffin-tin radii actually used will be adjusted by the program if the common V0, or similar options are used (see above). They may also be changed manually, or indeed refined against a well established model compound.


                C MTR1 1.34


Will change the value for MTR1 to 1.34 (suitable, for example, for Ga, Z=31).


If it is necessary to use a different value when an atom is used as a neighbour to that used when the potential is being calculated, either additional ATOM variables may be defined (with an MTR just used for overlaps) or the potential for each atom type may be calculated separately:


                CA POT 3


For example. The values may not be refined under these circumstances.


Other potential parameters that may be altered include: IONn, ALFn, CMAGn, where n is the atomic number. ALF is only used in conjunction with the X-α ground state exchange scheme, in accordance with equation [19]. ION is the ionic charge. Generally only +/- 1 is used as it is not possible to generate adequate anion charge densities for a free atom with a charge less than -1. Ionic phaseshifts are not usually used - the neutral atom charge densities are more reliable, and the net effect of using ionic phaseshifts is normally only a shift in EF.


Multiple excited atoms: CALC POT assumes that ATOM 1 is an excited atom. If potentials are calculated individually, an excited atom is indicated by using a -ve atom type (e.g. CA POT -1 would explicitly define atom type 1 as being an excited atom). Alternatively (and preferably) an excited atom status can be indicated by, for example:


                C ATOM4 BR*


LIST PHASE will indicate excited atoms with a '*'. Once so-defined, excited atom potentials will be calculated until scattering-atom status is resumed after C ATOM4 BR. When multiple spectra are in use, it will be necessary to use one of these methods to ensure that excited atom potentials are calculated properly.


Calculating Phaseshifts


Phaseshifts are calculated using:


                CALC PHASE


this will calculate phaseshifts for all atoms for which potentials are available. Phaseshifts depend on only a small number of options, they mostly depend on the potentials. One is the excited-state exchange term - usually the Hedin-Lundqvist method is used:


                SET EXCHANGE Hedin-Lundqvist (S E H)


the alternative is


                SET EXCHANGE Xalpha


Which uses a constant imaginary potential for the excited state.


Other options include whether to use scalar relativistic corrections - that is to include corrections to energy terms of the order of(E/c2), and corrections to the photo-electron momentum, but to ignore spin-orbit coupling and related terms. Although such schemes were successful in LAPW band structure calculations, and it is currently fashionable to include them in XAFS, the justification for them is poor. It may be better to ignore them by selecting:


                SET RELCOR OFF


Another option is to select the contribution to inelastic losses below the plasmon threshold, as described by Quinn (1962).


                SET QUINN ON/OFF


It is probably best to use this option as it helps reduce the discontinuity at the plasmon threshold energy.


A more important parameter is the core-hole lifetime. These are normally taken from tables, compiled from PES data on half-widths of peaks due to core excitations. There is some scope for variation however due to a number of factors:


1. Core widths are not totally immune to chemical factors.

2. Reduced experimental resolution is not explicitly accounted for, and looks rather like lifetime broadening (strictly it should be Gaussian whereas lifetime broadening is Lorenztian).

3. The theory behind the imaginary contribution to the excited state potential is valid only for a rather limited set of situations (a free electron gas in the plasmon pole approximation), and altering the core lifetime provides a good fudge if the electron inelastic scattering term is wrong.

4. The accuracy of the tables used in the program is not guaranteed.


With these factors in mind, tinkering with the core lifetime, or even refining it has some appeal. This may either be done, in response to a prompt, when the phaseshifts are calculated, or the parameter CW may be used.


When multiple edges are in use, different core lifetimes are required for different edges. Although a fix for problems occurring when two edges (e.g. K and L3) of the same element are in use is described below, it is better to calculate sets of both scattering and excited atom phaseshifts for each edge. In this case, instead of using the global parameter CW, the spectrum specific parameters CWi should be used. The index i is incremented for every atom number specifying an excited atom, and thus relates to a block of potentials or their associated parameters. It does not necessarily bear any relation to the spectrum index as used in READ EXP, although it normally ought to do so. In the table below (given by LIST PHASE), CW1 would apply to atoms 1 to 3, and CW2 to atoms 4 to 6. If parameters CWi are to be used, CW must be set to -1.


 1 ATOM 47 (AG*) ION 0.00 MTR 1.437 ALF 0.6667 CMAG 0.000 XE 0.000

 2 ATOM 35 (BR ) ION 0.00 MTR 1.396 ALF 0.6667 CMAG 0.000 XE 0.000

 3 ATOM 47 (AG ) ION 0.00 MTR 1.442 ALF 0.6667 CMAG 0.000 XE 0.000

 4 ATOM 35 (BR*) ION 0.00 MTR 1.396 ALF 0.6667 CMAG 0.000 XE 0.000

 5 ATOM 47 (AG ) ION 0.00 MTR 1.442 ALF 0.6667 CMAG 0.000 XE 0.000

 6 ATOM 35 (BR ) ION 0.00 MTR 1.396 ALF 0.6667 CMAG 0.000 XE 0.000


If the HL excited state option is not being used, then no inelastic losses are included. A term due to the electron inelastic losses should then also be included at this stage (or in CW). This will normally add 1 to 6 eV to the effective core width.


When the command CALC PHASE is executed, a prompt is issued:


                Do you require the atomic absorption [no] ?


The default option will depend on the setting of ATOMABS, the response will normally differ from the default only if XANES calculations are to be performed.


The next prompt is for the core hole width, as discussed above. If CW (or CWi) is defined, that is the default. Otherwise, a tabulated value is the default. If tabulated values are being used, a value rather higher than the default is normally appropriate. Experience suggests that in the current version of the program, twice the default value will normally give the best fit. It is sensible to check the tabulated value against published data, as the tables use approximate interpolated values only.


Once potentials and phaseshifts have been calculated, they can be written to files using the PRINT command (PRINT PHASE). They can be read in to later sessions using READ. The PLOT command can be used to examine phaseshifts graphically.


                P PHASE


Calculating the Theory


The EXAFS theory is updated in response to a number of commands, such as FIT, PLOT, PRINT.


FIT also gives fitting statistics. An example, for Cu-foil, is given below.


 Fit Index: with k**3 Weighting 3.0023

 R-Factor : with k**3 Weighting 27.8242

 Amplitude of Experiment 65.0893

 R(exafs) = 27.8242 Weight: 1.00

 R(distances)= 0.0000 Weight: 0.00

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 61.2 Np = 7. Chi^2 = 73.7025E-6


If you wish to update the FT as well (for example, so you can use CP 1 after the next update), type FIT FT.


Single scattering (SS) is always calculated using curved wave theory (CW). Multiple scattering (MS) may be calculated using curved wave theory, or in the small atom (SA) or Rehr and Albers (RA) approximations. These are selected using SET THEORY CURVED_WAVE (for CW) or SET THEORY SMALL_ATOM (for both SA and RA).


There are angular momentum restrictions on the MS CW theory (DLMAX for double scattering, TLMAX for higher orders). Use LIST DIMENSION to display the maximum allowed values. DLMAX also controls SA/RA theory, although it is only restricted to the maximum of LMAX in this case. If the theory is changed to CW, DLMAX will change. It will not be changed if the theory is switched back to SA/RA. This must be done manually to recover the previous result:


                CHANGE DLMAX LMAX


By default, the 'small-atom' option, is equivalent to the Rehr and Albers full-matrix approximation (NUMAX=2).


                C NUMAX 1


Reduces the accuracy


                C NUMAX 0


Gives the original small-atom approximation (Gurman, 1988).


Refinement


Refinement of parameters so as to achieve optimum agreement with experimental data is the primary purpose of the program.


The only command required is REFINE which, given a list of parameters to refine, will determine their optimum values and calculate statistical errors at the minimum it locates.


For example, to refine the variables EF, R1 and R2:


                REFINE 150            (no keyword, so LSR assumed, step parameter set to 150)


Enter parameter name or "=" to skip


                EF


Enter parameter name or "=" to skip


                R1


Enter parameter name or "=" to skip


                =


Least squares refinement using k**3 weighting


Initial parameters


1 EF 17.240 0.00272 17.51203

2 R1 1.500 0.00002 1.50159


Enter :     CONTINUE to refine interactively

                a number to edit, add to, or delete from the list


                3


We forgot R2, 3 means that we want to add parameter number 3 to the list. Note that there is no default for the above prompt, its just too easy to start the refinement accidently.


Enter parameter name or "=" to skip


                R2


Least squares refinement using k**3 weighting


Initial parameters


  1 R1 1.500 0.00002 1.50159

  2 EF 17.240 0.00272 17.51203

  3 R2 2.922 0.00003 2.92553


Enter :     CONTINUE to refine interactively

                a number to edit, add to, or delete from the list


                C             (for continue)


 R1 = 1.50000 EF = 17.23991 R2 = 2.92244

 Call 1 F 351.5847 R 177.353 F- 351.585 Rex 177.353 RD 0.000 Rx 0.00 636 27

 Select Next,Exit,Complete,Stats or Plot


                N 33 (or just 33)


Carry out 33 refinement cycles. The program will carry on altering the values of R1, R2 and EF until the fit-index reaches a minimum or the specified number of steps has been carried out.


In this case the refinement should end with:


 R1 = 1.95281 EF = 21.12186 R2 = 2.87818

 Call 50 F= 19.9091 R= 44.305 F(min)= 19.909 R(ex)= 44.305 R(dis)= 0.000

 Minimum Predicted, Accuracy = 0.2817E-02 Cond = 2 At Call 50

 Filename for statistics: [excora1.dat] ?


The program prints errors and correlations along with the best values of the parameters at the predicted minimum, after requesting a filename (default excora1.dat etc.) to provide a permanent record of the information (it also goes into the logfile). Type '=' if you do not require a statistics file.


The weighting used by the refinement is that same as that used by FIT, and can be altered using the SET option WEIGHTING.


The command uses numerical estimates of the derivatives whose values can depend on the step parameter. Convergence is often poor and refinements using a range of values of the step parameter are often required. A useful method of improving convergence is to refine different sub-sets of the variables required separately.


Refinement can often lead to physically unrealistic parameters, either as a result of underdeterminacy, strong correlations between parameters (as revealed in the correlation matrix produced as above), or because other parameters are wrong. For example, if EF is wrong, but only A parameters are being refined, they will refine to high values, as the errors due to the phase being wrong are reduced if the amplitude is reduced. The program uses soft constraints to reduce this effect. If a parameter is beyond a certain limiting value, there is a contribution to the fit-index proportional to the square of the excess. The most useful constraint is for A parameters. The limits can be set using DWMIN and DWMAX.


                C DWMIN .001;C DWMAX .03


Will in general keep A parameters between .001 and .03 during a refinement.


Multiple parameters may be refined using the list form for parameters (e.g. A[1-3,5]). Parameters may also be linked to refined variables using rules.


                RULE R2;R1*2

                REF;R1;C;C;


Will refine R1 and R2 (R2=2*R1)


A full list of options is presented in the command reference section on the REFINE command.


If you wish to compare the results of several refinements, SAVE will store both the parameters and their errors. TABLE

may then be used to display all the sets of parameters, with or without their errors.


Plotting the Spectra


The wide range of plotting commands are described more fully in the command reference sections for PLOT and COPLOT.


Amongst the more useful are:


                PLOT EXAFS


To plot the EXAFS spectrum


                COPLOT ( or CP )


To plot EXAFS and FT together


Other options include those to plot previous generations of theory with either EXAFS alone or in conjunction with the COPLOT command.


                P EX 1 (or just P 1)


will plot experiment, theory and the previous theory.


                CP 1


is similar. Note however, that for this to work, the previous theory must have been updated via a CP, P FT, PRINT or FIT FT, not just a FIT.


A full list of options is given in the command reference section on the PLOT command.


Output files


It is often necessary to save output as disc files. Parameters should be saved at regular intervals in case of program failure, or in case an unintentional change results in loss of the correct structure (but note that there is an UNDO and a RECOVER facility to cope with many situations). Phaseshifts should be saved to avoid having to calculate them each time and to ensure consistency in calculations. It is also useful to keep records of spectra, in case it is necessary to reproduce the results at a later stage, or to compare them with later calculations. Most of all, spectra are required as input to graphics packages and word-processors. Files for input to other programs may also be required.


All these forms of output may be produced using the command PRINT.


Many other commands can produce files. One obvious example is TABLE whose purpose is to produce formatted output for display or for inclusion in papers. REFINE produces files containing best-fit parameters, correlations and errors. EXTRACT produces files containing details of multiple scattering paths, and a filtered sum of paths.


All spectra may be written in column format for use with other plotting packages. Parameters may be written in Brookhaven or EXCURVE format, again using PRINT.


Disorder


Disorder is introduced by means of shell parameters

A, B, C and D. A, B and C are the second, third and fourth cumulants (see the theory section on disorder.

A is actually defined as 2xC2 (or 2), B as 10xC3 (Å3) and C as 100xC4 (Å4).


Two schemes are in use to calculate theory. In one the integral in equation (26) is calculated numerically (SET DIS EXACT). This will take into account spherical wave effects. The other (SET DISORDER APPROX) uses a conventional Debye-Waller term as given by equations (26-27). When only the second cumulant term is used, the difference between the two methods appears to be very small in the majority of cases. The approximate method is recommended therefore on the grounds of efficiency.


A is always the dominant term, but in some situations other terms are significant. Solids near their melting points are an obvious example. The effect in k-space of a distribution with a given set of cumulants can, in principal, be calculated accurately, provided spherical wave effects are ignored. In order to generate a pair distribution function for a given set of cumulants, however, a specific model is assumed - the anharmonic oscillator. In this model, the allowed value of higher cumulants is determined by the values of the lower ones. Thus in general, most values for the higher cumulants will not generate sensible values. For this reason the EXACT option is certainly not recommended when higher cumulants are in use. One situation where the two methods should give similar results, is if the values are commensurate with the anharmonic oscillator model. That is if:


(42)



 

Where α is the coefficient of linear expansion. It is possible to make use of this in determining the best values of the third cumulant. The model works very well for the first and fourth shells of Cu at reasonable temperatures (Edwards et al.,1997). The program will calculate B values automatically using this relationship provided both the coefficient of linear expansion (CLE) and the temperature (TEMP) is defined. CLE is actually 106 x the coefficient, TEMP is in K.

Use of this method avoids a big problem with using B parameters - they largely effect the phase, and are strongly correlated with R and EF, hence may lead to a good fit being obtained with erroneous distances.


A second scheme for treatment of disorder involves using A and D parameters to describe the convolution of a Gaussian with a truncated exponential. This model is appropriate for cases where a cumulant expansion does not rapidly converge, as in ionic conductors. D parameters should not be used in conjunction with B and C parameters.



Multiple Oxidation States


Where an atom occupies several sites, it is not unusual for it to have two different oxidation states. An obvious example is staurolite (Fe2,Mg)2(Al,Fe3)9O6(SiO4)4(O,OH)2. When this occurs, the chemical shift of the absorption edge (caused by differences in the screening of the nucleus by the different valence shells) will result in the associated components of the spectrum being out of phase at low energy. This can be accommodated by the atom-type dependent terms XEn, where n is the atom number associated with Tn. This is a correction to EF for each atom-type. It will be necessary to calculate a second set of phaseshifts for the central atom and each scattering atom, and to specify two clusters, about Fe2 and Fe3. The central atom of the second cluster should have CLUSn parameter of -2. There should be only two values for the XE parameters, i.e. all values associated with the same cluster should be the same. (The combined XAFS/PD program P more sensibly uses a cluster-dependent XE parameter, preventing the use of XE's as general fudge factors). There are other, and possibly better ways of treating multiple oxidation states, for example calculating two sets of phaseshifts with different V0 values.


Multiple Spectra


When two or more EXAFS spectra are in use, variables such as EF, AFAC, EMIN, EMAX etc. are unlikely to be the same for both. For these variables, as well as a common variable, which applies to all spectra, there are individual variables which apply to only one. These are indexed by spectrum number, as used in READ EXP. In some instances the common variable may be more appropriate - for example EF for different polarisation directions. It may also be useful to combine common and individual variables - AFAC may be the same for all but one of the spectra. The rules for combining variables, in the case of spectrum i is as follows:


                EF           The program uses EF+EFi

                AFAC      The program uses AFAC*AFACi

                EMIN       The program uses MAX(EMIN,EMINi)

                EMAX     The program uses MIN(EMAX,EMAXi)

                CW          The program uses CW unless CW=-1, when it will use CWi unless that is -1, but note that i is not a spectrum index here, it marks a 'block' of atom numbers which commences with an excited atom (see calculating phaseshifts in this chapter).

                VPI          The program uses VPI+VPIi

                WEX        The program uses WEX*WEXi

                BETH      There is no BETH - it uses BETHi (similarly with BEPHI, BEW)


The common variables may also be written, for example, EF0. This can be useful in resetting variables. e.g.


                C AFAC[0-3] 1


If only one spectrum has been used, the indexed variables can be ignored. If you are working with one spectrum, but a parameter file has been read which has been used with multiple spectra, check that the indexed parameters do not affect the result. To facilitate this, commands such as LIST will display the first spectrum indexed variables even when they are not required.


Differences in core-hole lifetime normally mean duplicating the scattering phaseshifts, using different values for the effective core-hole widths. It is also possible to use a single set of scattering phaseshifts, and to compensate for differences using spectrum dependent values of VPI.


Shell parameters for multiple spectra will normally require two clusters (see Reading the spectra in this chapter, and READ in Command Documentation for other possibilities). An example is shown below for AgBr (NaCl structure, Oh symmetry at each atom). Here cluster 1 is centred on Ag and cluster 2 on Br. Only one parameter can vary in this case, the cell parameter, so only ACELL is refined (it just scales all the distances). Note also that Ag-Br and Br-Ag Debye-Waller terms must be the same, so these are refined as A[1,6], A[2,7] etc. The atom types are defined in the table above - see Calculating the phaseshifts in this chapter.


Shell 0 N0 = 1.000 T0 = 1(AG) R0 = 0.000 A0 = 0.010 B0 = 0.000-1 0

Shell 1 N1 = 6.000 T1 = 2(BR) R1 = 2.867 A1 = 0.008 B1 = 0.000 1 0

Shell 2 N2 = 12.000 T2 = 3(AG) R2 = 4.054 A2 = 0.011 B2 = 0.000 1 0

Shell 3 N3 = 8.000 T3 = 2(BR) R3 = 4.965 A3 = 0.012 B3 = 0.000 1 0

Shell 4 N4 = 6.000 T4 = 3(AG) R4 = 5.734 A4 = 0.019 B4 = 0.000 1 0

Shell 5 N5 = 1.000 T5 = 4(BR) R5 = 0.000 A5 = 0.010 B5 = 0.000-2 0

Shell 6 N6 = 6.000 T6 = 5(AG) R6 = 2.867 A6 = 0.008 B6 = 0.000 2 0

Shell 7 N7 = 12.000 T7 = 6(BR) R7 = 4.054 A7 = 0.011 B7 = 0.000 2 0

Shell 8 N8 = 8.000 T8 = 5(AG) R8 = 4.965 A8 = 0.012 B8 = 0.000 2 0

Shell 9 N9 = 6.000 T9 = 6(BR) R9 = 5.734 A9 = 0.019 B9 = 0.000 2 0


When refining multiple spectra, it may be necessary to weight each one differently, to prevent the spectrum with the highest amplitude or the best signal to noise from dominating the fit. This is done by the weighting terms WEXi. There default value is 1. They may be adjusted to alter the relative weightings of the spectra. Ideally the sum of the terms in use should equal the number of spectra being used. e.g., for three spectra the scheme might :


                C WEX1 .5;.C WEX2 2;C WEX3 .5



Multiple Scattering


Multiple scattering is best implemented using the option


                SET MS ALL


This calculates all the paths within all the clusters, up to a maximum pathlength given by PLMAX. Paths may also be limited to those involving certain angles by MINANG and by magnitude using MINMAG. These and other related parameters are described in the parameter documentation, chapter 4. Their effect can be seen using EXTRACT (q.v.). PLMAX should be set to at least twice the distance of any strongly 'shadowed' atom - for example twice the fourth shell distance in Cu - this is higher than the default distance of 10Å.


By default, only 2nd and 3rd order paths are calculated (those involving 2 or 3 scattering events). It is possible to increase the order of scattering to 4 or 5 however by setting OMAX to 4 or 5. This still leaves a restriction that there can be no more than 2 different scattering atoms. This is relaxed by setting ATMAX to 3, 4 or 5 rather than 2.


There are two options for the choice of theory in multiple scattering calculations:


The default option is the approximation due to Rehr and Albers (1990). The alternative is the curved-wave theory (Gurman, Binsted and Ross, 1986) as used for single scattering. The former is implemented in three levels, using the parameter NUMAX to designate different matrix sizes. The minimum value, NUMAX=0, corresponds exactly to the small-atom theory (Gurman, 1988). They are selected using:


                SET THEORY Curved_wave


                or


                SET THEORY Small_atom


The parameters which control the number of angular momentum terms in expansions about scattering centres are very important. Strictly, the same value of LMAX should be used as for single scattering (typically around 25 for Cu foil). In practice, it is often possible to use much lower values if only light element scatterers are present and only low energies are required. The values required must be determined by inspection. The use of too low a value will result in MS amplitudes at high energy which are too high - sometimes an order of magnitude too high. The energy range is very critical, and whereas an LMAX of 12 may be acceptable at, say 800 eV, it may be far too low at 850 eV. For the curved_wave theory, there are absolute limits on angular momentum values of 12 for double scattering paths, and 9 for higher order paths. The values used are controlled by the parameters DLMAX and TLMAX respectively. For the small atom theory, DLMAX is used to control all orders of scattering and it has the same limit as LMAX (usually 25). With NUMAX=2, the small atom theory is almost as accurate as the curved wave theory. Although it is not significantly faster for low values of DLMAX, it is much faster for DLMAX>=12. The errors due to restricting DLMAX to lower values are in most instances much greater than using the approximate theory. The small atom theory, with NUMAX=2 is therefore recommended for all but near-edge calculations.


There are angular momentum restrictions on the MS CW theory (DLMAX for double scattering, TLMAX for higher orders). Use LIST DIMENSION to display the maximum allowed values. DLMAX also controls SA/RA theory, although it is only restricted to the maximum of LMAX in this case. If the theory is changed to CW, DLMAX will change. It will not be changed if the theory is switched back to SA/RA. This must be done manually to recover the previous result:


If you wish to compare the two theories, using a similar angular momentum basis, you should first restrict DLMAX using:


                CHANGE DLMAX TLMAX


To revert to maximum accuracy, DLMAX should be reset, whichever theory is used.



In order to inspect the current values of multiple scattering parameters, it is best to use the command

 

                LIST MSPARS


Typical output is:


OMIN 1.000 OMAX 3.000 PLMIN 0.000 PLMAX 10.000

MINANG -1.000 MINMAG 0.000 DLMAX 6.000 TLMAX 5.000

ATMAX 3.000 NUMAX 2.000 OUTPUT 0.000


It is important to try to ensure that important paths do not move in and out of the range allowed by PLMAX during refinement, as this will prevent convergence. There is a mechanism (EXTRACT FILTER) to 'fix' the set of paths to be calculated, but it is unreliable at present. The mechanism for calculating only the most important paths using MINMAG relies on the path indices (entries such as 7.02 in the table generated by extract) being constant. The set of path indices is always slightly greater than the number of entries calculated. The indices will remain constant, provided that the number of whole shells does not differ between calculations. If distances are altered to the extent that they differ by more than 5%, if the radii of two shells near to the path-length limit differ by less than the maximum change in bond length, or if the number of shells, order of scattering etc. are changed, then using MINMAG will give erroneous results. MINMAG is best used when only EF, AFAC and A parameters are varied, at least by novice users. If distances are to be included, they should be refined using a high value of the step parameter in REFINE.


path overflow: Although the number of paths which may be included in a calculation is not limited (the record is about 2 million), the number that may be stored is limited (the number is displayed at the start of the program). If the path dimension is exceeded, the entries will not appear in EXTRACT tables, and MINMAG and FILTER must not be used. The mechanism for rapid refinements when only AFAC and A parameters are varied will also fail (results will still be correct, but the calculations may be hundreds of times slower). If the path-number dimension, is exceeded, then EXTRACT will be valid but MINMAG and FILTER may not be used, and fast refinement of A and AFAC will not work.


site vacancies: Special difficulties arise when using site vacancies (see mixed sites) to model disordered sites. In this case the structure may contain two adjacent partially occupied sites which are very close to each other. In this case multiple scattering paths are required between the partially occupied sites except for mutually complementary sites which together represent a single atom. The interatomic vectors between such sites are usually small and may be restricted by use of the variable MINDIST. A path, whatever its length, is excluded if any single leg is less than MINDIST.



Units


Sometimes it is useful to subdivide the structure to facilitate either model-building or refinement. Usually this situation occurs with molecular compounds, where specific ligands are treated as separate entities. When building a model it is useful to be able to add or subtract an entire ligand, and it may also be useful to treat it as a more or less rigid entity during refinement. In addition, although it may be quite easy to determine which ligands are present and their distance from the central atom, it may be more difficult to determine the relationship between them in three-dimensions. As multiple scattering paths tend to be strongest when they include bonded distances, including intra-ligand paths but excluding inter-ligand paths may allow a reasonable fit to the spectrum, without having to develop a complete structural model. In EXCURVE parts of the structure treated in this way are called units. They are identified by a common unit number shared by their constituent atoms. The unit number of atoms which are not part of a unit is 0. A unit may be defined using, for example:


                C UN[1-4] 1


This defines unit 1, which may be, say, a CO3 group.


Units themselves have a number of parameters associated with them. If the position of a ligand is to be moved without altering its bonding distance, then it must be rotated about one of its atoms. The atom about which a rotation takes place is called the pivotal atom. It can be defined by a unit parameter (that is, a parameter indexed by unit number) called PIVn (n is the unit number). If PIVn is undefined, then whenever a rotation is performed, the atom nearest to the central atom at the time is used. Leaving PIV parameters undefined is dangerous, as refinement may at least temporarily alter the nearest atom, resulting in loss of coherency of the unit. In most circumstances the pivotal atom is part of the unit. In a few instances it may be outside the unit. For example, in P(Ph)3- compounds, it may be a good idea to define each phenyl group as a unit, but the bonded P atom as the pivotal atom. If a unit is to be moved nearer or farther from the central atom, one atom must be selected for translation. If the pivotal atom is both defined and within the unit, this atom will be used. Otherwise the nearest atom to the centre at the time will be selected, giving rise to the problems seen above. Each atom in the unit, other than the pivotal atom, has an angle associated with it which is expressed in the parameter ANGn (n is of course a shell index, not a unit index). For some purposes, the plane of a unit is important. As units of more than three atoms cannot in general be exactly planar, three atoms are selected to define the unit plane - PIVn, plus two more atoms defined by PLAn and PLBn (the program will select atoms if PLA/B are undefined). A unit must contain equal occupation numbers for all shells. The occupation numbers may however be more than one - the unit may be duplicated by the point symmetry.


Constrained Refinement


Constrained refinement uses rigid body constraints. That is, it involves movement of a complete unit, maintaining all of the interatomic distances and angles with the exception of those associated with the central atom. The only occasion on which the geometry might change, is when the central atom is itself part of a unit, as constrained refinement never results in movement of the central atom. Constrained refinement is turned on by setting the option constraints to on. Once this is done, various other parameters can be used to manipulate the unit. In addition to the parameters describing the coordinates of individual atoms within the unit, there are three rotational parameters -ROTn, TWSTn and TILTn. Formal definitions are given in the parameters section (chapter 4) - note however that they are shell parameters not unit parameters. Two types of motion are possible:


A.            Movement of the pivotal atom (see the definition above), either along a vector passing through the central atom (if X, Y, Z or R for the pivotal atom are changed), or by means of a rotation about an axis passing through the central atom (if TH, PHI, ROT, TWST and TILT for the pivotal atom are changed).


B.            Movement of one of the atoms other than the central atom or pivotal atom. In every case this involves a rotation about an axis passing through the pivotal atom while the position of the pivotal atom itself is unchanged.


Type a motion:


Movement of type A is achieved by changing or refining the shell variable associated with the shell for the pivotal atom. e.g., if the pivotal atom for unit 1 is in shell 7, then a command might be C R7 2.2 or (if the pivotal atom is the pivotal atom) C R[PIV1] 2.2. The latter form removes the need to remember the index of the pivotal atom, which might change, after a SORT or after new atoms have been added. The rules governing motion in each case are (c is the central atom, p is the pivotal atom, u is the vector c-p - see the parameter section, chapter 4 for more precise definitions):


R             motion is along the vector c-p so that the pivotal atom has the new R value requested.


TH           the unit is rotated about an axis through c and normal both to u and the z-axis, so that the new value of theta for the pivotal atom is achieved.


PHI          the unit is rotated about and axis though c and parallel to the z-axis so that the pivotal atom has the new coordinate requested.


X             the unit is translated along a vector through c parallel to the x-axis.


Y             translation parallel to the y-axis.


Z              translation parallel to the z-axis.


ANG        as the c-p-p angle is undefined (0) this is not a valid option.


ROT        the unit is rotated about the vector defined by VECA and VECB. The user must ensure that VECA refers to the central atom and VECB is neither 0 nor the pivotal atom.


TILT        the unit is rotated about the tilt axis nXu by the change in value.


TWST      the unit is rotated about n the normal to the unit plane.


All these type A motions are straightforward if the central atom is at the centre of the coordinate system (0,0,0). If this is not the case, motion is more complex as the parameter values to be satisfied are the absolute values not the values relative to the central atom. Under these circumstances, some values or PHI may be unobtainable, and the program does not allow TH to be changed at all. Note that none of these type A motions will effect the single scattering or intra-unit multiple scattering EXAFS except for R.


Type B motion:

 

Motions of type B are achieved by changing any shell variables associated with the unit other than those of the pivotal or central atoms. The atom given by PLA may often be appropriate.e.g.


                C R7 2.2 or C R[PLA1] 2.2. Note that C PANG1 235 is exactly equivalent to C ANG[PIV1] 235.


The rules governing motion in each case are:


R             The unit is rotated about the tilt axis uXn


TH           the unit is rotated about the tilt axis uXn


PHI          the unit is rotated about n the normal to th unit plane


X,Y          the unit is rotated about n


Z              the unit is rotated about the tilt axis uXn


ANG        the unit is rotated about uX(s-p), where s is the vector defining the shell in question


ROT        the unit is rotated the axis defined by VECA and VECB.


TWST      the unit is rotated about n


TILT        the unit is rotated about the tilt axis uXn


Sometimes, constrained refinement is required only for a single operation. It becomes tedious to switch it on, change a parameter and switch it off again. It is also normally disastrous to perform an operation when the constrinaed refinement status is not what you thought it was. For these cases, a single command CCHANGE (constrained change) is provided (see the command documentation, chapter 5).


Rules and Cell Parameters


A much simpler scheme for fixing one parameter in terms of another is to use the command RULE (see chapter 5). This allows, for example, the 4th shell to be maintained at twice the first shell distance. It can be used for any parameters, not just coordinates.

The parameters ACELL, BCELL, CCELL can be used to scale all the coordinates, as is appropriate for multi-shell fits to high symmetry solids, where shell ratios must be preserved to obtain a meaningful result. See the section on cell parameters in chapter 5.


Restrained Refinement


Restrained refinement is, like constrained refinement, a system for ensuring the coherence of well defined elements in the structure. It differs in that some distortion of the ideal distances is allowed, and there is no need to define units, or ensure that shells to be coupled have similar occupation numbers. It simply defines a set of preferred distances, which given suitable weightings will remain more or less fixed during refinement. The procedure is formally defined in the theory section, chapter 1, and examples are given in the paper by Binsted, Strange and Hasnain (1990). To get started:


Select a relative weighting for EXAFS and restraints:


                C WEX .5;C WD .5


Set up some ideal distances:


                C D2:1 1.2;C D3:2 1.1;C D3:1 1.3


and some bond-weightings


                C W2:1 1;C W3:2 1;C W3:1 1


FIT will display actual and ideal distances, and statistics. CHANGE (in chapter 5) and the parameter section (chapter 4) describe the variables and easy ways of changing them for complicated structures.



Metallo-proteins - amino acids, Brookhaven files and torsion angles


A number of options are provided primarily for use with proteins. These include additional unit parameters such as a unit name UNAMEi, torsion angles, to allow residues to be moved while the protein backbone remains intact. There are also easy ways to set up structures, either by reading from files in Brookhaven database format, reading .car files from the Cerius Explorer modelling program, or using a ligand database based on PROTIN restraint files. Additional unit parameters, as well as PIV, PLA, PLB etc. are defined if units are set up in this way. These parameters are most easily edited using the command PLOT UNIT n which has an edit facility. This is not usually the best way of displaying individual, complex units however, DRAW UNIT n is better, but does not have an edit facility.



Torsion angle refinement


Torsion angle refinement, like constrained refinement, involves simultaneous movement of atoms within a unit. In this case however, three of the four atoms defining the dihedral angle remain stationary while the others rotate until the desired angle is obtained. Three torsion angles may be defined. By default one (TORC) is defined by atoms c-p-a-b, while the others (TORA and TORB) are undefined except when a Brookhaven ( or .pdb ) file is read, when the atoms N-CA-CB-CG and CA-CB-CG-CD are used. The atoms defining the torsion angle for a unit may be changed at any time using PLOT UNIT which allows interactive changes to unit parameters. It is not relevant whether CONSTRAINTS is on or off when changing or refining torsion angles.


Brookhaven files


Brookhaven format files (often .pdb files on Unix systems) may be read using READ PARAMETERS BROOK (R PAR BR). The atom number of the central atom is requested, which allows atoms within MAXRAD angstroms of the central atom to be read. If these include atoms within many-atom residues, the whole residue is read. The variable MAXRAD is set to 5 Å by default. It may be changed if required. Brookhaven format files may be written using PRINT PARAMETERS BROOK. It is also possible to update a file, for which the EXCURVE parameters are a part, using PRINT PARAMETERS REPLACE. This is only possible if the same file has previously been read, as the atom numbers must correspond.


Cerius Explorer files


Cerius (.car) files, contain similar information to .pdb files, they may be also be read using: R PAR CAR.


The ligand database


The ligand database resides in the file ideals and is based on the database used by the crystallographic refinement program prolsq. It has been extended to include non-amino acid ligands and information for defining the default relationship to the central atom for use in EXAFS analysis. In order to use the database the shell for the pivotal atom and the coordinates of the pivotal atom should be selected. E.g.:


 C X3 1.3;C Y3 1.3;C Z3 0.


The ligand can then be selected using:


 C T3 (ligand name)


The ligand name may be an amino acid symbol (TYR, HIS etc.) or a chemical formula (CO3, SO4). A list of current names may be obtained using:


 C T3 ?


The ligand will be assigned to the next vacant unit number. The pivotal atom will be assigned to the specified shell, and shell numbers above NS will be used for the other atoms. The ligand name will be used for the unit name. The unit parameters PIV, PLA, PLB, will be set up, as will any relevant torsion angles. Bond angles and torsion angles will be defined from database information. The only undefined aspect of the ligand is the rotation about the vector u. This may be changed using the ROT parameter with VECA=VECB=0. As ROT has no absolute significance it is not possible to use the current setting to define the orientation. This coordinate has no effect on the theory unless inter-unit multiple scattering or XANES calculations are performed.


Idealisation and the Spin command


Because protein crystal refinements have been subject to generally weaker constraints on the interatomic distances and angles within amino-acid side-chains than is usual with EXAFS, it may be desirable to idealise the side chains. This is done by replacing them with amino-acids from the ligand database. The command used to do this is IDEALISE. The syntax is:


idealise ([spin/nospin]) unit-number


The optional keyword determines whether the spin command (described below) is also executed. If no unit number is specified, all units are idealised.

Idealisation assumes that all four main-chain atoms (N, O, C, CA) remain unchanged and that the torsion angles TORA and TORB remain unchanged. These two assumptions mean that the cumulative effect of small changes in interatomic distances, angles and torsion angles may result in very large movements of the atoms coordinated to the metal atom. The metal-ligand distance, the principal angle, and the torsion angle TORC can be optimised, without changing other distances or angles, using either the command spin or map. In each case TORA and TORB are varied. It is also possible to perform a general rotation about any bond, although unlike changing a torsion angle this will also result in changes to the main-chain atoms. A rotation can be achieved using a ROT parameter, after setting VECA and VECB to the correct shells numbers.


The command spin has the syntax:


spin [A or B or R]([long or short]) unit-number


e.g., spin along 2, spin blong 3


A signifies TORA, B TORB and R a general rotation ROT.

long or short determine the amount of output.


The unit number must be specified, and the unit parameters piv, pla and plb must be defined.


The command requests an optimum bond angle and central atom torsion angle, and determines the optimum value of TORA, etc. to achieve both these angles and the shortest metal-ligand distance.


One problem with spin is that the torsion angles cannot in general be optimised sequentially. An alternative is to use map to find the optimum value. To do this restrained refinement is used with the optimum distance (and/or angle) specified and with WEX a little higher than 0 and WD close to 1. TORA and TORB for the unit in question are used as map parameters.


Single Crystals and Surfaces


The analysis of both single crystal and surface spectra makes use of the polarisation dependence of the technique.


As the program can analyze both polarised and unpolarised spectra from the same sample simultaneously, it is necessary to specify how each spectrum is to be treated when it is read. Theory calculation can be considerably speeded up if several spectra can be calculated together. This is only possible if they are of the same edge, have the same energy range, and share a common value of EF. If this is the case, they may be treated as members of a polarisation set. The sequence number in each set is requested by READ EXPERIMENT.


                Sequence number in polarisation set [0]


                Entering 0 indicates no polarisation dependence

                                1 is the first or only member of a set

                                2 is a spectrum equivalent in every way except in terms of beam parameters

 

Once polarised spectra have been read, polarisation dependence is initiated using SET POLARISATION ON or SET POLARISATION EXACT and setting the appropriate beam parameters. ON simply takes the ratio of the amplitudes for the polarised and unpolarised cases in the small atom approximation. EXACT calculates the directional effects arising from angular part of the dipole matrix element for the full Z-matrix. It is much slower, and for multiple scattering calculations will only work at present for shells with single atoms (use EXPAND). For both single and multiple scattering, one effect of using ON is to ignore spherical-wave effects which are important very near the edge. It is exact, but totally useless, for cubic point groups ! In addition, for multiple scattering, the polarisation dependence is approximated by a scattering factor depending only on the angle between the first and last leg of the scattering path (γ). It is quite accurate for γ ~ 0, but very inaccurate for γ ~ 90. At γ = 90, it is zero, however important the path is. The approximation can therefore be extremely poor, for some paths. The EXACT polarisation dependence makes use of the Curved Wave theory option, and so is restricted in terms of angular momentum values in the same way. It is most useful in fitting the edge region, where curved wave effects are largest. It is however extremely slow.


When performing polarisation dependent calculations, two or three spectra will normally have been read, each referring to a different beam or polarisation direction. In this case, there are a set of beam parameters associated with each spectrum. The beam parameters are defined in terms of the cluster coordinates by BETHn and BEPHIn (beam θ and φ parameters) and an azimuthal parameter BEWn, the projection of the direction of the photon e-vector onto the xy plane. This system of reference is illustrated in Gurman, (1988). Selection of the correct beam parameters is facilitated by the command:


                LIST SPARS


which displays in addition to the above parameters, the actual direction of the e-vector in both cartesian and polar coordinates. The parameters have indices n given by the spectrum number, so if only a single spectrum has been read, the index is 1 (BETH1 etc). Typical output from the command is given below.

 

   Spectrum 1 Spectrum 2 Spectrum 3

 

   BETH1 = 0.000 BETH2 = 0.000 BETH3 = 90.000

   BEPHI1= 0.000 BEPHI2= 0.000 BEPHI3= 0.000

   BEW1 = 90.000 BEW2 = 0.000 BEW3 = 90.000

 

   EX1 = 1.000 EX2 = 0.000 EX3 = 0.000

   EY1 = 0.000 EY2 = 1.000 EY3 = 0.000

   EZ1 = 0.000 EZ2 = 0.000 EZ3 = -1.000

 

   ETH1 = 90.000 ETH2 = 90.000 ETH3 = 180.000

   EPHI1 = 0.000 EPHI2 = 270.000 EPHI3 = 0.000


Domain averaging. For some surfaces, although the normal incidence e//x and e//y are in principal different, because of random orientation of surface domains, no difference is seen in practice. In this instance it is necessary to average the theory over the two orthogonal directions. This is implemented by the command SET AVERAGE ON. When this is done the first two spectra are averaged - it is thus usually necessary to read one of the spectra twice - the theory will then be calculated twice, and the average used for each of the first two spectra. The program does not ensure that the beam direction is normal to the surface or that the two azimuthal angles are orthogonal as required so this must be done by the user. This procedure may also be used with twinned crystals.


Surface analysis may use a number of parameters not required elsewhere. The adsorbate layer is often defined by knowledge of the coverage, the LEED pattern, and the lattice spacing of the substrate. In this instance, the atoms forming this layer need not be refined. Below a few atomic layers, the substrate is also unlikely to differ greatly from the bulk phase, and may also be defined by knowledge of the bulk cell parameters. Between these to regions it is possible to define a surface layer. In many instances, refining the adsorbate-substrate distance, the relaxation of the surface layer, and reconstructions within it allows a large number of shells to be fitted, using a small number of parameters, providing a rigorous test of a particular model of the surface.


The adsorbate-substrate distance can be refined using DELTAZ which changes the Z-coordinates of all atoms below the XY plane. It is not necessary to specify constrained refinement in order to use this.


The surface layer is defined using ZMIN and ZMAX. The adsorbate is usually assigned coordinates with Z >= 0, with surface atoms lying below the XY plane, with Z -ve. In this case, ZMIN and ZMAX will be of the order -1.5 and -.5 respectively (for a monatomic surface layer). It is important that ZMIN and ZMAX are defined so that random changes in the coordinates during refinement do not cause atoms to move in and out of the layer.


Once the surface layer is defined, a simple model of surface relaxation may be tested by refining SURREL. This moves the substrate relative to the surface layer. The initial value of SURREL is 1, so refined values of the order of 1.1 are likely.


More complex relaxations may be achieved by refining the Z-coordinates of atoms in groups - e.g. Z[3,5,9,11], Z[4,6,8,12].


In order to treat reconstructions, it is also useful to define a surface cell. This is done using ACELL and BCELL. These parameters should be defined before any of the atom coordinates, the reason being that changing them will alter the x- and y- values of all the atoms in the cluster, even if constrained refinement is not selected. BCELL ( and for bulk crystals, CCELL) will reflect the point symmetry of the cluster. Thus if the symmetry is defined as C4v, changing ACELL will also change BCELL. Once the cell is defined, The parameters SDXn, and SDYn can be used to effect reconstructions. Although this approach may have limited applications, it can be applied to some quite complex reconstructions. See for example Binsted and Norman [n].


Another type of transformation may be achieved using SURROT which rotates atoms about the origin of their surface cell.


All these transformations are restricted by the requirement that they are compatible with the point symmetry of the cluster, and therefore are of greatest use with clusters described by low symmetry.

A simple demonstration of some of these options is given in the examples section of the manual (example 3). Further discussion and examples appear in the Parameters and Related Topics section under surface parameters.


Some typical steps surface analysis


1. Set up the initial parameters ( e.g. using PAXAS ) so the adsorbate atoms are at Z=0 or above. Ensure all the shells are compatible with the point group.


2. Define the point group.


3. Change ZMIN and ZMAX to refine the surface layer: -1.0 and -0.1 will often suffice.


4. Set the beam polarisation parameters for each experiment to be analyzed.


5. Set SURFACE to ON.


6. Adjust the adsorbate-substrate distance using DELTAZ.


7. Adjust the surface relaxation using SURREL.


8. Adjust the bulk spacing using ACELL, BCELL, CCELL as required by symmetry (use ACELL[1,3] or ACELL[1-3] for isotropic refinement in non-cubic point groups.


9. Adjust the displacements of the adsorbate and reconstruction of the surface layer using SDX and SDY.


Whole-spectrum fitting


Whole-spectrum fitting is the analysis of the total absorbance spectrum, including both the atomic and scattering contributions, over the whole energy range - from below the edge to the limit of measurable EXAFS. The procedure is selected using


                SET ATOMIC_ABS ON


It requires atomic transition rates, calculated for real (rather than complex) potentials, so potentials and phaseshifts should be re-calculated after the option is selected. It also requires that EMIN is given a negative value, so the pre-edge region can be seen. The data to be fitted should consist of absorbance vs. either eV above the edge, or absolute photon energy. If the latter, or if the edge position is not accurately defined, the variable E0 can be used to generate the correct energy scale. The edge position so defined should accurately reflect the position of the Fermi level when the spectrum is read. There is no suitable 'fudge factor' to alter the edge position after it is read in.


Other parameters required are TEMP - this defines the effective temperature used to define a T-dependent Fermi function, which is convoluted with the edge. As this is also used to approximate lifetime and resolution, a value very much higher than the actual temperature may be needed to match the experimental resolution.


The parameters PRE0i, PRE1i, PRE2i correct for residual pre-edge background (the index i is only required for multiple spectra).


The parameters POST0i ... POST8i and OFFSET (POSTn is a polynomial in (eV-OFFSET) correct the theoretical atomic transition rate - this must be accurate to a few % in order for the EXAFS to be refinable - an impossible task theoretically.


The procedure is discussed in more detail in Binsted and Hasnain, 1996. Results obtainable now that most of the improvements recommended in the program have been introduced are much better however.



Startup files



The first step is usually to set up a startup file. This contains commands to read in spectra, set options that are invariably used, read parameter and phaseshift files etc. It is not absolutely essential to do this as the commands can be entered at the terminal in exactly the same format, but it is difficult to remember as well as tedious to enter a dozen or more lines every time the program is used.


A startup file may look like this ( you can include comments starting with ! )


!Set up some aliases for plotting hard copies

!make sure alias names are otherwise incomprehensible to the program

!T0 is 'plot the exafs as hard copy'

alias T0

gs dev 2;p;;gs dev 1

!T1 is a hard-copy coplot

alias T1

gs dev 2;cp;;gs dev 1

!T2 plots 3 spectra in separate frames

alias T2

gs fr sel;p;1;2;3;;gs fr 1

!T3 plots 3 FT's in 3 frames

alias T3

gs fr sel;p ft;1;2;3;;gs fr 1

!read in two EXAFS spectra

r ex 1;ba2ino3f.ex1;1;12;BA K;;

r ex 2;ba2ino3f.ex2;1;12;IN K;;

!read in excurve parameters

r par;expara1

!set the weighting for the refinement

s w k3

!set a few phaseshift related options

ft nd 2;s rel of;s ground x;s tort v

!set the limits for DW factors

c dwmin 0;c dwmax .03

!set the value of CW

c CW 3

!calculate some phaseshifts

ca pot;;;;;5;;;;

ca ph;;;;;;;;;;;


All this could be put in a file called, for example stba2 ( traditionally excurve command files start with st).


To run it, start the program:


excurve

%stba2( run the startup file)

 

You can then enter further input from the terminal.



Bond Valence Sums

The bond valence sum, given by Brown as:


(43)




ole.gif(43)


is a useful check of the validity of cluster coordinates. It may be check using FIT BOND_VALENCE, which uses values of ION (or default values if ION parameters are zero), and BOND to establish the cuttoff for bonded atoms. Note that ION, which is index by atom-type also effects phaseshift calculations, and should be reset after use for bond valence calculations.





3. Examples


The examples below are essentially the same as the examples used to demonstrate the program.


Comment lines start with a ! as in EXCURVE command files


Program output other than prompts is either indented by two spaces or in fixed-space font (tables)


Prompts issued by the program are not indented


User responses are indented by eight spaces and in bold. [return] signifies a carriage return.


Some of the output below is, by default, written only to the log file exout.lis. Options are available to send more output !to he terminal if required.


C OUTPUT 1, 2 ,3 etc. gives more terminal output throughout


The CALC command prompts for the amount of output produced during potential and phaseshift calculations


Example 1. Refinement of Copper Foil


!Fitting Cu foil (100 K) - typical run time ~ 6 hours


!Read in the data


ENTER COMMAND:


                r ex


Filename for Experiment 1 ?


                culn.exn


Point frequency [1] ?


                [return]


Column combination [12] ?


                [return]


Edge ? [CU K]


                [return]


Sequence-number in polarisation set [0]


                [return]


Number of clusters for this experiment [1]


                [return]


!The next lines are the headers on the data file


  EXAFS :                 CULN.EX3

  EV                          EXAFS


  Number of points read: 290



!Define the atom-types


ENTER COMMAND:


                c atom[1-2] cu


!Calculate the potentials using all default options


ENTER COMMAND:


                ca pot;;;;;;;;;;;

 

  Z= 29 (CU) 1s1/2 1 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

             3d5/2 6 4s1/2 2 - total 29

 

  Z= 29 (CU) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

             3d5/2 6 4s1/2 1 - total 29


  Excited atom code : 1 Log grid increment : 0.02784

  Lattice constant : 2.56000 Muffin-tin radius : 1.28000 349

  Atomic volume : 11.86329 Wigner-seitz radius: 1.41483 352

  Exchange constant : 0.66670 Madelung constant : 0.00000

     I R RHO(AT) RHO(SUP) RV(AT) RV(SUP) RV(MT) V(MT))

     50 0.0006 0.0478 0.0478 -57.8672 -57.8672 -57.8932 -0.987E+05

    100 0.0024 0.6551 0.6551 -57.4673 -57.4673 -57.5661 -0.244E+05

    150 0.0095 6.5809 6.5809 -55.8846 -55.8856 -56.2250 -0.592E+04

    200 0.0382 20.6102 20.6103 -50.2474 -50.2514 -51.0456 -0.134E+04

    250 0.1537 41.2852 41.2869 -34.3744 -34.3911 -36.0022 -0.234E+03

    300 0.6183 24.1379 24.1672 -10.3973 -10.4697 -12.6942 -0.205E+02

    348 2.3524 1.2220 2.2412 -0.7806 -1.4629 -3.2688 -0.139E+01

    349 2.4188 1.1539 2.2887 -0.7235 -1.4591 -3.2973 -0.136E+01

    350 2.4871 1.0892 2.3569 -0.6691 -1.4640 -3.3396 -0.134E+01

  CU (CU) Rho0: 0.3775 Efermi: -5.566 V0: -18.149 Electrons: 28.903 (Z= 29)

 

  Z= 29 (CU) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

              3d5/2 6 4s1/2 1 - total 29

 

  Z= 29 (CU) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

              3d5/2 6 4s1/2 1 - total 29

 

  Log grid increment : 0.02784

  Lattice constant : 2.56000 Muffin-tin radius : 1.28000 349

  Atomic volume : 11.86329 Wigner-seitz radius: 1.41483 352

  Exchange constant : 0.66670 Madelung constant : 0.00000

       I R RHO(AT) RHO(SUP) RV(AT) RV(SUP) RV(MT) V(MT))

     50 0.0006 0.0845 0.0845 -57.8385 -57.8385 -57.8698 -0.986E+05

    100 0.0024 1.1583 1.1583 -57.3521 -57.3520 -57.4714 -0.243E+05

    150 0.0095 11.6431 11.6431 -55.4412 -55.4422 -55.8521 -0.588E+04

    200 0.0382 35.3221 35.3222 -49.0428 -49.0468 -49.9952 -0.131E+04

    250 0.1537 39.7602 39.7619 -33.3862 -33.4030 -34.9944 -0.228E+03

    300 0.6183 22.4335 22.4629 -10.3392 -10.4121 -12.5856 -0.204E+02

    348 2.3524 1.1058 2.1223 -0.6822 -1.3663 -3.1437 -0.134E+01

    349 2.4188 1.0323 2.1638 -0.6330 -1.3705 -3.1788 -0.131E+01

    350 2.4871 0.9641 2.2280 -0.5863 -1.3831 -3.2281 -0.130E+01

  CU (CU) Rho0: 0.3574 Efermi: -5.456 V0: -17.590 Electrons: 29.055 (Z= 29)


!Calculate the phaseshifts - increment the core width to allow for experimental resolution


ENTER COMMAND:


                ca ph;;2.761


!Define the structure


ENTER COMMAND:


                c acell 2.5*1.414213562


ENTER COMMAND:


                c r1 2.5


ENTER COMMAND:


                c t[1-20] 2


!Use a 7-shell cluster initially


ENTER COMMAND:


                c ns 7;str fcc


!Set the maximum length for MS paths


ENTER COMMAND:


                c plmax 14


!Guess some initial values for the Debye-Waller factors


ENTER COMMAND:


                c a1 .01;c a[2-20] .02


!Initial value of EF (the refinement will not work well if you start from 0)


ENTER COMMAND:


                c ef 1


!Inspect the parameters


ENTER COMMAND:

 

                l               



  LMAX = 25.000 DLMAX= 25.000 TLMAX= 9.000 WP = 0.100 NS = 7.000

  EF = 1.000 VPI = 0.000 AFAC = 1.000 EMIN = 3.000 EMAX =3000.000

  EF1 = 0.000 VPI1 = 0.000 AFAC1= 1.000 EMIN1=-311.500 EMAX1=1525.540

  Shell 0 N0 = 1.000 T0 = 1(CU) R0 = 0.000 A0 = 0.010 B0 = 0.000-1 0

  Shell 1 N1 = 12.000 T1 = 2(CU) R1 = 2.500 A1 = 0.010 B1 = 0.000 1 0

  Shell 2 N2 = 6.000 T2 = 2(CU) R2 = 3.536 A2 = 0.020 B2 = 0.000 1 0

  Shell 3 N3 = 24.000 T3 = 2(CU) R3 = 4.330 A3 = 0.020 B3 = 0.000 1 0

  Shell 4 N4 = 12.000 T4 = 2(CU) R4 = 5.000 A4 = 0.020 B4 = 0.000 1 0

  Shell 5 N5 = 24.000 T5 = 2(CU) R5 = 5.590 A5 = 0.020 B5 = 0.000 1 0

  Shell 6 N6 = 8.000 T6 = 2(CU) R6 = 6.124 A6 = 0.020 B6 = 0.000 1 0

  Shell 7 N7 = 48.000 T7 = 2(CU) R7 = 6.614 A7 = 0.020 B7 = 0.000 1 0


!Switch on MS - only third order, two different scatterers so far


ENTER COMMAND:


                s ms al


!Refine EF, ACELL and A1


ENTER COMMAND:


                ref


ENTER COMMAND:


  Parameter refinement with constraints off:


                ef;acell;a1;=

 

  Least squares refinement using k**2 weighting

 

  Initial parameters


   1 EF 1.000 0.27212 0.00000 27.21164 0.03675

   2 ACELL 3.536 0.00212 0.00000 0.21167 16.70298

   3 A1 0.010 0.00028 0.00000 0.02800 0.35711

 

  Enter:     Write to save the list of variables

                 Continue to refine interactively

                 a number to edit, add to, or delete from the list


                c


  EF = 1.00000 ACELL = 3.53553 A1 = 0.01000

  Call 1 F 66.0630 R 76.554 F- 66.063 Rex 76.554 RD 0.00 Rx 0.000 192 7


Select Next,Exit,Complete,Stats or Plot


!Plot toggles plotting during refinement


                p

 

  EF = 1.27212 ACELL = 3.53553 A1 = 0.01000

  Call 2 F 54.5289 R 68.497 F- 52.937 Rex 68.497 RD 0.00 Rx 0.000 192 7


Select Next,Exit,Complete,Stats or Plot


!Next n (or just n) disables prompts for the next n cycles


                333


  EF = 1.00000 ACELL = 3.53765 A1 = 0.01000

  Call 3 F 53.6014 R 67.680 F- 52.937 Rex 67.680 RD 0.00 Rx 0.000 192 7

  EF = 1.00000 ACELL = 3.53553 A1 = 0.01028

  Call 4 F 52.6384 R 67.541 F- 52.638 Rex 67.541 RD 0.00 Rx 0.000 192 7

  EF = -0.76881 ACELL = 3.53020 A1 = 0.01060

  Call 5 F 43.8959 R 64.220 F- 43.896 Rex 64.220 RD 0.00 Rx 0.000 192 7

  EF = -2.21235 ACELL = 3.53958 A1 = 0.01100

  Call 6 F 36.2281 R 58.990 F- 36.228 Rex 58.990 RD 0.00 Rx 0.000 192 7

  EF = -3.76135 ACELL = 3.55790 A1 = 0.01134

  Call 7 F 27.6812 R 51.503 F- 27.681 Rex 51.503 RD 0.00 Rx 0.000 192 7

  EF = -6.25711 ACELL = 3.56873 A1 = 0.01136

  Call 8 F 18.7336 R 43.870 F- 18.734 Rex 43.870 RD 0.00 Rx 0.000 192 7

  EF = -7.88148 ACELL = 3.58281 A1 = 0.01070

  Call 9 F 13.7414 R 37.167 F- 13.741 Rex 37.167 RD 0.00 Rx 0.000 192 7

  EF = -7.92222 ACELL = 3.58326 A1 = 0.01097

  Call 10 F 13.7654 R 37.431 F- 13.741 Rex 37.431 RD 0.00 Rx 0.000 192 7

  EF = -8.08531 ACELL = 3.58141 A1 = 0.01070

  Call 11 F 13.8338 R 36.869 F- 13.741 Rex 36.869 RD 0.00 Rx 0.000 192 7

  EF = -9.58525 ACELL = 3.59704 A1 = 0.01040

  Call 12 F 11.4548 R 33.323 F- 11.455 Rex 33.323 RD 0.00 Rx 0.000 192 7

  EF = -9.92608 ACELL = 3.60063 A1 = 0.01028

  Call 13 F 11.3707 R 33.062 F- 11.371 Rex 33.062 RD 0.00 Rx 0.000 192 7


  Minimum Predicted, Accuracy = 0.3743E-01 Cond = 2 At Call 13


Filename for statistics ?

Filename: [excora1.dat] ?


                <return>


  Call 13, R(min)= 11.3707


  Best Values Are :


  EF = -9.92608

  ACELL = 3.60063

  A1 = 0.01028


!Now include all third order paths. Refine the DW factors for the

!first 6 shells (4th order terms are required at the distance

!of the 7th shell)


ENTER COMMAND:


                c atmax 3


ENTER COMMAND:


                ref


Enter parameter name or "=" to skip


                ef;acell;a1;a2;a3;a4;a5;a6;=

 

  Least squares refinement using k**2 weighting

 

 

  Initial parameters


   1 EF -9.926 0.27212 0.00000 27.21164 -0.36477

   2 ACELL 3.601 0.00212 0.00000 0.21167 17.01051

   3 A1 0.010 0.00029 0.00000 0.02878 0.35711

   4 A2 0.020 0.00056 0.00000 0.05601 0.35711

   5 A3 0.020 0.00056 0.00000 0.05601 0.35711

   6 A4 0.020 0.00056 0.00000 0.05601 0.35711

   7 A5 0.020 0.00056 0.00000 0.05601 0.35711

   8 A6 0.020 0.00056 0.00000 0.05601 0.35711

 

Enter:      Write to save the list of variables

                Continue to refine interactively

                a number to edit, add to, or delete from the list


                c;p;c;;


  EF = -9.92608 ACELL = 3.60063 A1 = 0.01028

  A2 = 0.02000 A3 = 0.02000 A4 = 0.02000

  A5 = 0.02000 A6 = 0.02000

  Call 1 F 9.0099 R 29.860 F- 9.010 Rex 29.860 RD 0.00 Rx 0.000 192 7

  EF = -9.65396 ACELL = 3.60063 A1 = 0.01028

  A2 = 0.02000 A3 = 0.02000 A4 = 0.02000

  A5 = 0.02000 A6 = 0.02000

  Call 2 F 9.6026 R 30.736 F- 9.010 Rex 30.736 RD 0.00 Rx 0.000 192 7



       etc.


  EF = -10.37898 ACELL = 3.59946 A1 = 0.01022

  A2 = 0.01639 A3 = 0.01365 A4 = 0.01434

  A5 = 0.01799 A6 = 0.01818

  Call 22 F 6.1436 R 24.564 F- 6.144 Rex 24.564 RD 0.00 Rx 0.000 192 7


  Minimum Predicted, Accuracy = 0.6371E-02 Cond = 2 At Call 22


  EF = -10.37898 ACELL = 3.59946 A1 = 0.01022

  A2 = 0.01639 A3 = 0.01365 A4 = 0.01434

  A5 = 0.01799 A6 = 0.01818

  Call 23 F 6.1436 R 24.564 F- 6.144 Rex 24.564 RD 0.00 Rx 0.000 192 7


       etc.


  EF = -10.37898 ACELL = 3.59946 A1 = 0.01022

  A2 = 0.01639 A3 = 0.01365 A4 = 0.01434

  A5 = 0.01799 A6 = 0.01874

  Call 31 F 6.1454 R 24.571 F- 6.144 Rex 24.571 RD 0.00 Rx 0.000 192 7


 

  Fit index * k**2 : 0.6145E-03 R-factor : 24.5712 Chisqu : 0.3329E-05

  Rexafs 24.5712 Rdist 0.0000


!Now extend the model to 10 shells, with all 5th order paths

!This will take ages


ENTER COMMAND


                c ns 10


ENTER COMMAND:


                str fcc q

                c plmax 16;c omax 5;c atmax 5


!Refine the DW factors only


ENTER COMMAND


                ref;a1;a2;a3;a4;a5;a6;a7;a8;a[9-10];=

 

  Least squares refinement using k**2 weighting


  Initial parameters


   1 A1 0.010 0.00029 0.46548 0.02861 0.35711

   2 A2 0.016 0.00046 0.00391 0.04589 0.35711

   3 A3 0.014 0.00038 0.00052 0.03824 0.35711

   4 A4 0.014 0.00040 0.00426 0.04017 0.35711

   5 A5 0.018 0.00050 0.00154 0.05038 0.35711

   6 A6 0.018 0.00051 0.00186 0.05092 0.35711

   7 A7 0.020 0.00056 0.00602 0.05601 0.35711

   8 A8 0.020 0.00056 0.01806 0.05601 0.35711

   9 A[9-10] 0.020 0.00056 0.00000 0.05601 0.35711


Enter:      Write to save the list of variables

                Continue to refine interactively

                a number to edit, add to, or delete from the list


                c;p;c;


  A1 = 0.01022 A2 = 0.01639 A3 = 0.01365

  A4 = 0.01434 A5 = 0.01799 A6 = 0.01818

  A7 = 0.02000 A8 = 0.02000 A[9-10] = 0.02000

  Call 1 F 4.5154 R 20.310 F- 4.515 Rex 20.310 RD 0.00 Rx 0.000 192 10

  A1 = 0.01050 A2 = 0.01639 A3 = 0.01365

  A4 = 0.01434 A5 = 0.01799 A6 = 0.01818

  A7 = 0.02000 A8 = 0.02000 A[9-10] = 0.02000

  Call 2 F 4.5573 R 20.519 F- 4.515 Rex 20.519 RD 0.00 Rx 0.000 192 10


       etc.


  A1 = 0.01020 A2 = 0.01596 A3 = 0.01355

  A4 = 0.01395 A5 = 0.01708 A6 = 0.01176

  A7 = 0.01450 A8 = 0.01388 A[9-10] = 0.02227

  Call 15 F 4.3090 R 19.786 F- 4.309 Rex 19.786 RD 0.00 Rx 0.000 192 10


  Minimum Predicted, Accuracy = 0.3193E-02 Cond = 2 At Call 15


  Call 15, R(min)= 4.3090


  Best Values Are :

  A1 = 0.01020

  A2 = 0.01596

  A3 = 0.01355

  A4 = 0.01395

  A5 = 0.01708

  A6 = 0.01176

  A7 = 0.01450

  A8 = 0.01388

  A[9-10] = 0.02227


!Save the parameters, and create a table of MS paths (using the default filename in each case


ENTER COMMAND:


                pr par;

 

  Fit Index: with k^2 Weighting 0.4309

  R-Factor : with k^2 Weighting 19.7860

  Amplitude of Experiment 53.8497

  R(exafs) = 19.7860 Weight: 1.00

  R(distances)= 0.0000 Weight: 0.00

  R(angles) = 0.0000 Weight: 0.00

  N(ind) = 31.5 Np = 1. Chi^2 = 2.3179E-6


Parameters printed in expara1.dat


ENTER COMMAND

 

                extr q;


Paths printed in extaba1.dat


!Plot the final result


ENTER COMMAND


                cp


!Obtain a hard copy


ENTER COMMAND:


                gs dev p;cp


!Finish


ENTER COMMAND:


                END

 

A much better fit can be obtained using 20 shells at considerable extra computational expense.



fig2.gif

Figure 2 - 10 shell fit to Cu foil














Example 1a. Whole Spectrum Refinement of Whole Sectrum Refinement ofCopper Foil



!Select the plotter amd set up some aliases


                gs plot ps_file


                alias pcp;gs dev p;cp;gs dev t


                alias pp;gs dev p;p;gs dev t


!Set the e0 value in order to read the experiment


                c e0 8979.66


                r ex;culn.bsa;;;;;;;;;;;;;;;;;;


!Read the paramaters - from a seven shell EXAFS refinement


                r par;cu.par


!!Define the symmetry


                sym oh


!Select the whole-spectrum option


                s atom on


!Allow calculation below the edge


                c emin -3


!Select the core wdith (1 ev for experimental resolution)


                c cw 2.761


!Include multiple scattering


                s ms al


!Calculate potentials and phaseshifts


!!These are defaults - using different options can give better results


                ca pot;;;;;;;;;;;;;;;


                ca ph;;;;;;;;;;;;;;;;


!Select 5th order correction


                c npost 5


!Refine the post-edge polynomial correction parameters,


! plus effective temperature and the E0 correction


! First step will be slow


                ref post


                6;offset;7;temp;8;de0


                c;p;c;=


                cp


!Turn off the k^2 weighting to see the edge


                s we n


                p


!Display the atomic-background parameters


l back



fig2b.gif

Figure 3 - Unweighted whole spectrum fit to Cu foil

fig2a.gif

Figure 4 - Whole spectrum fit to k^2 weighted Cu foil



Example 2. Gallium Antimonide


Find the cell parameter and Debye-Waller factors of GaSb by simultaneously fitting the Ga K-edge and Sb K-edge

The compound has the cubic sphalerite structure, with Sb and Ga each in 4-fold coordination. The author wishes to thank Dr.A.Sapelkin for permission to use this data.



!Read the data for the gallium edge


ENTER COMMAND:


                r ex 1


Filename for Experiment 1 ?


                cgasb.exb


Point frequency [1] ?


                1


Column combination [12] ?


                32


Edge ? [CU K]


                ga k


Sequence-number in polarisation set [0] ?


                [return]


Number of clusters for this experiment [1] ?


                [return]


  HARTREES ABSORPTION EV


  Number of points read: 359


  SPECTRUM : 1 359 0.670 1511.020


!Read the data for the antimony edge


ENTER COMMAND:


                r ex 2;csbga.exb;;32;sb k;;;;


  HARTREES ABSORPTION EV


  Number of points read: 437


  SPECTRUM : 2 437 0.270 0.081 1493.870 0.000


!Read some pre-existing phaseshift files


ENTER COMMAND:


                r ph


Enter number of phaseshift files


                6


Filename for central atom ?


                exphsa1.gac


  EXCURVE >>> 23/ 3/98 20:52:05


  GA phaseshifts (Z= 31).


  mtr 1.4100 alpha 0.667 madelung const. 0.00 hole-code 1 V0 -17.3443

  Ef -5.6451 RHO0 0.3384 Rlife 7.0000

  Number Of Energy Points: 90


Filename for second atom ?


                .sb;.ga;.sbc;.ga2;.sb2



  SB phaseshifts (Z= 51).


  mtr 1.5900 alpha 0.667 madelung const. 0.00 hole-code 0 V0 -16.6932

  Ef -6.2505 RHO0 0.2854 Rlife 7.0000

  Number Of Energy Points: 90



  GA phaseshifts (Z= 31).


  mtr 1.4100 alpha 0.667 madelung const. 0.00 hole-code 0 V0 -17.0346

  Ef -5.9492 RHO0 0.3121 Rlife 7.0000

  Number Of Energy Points: 90



  SB phaseshifts (Z= 51).


  mtr 1.5900 alpha 0.667 madelung const. 0.00 hole-code 1 V0 -16.3918

  Ef -5.7126 RHO0 0.2951 Rlife 7.0000

  Number Of Energy Points: 90



  GA phaseshifts (Z= 31).


  mtr 1.4100 alpha 0.667 madelung const. 0.00 hole-code 0 V0 -17.0346

  Ef -5.9492 RHO0 0.3121 Rlife 7.0000

  Number Of Energy Points: 90



  SB phaseshifts (Z= 51).


  mtr 1.5900 alpha 0.667 madelung const. 0.00 hole-code 0 V0 -16.6932

  Ef -6.2505 RHO0 0.2854 Rlife 7.0000

  Number Of Energy Points: 90


!Generate the structure - this is made slightly more

!complicated by the need to generate two clusters, one for each edge

!First set the atom parameters


                c atom[1,3,5] ga;c atom[2,4,6] sb


!Set the first shell distance to 6.095/sqrt(16/3) - the approximate

!crystallographic value at RT


                c r1 2.63921


!Set the atom types for the first two shells and the cluster size


                c t1 sb;c t2 ga;c ns 13


!define the structure


ENTER COMMAND:


                str sph q


ENTER COMMAND:


                l


 LMAX = 25.000 DLMAX= 25.000 TLMAX= 9.000 WP = 0.100 NS = 13.000

 EF = 0.000 VPI = 0.000 AFAC = 1.000 EMIN = 3.000 EMAX =3000.000

 EF1 = 0.000 VPI1 = 0.000 AFAC1= 1.000 EMIN1= 0.670 EMAX1=1511.020

 EF2 = 0.000 VPI2 = 0.000 AFAC2= 1.000 EMIN2= 0.670 EMAX2=1511.020

 

Shell 0 N0 = 1.000 T0 = 1(GA) R0 = 0.000 A0 = 0.010 B0 = 0.000-1 0

Shell 1 N1 = 4.000 T1 = 6(SB) R1 = 2.639 A1 = 0.010 B1 = 0.000 1 0

Shell 2 N2 = 12.000 T2 = 5(GA) R2 = 4.310 A2 = 0.010 B2 = 0.000 1 0

Shell 3 N3 = 12.000 T3 = 6(SB) R3 = 5.054 A3 = 0.010 B3 = 0.000 1 0

Shell 4 N4 = 6.000 T4 = 5(GA) R4 = 6.095 A4 = 0.010 B4 = 0.000 1 0

Shell 5 N5 = 12.000 T5 = 6(SB) R5 = 6.642 A5 = 0.010 B5 = 0.000 1 0

Shell 6 N6 = 12.000 T6 = 5(GA) R6 = 7.465 A6 = 0.010 B6 = 0.000 1 0

Shell 7 N7 = 12.000 T7 = 5(GA) R7 = 7.465 A7 = 0.010 B7 = 0.000 1 0

Shell 8 N8 = 4.000 T8 = 6(SB) R8 = 7.918 A8 = 0.010 B8 = 0.000 1 0

Shell 9 N9 = 12.000 T9 = 6(SB) R9 = 7.918 A9 = 0.010 B9 = 0.000 1 0

Shell 10 N10= 12.000 T10= 5(GA) R10 = 8.620 A10 = 0.010 B10 = 0.000 1 0

Shell 11 N11= 24.000 T11= 6(SB) R11 = 9.015 A11 = 0.010 B11 = 0.000 1 0

Shell 12 N12= 24.000 T12= 5(GA) R12 = 9.637 A12 = 0.010 B12 = 0.000 1 0

Shell 13 N13= 12.000 T13= 6(SB) R13 = 9.992 A13 = 0.010 B13 = 0.000 1 0


!Remove any existing file PAR1 (O/S dependent)


ENTER COMMAND:


                ^del par1


!store the result for the Ga edge


ENTER COMMAND:


                pr par

 

 Fit Index: with k^2 Weighting 3.4382

 R-Factor : with k^2 Weighting 116.5080

 Amplitude of Experiment 101.5911

 R(exafs) = 116.5080 Weight: 1.00

 R(distances)= 0.0000 Weight: 0.00

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 88.4 Np = 1. Chi^2 = 4.8704E-6

 

Filename: [expara4.dat ] ?


                par1


  Parameters printed in par1


!Repeat for the Sb edge - remember to redefine the central atom type


ENTER COMMAND:


                c t0 sb;c t1 ga;c t2 sb;str sph q


ENTER COMMAND:


                l


 LMAX = 25.000 DLMAX= 25.000 TLMAX= 9.000 WP = 0.100 NS = 13.000

 EF = 0.000 VPI = 0.000 AFAC = 1.000 EMIN = 3.000 EMAX =3000.000

 EF1 = 0.000 VPI1 = 0.000 AFAC1= 1.000 EMIN1= 0.670 EMAX1=1511.020

 EF2 = 0.000 VPI2 = 0.000 AFAC2= 1.000 EMIN2= 0.670 EMAX2=1511.020

 Shell 0 N0 = 1.000 T0 = 6(SB) R0 = 0.000 A0 = 0.010 B0 = 0.000-1 0

 Shell 1 N1 = 4.000 T1 = 5(GA) R1 = 2.639 A1 = 0.010 B1 = 0.000 1 0

 Shell 2 N2 = 12.000 T2 = 6(SB) R2 = 4.310 A2 = 0.010 B2 = 0.000 1 0

 Shell 3 N3 = 12.000 T3 = 5(GA) R3 = 5.054 A3 = 0.010 B3 = 0.000 1 0

 Shell 4 N4 = 6.000 T4 = 6(SB) R4 = 6.095 A4 = 0.010 B4 = 0.000 1 0

 Shell 5 N5 = 12.000 T5 = 5(GA) R5 = 6.642 A5 = 0.010 B5 = 0.000 1 0

 Shell 6 N6 = 12.000 T6 = 6(SB) R6 = 7.465 A6 = 0.010 B6 = 0.000 1 0

 Shell 7 N7 = 12.000 T7 = 6(SB) R7 = 7.465 A7 = 0.010 B7 = 0.000 1 0

 Shell 8 N8 = 4.000 T8 = 5(GA) R8 = 7.918 A8 = 0.010 B8 = 0.000 1 0

 Shell 9 N9 = 12.000 T9 = 5(GA) R9 = 7.918 A9 = 0.010 B9 = 0.000 1 0

 Shell 10 N10= 12.000 T10= 6(SB) R10 = 8.620 A10 = 0.010 B10 = 0.000 1 0

 Shell 11 N11= 24.000 T11= 5(GA) R11 = 9.015 A11 = 0.010 B11 = 0.000 1 0

 Shell 12 N12= 24.000 T12= 6(SB) R12 = 9.637 A12 = 0.010 B12 = 0.000 1 0

 Shell 13 N13= 12.000 T13= 5(GA) R13 = 9.992 A13 = 0.010 B13 = 0.000 1 0


ENTER COMMAND:


                ^del par2


                pr par;par2

 

 Fit Index: with k^2 Weighting 2.0194

 R-Factor : with k^2 Weighting 94.2218

 Amplitude of Experiment 101.4107

 R(exafs) = 94.2218 Weight: 1.00

 R(distances)= 0.0000 Weight: 0.00

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 88.5 Np = 1. Chi^2 = 2.8606E-6

 

  Parameters printed in par2


!Now re-read the parameters for each cluster


ENTER COMMAND:


                r par;par1


 

  Experiment in : cgasb.exb

 

  Fit index with K**2 weight: 0.3438E-02 R-factor :116.5080 Chisqu : 4.87043


ENTER COMMAND:


                r par add;par2


 

  Experiment in : cgasb.exb

 

  Fit index with K**2 weight: 0.2019E-02 R-factor : 94.2218 Chisqu : 2.86061

 

!Fix the cluster parameters for the second cluster


ENTER COMMAND:


                c clus14 -2;c clus[15-ns] 2


!Select the useful energy range


ENTER COMMAND:


                c emin 5;c emax 1250


!Make sure the point group (Td) is defined for both clusters


ENTER COMMAND:


                sym td;td


!Select the MS parameters - 5th order but paths


!involve only 3 DIFFERENT scatterers - initially only include paths to 12 angstroms


ENTER COMMAND:


                c atmax 3;c omax 5;c plmax 12


!Turn the MS on (the ALL option selects all paths in the cluster within filter limits)


ENTER COMMAND:


                s ms al


!Select some initial DW factors


ENTER COMMAND:


                c a[1-ns] .02


ENTER COMMAND:


                c a[1,15] .005;c a[2-4,16-18] .015


!Two energy zero terms are also needed - set these to some value other than 0 at the start


ENTER COMMAND:


                c ef1 20;c ef2 1


ENTER COMMAND:


                l


 LMAX = 25.000 DLMAX= 25.000 TLMAX= 9.000 WP = 0.100 NS = 27.000

 EF = 0.000 VPI = 0.000 AFAC = 1.000 EMIN = 5.000 EMAX =1250.000

 EF1 = 5.000 VPI1 = 0.000 AFAC1= 1.000 EMIN1= 0.670 EMAX1=1511.020

 EF2 = 5.000 VPI2 = 0.000 AFAC2= 1.000 EMIN2= 0.670 EMAX2=1511.020

 Shell 0 N0 = 1.000 T0 = 1(GA) R0 = 0.000 A0 = 0.010 B0 = 0.000-1 0

 Shell 1 N1 = 4.000 T1 = 6(SB) R1 = 2.639 A1 = 0.005 B1 = 0.000 1 0

 Shell 2 N2 = 12.000 T2 = 5(GA) R2 = 4.310 A2 = 0.015 B2 = 0.000 1 0

 Shell 3 N3 = 12.000 T3 = 6(SB) R3 = 5.054 A3 = 0.015 B3 = 0.000 1 0

 Shell 4 N4 = 6.000 T4 = 5(GA) R4 = 6.095 A4 = 0.015 B4 = 0.000 1 0

 Shell 5 N5 = 12.000 T5 = 6(SB) R5 = 6.642 A5 = 0.020 B5 = 0.000 1 0

 Shell 6 N6 = 12.000 T6 = 5(GA) R6 = 7.465 A6 = 0.020 B6 = 0.000 1 0

 Shell 7 N7 = 12.000 T7 = 5(GA) R7 = 7.465 A7 = 0.020 B7 = 0.000 1 0

 Shell 8 N8 = 4.000 T8 = 6(SB) R8 = 7.918 A8 = 0.020 B8 = 0.000 1 0

 Shell 9 N9 = 12.000 T9 = 6(SB) R9 = 7.918 A9 = 0.020 B9 = 0.000 1 0

 Shell 10 N10= 12.000 T10= 5(GA) R10 = 8.620 A10 = 0.020 B10 = 0.000 1 0

 Shell 11 N11= 24.000 T11= 6(SB) R11 = 9.015 A11 = 0.020 B11 = 0.000 1 0

 Shell 12 N12= 24.000 T12= 5(GA) R12 = 9.637 A12 = 0.020 B12 = 0.000 1 0

 Shell 13 N13= 12.000 T13= 6(SB) R13 = 9.992 A13 = 0.020 B13 = 0.000 1 0

 Shell 14 N14= 1.000 T14= 6(SB) R14 = 0.000 A14 = 0.020 B14 = 0.000-2 0

 Shell 15 N15= 4.000 T15= 5(GA) R15 = 2.639 A15 = 0.005 B15 = 0.000 2 0

 Shell 16 N16= 12.000 T16= 6(SB) R16 = 4.310 A16 = 0.015 B16 = 0.000 2 0

 Shell 17 N17= 12.000 T17= 5(GA) R17 = 5.054 A17 = 0.015 B17 = 0.000 2 0

 Shell 18 N18= 6.000 T18= 6(SB) R18 = 6.095 A18 = 0.015 B18 = 0.000 2 0

 Shell 19 N19= 12.000 T19= 5(GA) R19 = 6.642 A19 = 0.020 B19 = 0.000 2 0

 Shell 20 N20= 12.000 T20= 6(SB) R20 = 7.465 A20 = 0.020 B20 = 0.000 2 0

 Shell 21 N21= 12.000 T21= 6(SB) R21 = 7.465 A21 = 0.020 B21 = 0.000 2 0

 Shell 22 N22= 4.000 T22= 5(GA) R22 = 7.918 A22 = 0.020 B22 = 0.000 2 0

 Shell 23 N23= 12.000 T23= 5(GA) R23 = 7.918 A23 = 0.020 B23 = 0.000 2 0

 Shell 24 N24= 12.000 T24= 6(SB) R24 = 8.620 A24 = 0.020 B24 = 0.000 2 0

 Shell 25 N25= 24.000 T25= 5(GA) R25 = 9.015 A25 = 0.020 B25 = 0.000 2 0

 Shell 26 N26= 24.000 T26= 6(SB) R26 = 9.637 A26 = 0.020 B26 = 0.000 2 0

 Shell 27 N27= 12.000 T27= 5(GA) R27 = 9.992 A27 = 0.020 B27 = 0.000 2 0


!Plot the result (this will be slow)


ENTER COMMAND:


                cp


!Refine the structure - as it is cubic, only ACELL can sensibly be refined - it will just scale all the distances


ENTER COMMAND:


                ref 80


  Parameter refinement with constraints off:

  Enter parameter name or = :


                acell

                ef1

                ef2

                =


 Least squares refinement using k**2 weighting

  

 Initial parameters

   1 ACELL 1.000 0.00532 0.00000 0.21167 4.72432

   2 EF1 20.000 0.68353 0.00000 27.21164 0.73498

   3 EF2 1.000 0.68353 0.00000 27.21164 0.03675

 

Enter :     Write to save the list of variables

                Continue to refine interactively

                a number to edit, add to, or delete from the list


!This is correct so no editing needed


                c

 

 ACELL = 1.00000 EF1 = 20.00000 EF2 = 1.00000

 Call 1 F 2.7502 R 32.476 F- 2.750 Rex 32.48 RD 0.00 Rx 0.00 636 27


!The continue option will complete the refinement without further prompts


Select Next,Exit,Complete,Stats or Plot


                p;c


 ACELL = 1.00532 EF1 = 20.00000 EF2 = 1.00000

 Call 2 F 5.3635 R 46.184 F- 2.750 Rex 46.18 RD 0.00 Rx 0.00 636 27

 ACELL = 1.00000 EF1 = 20.68353 EF2 = 1.00000

 Call 3 F 2.6433 R 32.044 F- 2.643 Rex 32.04 RD 0.00 Rx 0.00 636 27

 ACELL = 1.00000 EF1 = 20.68353 EF2 = 1.68353

 Call 4 F 2.8511 R 33.532 F- 2.643 Rex 33.53 RD 0.00 Rx 0.00 636 27

 ACELL = 0.99875 EF1 = 21.21262 EF2 = 0.59809

 Call 5 F 2.3736 R 30.243 F- 2.374 Rex 30.24 RD 0.00 Rx 0.00 636 27

 ACELL = 0.99843 EF1 = 21.84350 EF2 = 0.42212

 Call 6 F 2.3325 R 29.980 F- 2.333 Rex 29.98 RD 0.00 Rx 0.00 636 27

 ACELL = 1.00352 EF1 = 22.04184 EF2 = 0.42212

 Call 7 F 4.5556 R 42.192 F- 2.333 Rex 42.19 RD 0.00 Rx 0.00 636 27

 ACELL = 0.99841 EF1 = 21.83211 EF2 = 0.20828

 Call 8 F 2.3242 R 29.906 F- 2.324 Rex 29.91 RD 0.00 Rx 0.00 636 27

 ACELL = 0.99750 EF1 = 22.21673 EF2 = 0.76116

 Call 9 F 2.4023 R 30.615 F- 2.324 Rex 30.62 RD 0.00 Rx 0.00 636 27

 ACELL = 0.99891 EF1 = 21.42129 EF2 = -0.33415

 Call 10 F 2.3064 R 29.660 F- 2.306 Rex 29.66 RD 0.00 Rx 0.00 636 27

 Minimum Predicted, Accuracy = 0.1541E-02 Cond = 2 At Call 10

 

 Fit index * k^2: 0.2306 Rdistances: 0.0000 Chisqu: 0.3662E-06

 Rexafs: 29.6604 Rxray: 0.0000 Rd: 0.0000

 Call 10, R(min)= 2.3064


 Best Values Are :

  1 ACELL = 0.99891 +/- 0.00067 (2 sigma)

  2 EF1 = 21.42129 +/- 0.48710 (2 sigma)

  3 EF2 = -0.33415 +/- 0.51268 (2 sigma)

 


!Replot

 

ENTER COMMAND:


                cp


ENTER COMMAND:


!Add some more MS paths


ENTER COMMAND:


                c plmax 16


!The DW factors for Ga-Sb and Sb-Ga at the same distance must be the same

!Here it is also assumed that Ga-Ga and Sb-Sb DW factors are the same

!(this turns out to be a reasonable approximation)


ENTER COMMAND:


                ref;a[1,15];a[2,16];a[3,17];a[4,18];a[5,19];a[6,7,20,21];a[8,9,22,23];=


 Parameter refinement with constraints off:

 

 Least squares refinement using k**2 weighting

 

  Initial parameters

   1 A[1,15] 0.005 0.00014 0.00000 0.01400 0.35711

   2 A[2,16] 0.015 0.00042 0.00000 0.04200 0.35711

   3 A[3,17] 0.015 0.00042 0.00000 0.04200 0.35711

   4 A[4,18] 0.015 0.00042 0.00000 0.04200 0.35711

   5 A[5,19] 0.020 0.00056 0.00000 0.05601 0.35711

   6 A[6,7,20,2 0.020 0.00056 0.00000 0.05601 0.35711

   7 A[8,9,22,2 0.020 0.00056 0.00000 0.05601 0.35711

       Continue to refine interactively

       a number to edit, add to, or delete from the list

 

                c;p


!First cycle will be slow


 Call 1 F 2.1960 R 28.800 F- 2.196 Rex 28.80 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 2 F 2.1843 R 28.745 F- 2.184 Rex 28.74 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01542 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000


!Selecting complete avoids all further prompts but the last - which is for the filename for the statistics


  Select Next,Exit,Complete,Stats or Plot


                c


 A[1,15] = 0.00514 A[2,16] = 0.01542 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 3 F 2.2438 R 29.107 F- 2.184 Rex 29.11 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01542

 A[4,18] = 0.01500 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 4 F 2.1939 R 28.784 F- 2.184 Rex 28.78 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01500

 A[4,18] = 0.01542 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 5 F 2.1849 R 28.736 F- 2.184 Rex 28.74 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02056 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 6 F 2.1818 R 28.704 F- 2.182 Rex 28.70 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02056 A[6,7,20= 0.02056

 A[8,9,22= 0.02000

 Call 7 F 2.1869 R 28.721 F- 2.182 Rex 28.72 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00514 A[2,16] = 0.01500 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02056 A[6,7,20= 0.02000

 A[8,9,22= 0.02056

 Call 8 F 2.1835 R 28.717 F- 2.182 Rex 28.72 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00527 A[2,16] = 0.01088 A[3,17] = 0.01440

 A[4,18] = 0.01496 A[5,19] = 0.02071 A[6,7,20= 0.01953

 A[8,9,22= 0.01984 A[1,15] = 0.00514 A[2,16] = 0.01542 A[3,17] = 0.01500

 A[4,18] = 0.01500 A[5,19] = 0.02000 A[6,7,20= 0.02000

 A[8,9,22= 0.02000

 Call 9 F 1.7333 R 25.821 F- 1.733 Rex 25.82 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00513 A[2,16] = 0.01048 A[3,17] = 0.01355

 A[4,18] = 0.01438 A[5,19] = 0.02213 A[6,7,20= 0.01508

 A[8,9,22= 0.01719

 Call 10 F 1.6575 R 25.037 F- 1.658 Rex 25.04 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00518 A[2,16] = 0.01055 A[3,17] = 0.01344

 A[4,18] = 0.01372 A[5,19] = 0.02242 A[6,7,20= 0.01335

 A[8,9,22= 0.01463

 Call 11 F 1.6566 R 24.974 F- 1.657 Rex 24.97 RD 0.00 Rx 0.00 636 27

 A[1,15] = 0.00518 A[2,16] = 0.01050 A[3,17] = 0.01339

 A[4,18] = 0.01417 A[5,19] = 0.02257 A[6,7,20= 0.01347

 A[8,9,22= 0.01708

 Call 12 F 1.6538 R 24.985 F- 1.654 Rex 24.98 RD 0.00 Rx 0.00 636 27


 Minimum Predicted, Accuracy = 0.7764E-03 Cond = 2 At Call 12


Filename: [excora6.dat ] ?


                [return]

 

 Value of fit index at predicted minimum 1.6538

 

 Fit index * k^2: 0.1654 Rdistances: 0.0000 Chisqu: 0.2626E-06

 Rexafs: 24.9848 Rxray: 0.0000 Rd: 0.0000


 Call 12, R(min)= 1.6538

 Best Values Are :

  1 A[1,15]                 = 0.00518 +/- 0.00018 (2 sigma)

  2 A[2,16]                 = 0.01050 +/- 0.00071 (2 sigma)

  3 A[3,17]                 = 0.01339 +/- 0.00139 (2 sigma)

  4 A[4,18]                 = 0.01417 +/- 0.00488 (2 sigma)

  5 A[5,19]                 = 0.02257 +/- 0.00195 (2 sigma)

  6 A[6,7,20,21]         = 0.01347 +/- 0.00356 (2 sigma)

  7 A[8,9,22,23]         = 0.01708 +/- 0.00519 (2 sigma)


Correlation matrix printed in excora6.dat


!Display the final R-factor and plot the results

fig3.gif

Figure 5 - Fit to Ga and Sb K-edges of GaSb


ENTER COMMAND:


                fit

 

 Fit Index: with k^2 Weighting 0.1654

 R-Factor : with k^2 Weighting 24.9848

 Amplitude of Experiment 102.4680

 R(exafs) = 24.9848 Weight: 1.00

 R(distances)= 0.0000 Weight: 0.00

 R(angles) = 0.0000 Weight: 0.00

 

 

ENTER COMMAND:


                cp


ENTER COMMAND:


                end

 

Total cpu time used = 1289.76 Elapsed time = 1290.00







Example 3. Cu-Zn Superoxide dismutase


Start the program - this example requires a version with large dimension limits


                excurve big


!Start the example in file stsod


                %stsod


!Henceforth the i/o is as for direct input from the terminal - some of this is supressed when the command file is run unless GSET PROMPT MAX is selected


!Read the Cu K-edge data


ENTER COMMAND:


                r ex 1


Filename for Experiment 1 ?


                r51991a.SODCU.exback


Point frequency [1] ?


                [return]

 

Column combination [12] ?

 

                32

 

Sequence-number in polarisation set [0]

 

                [return]

 

 

Edge ? [CU K]

 

                cu k

 

Number of clusters for this experiment [1]

 

                [return]

 

!These are the title records for this experiment

 

     0.00000 0.08302 25.23699 Background subtracted spectrum

 304 Hartrees Absorption Ev Edgenor pre

 

Number of points read: 304

 

!Read the Zn K-edge data (avoid prompts this time)

 

ENTER COMMAND:

 

                r ex 2;r52042a.SODZN.exback;1;32;zn k;;;;

 

     0.00000 0.08706 27.33692 Background subtracted spectrum

 314 Hartrees Absorption Ev Edgenor pre

 

Number of points read: 314

 

!Set up the atom types - the * indicates a central atom. Here we are using the same

!scattering phaseshifts for both Cu and Zn edges (the imaginary parts should really

! be slightly different).

 

ENTER COMMAND:

 

                c atom1 cu*;c atom2 c;c atom3 n;c atom4 o;c atom5 zn;c atom6 cu;c atom7 zn*

 

!Set the search radius for residues and bond distance for molecular graphics etc.

 

ENTER COMMAND:

 

                c maxrad 8.5

 

ENTER COMMAND:

 

                c bond 2.1

 

!Read the .pdb files

 

ENTER COMMAND:

 

                r par br

 

Reading data with format: BROOKHAVEN (.pdb)

Filename for parameters ?

 

                sod

 

Enter Cluster Number: [1]

 

                [return]

 

Central atom number [1 ]

 

                2168

 

!This is how to set up an indepenent cluster for Zn

!r par br;sod.pdb;2;2169;;;;

 

!Here the clusters are to be linked however

 

 

!Calculate potentials - the order depends on how the atom variables are defined

 

                ca pot;c;n;1;c;c;n;n;n;n;

 

Calculating potentials for all atoms:

 

   Z= 29 (CU) 1s1/2 1 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

             3d5/2 6 4s1/2 2 - total 29

 

 Z= 7 (N) 1s1/2 2 2s1/2 2 2p1/2 1 2p3/2 2 - total 7

 

CU (N ) Rho0: 0.5100 Efermi: -3.014 V0: -18.393 Electrons: 29.145 (Z= 29)

 

 

! ..... output for additional atoms follows ....

 

 

 Z= 16 (S) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 2 - total 16

 

 

 Z= 30 (ZN) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

             3d5/2 6 4s1/2 2 - total 30

 

S (ZN) Rho0: 0.4364 Efermi: -3.665 V0: -17.525 Electrons: 15.657 (Z= 16)

 

!Calculate phaseshifts

 

                ca ph

 

Calculating phaseshifs for all atoms:

 

Enter core width (FWHM eV) [ 1.761]

 

                [return]

 

Enter core width (FWHM eV) [ 1.936]

 

                [return]

 

!Sort in order of radius

 

                sort

 

Shells Have Been Put in Order of Ascending R

 

!Generate a second cluster centred on the Zn at 6 angstroms

!The cluster is to be a LINKED cluster

 

ENTER COMMAND:

 

                gen link 2

 

Enter atom number for cluster 2

 

                53

 

!The Zn was in shell 53 of the Cu cluster (cluster 1)

 

!Remember to change the atom-type for the excited atoms in cluster 2

 

!Sort again

 

                sort

 

Shells Have Been Put in Order of Ascending R

 

!Remove the unwanted part of the Zn cluster

 

ENTER COMMAND:

 

                c un[284-ns] 0

 

ENTER COMMAND:

 

                c ns 283

 

 

!Set some initial values of EF

 

ENTER COMMAND:

 

                c ef[1-2] -2

 

!Set up DW factors based on model compounds

 

ENTER COMMAND:

 

                c a[1-4] .005;c a[5-14] .009;c a[15-26] .016;c a[26-250] .025

 

 

!Zn cluster model compounds

 

ENTER COMMAND:

 

                c a[252-255] .005;c a[256-265] .009;c a[266-275] .016;c a[276-ns] .025

 

!Define the symmetry

 

ENTER COMMAND:

 

                sym c1;c1

 

 

!Draw the 2 clusters

 

ENTER COMMAND:

 

                dr cl 1

 

                dr cl 2

 

ENTER COMMAND:

 

!Plot the result

 

ENTER COMMAND:

 

                cp

 

!Refine the EFs and central atom positions

 

ENTER COMMAND:

 

                ref 50;ef1;ef2;x0;y0;z0;x53;y53;z53;=

 

Parameter refinement with constraints off:

 

 Least squares refinement using k**2 weighting

 

 

 Initial parameters

   1 EF1 -2.000 2.72116 0.00000 27.21164 -0.07350

   2 EF2 -2.000 2.72116 0.00000 27.21164 -0.07350

   3 X0 0.001 0.02117 0.00000 0.21167 0.00472

   4 Y0 0.001 0.02117 0.00000 0.21167 0.00472

   5 Z0 0.001 0.02117 0.00000 0.21167 0.00472

   6 X53 -3.014 0.02117 0.00000 0.21167 -14.23909

   7 Y53 3.907 0.02117 0.00000 0.21167 18.45790

   8 Z53 -3.572 0.02117 0.00000 0.21167 -16.87525

 

Enter :      Write to save the list of variables

                Continue to refine interactively

a number to edit, add to, or delete from the list

 

                c

 

 EF1 = -2.00000 EF2 = -2.00000 X0 = 0.00100

 Y0 = 0.00100 Z0 = 0.00100 X53 = -3.01400

 Y53 = 3.90700 Z53 = -3.57200

Call 1 F 20.9503 R 79.159 F- 20.950 Rex 79.16 RD 0.00 Rx 0.00 594 283

 EF1 = 0.72116 EF2 = -2.00000 X0 = 0.00100

 Y0 = 0.00100 Z0 = 0.00100 X53 = -3.01400

 Y53 = 3.90700 Z53 = -3.57200

Call 2 F 23.8008 R 83.411 F- 20.950 Rex 83.41 RD 0.00 Rx 0.00 594 283

 

!Additional output follows ...............

 

 EF1 = 0.83020 EF2 = 1.20080 X0 = 0.31601

 Y0 = -0.03229 Z0 = 0.17469 X53 = -2.97089

 Y53 = 3.82933 Z53 = -3.66482

Call 30 F 9.4960 R 51.599 F- 9.496 Rex 51.60 RD 0.00 Rx 0.00 594 283

 PRED+2.PPAR.AP.(DMAX-AP) le ACCURACY

 Minimum Predicted, Accuracy = 0.4685E-01 Cond = 2 At Call 30

 

Filename for statistics ?

Filename: [excora1.dat] ?

 

 

                [return]

 

 

 *** Correlation matrix and statistical errors ***

 

        EF1 EF2 X0 Y0 Z0 X53 Y53 Z53

 EF1 1.00 -0.14 0.47 -0.27 0.42 0.16 0.00 0.17

 EF2 -0.14 1.00 -0.23 0.00 -0.19 0.09 0.19 -0.13

 X0 0.47 -0.23 1.00 0.38 0.58 0.04 -0.17 0.24

 Y0 -0.27 0.00 0.38 1.00 -0.22 -0.33 -0.37 -0.23

 Z0 0.42 -0.19 0.58 -0.22 1.00 0.38 0.33 0.65

 X53 0.16 0.09 0.04 -0.33 0.38 1.00 0.52 0.39

 Y53 0.00 0.19 -0.17 -0.37 0.33 0.52 1.00 0.69

 Z53 0.17 -0.13 0.24 -0.23 0.65 0.39 0.69 1.00

 DSTEP 2.721 2.721 0.021 0.021 0.021 0.021 0.021 0.021

 

 Value of fit index at predicted minimum 9.4960

 

 

Fit index * k^2 : 0.9496 Rdistances : 0.0000 Chisqu : 0.1613E-05

Rexafs 51.5987 Rxray 0.0000 Rd 0.0000

 

 

!Repeat the refinement, avoiding all further prompts

 

ENTER COMMAND:

 

                ref res 100;c;p;c;=

 

  1 EF1 = 0.83020 +/- 0.58330 (2 sigma)

  2 EF2 = 1.20080 +/- 0.43868 (2 sigma)

  3 X0 = 0.31601 +/- 0.04502 (2 sigma)

  4 Y0 = -0.03229 +/- 0.04876 (2 sigma)

  5 Z0 = 0.17469 +/- 0.03559 (2 sigma)

  6 X53 = -2.97089 +/- 0.02298 (2 sigma)

  7 Y53 = 3.82933 +/- 0.04581 (2 sigma)

  8 Z53 = -3.66482 +/- 0.03874 (2 sigma)

 

Parameter refinement with correlation off:

 

 EF1 = 0.83020 EF2 = 1.20080 X0 = 0.31601

 Y0 = -0.03229 Z0 = 0.17469 X53 = -2.97089

 Y53 = 3.82933 Z53 = -3.66482

Call 1 F 9.4960 R 51.599 F- 9.496 Rex 51.60 RD 0.00 Rx 0.00 594 283

 EF1 = 1.10232 EF2 = 1.20080 X0 = 0.31601

 Y0 = -0.03229 Z0 = 0.17469 X53 = -2.97089

 Y53 = 3.82933 Z53 = -3.66482

Call 2 F 9.5108 R 51.911 F- 9.496 Rex 51.91 RD 0.00 Rx 0.00 594 283

 

 

 

!Additional output follows ...............

 

 

 

 EF1 = 1.08041 EF2 = 0.84231 X0 = 0.35989

 Y0 = -0.01875 Z0 = 0.20371 X53 = -2.97934

 Y53 = 3.79551 Z53 = -3.66970

Call 32 F 9.2000 R 49.948 F- 9.198 Rex 49.95 RD 0.00 Rx 0.00 594 283

 PRED+2.PPAR.AP.(DMAX-AP) le ACCURACY

 Minimum Predicted, Accuracy = 0.6715E-02 Cond = 2 At Call 32

 

 *** Correlation matrix and statistical errors ***

 

        EF1 EF2 X0 Y0 Z0 X53 Y53 Z53

 EF1 1.00 0.01 0.51 -0.31 0.42 -0.01 0.00 -0.01

 EF2 0.01 1.00 0.01 0.00 0.00 0.11 0.21 -0.14

 X0 0.51 0.01 1.00 0.20 0.55 -0.03 -0.01 0.01

 Y0 -0.31 0.00 0.20 1.00 -0.38 -0.01 0.00 0.01

 Z0 0.42 0.00 0.55 -0.38 1.00 -0.02 -0.01 0.01

 X53 -0.01 0.11 -0.03 -0.01 -0.02 1.00 0.69 0.55

 Y53 0.00 0.21 -0.01 0.00 -0.01 0.69 1.00 0.65

 Z53 -0.01 -0.14 0.01 0.01 0.01 0.55 0.65 1.00

 DSTEP 0.272 0.272 0.002 0.002 0.002 0.002 0.002 0.002

 

 Value of fit index at predicted minimum 9.1981

 

 

Fit index * k^2 : 0.9200 Rdistances : 0.0000 Chisqu : 0.1563E-05

Rexafs 49.9477 Rxray 0.0000 Rd 0.0000

  1 EF1 = 1.08393 +/- 0.52541 (2 sigma)

  2 EF2 = 0.83260 +/- 0.38846 (2 sigma)

  3 X0 = 0.35998 +/- 0.04687 (2 sigma)

  4 Y0 = -0.01880 +/- 0.04269 (2 sigma)

  5 Z0 = 0.20375 +/- 0.04408 (2 sigma)

  6 X53 = -2.97803 +/- 0.02579 (2 sigma)

  7 Y53 = 3.79946 +/- 0.06112 (2 sigma)

  8 Z53 = -3.66646 +/- 0.05609 (2 sigma)

 

ENTER COMMAND:

 

!And again ......

 

       ref res 150;c;p;c;=

 

Parameter refinement with correlation off:

 

 EF1 = 1.08393 EF2 = 0.83260 X0 = 0.35998

 Y0 = -0.01880 Z0 = 0.20375 X53 = -2.97803

 Y53 = 3.79946 Z53 = -3.66646

Call 1 F 9.1981 R 49.963 F- 9.198 Rex 49.96 RD 0.00 Rx 0.00 594 283

 

 

!Additional output follows ...............

 

 

 EF1 = 1.18360 EF2 = 0.71829 X0 = 0.40260

 Y0 = 0.01504 Z0 = 0.22739 X53 = -2.97873

 Y53 = 3.79873 Z53 = -3.66719

Call 30 F 9.0944 R 49.019 F- 9.094 Rex 49.02 RD 0.00 Rx 0.00 594 283

 

 PRED+2.PPAR.AP.(DMAX-AP) le ACCURACY

 Minimum Predicted, Accuracy = 0.2057E-02 Cond = 2 At Call 30

 

 *** Correlation matrix and statistical errors ***

 

        EF1 EF2 X0 Y0 Z0 X53 Y53 Z53

 EF1 1.00 0.01 0.29 -0.38 0.31 0.00 0.01 -0.01

 EF2 0.01 1.00 0.00 -0.01 0.00 0.11 0.18 -0.17

 X0 0.29 0.00 1.00 0.34 0.55 0.00 0.00 -0.01

 Y0 -0.38 -0.01 0.34 1.00 -0.28 0.00 -0.01 0.01

 Z0 0.31 0.00 0.55 -0.28 1.00 -0.01 0.00 -0.01

 X53 0.00 0.11 0.00 0.00 -0.01 1.00 0.71 0.53

 Y53 0.01 0.18 0.00 -0.01 0.00 0.71 1.00 0.65

 Z53 -0.01 -0.17 -0.01 0.01 -0.01 0.53 0.65 1.00

 DSTEP 0.027 0.027 0.000 0.000 0.000 0.000 0.000 0.000

 

 Value of fit index at predicted minimum 9.0944

 

 

Fit index * k^2 : 0.9094 Rdistances : 0.0000 Chisqu : 0.1545E-05

Rexafs 49.0189 Rxray 0.0000 Rd 0.0000

  1 EF1 = 1.18360 +/- 0.47498 (2 sigma)

  2 EF2 = 0.71829 +/- 0.37500 (2 sigma)

  3 X0 = 0.40260 +/- 0.04543 (2 sigma)

  4 Y0 = 0.01504 +/- 0.05078 (2 sigma)

  5 Z0 = 0.22739 +/- 0.04305 (2 sigma)

  6 X53 = -2.97873 +/- 0.02577 (2 sigma)

  7 Y53 = 3.79873 +/- 0.05970 (2 sigma)

  8 Z53 = -3.66719 +/- 0.05730 (2 sigma)0

 

ENTER COMMAND:

 

!Switch on MS

 

ENTER COMMAND:

 

                s ms un

 

ENTER COMMAND:

 

                ref res;c;p;c;=

 

Parameter refinement with constraints off:

 

 EF1 = 1.18360 EF2 = 0.71829 X0 = 0.40260

 Y0 = 0.01504 Z0 = 0.22739 X53 = -2.97873

 Y53 = 3.79873 Z53 = -3.66719

Call 1 F 9.1004 R 47.329 F- 9.100 Rex 47.33 RD 0.00 Rx 0.00 594 283

 EF1 = 1.45572 EF2 = 0.71829 X0 = 0.40260

 Y0 = 0.01504 Z0 = 0.22739 X53 = -2.97873

 Y53 = 3.79873 Z53 = -3.66719

Call 2 F 9.7217 R 48.225 F- 9.100 Rex 48.23 RD 0.00 Rx 0.00 594 283

 

 

!Additional output follows ...............

 

 

 EF1 = -1.87525 EF2 = -0.66724 X0 = 0.41083

 Y0 = 0.02129 Z0 = 0.27967 X53 = -2.96679

 Y53 = 3.80051 Z53 = -3.62263

Call 38 F 3.3382 R 32.309 F- 3.335 Rex 32.31 RD 0.00 Rx 0.00 594 283

Fit index is not decreasing

 

 *** Correlation matrix and statistical errors ***

 

        EF1 EF2 X0 Y0 Z0 X53 Y53 Z53

 EF1 1.00 0.11 0.42 -0.39 0.35 0.14 0.31 -0.32

 EF2 0.11 1.00 0.19 0.00 0.29 0.16 -0.02 0.03

 X0 0.42 0.19 1.00 0.11 0.75 0.28 0.49 -0.12

 Y0 -0.39 0.00 0.11 1.00 0.16 0.08 0.03 0.68

 Z0 0.35 0.29 0.75 0.16 1.00 0.40 0.66 -0.03

 X53 0.14 0.16 0.28 0.08 0.40 1.00 0.27 -0.14

 Y53 0.31 -0.02 0.49 0.03 0.66 0.27 1.00 -0.36

 Z53 -0.32 0.03 -0.12 0.68 -0.03 -0.14 -0.36 1.00

 DSTEP 0.272 0.272 0.002 0.002 0.002 0.002 0.002 0.002

 

 Value of fit index at predicted minimum 3.3348

 

 

Fit index * k^2 : 0.3338 Rdistances : 0.0000 Chisqu : 0.5671E-06

Rexafs 32.3089 Rxray 0.0000 Rd 0.0000

  1 EF1 = -1.91691 +/- 0.24213 (2 sigma)

  2 EF2 = -0.63885 +/- 0.27333 (2 sigma)

  3 X0 = 0.41076 +/- 0.02465 (2 sigma)

  4 Y0 = 0.02186 +/- 0.01918 (2 sigma)

  5 Z0 = 0.27986 +/- 0.02877 (2 sigma)

  6 X53 = -2.96714 +/- 0.01137 (2 sigma)

  7 Y53 = 3.79991 +/- 0.01202 (2 sigma)

  8 Z53 = -3.62449 +/- 0.01431 (2 sigma)

 

!Draw the clusters again

 

ENTER COMMAND:

 

                dr cl 1

 

                dr cl 2

 

!Plot the result

 

ENTER COMMAND:

 

                cp

 

ENTER COMMAND:

 

 

!Create a modified .pdb file

 

ENTER COMMAND:

 

                pr par rep;

 

 Fit Index: with k^2 Weighting 0.3335

 R-Factor : with k^2 Weighting 32.3093

 Amplitude of Experiment 101.2935

 R(exafs) = 32.3093 Weight: 1.00

 R(distances)= 0.0000 Weight: 0.00

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 110.5 Np = 1. Chi^2 = 0.5665E-6

Filename: [exbrka5.pdb] ?

 

File to be modified filename ?

 

                sod.pdb

 

!sod.pdb is modified and written to exbrka5.pdb - sod.pdb is not itself changed

 

Parameters printed in exbrka5.pdb


 

fig4a.gif

Figure 6 - Cu site of Superoxide Dismutase

fig4b.gif

Figure 7 - Result of refining metal atom positions of Superoxide Dismutase

 


Example 4. Tetrakis imidazole Copper(II) Nitrate

 

 

 

Example 5. Simple demonstration of Surface parameters

 

! Define the symmetry of a four-fold hollow site

 

 sym c4v

 

! Define the surface cell

 

 c acell 2.4

 

! Define the atom types

 

 c atom1 s;c atom2 ni;c atom3 s

 

! Define the shell parameters

 

 c ns 3;c t[1-2] ni;c t3 s

 c x1 1.2;c y1 1.2;c z1 -1;c n1 4

 c x2 0;c y2 0;c z2 -2.2;c n2 1

 c x3 2.4;c y3 2.4;c z3 0;c n3 4

 

! Define the surface layer

 

 c zmin -1.5;c zmax .5

 

! List the cartesian coordinates

 l car log

 

 EF = 0.000 VPI = 0.000 AFAC= 0.800 EMIN= 3.000 EMAX=1650.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 3.000

 Shell 1 N1 = 4.000 T1 = 2(NI) X1 = 1.200 Y1 = 1.200 Z1 = -1.000

 Shell 2 N2 = 1.000 T2 = 2(NI) X2 = 0.000 Y2 = 0.000 Z2 = -2.200

 Shell 3 N3 = 4.000 T3 = 3(S ) X3 = 2.400 Y3 = 2.400 Z3 = 0.000

 

! List the radial coordinates

 l log

 

 EF = 0.000 VPI = 0.000 AFAC= 0.800 EMIN= 3.000 EMAX=1650.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 3.000

 Shell 1 N1 = 4.000 T1 = 2(NI) R1 = 1.970 A1 = 0.010 B1 = 0.000

 Shell 2 N2 = 1.000 T2 = 2(NI) R2 = 2.200 A2 = 0.010 B2 = 0.000

 Shell 3 N3 = 4.000 T3 = 3(S ) R3 = 3.394 A3 = 0.010 B3 = 0.000

 

! Draw the structure

 dr

! Test the effect of DELTAZ

 c deltaz .1

 l car log

 

 EF = 0.000 VPI = 0.000 AFAC= 0.800 EMIN= 3.000 EMAX=1650.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 3.000

 Shell 1 N1 = 4.000 T1 = 2(NI) X1 = 1.200 Y1 = 1.200 Z1 = -0.900

 Shell 2 N2 = 1.000 T2 = 2(NI) X2 = 0.000 Y2 = 0.000 Z2 = -2.100

 Shell 3 N3 = 4.000 T3 = 3(S ) X3 = 2.400 Y3 = 2.400 Z3 = 0.000

 

! Reset DELTAZ

 

 c deltaz 0

 

! Test the effect of SDX2 - the 2 refers to Nickel scattering atoms - not shell 2

 

 c sdx2 .1

 

 l car log

 

 EF = 0.000 VPI = 0.000 AFAC= 0.800 EMIN= 3.000 EMAX=1650.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 3.000

 Shell 1 N1 = 4.000 T1 = 2(NI) X1 = 1.440 Y1 = 1.200 Z1 = -1.000

 Shell 2 N2 = 1.000 T2 = 2(NI) X2 = 0.000 Y2 = 0.000 Z2 = -2.200

 Shell 3 N3 = 4.000 T3 = 3(S ) X3 = 2.400 Y3 = 2.400 Z3 = 0.000

 

 c sdx2 0

 

! Test the effect of SURREL

 

 c surrel 1.1

 

 l car log

 

 EF = 0.000 VPI = 0.000 AFAC= 0.800 EMIN= 3.000 EMAX=1650.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 3.000

 Shell 1 N1 = 4.000 T1 = 2(NI) X1 = 1.200 Y1 = 1.200 Z1 = -1.000

 Shell 2 N2 = 1.000 T2 = 2(NI) X2 = 0.000 Y2 = 0.000 Z2 = -2.080

 Shell 3 N3 = 4.000 T3 = 3(S ) X3 = 2.400 Y3 = 2.400 Z3 = 0.000

 

 c surrel 1

 

 

 

 

Example 6. Fe tris(DMPP)

 

(Data kindly donated by Dr. Walkiria Schlindwein)

 

 

The command file to perform these calculations is listed below, followed by a detailed description

 

!Set up an empty site - as the ligand is bidentate, this will be used for the pivotal atom

site e;c;0;=

!Read the Fe K-edge data

r ex;r41799.exb;1;32;fe k;;;

!Set emergy limits to the range where background subtraction is adequate

c emin 19.8;c emax 590

!Read in crystallographic parameters

r par br;fedmpp1;1;1

!Remove the hydrogen atoms and sort in order of distance

sort del 5

!Draw the original structure

dr

!Remove furthest atoms

c ns 31

!Check the orientation of 'rotation axis' using the 3rd shell N atoms

!(the molecule has approximate C3 symmetry)

plane;23;24;25;0;0;1

!The axis is almost exactly parallel to z - no need to rotate it

!Divide the cluster into 3 units, + one odd atom

!(necessary because the .pdb file defined everything as one residue)

c un[1-ns] 0

c un[1,4,7,9,13,16,20,23,26,29] 1

c un[2,6,8,11,14,17,21,24,27,30] 2

c un[3,5,10,12,15,18,22,25,28,31] 3

!Put the single O atom on the z-axis

c th19 0

!Remove units 1 and 3, increase the occupation number for unit 2

c uoc[1,3] 0

c uoc2 3

!Remove empty shells

sort del

!Create the pivotal atom between atoms 1 and 2

c ns ns+1

c x[ns] .5*x1+.5*x2

c y[ns] .5*y1+.5*y2

c z[ns] .5*z1+.5*z2

!Ensure the occupation number and unit are the same as the other atoms

!The occupation number should be changed first

c n[ns] 3;c un[ns] 2

!Rename unit 2 as unit 1

c un[1-6,8-ns] 1

!Define the extra shell as the pivotal atom for unit 1

c piv1 ns

!Define the symmetry

sym c3

!Draw the symmetrised structure on top of the original

dr noc

!Define an atom parameter for the empty site

c atom5 e

!Define the atom type for the extra atom

c t[ns] e

!Calculate the potentials

ca pot;C;O;1;FE;C;;;

!Use the constant interstitial potential option

s con v

ca pot;C;O;1;FE;C;;;

!Calculate the phaseshifts

!The core-hole lifetime is adjusted, so the amplitude is correct

!For AFAC=1

c cw .5

ca ph;;;;;;;;;;;;;;;;;;;

!Set up rules for DW factors - makes refinements easier

rule a2;a1

rule a4;a3

rule a6;a5

rule a9;a8

rule a10;a8

rule a11;a8

!Set DW factor limits

c dwmin .003;c dwmax .025

!Set starting value for EF

c ef -2

!Refine EF and A values without MS

ref ef+a

c;c;=

!Set up MS parameters

c atmax 5;c omax 5;c plmax 12

s ms units

!Re-refine As

ref a;c;c;=

!Constrained refinement

s cor on

!Reduce MS using filter

c minmag .005

!Refine the pivotal atom distance

ref;r12;=;c;c;

!Refine the DW factors

ref a;c;c;=

!Turn off constrained refinement

s cor of

!Use restrained refinement

c wd .5;c wex .5

c d:

c w: -5

1;1.5

c w: -2

1.5;2.3

fit

ref x+y+z

c;c;

ref a;c;c;=

!Remove filters and re-refine DW factors

c minmag 0

ref a;c;c;=

 

 

EXCURVE 9.26 >>> 29/09/02 at 06:12:21

 

ENTER COMMAND:

 

Start the command file

 

%stm

 

Set up an empty site - as the ligand is bidentate, this

will be used for the pivotal atom

 

site e;c;0;=

 

Read the Fe K-edge data

 

r ex;r41799.exb;1;32;fe k;;;

 

 

Set energy limits to the range where background subtraction is adequate

 

c emin 19.8;c emax 590

 

Read in crystallographic parameters

 

r par br;fedmpp1;1;1

 

Reading data with format: BROOKHAVEN (.pdb)

 

Remove the hydrogen atoms and sort in order of distance

 

sort del H

 

Draw the original structure

 

dr

 

Remove furthest atoms

 

c ns 31

 

Check the orientation of 'rotation axis' using the 3rd shell N atoms

(the molecule has approximate C3 symmetry)

 

plane;23;24;25;0;0;1

 

The axis is almost exactly parallel to z - no need to rotate it

Divide the cluster into 3 units, + one odd atom

(necessary because the .pdb file defined everything as one residue)

 

c un[1-ns] 0

c un[1,4,7,9,13,16,20,23,26,29] 1

c un[2,6,8,11,14,17,21,24,27,30] 2

c un[3,5,10,12,15,18,22,25,28,31] 3

 

Put the single O atom on the z-axis

 

c th19 0

 

Remove units 1 and 3, increase the occupation number for unit 2

 

c uoc[1,3] 0

c uoc2 3

 

Remove empty shells

 

sort del

 

Create the pivotal atom between atoms 1 and 2

 

c ns ns+1

c x[ns] .5*x1+.5*x2

c y[ns] .5*y1+.5*y2

c z[ns] .5*z1+.5*z2

 

Ensure the occupation number and unit are the same as the other atoms

The occupation number should be changed first

 

c n[ns] 3;c un[ns] 2

 

Rename unit 2 as unit 1

 

c un[1-6,8-ns] 1

 

Define the extra shell as the pivotal atom for unit 1

 

c piv1 ns

 

Define the symmetry

 

sym c3

 

Draw the symmetrised structure on top of the original

 

dr noc

 

 

Define the atom type for the extra atom

 

c t[ns] e

 

Calculate the potentials

 

ca pot;C;O;1;FE;C;;;

 

 

 Z= 26 (FE) 1s1/2 1 2s1/2 2 2p1/2 2 2p3/2 4 3s1/2 2 3p1/2 2 3p3/2 4 3d3/2 4

             3d5/2 3 4s1/2 2 - total 26

 

 Z= 8 (O) 1s1/2 2 2s1/2 2 2p1/2 2 2p3/2 2 - total 8

NPTS = 349 JWS = 353 NEND = 451 NEND(2) = 451

 

Excited atom code : 1 Log grid increment : 0.02779

Lattice constant : 2.26000 Muffin-tin radius : 1.26000 349

Atomic volume : 10.88370 Wigner-seitz radius: 1.37477 352

Exchange constant : 0.66670 Madelung constant : 0.00000

 

   I R RHO(AT) RHO(SUP) RV(AT) RV(SUP) RV(MT) V(MT))

   50 0.0006 0.0330 0.0330 -51.8887 -51.8887 -51.9117 -0.887E+05

  100 0.0024 0.4607 0.4607 -51.5524 -51.5524 -51.6402 -0.220E+05

  150 0.0094 4.8826 4.8826 -50.2211 -50.2211 -50.5279 -0.536E+04

  200 0.0379 17.9767 17.9767 -45.4394 -45.4402 -46.1972 -0.122E+04

  250 0.1520 34.1266 34.1275 -31.8463 -31.8519 -33.3602 -0.220E+03

  300 0.6100 18.1612 18.1782 -11.1538 -11.1795 -13.2020 -0.216E+02

  348 2.3158 1.3239 2.6169 -1.0125 -1.4249 -3.3026 -0.143E+01

  349 2.3811 1.2571 2.7524 -0.9452 -1.4034 -3.3311 -0.140E+01

  350 2.4482 1.1941 2.9309 -0.8808 -1.3916 -3.3779 -0.138E+01

FE (O ) Rho0: 0.4987 Efermi: -3.578 V0: -18.728 Electrons: 25.667 (Z= 26)

 

 

              etc.

 

Calculate the phaseshifts

The core-hole lifetime is adjusted, so the amplitude is correct

For AFAC=1

 

c cw .5

ca ph;;;;;;;;;;;;;;;;;;;

 

Set up rules for DW factors - makes refinements easier

 

rule a2;a1

rule a4;a3

rule a6;a5

rule a9;a8

rule a10;a8

rule a11;a8

 

Set DW factor limits

 

c dwmin .003;c dwmax .025

 

Set starting value for EF

 

c ef -2

 

Refine EF and A values without MS

 

ref ef+a

 

 Least squares refinement using k**2 weighting

 

 

 Initial parameters

   1 EF -2.000 0.27212 0.00000 27.21164 -0.07350

   2 A1 0.022 0.00063 0.00000 0.06301 0.35711

   3 A3 0.022 0.00063 0.00000 0.06301 0.35711

   4 A5 0.022 0.00063 0.00000 0.06301 0.35711

   5 A7 0.022 0.00063 0.00000 0.06301 0.35711

   6 A8 0.022 0.00063 0.00000 0.06301 0.35711

 

c;c;=

 

 EF = -2.00000 A1 = 0.02250 A3 = 0.02250

 A5 = 0.02250 A7 = 0.02250 A8 = 0.02250

Call 1 F 15.3191 R 45.164 F- 15.319 Rex 45.16 RD 0.00 Rx 0.00 220 12

 EF = -1.72788 A1 = 0.02250 A3 = 0.02250

 A5 = 0.02250 A7 = 0.02250 A8 = 0.02250

Call 2 F 16.2460 R 46.154 F- 15.319 Rex 46.15 RD 0.00 Rx 0.00 220 12

 EF = -2.00000 A1 = 0.02313 A3 = 0.02250

 A5 = 0.02250 A7 = 0.02250 A8 = 0.02250

Call 3 F 15.7096 R 45.872 F- 15.319 Rex 45.87 RD 0.00 Rx 0.00 220 12

 

 

       etc.

 

 

 EF = -3.62000 A1 = 0.00709 A3 = 0.02313

 A5 = 0.02464 A7 = 0.01724 A8 = 0.00770

Call 74 F 3.8024 R 21.746 F- 3.802 Rex 21.75 RD 0.00 Rx 0.00 220 12

 

 Minimum Predicted, Accuracy = 0.1083E-01 Cond = 2 At Call 74

 

 *** Correlation matrix and statistical errors ***

 

        EF A1 A3 A5 A7 A8

 EF 1.00 0.18 -0.35 -0.28 -0.12 0.19

 A1 0.18 1.00 -0.13 -0.11 -0.08 0.05

 A3 -0.35 -0.13 1.00 0.71 0.18 -0.55

 A5 -0.28 -0.11 0.71 1.00 0.48 -0.66

 A7 -0.12 -0.08 0.18 0.48 1.00 0.34

 A8 0.19 0.05 -0.55 -0.66 0.34 1.00

 DSTEP 0.272 0.001 0.001 0.001 0.001 0.001

 

 Value of fit index at predicted minimum 3.8024

 

 

Fit index * k^2 : 0.3802 Rdistances : 0.0000 Chisqu : 0.1845E-05

Rexafs : 21.7463 Rxray : 0.0000 Rd : 0.0000

 

Best Values Are:

 

  1 EF = -3.62719 +/- 0.23554 (2 sigma)

  2 A1 = 0.00709 +/- 0.00108 (2 sigma)

  3 A3 = 0.00770 +/- 0.00462 (2 sigma)

  4 A5 = 0.02464 +/- 0.00564 (2 sigma)

  5 A7 = 0.01724 +/- 0.07940 (2 sigma)

  6 A8 = 0.02209 +/- 0.03739 (2 sigma)

       

Set up MS parameters

 

                c atmax 5;c omax 5;c plmax 12

                s ms units

 

Re-refine “A”s

 

                ref a;c;c;=

 

 A1 = 0.00709 A3 = 0.00770 A5 = 0.02464

 A7 = 0.01724 A8 = 0.02209

Call 1 F 1.8720 R 14.555 F- 1.872 Rex 14.56 RD 0.00 Rx 0.00 220 12

 A1 = 0.00729 A3 = 0.00770 A5 = 0.02464

 A7 = 0.01724 A8 = 0.02209

Call 2 F 1.8830 R 14.511 F- 1.872 Rex 14.51 RD 0.00 Rx 0.00 220 12

 A1 = 0.00709 A3 = 0.00792 A5 = 0.02464

 A7 = 0.01724 A8 = 0.02209

Call 3 F 1.8790 R 14.609 F- 1.872 Rex 14.61 RD 0.00 Rx 0.00 220 12

 

              etc.

 

 

 A1 = 0.00676 A3 = 0.00621 A5 = 0.00638

 A7 = 0.02450 A8 = 0.01274

Call 38 F 1.3343 R 12.559 F- 1.334 Rex 12.56 RD 0.00 Rx 0.00 220 12

 

 Minimum Predicted, Accuracy = 0.1324E-02 Cond = 2 At Call 38

 

 *** Correlation matrix and statistical errors ***

 

        A1 A3 A5 A7 A8

 A1 1.00 -0.03 0.00 0.01 0.03

 A3 -0.03 1.00 -0.37 0.28 0.04

 A5 0.00 -0.37 1.00 0.77 -0.12

 A7 0.01 0.28 0.77 1.00 -0.31

 A8 0.03 0.04 -0.12 -0.31 1.00

 DSTEP 0.000 0.000 0.001 0.000 0.001

 

 Value of fit index at predicted minimum 1.3343

 

 

Fit index * k^2 : 0.1334 Rdistances : 0.0000 Chisqu : 0.6473E-06

Rexafs : 12.5593 Rxray : 0.0000 Rd : 0.0000

 

Best values are:

 

  1 A1 = 0.00676 +/- 0.00061 (2 sigma)

  2 A3 = 0.00621 +/- 0.00198 (2 sigma)

  3 A5 = 0.00638 +/- 0.00319 (2 sigma)

  4 A7 = 0.02450 +/- 0.00058 (2 sigma)

  5 A8 = 0.01274 +/- 0.00982 (2 sigma)

 

Constrained refinement

 

                s cor on

 

Reduce MS using filter

 

                c minmag .005

 

Refine the pivotal atom distance

 

                ref;r12;=;c;c;

 

 R12 = 1.54021

Call 1 F 1.2404 R 11.867 F- 1.240 Rex 11.87 RD 0.00 Rx 0.00 220 12

 R12 = 1.54184

Call 2 F 1.2613 R 11.864 F- 1.240 Rex 11.86 RD 0.00 Rx 0.00 220 12

 

 Minimum Predicted, Accuracy = 0.8771E-03 Cond = 2 At Call 2

 

Correlation matrix printed in excorb9.dat

 

Refine the DW factors

 

ref a;c;c;=

 

 A1 = 0.00676 A3 = 0.00621 A5 = 0.00638

 A7 = 0.02450 A8 = 0.01274

Call 1 F 1.2403 R 11.867 F- 1.240 Rex 11.87 RD 0.00 Rx 0.00 220 12

 A1 = 0.00695 A3 = 0.00621 A5 = 0.00638

 A7 = 0.02450 A8 = 0.01274

Call 2 F 1.2454 R 11.904 F- 1.240 Rex 11.90 RD 0.00 Rx 0.00 220 12

 

              etc.

 

 A1 = 0.00667 A3 = 0.00602 A5 = 0.00777

 A7 = 0.02451 A8 = 0.01292

Call 10 F 1.2332 R 11.773 F- 1.233 Rex 11.77 RD 0.00 Rx 0.00 220 12

 

 Minimum Predicted, Accuracy = 0.8771E-03 Cond = 2 At Call 10

 

 *** Correlation matrix and statistical errors ***

 

        A1 A3 A5 A7 A8

 A1 1.00 -0.01 0.01 0.00 0.02

 A3 -0.01 1.00 -0.10 -0.08 0.04

 A5 0.01 -0.10 1.00 0.39 -0.17

 A7 0.00 -0.08 0.39 1.00 -0.11

 A8 0.02 0.04 -0.17 -0.11 1.00

 DSTEP 0.000 0.000 0.000 0.001 0.000

 

 Value of fit index at predicted minimum 1.2332

 

 

Fit index * k^2 : 0.1233 Rdistances : 0.0000 Chisqu : 0.5983E-06

Rexafs : 11.7731 Rxray : 0.0000 Rd : 0.0000

 

Best Values Are:

 

  1 A1 = 0.00667 +/- 0.00058 (2 sigma)

  2 A3 = 0.00602 +/- 0.00180 (2 sigma)

  3 A5 = 0.00777 +/- 0.00309 (2 sigma)

  4 A7 = 0.02451 +/- 0.00006 (2 sigma)

  5 A8 = 0.01292 +/- 0.00787 (2 sigma)

 

Turn off constrained refinement

 

                s con of

 

Use restrained refinement

 

                c wd .5;c wex .5

                c d:

                c w: -5

                1;1.5

                c w: -2

 

                1.5;2.3

 

                fit

 

 Atom(I) Atom(J) Ideal Theory Difference Error % Weighting Error*Weight*1

   1(O ) 0(FE) 1.998 1.998 0.0000 0.00 2.000 0.0000

   2(O ) 0(FE) 2.046 2.046 0.0000 0.00 2.000 0.0000

   3(C ) 1(O ) 1.346 1.346 0.0000 0.00 5.000 0.0000

   4(C ) 2(O ) 1.288 1.288 0.0000 0.00 5.000 0.0000

   4(C ) 3(C ) 1.410 1.410 0.0000 0.00 5.000 0.0000

   5(C ) 3(C ) 1.400 1.400 0.0000 0.00 5.000 0.0000

   6(C ) 4(C ) 1.424 1.424 0.0000 0.00 5.000 0.0000

   8(C ) 5(C ) 1.469 1.469 0.0000 0.00 5.000 0.0000

   9(N ) 5(C ) 1.362 1.362 0.0000 0.00 5.000 0.0000

  10(C ) 6(C ) 1.352 1.352 0.0000 0.00 5.000 0.0000

  10(C ) 9(N ) 1.368 1.368 0.0000 0.00 5.000 0.0000

  11(C ) 9(N ) 1.476 1.476 0.0000 0.00 5.000 0.0000

  12(E ) 0(FE) 1.540 1.540 0.0000 0.00 2.000 0.0000

  12(E ) 1(O ) 1.310 1.310 0.0000 0.00 5.000 0.0000

  12(E ) 2(O ) 1.310 1.310 0.0000 0.00 5.000 0.0000

  12(E ) 3(C ) 1.365 1.365 0.0000 0.00 5.000 0.0000

  12(E ) 4(C ) 1.368 1.368 0.0000 0.00 5.000 0.0000

 

 Fit Index: with k^2 Weighting 0.0308

 R-Factor : with k^2 Weighting 11.7731

 Amplitude of Experiment 52.4801

 R(exafs) = 11.7731 Weight: 0.50

 R(distances)= 0.0000 Weight: 0.50

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 24.4 Np = 1. Chi^2 = 0.1357E-6

 

                ref x+y+z

 

 Least squares refinement using k**2 weighting

 

 

 Initial parameters

   1 X1 -1.411 0.00212 0.00000 0.21167 -6.66601

   2 X2 -0.389 0.00212 0.00000 0.21167 -1.83776

   3 X3 -1.759 0.00212 0.00000 0.21167 -8.31009

   4 X4 -1.202 0.00212 0.00000 0.21167 -5.67863

 

                      etc.

 

  30 Z11 -1.432 0.00212 0.00000 0.21167 -6.76522

 

                c;c;

 

 X1 = -1.41100 X2 = -0.38900 X3 = -1.75900

 X4 = -1.20200 X5 = -2.63800 X6 = -1.56100

 X8 = -3.19600 X9 = -2.95800 X10 = -2.42501

 X11 = -3.85700 Y1 = -0.87100 Y2 = -1.62800

 Y3 = -2.07800 Y4 = -2.45100 Y5 = -2.92700

 Y6 = -3.72800 Y8 = -2.57400 Y9 = -4.12800

 Y10 = -4.51100 Y11 = -5.08400 Z1 = -1.11400

 Z2 = 1.17700 Z3 = -0.63000 Z4 = 0.61100

 Z5 = -1.31300 Z6 = 1.12800 Z8 = -2.62500

 Z9 = -0.75700 Z10 = 0.44300 Z11 = -1.43200

Call 1 F 0.3083 R 11.773 F- 0.308 Rex 11.77 RD 0.00 Rx 0.00 237 12

 

              etc.

 

 X1 = -1.40884 X2 = -0.38901 X3 = -1.75689

 X4 = -1.20198 X5 = -2.63797 X6 = -1.55889

 X8 = -3.19389 X9 = -2.95588 X10 = -2.42497

 X11 = -3.85700 Y1 = -0.86891 Y2 = -1.62802

 Y3 = -2.07794 Y4 = -2.44889 Y5 = -2.92696

 Y6 = -3.72796 Y8 = -2.57191 Y9 = -4.12796

 Y10 = -4.51099 Y11 = -5.08399 Z1 = -1.11391

 Z2 = 1.17912 Z3 = -0.62796 Z4 = 0.61102

 Z5 = -1.31297 Z6 = 1.13011 Z8 = -2.62498

 Z9 = -0.75493 Z10 = 0.44305 Z11 = -1.43200

Call 35 F 0.3423 R 12.319 F- 0.303 Rex 12.20 RD 0.12 Rx 0.00 237 12

 

Correlation matrix printed in excorc1.dat

 

                ref a;c;c;=

 

 A1 = 0.00667 A3 = 0.00602 A5 = 0.00777

 A7 = 0.02451 A8 = 0.01292

Call 1 F 0.3030 R 11.920 F- 0.303 Rex 11.80 RD 0.12 Rx 0.00 237 12

 A1 = 0.00686 A3 = 0.00602 A5 = 0.00777

 A7 = 0.02451 A8 = 0.01292

Call 2 F 0.3052 R 11.977 F- 0.303 Rex 11.86 RD 0.12 Rx 0.00 237 12

              etc.

 

 A1 = 0.00649 A3 = 0.00602 A5 = 0.00774

 A7 = 0.02451 A8 = 0.01285

Call 7 F 0.3020 R 11.890 F- 0.302 Rex 11.77 RD 0.12 Rx 0.00 237 12

 

 Minimum Predicted, Accuracy = 0.2143E-03 Cond = 2 At Call 7

 

 *** Correlation matrix and statistical errors ***

 

        A1 A3 A5 A7 A8

 A1 1.00 -0.01 0.00 -0.02 0.01

 A3 -0.01 1.00 -0.09 0.00 0.04

 A5 0.00 -0.09 1.00 -0.01 -0.15

 A7 -0.02 0.00 -0.01 1.00 -0.03

 A8 0.01 0.04 -0.15 -0.03 1.00

 DSTEP 0.000 0.000 0.000 0.001 0.000

 

 Value of fit index at predicted minimum 0.3020

 

 

Fit index * k^2 : 0.3020E-01 Rdistances : 0.1158 Chisqu : 0.1329E-06

Rexafs : 11.7739 Rxray : 0.0000 Rd : 0.1158

 

  1 A1 = 0.00649 +/- 0.00055 (2 sigma)

  2 A3 = 0.00602 +/- 0.00169 (2 sigma)

  3 A5 = 0.00774 +/- 0.00303 (2 sigma)

  4 A7 = 0.02451 +/- 0.00003 (2 sigma)

  5 A8 = 0.01285 +/- 0.00758 (2 sigma)

 

Remove filtersand re-refine DW factors

 

                c minmag 0

                ref a;c;c;=

 

 A1 = 0.00649 A3 = 0.00602 A5 = 0.00774

 A7 = 0.02451 A8 = 0.01285

Call 1 F 0.3302 R 12.683 F- 0.330 Rex 12.57 RD 0.12 Rx 0.00 237 12

 A1 = 0.00667 A3 = 0.00602 A5 = 0.00774

 A7 = 0.02451 A8 = 0.01285

Call 2 F 0.3306 R 12.690 F- 0.330 Rex 12.57 RD 0.12 Rx 0.00 237 12

 

              etc.

 

 A1 = 0.00651 A3 = 0.00589 A5 = 0.00632

 A7 = 0.02451 A8 = 0.01444

Call 10 F 0.3275 R 12.747 F- 0.327 Rex 12.63 RD 0.12 Rx 0.00 237 12

 

 Minimum Predicted, Accuracy = 0.2335E-03 Cond = 2 At Call 10

 

 *** Correlation matrix and statistical errors ***

 

        A1 A3 A5 A7 A8

 A1 1.00 -0.01 0.01 0.00 0.03

 A3 -0.01 1.00 -0.09 0.01 0.07

 A5 0.01 -0.09 1.00 -0.14 -0.14

 A7 0.00 0.01 -0.14 1.00 0.12

 A8 0.03 0.07 -0.14 0.12 1.00

 DSTEP 0.000 0.000 0.000 0.001 0.000

 

 Value of fit index at predicted minimum 0.3275

 

 

Fit index * k^2 : 0.3275E-01 Rdistances : 0.1158 Chisqu : 0.1441E-06

Rexafs : 12.6309 Rxray : 0.0000 Rd : 0.1158

 

Best Values Are:

 

  1 A1 = 0.00651 +/- 0.00057 (2 sigma)

  2 A3 = 0.00589 +/- 0.00176 (2 sigma)

  3 A5 = 0.00632 +/- 0.00293 (2 sigma)

  4 A7 = 0.02451 +/- 0.00003 (2 sigma)

  5 A8 = 0.01444 +/- 0.00787 (2 sigma)

 

                fit

 

 Atom(I) Atom(J) Ideal Theory Difference Error % Weighting Error*Weight*1

   1(O ) 0(FE) 1.998 1.995 0.0024 0.12 2.000 0.0000

   2(O ) 0(FE) 2.046 2.047 -0.0012 -0.06 2.000 0.0000

   3(C ) 1(O ) 1.346 1.349 -0.0027 -0.20 5.000 -0.0001

   4(C ) 2(O ) 1.288 1.287 0.0004 0.03 5.000 0.0000

   4(C ) 3(C ) 1.410 1.407 0.0033 0.23 5.000 0.0002

   5(C ) 3(C ) 1.400 1.402 -0.0024 -0.17 5.000 -0.0001

   6(C ) 4(C ) 1.424 1.425 -0.0014 -0.10 5.000 -0.0001

   8(C ) 5(C ) 1.469 1.468 0.0003 0.02 5.000 0.0000

   9(N ) 5(C ) 1.362 1.362 -0.0004 -0.03 5.000 0.0000

  10(C ) 6(C ) 1.352 1.354 -0.0014 -0.10 5.000 -0.0001

  10(C ) 9(N ) 1.368 1.365 0.0027 0.20 5.000 0.0001

  11(C ) 9(N ) 1.476 1.478 -0.0023 -0.15 5.000 -0.0001

 

 Fit Index: with k^2 Weighting 0.0327

 R-Factor : with k^2 Weighting 12.7468

 Amplitude of Experiment 52.4801

 R(exafs) = 12.6309 Weight: 0.50

 R(distances)= 0.1158 Weight: 0.50

 R(angles) = 0.0000 Weight: 0.00

 N(ind) = 24.4 Np = 1. Chi^2 = 0.1441E-6

 

 


 

fig5a.gif

Figure 8 - Structure of Fe(DMPP)3, including dummy atoms for positioning the ligands.

fig5b.gif

Figure 9 - Fit to Fe-edge of Fe(DMPP)3

 


4. Parameters and Related Topics

 

Parameters are of thirteen types:

 

 1. Cell parameters ACELL,BCELL,ALPHA

 2. Shell parameters are indexed by shell numbers - N1,T2,X3

 3. Unit parameters are indexed by unit number - PANG1,PIV1,UOC2

 4. Phaseshift parameters are indexed by atom type - MTR1,ALF2

 5. Site parameters are indexed by site number - PERCA1, PERCB2

 6. Spectrum parameters are either unindexed (common parameters) or indexed by spectrum number - WEX,EF1,AFAC2

      There are five groups of unindexed parameters:

 7. Theory parameters, including those concerned with phaseshift and multiple scattering calculations - LMAX, MINANG

 8. Control parameters, influencing refinement, output etc. - BOND, SIZE, MAXRAD

 9. Fourier transform parameters - WP, RMIN, RMAX

10. Surface parameters - ZMIN, DELTAX, SURREL

11. XANES parameters are used only by XANES calculations - XEMIN, XLOUT

12. Restrained refinement parameters are indexed by two shell numbers - D3:1,V5:0

13. Bond parameters are index by atom numbers - B253:72

 

Terminology

 

  Central atom - each of the clusters represented in the parameter table has one central atom. Cluster 1 has the central atom in shell 0, i.e. has coordinates X0, Y0, Z0 or R0, θ0, φ0. It is often, but not necessarily, at the centre of the coordinate system. The central atom of other clusters may occupy any shell, and is distinguished by a negative cluster number. The central atom is abbreviated by c below.

 

  Absolute and Relative coordinates - the spatial coordinates X, Y, Z, R, θ and φ are all absolute coordinates. If the central atom is not at the origin in these coordinates the theory is determined by the relative coordinates, with the central atom at (0,0,0). It is possible to display, but not to directly change the relative coordinates using LIST RADIAL. Compare the cordinates given by this command with those given by L SPHERICAL and L CART. To avoid complications it is usually preferable to leave the central atom at absolute position (0,0,0) and to move the ligands. One occasion when this may not be the case is in protein refinements where the main-chain atomic positions are to be retained, but the central atom and ligands such as bicarbonate or hydroxyl are to be moved.

 

  Clusters - the parameter table represents one or more clusters which consists of atoms surrounding crystallographically distinct excited atom sites. A cluster may also be an average over several such sites.

 

  Shell - a shell consists of a set of atoms equidistant from the origin (usually the central atom but see above). Neither the θ nor φ values of the other atoms in the same shell need be the same. If the point symmetry of each central atom is defined, then the coordinates of all the atoms in a shell are defined. If no point symmetry is specified, then for the purpose of theory calculation the coordinates of all te atoms in a shell are assumed to be the same. Many program commands and options are unavailable if the symmetry is undefined.

 

  Unit - a unit is a set of atoms, for example those comprising one ligand, identified by a common, non-zero, unit number. The unit is to allow constrained/restrained refinement, restricted (intra-unit) multiple scattering, and easy addition to, or removal of, ligands from a cluster.

 

  Pivotal atom - the pivotal atom of a unit is the atom about which rotations of the unit are defined. If no pivotal atom is defined, the nearest atom to the centre is assumed. As the nearest atom may change giving unexpected results, it is advisable to set the parameter PIVn to one of the atoms in the unit (i.e. to a shell number) to avoid ambiguity. PIVn then defines the pivotal atom for unit n. In some circumstances, PIVn may be outside the unit (see torsion angles below), it does not then define the pivotal atom. The pivotal atom is abbreviated by p below. The vector c-p is abbreviated by u.

 

  Unit plane - the unit plane is defined by p-a-b, where p is the pivotal atom, a is an atom defined by the unit parameter PLA and b is an atom defined by the unit parameter PLB. The unit plane is defined by the vector n which is a normal to the plane through p. If either p, a or b are undefined ( or equivalent ) then n is taken as a normal to u in the vertical plane. If p is undefined or u is parallel to the z-axis, n is taken as the z-axis.

 

  Principal angle - the principal angle is the angle c-p-a. Its sign is determined by the sign of the z-component of the vector cross-product uX(a-p). If this is zero, the y- or if necessary the -x component is used.

 

Parameter Definitions

 

 1. Cell parameters (neither essential, nor used rigorously in EXCURVE, and mainly used for scaling of atomic distances)

 

  ACELL                   crystallographic cell dimension a

  BCELL                   crystallographic cell dimension b

  CCELL                   crystallographic cell dimension c

  ALPHA                   crystallographic cell parameter α

  BETA                     crystallographic cell parameter β

  GAMMA                 crystallographic cell parameter γ

 

 

2. Shell parameters

 

  N            shell occupancy

  T             atom type (element symbol)

  R            radial distance of one of the atoms in the shell (Å)

  A            Debye-Waller term 2 (Å2) (or 2 C2 where C2 is the second cumulant of the pair distribution function)

  B            third cumulant C3x10 ( Å3)

  C            fourth cumulant C4 x100 ( Å4)

  D            exponent for truncated exponential disorder

  UN          number of the unit of which the shell is a part, or 0

  ANG       angle c-p-i for shell i. c = central, p = pivotal atom (0)

  TH          polar coordinate θ of one of the atoms in the shell (0)

  PHI         polar coordinate φ of one of the atoms in the shell (0)

  X            cartesian coordinate x of one of the atoms (Å)

  Y            cartesian coordinate y (Å)

  Z             cartesian coordinate z (Å)

  ROT       rotation about u (unit vector c-p) or VECA-VECB (0)

  TWST     rotation about n (normal to unit plane)(0)

  TILT       rotation about nXu (tilt axis)(0)

  CLUS     cluster to which shell belongs, -ve for an excited atom

  LINK      shell to which the shell is linked, in linked clusters

 

 3. Unit parameters

 

  PIV         pivotal atom for the unit

  PLA        atom a defining the unit plane, and the principal angle

  PLB        atom b defining the unit plane

  TORA     torsion angle ψ (N-CA-CB-CG)

  TORB     torsion angle ϖ (CA-CB-CG-CD)

  TORC     torsion angle at centre (c-p-a-b)

  PANG    principal angle c-p-a

  UOC       unit occupancy - changes N for all atoms in the unit

 

All the unit parameters above can be changed using the command CHANGE. The torsion angle parameters can be refined using REFINE as well as being read from files. A number of other unit variables can only be modified by reading from the ligand database, or from a Brookhaven (.pdb) file or by changing them interactively using PLOT UNIT. These are:

 

  UNAME                  the name of the unit

  NTORA[1-4]           the atoms defining torsion angle A

  NTORB[1-4]           the atoms defining torsion angle B

  RESNAME             the name of the ligand ( residue in .PDB files)

  RESNUM               residue number

 

 4. Phaseshift parameters (indexed by ATOM TYPE)

 

  ATOM                    atomic number associated with an atom type

  MTR                       muffin-tin radius

  ION                         ionic charge

  ALF                        exchange term for X-α ground state exchange

  CMAG                    Correction to Madelung potential

  XE                          Atom-type specific correction to EF

 

The following parameters are, like the parameters above, indexed by atomi type, but are involved in changing the structure, not the phaseshifts

 

  SDXi                       Displacement in x-direction for atoms of type i with Z between ZMIN and ZMAX

  SDYi                       Displacement in y-direction for atoms of type i with Z between ZMIN and ZMAX

  SDZi                       Displacement in z-direction for atoms of type i with Z between ZMIN and ZMAX

 

Other parameters which effect phaseshifts include EF0, RHO0 and V0 (see theory parameters).

 

 5. Site parameters

 

Parameters used for adjusting the occupancy of mixed sites

 

  PERCAi                                  Fraction of component A in site i

  PERCBi                                  Fraction of component B in site i

  PERCCi                 Fraction of component C in site i

 

 6. Spectrum parameters

 

Most of these variables have both a common term which is unindexed, and a term indexed by its spectrum number. The common variable applies to all spectra, the individual variables apply to only one. These are indexed by spectrum number, as used in READ EXP. Variables of this type are indicated by an optional index below. e.g. EF(i). A few variables must be indexed: these are indicated by BEWi etc.

 

  EF(i)                       edge position (fermi energy), relative to calculated vacuum zero

  VPI(i)                      energy-independent correction imaginary potential

  AFAC(i)                  amplitude reduction due to many-electron processes etc.

  EMIN(i)                   minimum energy for EXAFS theory calculations

  EMAX(i)                 maximum energy for EXAFS theory calculations

  WEX(i)                   weighting for EXAFS component of the fit-index

  CW(i)                      the effective core-hole width, in eV. Theoretical values used if -1

  BETH(i)                                  beam direction - theta value, for spectrum i

  BEPHI(i)                 beam direction - phi value, for spectrum i

  BEW(i)                   polarisation azimuth, for experimental spectrum i

  PRE0(i),PRE1(i),PRE2(i)

                                coefficients of pre-edge correction factor for whole-spectrum fitting

  POST0(i),POST1(i)..POST8(i)

                                coefficients of polynomial correction factor for whole-spectrum fitting

 

In some instances it may be useful to combine common and individual variables - e.g., AFAC may be the same for all but one of the spectra. The rules for combining variables, in the case of spectrum i is as follows:

 

  EF                          The program uses EF+EFi

  AFAC                     The program uses AFAC*AFACi

  EMIN                      The program uses MAX(EMIN,EMINi)

  EMAX                     The program uses MIN(EMAN,EMANi)

  VPI                         The program uses VPI+VPIi

  WEX                       The program uses WEX*WEXi

  BETH                     There is no BETH - it uses BETHi (similarly with BEPHI, BEW)

 

The common variables may also be written, for example, EF0. This can be useful in resetting variables. e.g.

 

                C AFAC[0-3] 1

 

7. Theory parameters

 

  ATMAX                  maximum number of different atoms in a MS path

  DE0                        refinable correction to E0, for whole spectrum fitting

  NS                          the number of shells used for calculations

  LMAX                     maximum angular momentum for single scattering theory

  KMIN                      minimum wave vector for EXAFS theory

  KMAX                    maximum wave vector for EXAFS theory

  OMIN                      minimum order of scattering for theory calculations

  OMAX                    maximum order of scattering for theory calculations

  DLMAX                  maximum angular momentum for double-scattering theory

  TLMAX                  maximum angular momentum for triple-scattering theory

  DWMIN                  minimum reasonable value of A

  DWMAX                 maximum reasonable value of A

  TEMP                     temperature (K) - used in calculating edge-width (whole-spectrum fitting) and C3 (if CLE ne 0)

  CLE                        coefficient of linear expansion - if ne 0, used to calculate T-dependent C3 in anharmonic oscillator model

  E0                           absolute edge position - for whole-spectrum fitting only

  NIND                      number of independent points in χ2 calculation

  V0                           global interstitial potential value for potential calculation (eV)

  FE0                        global Fermi energy value for potential calculation (eV)

  RHO0                     global charge density value for potential calculation (4/3πr2 x e/(bohr rad)3)

  OFFSET                 fitting parameter defining the independent variables origin in the whole-spectrum polynomial correction

  MINANG                minimum angle for multiple scattering paths

  MINDIST                minimum distance for inter-atomic paths in multiple scattering paths

  MINMAG                minimum magnitude in principal path selection

  PLMIN                    minimum pathlength for multiple scattering paths

  PLMAX                  maximum pathlength for multiple scattering paths

 

 8. Control parameters

 

  D1A                        parameter A for use with CHANGE D1

  D1B                        parameter B for use with CHANGE D1

  D2A                        parameter A for use with CHANGE D2

  D2B                        parameter B for use with CHANGE D2

  OUTPUT                determines the output level

  BOND                    minimum bonding distance for plots etc.

  SIZE                       atom size in plots (% of MTR)

  VX                          x-coordinate of viewing position for 3D plots

  VY                          y-coordinate of viewing position for 3D plots

  VZ                          z-coordinate of viewing position for 3D plots

  M[1-9]                    memories

  WD                         weighting for structural component of the fit-index

  WA                         weighting for angle component of the fit-index

  NGRID                   number of points in grid used for potential calculations

  DFAC                     Relates maximum to initial step size in REFINE

  MAXRAD               maximum radius for inclusion of ligands from Brookhaven format file

  NPARS                  number of refined parameters used in χ2 calculation

  WNOISE                k-weighting of noise component of theory

  SPARE8                 select specific scattering angular momentum components - must be -1 for curve-fitting

  SPAR11                 suppress pi-shift if 99 and controls the way matrix elements are calculated from complex potentials- should normally be 97

  VECA                     shell A used in defining a rotation vector

  VECB                     shell B used in defining a rotation vector

  YMIN                      y-axis minimum for plots (for GSET RANGE YMIN/YMAX)

  YMAX                    y-axis maximum

 

 9. Fourier Transform parameters

 

  RMIN                      minimum distance for Fourier transforms

  RMAX                    maximum distance for Fourier transforms

  WP                         Fourier transform window parameter

 

10. Surface parameters

 

  ZMIN                      minimum depth of surface layer

  ZMAX                     maximum depth of surface layer

  DELTAX                 substrate displacement in x-direction

  DELTAY                 substrate displacement in y-direction

  DELTAZ                 substrate displacement in z-direction

  SURROT                surface rotation - rotation of top layer of substrate

  SURREL                surface relaxation - increase in top layer spacing relative to bulk

 

 11. XANES parameters

 

  XMIN                      minimum energy for XANES theory calculations

  XMAX                     maximum energy for XANES theory calculations

  XNP                        number of points in XANES calculations

  XLMAX                  maximum angular momentum for XANES calculations

  XLOUT                   maximum angular momentum for single centre expansion

  XOPT                     determines treatment of central atom phase.

 

 12. Restrained refinement parameters

 

These are indexed by two shell numbers, n and m

 

  Dn:m                      ideal value of distance n-m, e.g. D3:2 is the distance between atoms in shells 3 and 2

  Wn:m                     weighting for distance n-m

  An:m                      ideal value of angle 0-n-m

  Vn:m                      weighting for angle 0-n-m

 

 13. Bond parameters

 

These are indexed by two atom numbers, n and m. They are used only by DRAW

 

  Bn:m                      if non-zero, indicates a bond between atom numbers n and m. The atom numbers are given by the ID column in SYMMETRY output.

 

 

Parameter usage

 

 1. The crystallographic cell parameters

 

The cell parameters ACELL, BCELL, CCELL, ALPHA, BETA, and GAMMA have a number of uses. They are used to add the cell outline to pictures created with DRAW, they are used to calculate and display fractional coordinates, and they are used to allow simultaneous changes to all shells in accordance with changes in the cell parameters. The cell parameters are subject to symmetry conditions, e.g. for cubic point groups (T, Td, O, Oh ) A=B=C, α=β=γ=90. For this reason the point symmetry of the cluster should be defined before they are changed, using the command SYMMETRY. As changing the cell parameters also moves atoms, it is also important that the cell parameters are entered before the atomic coordinates. If this procedure has not been followed, the best solution is to write the parameters to a file using PRINT PARAMS, and then edit the file so that the cell parameters are correct before reading it again. The fractional coordinates of atoms may be listed using the command LIST FRAC.

 

Normally, it is not necessary to enter actual values of the cell parameters. For example, to determine the lattice constant of a cubic metal, it is simply to necessary to refine ACELL. The extent it differs from the starting value of 1 will indicate the fractional change in the cell parameter compared to the stating value. This provides an easy way of refining the coordinates of all the atoms, without having to use constrained refinement (constraints on) or the RULE command.

 

One use of CCELL, is to simulate the effect of surface relaxation. If only adsorbate atoms and two layers of substrate atoms are included, then the inter-layer spacing will vary. The adsorbate-substrate spacing will also change as a result, but this can be corrected by adjusting DELTAZ as described below (surface parameters).

 

 2. Shell parameters

 

  N                            If the point symmetry of the cluster is defined, the occupation numbers must be an integer number consistent with the symmetry position occupied. This may sometimes mean that a shell of atoms must be split into two - as for HCP structures where c/a is exactly (8/3)1/2.

 

  T                             The atom type is stored as a number, which is the same as that used in reading phaseshift files and in indexing phaseshift variables, including the ATOMn variables, where the index n corresponds to the value of T. If the ATOM variables are defined, then T may be assigned an element symbol instead of a number.

 

  R                            When the central atom of the cluster is at the centre of the coordinate system, the R values of all the atoms in a shell are there same. This is not the case, however, when the central atom has other coordinates.

 

  ROT                       ROT defines a rotation about an axis, but there is no absolute reference for the rotation, so only the change in its value is significant. For this reason it is often simpler to enter commands such as C ROT13 ROT13+90. The ROT parameters provide a convenient means of changing the fundamental coordinates x, y, z, r, θ, and φ, they play no prat in the theory. If a new set of parameters is read while ROT parameters are non-zero, then the starting point for any changes to the new data will be non-zero. As this is potentially confusing, these parameters are set to zero whenever a new parameter file is read. The axis used is determined by the parameters VECA and VECB which determine two points defining the rotation vector. VECA is always a shell number ( 0 for central atom of cluster 1). VECB may be a positive shell number, negative, or zero:

 

  VECB > 0               the second point is shell VECA ( not shell 0)

 

  VECB = 0               the second point is the pivotal atom for the unit to which the shell belongs ( the unit must be defined).

 

  VECB < 0               VECB is a code defining a direction relative to VECA. These codes are -1 for <100>, -2 for <010>, -3 for <001>, and -4 for <111>. What -5 does is a complete mystery.

 

Note that if, as is often the case, the central atom in shell 0 is required, this must be specified as VECA not VECB.

 

  CLUS                     This parameter determines which cluster the shell belongs to and whether the shell is an excited atom or not. An excited atom is signified by a negative value.

 

  LINK                      If two excited atoms are in close proximity, such as for Fe atoms in cubane, it would be normal to link one cluster with the other. This is achieved by setting the LINK parameter for a shell in one cluster to a shell in another, and defining an offset vector for the second cluster. This is normally done by means of the command GENERATE, but LINKS may be inspected or changed manually.

 

Many shell parameters are effected when constrained refinement is used. Details are discussed in the section Constrained Refinement in the program Guide (chapter 2).

 

 

 3. Unit parameters

 

Torsion angles - The program allows torsion angles to be defined and then changed for certain atoms within units. Changing a torsion angle, like constrained refinement, involves simultaneous movement of atoms within a unit. In this case however, three of the four atoms defining the dihedral angle remain stationary while the others rotate until the desired angle is obtained. Three torsion angles may be defined. By default one (TORC) is defined by atoms c-p-a-b, while the others (TORA and TORB) are undefined except when a Brookhaven ( or .pdb ) file is read, when the atoms N-CA-CB-CG and CA-CB-CG-CD are used (if there is no CG, NG or CG1 etc. may be used). The atoms defining the torsion angle for a unit may be changed at any time using PLOT UNIT which allows interactive changes to unit parameters. It is not relevant whether CONSTRAINTS is on or off when changing or refining torsion angles. Note that the program has no sense of which part of the unit is to remain stationary during rotation. The atoms defining the rotation axis (e.g. -CA-CB- ) will of course be unchanged. Otherwise those with residue names C, N, O, CA and the central atom, will remain unchanged, all others will be rotated. For this reason torsion angles are not generally used except in conjunction with parameters read from .pdb or .car files, or with structures created using the ligand database.

 

In order to make TORCi more useful. p is taken as PIVi, even if it is not within a unit. This has a special application in moving the side chains of complex polydentate ligands.

 

The ligand database - The ligand database resides in the file ideals and is based on the database used by the crystallographic refinement program prolsq. It has been extended to include non-amino acid ligands and information for defining the default relationship to the central atom for use in EXAFS analysis. In order to use the database the shell for the pivotal atom and the coordinates of the pivotal atom should be selected. E.g.:

 

 C X3 1.3;C Y3 1.3;C Z3 0.

 

The ligand can then be selected using:

 

 C T3 (ligand name)

 

The ligand name may be an amino acid symbol (TYR, HIS etc.) or a chemical formula (CO3, SO4). A list of current names may be obtained using:

 

 C T3 ?

 

The ligand will be assigned to the next vacant unit number. The pivotal atom will be assigned to the specified shell, and shell numbers above NS will be used for the other atoms. The ligand name will be used for the unit name. The unit parameters PIV, PLA, PLB, will be set up, as will any relevant torsion angles. Bond angles and torsion angles will be defined from database information. The only undefined aspect of the ligand is the rotation about the vector u. This may be changed using the ROT parameter with VECA=VECB=0. As ROT has no absolute significance it is not possible to use the current setting to define the orientation. This coordinate has no effect on the theory unless inter-unit multiple scattering or XANES calculations are performed.

 

 4. Phaseshift parameters

 

MTR values are set to default values (dependent on ION values), whenever ATOM values are changed. They may thereafter be changed or refined. Potentials and phaseshifts are automatically updated during refinements, but not when MTR values are changed manually If the COMMON V, EF or RHO options are in use, the Muffin-tin radius is initially set to the corresponding MTR value. The value of the Muffin-tin radius is then refined. The value used is written to the terminal and logfile during potential calculations, and to the phaseshift files genereated by PRINT PHASE, but the values of MTR variables are not changed..

 

 5. Site parameters

 

At present, the atoms associated with a site definition can only be defined by the SITE command, whereas the occupancy factors, PERCA1 etc. are parameters. The PERC parameters are only meaningful within the context of the site definition. It is therefore necessary to define the site before reading a parameter file, which contains no record of either the site name or its constituent atoms.

The ATOM parameters which allow T parameters to refer to the sites, are stored as numbers, not simbols. The order in which the sites are defined must therefore be the same as that in which they are used in any parameter files that are read .For further discussion of site parameters see the section Mixed Sites in the Program Guide (Chapter 2).

 

 6a. Spectrum parameters - beam polarisation parameters

 

Beam parameters are used in polarised (single crystal or surface) EXAFS to describe the orientation of the beam in terms of the axial system used to describe the crystal. There are sets of beam parameters for each experimental spectrum.

(e.g., BETH1, BETH2, BETH3). The beam orientation is given by BETH1 and BEPHI1 etc., the polarisation direction by BEW1. The default settings are for the polarisation e vector parallel to x, y and z respectively. The parameter values and the corresponding e vector directions are shown below.

 

  l spars

 

   Spectrum 1 Spectrum 2 Spectrum 3

 

   BETH1 = 0.000 BETH2 = 0.000 BETH3 = 90.000

   BEPHI1= 0.000 BEPHI2= 0.000 BEPHI3= 0.000

   BEW1 = 90.000 BEW2 = 0.000 BEW3 = 90.000

 

   EX1 = 1.000 EX2 = 0.000 EX3 = 0.000

   EY1 = 0.000 EY2 = 1.000 EY3 = 0.000

   EZ1 = 0.000 EZ2 = 0.000 EZ3 = -1.000

 

   ETH1 = 90.000 ETH2 = 90.000 ETH3 = 180.000

   EPHI1 = 0.000 EPHI2 = 270.000 EPHI3 = 0.000

 

 7a. Theory parameters - multiple scattering parameters

 

A number of parameters apply only to MS. DLMAX and TLMAX determine the number of angular momentum terms for double and triple scattering respectively. Although the number of terms required is usually less than for single scattering, the maximum allowed values (often 12 and 9, although some versions allow 15 and 12), may not be sufficient for heavy atom scatterers, and care should be taken in reducing these parameters, even for light atoms.

 

Several parameters restrict the number of paths that are calculated. These parameters can also be used to isolate contributions using EXTRACT     if a full set of paths have been previously calculated.

 

PLMIN                     is the minimum path length ( usually 0 )

PLMAX                   is the maximum path length (default is 10)

MINANG                 is the minimum angle - scattering within a triplet of atoms, or a quadruplet derived from it, will not be calculated unless one of the bond angles exceeds this value.

OMIN                       is the minimum order - default is 1

OMAX                     is the maximum order - default 3, maximum 5 - use of a higher order will considerably slow down the calculations.

ATMAX                   determines the maximum number of scattering atoms in a path - default is 2. 3, 4 or 5 may be selected at high computational expense.

MINMAG                 determines a cut-off below which previously calculated paths will be ignored. Default is 0. This should be used with great care. If one of the above parameters is changed, or any bond length changes by more than a few percent, the path indices will change, causing the wrong paths to be omitted. Path indices may be inspected using EXTRACT. A safe way to use this, is to set MINMAG to 0, calculate a spectrum with small atom or low DLMAX and TLMAX, set MINMAG to a sensible cut-off, and recalculate the spectrum using a higher angular momentum.

MINDIST                 determines the minimum permitted distance in any MS path. When site vacancies are being used it can be used to avoid including a disordered site twice in the same path.

 

The command LIST MSPARS will give the current values of most multiple scattering parameters.

 

When using the SMALL_ATOM option (SET THEORY SMALL_ATOM), the precision may be selected using NUMAX, which determines the size of the scattering matrix. 0 uses the approximation of Gurman (1988), 1 and 2 use the Rehr and Albers (1990) method, where the value of NUMAX determines the matrix size.

 

 7b. Theory parameters - energy parameters

 

 7c. Theory parameters - whole-spectrum parameters

 

 

 8. Control parameters

 

BOND has several uses in the program. It determines which bonds are included in plots produced by DRAW, and which distances and angles are included in the orresponding tables. It has a similar function in PLOT UNIT, and is also used to determine which shells are included in calculating bond valence sums. If BOND is zero, a value slightly greater than the first shell distance of the first cluster is assumed for DRAW and PLOT. When reading parameters in Brookhaven .pdb format, then if BOND is zero, it will be changed to a value slightly greater than the first shell distance.

 

OUTPUT has a default value of 0. Increasing its value will increase the amount of output to both the terminal and the log file. It is a good idea to use a value of at least 1 for long MS calculations, so the program does not appear to hang up.

 

 9. Fourier transform parameters

 

RMAX effects the range in R-space of plots produced by PLOT FT, COPLOT and PLOT PATHS, but not FFILTER, which has other mechanisms for determining the range in R-space.

 

10a. Surface parameters - surface displacement parameters

 

The general surface displacement parameters DELTAX, DELTAY, DELTAZ and those indexed by atoms type, the surface layer displacement parameters - SDX, SDY, and SDZ, are used for correlated movement of surface atoms. They are specific to surfaces, are indifferent to the status of the CONSTRAINTS option and do not require the use of units. One other thing they have in common is that their origin is undefined. They have no absolute meaning and are provided as a convenient means of changing the fundamental coordinates x, y, z, r, θ, and φ.

DELTAX etc. will move all atoms other than those in the z >=0 adsorbate layer in the required direction (in the cartesian rather than the crystallographic cell). For example DELTAX or DELTAY will simulate movement of the adsorbate off a high symmetry site, while DELTAZ will alter the adsorbate-substrate distance. Note that because all atoms, including those in special positions, are moved, the use of these parameters is highly subject to the point symmetry of the cluster. Movement of DELTAZ is not permitted in point groups with a centre, a horizontal mirror plane, a horizontal diad or cubic symmetry. However, as these are improbably in a surface simulation these restrictions should not prove a problem. DELTAX and DELTAY however are incompatible with a principal axis higher than 1, and are effectively restricted to use with ci and cx. cx is a specially defined point group symbol representing cσ in an alternative orientation with the mirror plane parallel to x. As DELTAX etc. have no absolute origin as a reference point, only changes in its value are relevant, so atoms are moved by the difference between the new and old values.

SDX etc. operate in a manner analogous to DELTAX etc.. The differences are that SDX only moves atoms in the top substrate layer, or surface layer, and is indexed by atom type, so that only certain atoms are moved. The surface layer is defined to mean any atom with a z-coordinate between ZMIN and ZMAX angstroms. If the atoms to be moved are in a general position then there are no symmetry restrictions on which movements are allowed. If atoms are in a special position with respect to a point symmetry operator, such as lying on the principal axis, then symmetry restrictions will apply. These will not be checked when the change is made, as with DELTAX, and will result in errors the next time the coordinates of all the atoms are expanded using the point group symmetry. If it is necessary to distinguish crystallographically distinct sites occupied by the same atom type, it will be necessary to duplicate phaseshifts, and assign two different atom types to the same element.

The action resulting from such movements will clearly depend on which of the set of symmetry related atoms are given in the table of shell parameters. With DELTAX the symmetry rules ensured that all the atoms were translated in the same direction. With SDX however, the action of vertical mirror planes will cause contrary motion of individual atoms and non-unitary principal axes will cause rotations. Indeed, the principal use of these variables is to simulate surface reconstructions which involve rotations of atoms, in contrary directions for adjacent adsorbate sites. The effect of the symmetry operator will be different depending on which atom in a shell has been selected for each shell ( they will simulate the effect of different crystallographic space groups). In general, only one of the possible choices is correct, and this will not be the case which is usually selected. An example of a parameter table ( for reconstructed p4g N on Ni(100) is given below.

 

                l car

 

 E0 = 3.000 VPI = -4.000 AFAC= 0.800 EMIN= 3.000 EMAX=3000.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 10.000

 Shell 1 N1 = 4.000 T1 = 28(NI) X1 = 2.400 Y1 = 0.000 Z1 = -1.000

 Shell 2 N2 = 4.000 T2 = 28(NI) X2 = -2.400 Y2 = 4.800 Z2 = -1.000

 Shell 3 N3 = 4.000 T3 = 28(NI) X3 = -2.400 Y3 = -4.800 Z3 = -1.000

 Shell 4 N4 = 4.000 T4 = 28(NI) X4 = -7.200 Y4 = 0.000 Z4 = -1.000

 Shell 5 N5 = 4.000 T5 = 8 (O ) X5 = 0.000 Y5 = 4.800 Z5 = 0.000

 Shell 6 N6 = 4.000 T6 = 8 (O ) X6 = 4.800 Y6 = 4.800 Z6 = 0.000

 Shell 7 N7 = 1.000 T7 = 28(NI) X7 = 0.000 Y7 = 0.000 Z7 = -2.200

 Shell 8 N8 = 4.000 T8 = 28(NI) X8 = 4.800 Y8 = 0.000 Z8 = -2.200

 Shell 9 N9 = 4.000 T9 = 28(NI) X9 = 2.400 Y9 = 2.400 Z9 = -2.200

 Shell 10 N10= 4.000 T10= 28(NI) X10 = 4.800 Y10 = 4.800 Z10 = -2.200

 

       l frac

 

Cell parameters: 9.6000 9.6000 1.0000

 

   Shell X Y Z

 

    0 O 0 0.0000 0 0.0000 0 0.0000

    1 NI 0 0.2500 0 0.0000 -1 0.0000

    2 NI -1 0.7500 0 0.5000 -1 0.0000

    3 NI -1 0.7500 -1 0.5000 -1 0.0000

    4 NI -1 0.2500 0 0.0000 -1 0.0000

    5 O 0 0.0000 0 0.5000 0 0.0000

    6 O 0 0.5000 0 0.5000 0 0.0000

    7 NI 0 0.0000 0 0.0000 -3 0.8000

    8 NI 0 0.5000 0 0.0000 -3 0.8000

    9 NI 0 0.2500 0 0.2500 -3 0.8000

    10 NI 0 0.5000 0 0.5000 -3 0.8000

 

 c sdy2 .02

 

 l car

 

 EF = 3.000 VPI = -4.000 AFAC= 0.800 EMIN= 3.000 EMAX=3000.000

 RMIN= 0.100 RMAX= 10.000 WIND= 2.000 WP = 0.100 NS = 10.000

 Shell 1 N1 = 4.000 T1 = 28(NI) X1 = 2.400 Y1 = 0.192 Z1 = -1.000

 Shell 2 N2 = 4.000 T2 = 28(NI) X2 = -2.400 Y2 = 4.992 Z2 = -1.000

 Shell 3 N3 = 4.000 T3 = 28(NI) X3 = -2.400 Y3 = -4.608 Z3 = -1.000

 Shell 4 N4 = 4.000 T4 = 28(NI) X4 = -7.200 Y4 = 0.192 Z4 = -1.000

 Shell 5 N5 = 4.000 T5 = 8 (O ) X5 = 0.000 Y5 = 4.800 Z5 = 0.000

 Shell 6 N6 = 4.000 T6 = 8 (O ) X6 = 4.800 Y6 = 4.800 Z6 = 0.000

 Shell 7 N7 = 1.000 T7 = 28(NI) X7 = 0.000 Y7 = 0.000 Z7 = -2.200

 Shell 8 N8 = 4.000 T8 = 28(NI) X8 = 4.800 Y8 = 0.000 Z8 = -2.200

 Shell 9 N9 = 4.000 T9 = 28(NI) X9 = 2.400 Y9 = 2.400 Z9 = -2.200

 Shell 10 N10 = 4.000 T10= 28(NI) X10 = 4.800 Y10 = 4.800 Z10 = -2.200

 

 l frac

 

Cell parameters: 9.6000 9.6000 1.0000

 

     Shell X Y Z

 

        0 O 0 0.0000 0 0.0000 0 0.0000

        1 NI 0 0.2500 0 0.0200 -1 0.0000

        2 NI -1 0.7500 0 0.5200 -1 0.0000

        3 NI -1 0.7500 -1 0.5200 -1 0.0000

        4 NI -1 0.2500 0 0.0200 -1 0.0000

        5 O 0 0.0000 0 0.5000 0 0.0000

        6 O 0 0.5000 0 0.5000 0 0.0000

        7 NI 0 0.0000 0 0.0000 -3 0.8000

        8 NI 0 0.5000 0 0.0000 -3 0.8000

        9 NI 0 0.2500 0 0.2500 -3 0.8000

       10 NI 0 0.5000 0 0.5000 -3 0.8000

 

If a new parameter file is read while DELTAX, SDX etc. are non-zero, then the starting point for any changes to the new data will be non-zero. As this is potentially confusing, these parameters are set to zero whenever a new set of parameters is read.

 

10b. Surface parameters - the surface relaxation parameter SURREL

 

SURREL alters the surface relaxation - that is, the distance between the top two substrate layers of a surface relative to the bulk interlayer spacing. The default value is 1. As with SDX etc. the surface layer is defined as that between ZMIN and ZMAX. When changing SURREL care should be taken to ensure that as a result of the change, atoms within the surface layer do not move out of it, and that atoms outside the surface layer do not move into it.

 

 11. XANES parameters

 

 12. Restrained refinement parameters

 

 13. Bond parameters


5. Command Reference

 

 

ALIAS

 

 

ALIAS is used to define commands.

 

Syntax:                    ALIAS alias_name [DEL]

                                ALIAS [LIST]

                                ALIAS DELETE [n]

 

Abbreviations:         AL

 

This command allows users to define their own commands or abbreviations. For example:

 

                ALIAS TEMPCOM

 

results in the prompt:

 

                Enter definition of TEMPCOM:

 

You can then type in any command or list of commands e.g.:

 

                gset dev 2;gset plotter ps_file

 

and for the rest of the session TEMPCOM will result in the execution of the list of commands.

 

If LIST is specified or else the command is entered without a keyword, then ALIAS lists the current aliases.

 

The number of aliases which may be defined is displayed using LIST DIMENSION. An alias may be up to 80 characters long. If the maximum number of aliases are already defined, the last n may be deleted using ALIAS DELETE n. If n is unspecified, the default is 1. DELETE may not be abbreviated, so that alias names such as DEL are allowed.

 

A specific alias may be deleted using:

 

                ALIAS alias_name DEL

 

Aliases containing special characters such as *, % and ! should be enclosed in quotes:

 

                ALIAS LL;'^ls -l'

 

Once defined, an alias may be used whenever a command name may be used.

An alias name must not conflict with an existing command or abbreviation. For example :

 

                ALIAS R;C R1 2

 

Will have no effect, as R will always be interpreted as READ, for which it is a permitted abbreviation.

 

 

ANGLE

 

 

ANGLE is used to calculate an angle with vertex (0,0,0)

 

Syntax:                    ANGLE [cluster_number]

 

Abbreviations:         AN

 

This command calculates the angle at (0,0,0) for two atoms. The program requests the spherical polar coordinates for two atoms. Normally the TH and PHI parameters for two shells are used, but any value or expression is valid.

 

                ANGLE

 

results in the prompt:

 

Enter theta for atom A

 

                TH1

 

......

 

Enter phi for atom B

 

                PHI4

 

Will calculate the angle 1-0-4

 

CALC

 

CALC is used to calculate potentials and phaseshifts.

 

Syntax:                    CALC POTENTIALS n

                                CALC PHASESHIFTS n

 

Abbreviations:         CA PO/PH

 

Option:                    atom number n

 

If the number n is defined then the calculation is performed for that atom number only (the atom numbers are those used in Tn parameters and elsewhere, usually 1 for the central atom, 2 for the first scattering atom etc.). If n is negative then the calculation is done for an atom of that type treated as a central excited atom. If n is omitted then the calculations are done for all defined atom types. Atom types are defined when the corresponding ATOMn variables are set to an atomic symbol or number.

 

                e.g.          C ATOM1 CU;C ATOM3 O;CA POT

 

Will calculate potentials for the Cu central atom (n=1) and the O scattering atom (n=3). The n=2 potential will be omitted unless ATOM2 has been previously defined.

 

Atom 1 is always an excited atom. If multiple edges are being fitted, additional excited atoms are required. These may be specified using:

 

                CA POT -4

 

To make atom 4 an excited atom, or better, by initially defining the relevant atom variables as excited atoms.

 

                C ATOM1 GA*;C ATOM4 SB*

 

For the Ga and Sb edges of GaSb. This procedure may be made mandatory in future releases. Atoms are also defined as excited atoms, if excited atom phaseshifts are read for that atom number. However they are defined, excited atoms are indicated by a * symbol when using LIST PHASE.

 

The potentials or phaseshifts are calculated using the approximations and methods outlined in the theory section.

 

Options which apply to potential calculations include those available through SET GROUND_STATE, SET EXCHANGE, SET COMMON ( see the help on SET ).

 

Options which apply to phaseshift calculations include those available through SET QUINN, SET RELCOR ( see the help on SET ).

 

Variables which apply to potential calculations for atom n, include ATOMn, MTRn, IONn, and CMAGn. Other variables affecting potential calculations, when using COMMON options, include V0, FE0 and RHO0.

 

The principal variables effecting phaseshift calculations are the core width parameters CW, CW1, CW2 etc. If CW is defined (i.e. if it is positive or zero), it will be used as the default core width for all phaseshift calculations. If CW1 etc. are defined (i.e. if they are positive or zero), they will be used as defaults for phaseshifts relating to experiment number 1 etc. These parameters should be set to -1 if not required, when program defaults will be used. The default values may be modified when CALC PH is executed.

 

CALC issues a number of prompts which are described in the sections Calculating Potentials and Calculating Phaseshifts of the program guide section, chapter 2. An example potential calculation is described in the examples section, chapter 3.

 

For Whole-spectrum fitting - using SET ATOMIC_ABS ON, slightly different rules apply - a potential will be calculated for an 'ATOM 0'. This duplicates the potential for the central atom, using an entirely real potential, as the treatment of inelastic effects is inappropriate for calculation of dipole transition rates. It is not necessary to change 'ATOM0' - there is no such variable. For this reason, the option to calculate the atomic absorption for a complex potential should be regarded as redundant.

 

 

CCHANGE

 

CCHANGE is used to change multiple atomic coordinates using constraints, irrespective of the current status of the CONSTRAINTS option.

 

Syntax:                    CCHANGE variable_name new_value

 

Abbreviations:         CC

 

Notes:

 

CCHANGE R1 is exactly equivalent to using

 

                 SET CONSTRAINTS ON;C R1;SET CONSTRAINTS OFF

 

All the atoms in the same unit as R1 will be moved so as to preserve the geometry of the unit. See documentation sections on units and constraints.

 

Note that if this method is used, subsequent refinements will not be constrained. The command is most useful in getting an approximate fit 'by hand' before using restrained refinement (q.v.).  

 

 

CHANGE

 

 

CHANGE is used to alter the values of the parameters described in section 4.

 

Syntax:                    CHANGE variable_name new_value

                                CHANGE CENTRE [cluster_number]

 

Abbreviations:         CH or C

 

Notes:

 

The effect is to change the value of variable_name to new_value.

 

Variable_name may be one of:

 

a) A parameter name, R1, EMIN etc. ( see the parameters section for a full list). Note that the program will not allow some parameters to be changed to values outside a specified range. Some parameters ( EMIN, EMAX, EF, KMIN, KMAX ) are interconnected and may change if you change the others (The relationship between KMIN and EMIN depends not only on EF, but also on the energy dependent self-energy, and may change when the theory is updated). New_value is usually a number, but in the case of parameters such as Tn, ATOMn new_value may be either an atomic number or chemical symbol:

 

                C ATOM1 CU is equivalent to C ATOM1 29

 

New_value may always be an arithmetic expression including other parameters, as in:

 

                C R2 R1*1.5

 

Parameters D1A, D1B, D2A and D2B are CHANGEd to the name of another parameter ( see d) below ).

 

b) A parameter list, R[1-3] etc. This format may be used with shell parameters N, T, R, A, UN, ANG, TH, PHI etc., with phaseshift parameters, MTR, ATOM etc., and with other indexed parameters such as memories, M1 etc.

Values may be changed for a range of shells. The format is similar to the Unix 'wildcard' format for filenames. The list is placed in square brackets [] after the parameter name. Thus 'CHANGE N[1-4] 7' will change N1, N2, N3 and N4 to 7. Several ranges may be specified in one set of [] by separating them with commas. Thus N[1,3-5,7] refers to N1, N3, N4, N5 and N7. Parameters may also be used inside the []. Thus N[1-NS] refers to all N values from 1 to the current value of NS. When used in this way CHANGE only reports the first and last values changed.

Identical rules apply to parameter lists in the command REFINE.

 

c) A shell symbol, S1, S2, S3, etc. New_value should be the number of the shell whose parameter values you wish to copy to the shell being changed. e.g.:

 

                C S2 1

 

Will produce the result that shell 2 is identical to shell 1.

 

If new_value is unspecified, you will be prompted for new values for all the parameters of that shell. Enter '=' when sufficient parameters have been changed. This allows all the parameters for a shell to be entered using a single CHANGE command.

 

d) DF1 or DF2. The difference between parameters D1A and D1B or D2A and D2B will be set to new_value. D1A and D1B must previously have been set to the names of two parameters indexed by shell. If DF1 is set then during an REFINE or MAP the difference between the two parameters D1A and D1B will be maintained. Thus 'C D1A R1; C D1B R2; C DF1 1.0 ' will maintain a distance of 1.0 between shell 1 and shell 2. This can be useful if there are close peaks in an

EXAFS spectrum.

 

e) Table symbols Dn:m or Wn:m ( n and m integers ). These parameters are used in restrained refinement. 'C D1:0 3.4' for example sets the distance between shell 1 and the central atom to be 3.4; 'C D3:2 2.6' sets the distance from shell 3 to shell 2 to be 2.6. ( The larger shell index must come first. ) Wn:m is the weight given in restrained refinement to the distance Dn:m. (See the section on restrained refinement for more details.)

 

Special notation permits multiple changes:

 

                C D:

 

Sets all restrained distances equal to the corresponding current inter-shell distance.

 

                C W: 1

 

Sets all the weights to 1, unless the corresponding Dn:m is zero.

 

f) Table symbols Bn:m (n and m integers). These parameters are used in specifying non-standard bond distances in the commands DRAW and DISPLAY. n and m are the numbers associated with individual atoms - that is the numbers generated by the SYMMETRY command, not the shell numbers. One difficulty that may be encountered, is that the order of the atoms, and therefore the significance of the numbers, may change with small changes in the coordinates of the atoms. These parameters have not been tested since changes in the symmetry code and may not function correctly. They are due to be revised.

 

g) Table symbols An:m, Vn:m (n and m integers). These parameters are used in restrained refinements using angles. They are analogous to Dn:m and Wn:m used in distance restraints.

 

h) CENTRE. The effect of this is to re-centre the cluster specified by the numeric option. If the central atom has been moved, its new coordinates will be set to 0,0,0 and the coordinates of the other atoms in the cluster moved by the same amount. The move will be remembered when using WRITE PARAMETERS BR to produce a .pdb file. The default cluster number is 1.

 

Correlation

 

CHANGE is affected by the SET CONSTRAINTS option (which may be OFF, ON or ALL).

 

Changes to torsion angles (using TORTA1 etc.) will only be effective if CONSTRAINTS is OFF.

Changes to SURREL, SURROT, SDX, TRANSX, ACELL etc. will ignore the status of the CONSTRAINTS option (in general it should be OFF if these options are used).

If RULES have been defined, related parameters will be update whenever a parameter is changed. The use of RULES will override any changes due to use of CONSTRAINTS. In general, RULES should only be used when CONSTRAINTS is OFF.

If a parameter is the subject rather than the object of a rule, CHANGE will have no effect.

 

 

COMPARE

 

 

COMPARE is used to compare a new experimental spectrum with the current experiment and/or theory.

 

Syntax:                    COMPARE EV/K/KEV option

 

Abbreviations:         COM

 

Notes:

 

The name of the additional experimental file is requested. If the wavevector is being used as the X-axis then an energy shift may be specified to permit alignment of spectra. The energy shift is added to EF and the new value is used in calculating the wave vector for both the plot and the Fourier transform.

The keyword determines wether the spectrum is tabulated in eV, wavevector or keV. E0 is used with eV and keV (e.g. if absolute energy rather than energy relative to the edge is used). E0 is ignored for K. The energy zero may be added to the offset described above. The default keyword is EV.

 

option = 0                Only the experiments are displayed (default).

 

option = 1                The theory is displayed as well as the experiments.

 

 

CONFIG

 

CONFIG is used to change hardware dependent features such as fonts and line width. These are stored in the file excurve.cfg.

 

Syntax:                    CONFIG  LIST/WRITE/FONTLIST/item

 

Abbreviations:         CON

 

Notes:

 

LIST                        display items that may be altered (default)

FONTLIST               display list of fonts (only a few of this list may be available on a particular device)

WRITE                    write a new excurve.cfg file

 

LWIDTH                  determines minimum line width for hard copy

TERMFONT            font for windows terminal

PRINTFONT           font for hard copy

TERMTEXTSIZE     determines font size for terminal

PRINTTEXTSIZE    determines font size for hard copy

XOFFSET               hard copy left margin

YOFFSET               hard copy bottom margin

PLOTTER               determines the default plotter as in GSET PLOTTER

                                (COLOUR/MONO etc. for Windows, HP/PS etc. for Linux)

 

The font and textsize options are not yet implemented in the Linux version

 

COPLOT

 

 

COPLOT displays EXAFS and Fourier Transforms together.

 

Syntax:                    COPLOT option

 

Abbreviations:         COP or CP

 

Notes:

 

COPLOT produces EXAFS and Fourier transform plots. By default, these are in frames 1 and 2 (top and bottom left) of a 4-frame page for the first spectrum, frames 3 and 4 for te second. If the GSET option FRAMES is set to SELECT then you will be prompted for the frame numbers permitting other formats. If you wish to produce plots in other combinations then use GSET FRAMES SELECT and the PLOT command to produce the individual frames.

 

Option may be 0 (default), 1 or 2. 1 causes the previous generation of theory to be displayed alongside the current one. 2 displays 2 previous generations. Option 2 is not available if the number of experimental points exceeds half the dimension of the array (this is displayed by LIST DIMENSION). The display is also affected by the other GSET options as with PLOT.

 

DEBYE

 

 

DEBYE Calculates disorder using Debye theory, displays heat capacities, MSD's EXAFS Debye Waller, factors etc.

Debye-Waller parameters An are calculated which can then be used for fitting.

 

Syntax:                    DEBYE

 

Abbreviations:         DEB or DE

 

Notes:

 

Uses the current values of parameters ACELL etc, Tn, TEMP, and point group, all of which must be defined.

 

Further information requested is the number of atoms per unit cell (e.g. 4 for FCC, 2 for BCC), and the Debye temperature.

 

 

DISPLAY

 

DISPLAY is used to display interatomic distances and angles for a cluster whose point symmetry has been defined.

 

Syntax:                    DISPLAY ATOM/CLUSTER/SHELL [atom, cluster or shell number]

 

Abbreviations:         DI

 

Notes:

 

This command displays a table of interatomic distances and angles. The positions used are calculated from the shell variables and the point symmetry of the cluster. The point group must be specified by using the SYMMETRY command. If this has not been done, or if a structural variable has been changed since the last use of SYMMETRY then SYMMETRY will be executed automatically (without output). ( see the section on the SYMMETRY command). SYMMETRY generates labels for every atom in the structure. The first column out output is the atom number (1,2,3....n). The second is a shell number with a symmetry index (e..g 1, 1a, 1b, 1c, 2, 2a, 3 ). The order is that required by XANES calculations.

 

 

DISPLAY with no parameters, displays distances and angles with the central atom as vertex, for all clusters.

 

DISPLAY CLUSTER n restricts the display to cluster n.

 

With CLUSTER the output is restricted to distances between each atom in the asymmetric unit and all other atoms.

 

DISPLAY SHELL n shows all interatomic distances and angles related to shell n.

 

DISPLAY ATOM n shows all interatomic distances and angles involving atom number n.

 

With ATOM and SHELL keywords, all relevant distances are displayed. If n is omitted, all distances in the structure are displayed.

 

For ATOM , atoms are labelled with numbers generated by the SYMMETRY command (the 'ID' column).

For the other keywords, the atoms are labeled by shell number.

 

Information generated by this command may be written to a file using the PRINT GEOM command.

 

DRAW

 

DRAW will display a simple plot of the clusters surrounding each central atom, or of individual units. The point symmetry of each cluster must be defined.

 

Syntax:                    DRAW keyword [cluster/unit number]

 

Abbreviations:         DR

 

Keywords:                               CLUSTER (default) draw the structure on new axes

                                PATH                      draw the atoms of a multiple scattering path

                                UNIT                        draw an excurve 'unit' (part of the cluster defined by common 'unit numbers')

                                NOCLEAR               overlay the structure on an existing display

                                POSITIVE               use absolute values of the coordinates of the point of projection

 

Notes:

 

This command displays a projection of the three dimensional atomic positions. These positions should have been calculated from the shell variables by using the SYMMETRY command. If this has not been done, or if a structural variable has been changed since the last use of SYMMETRY then SYMMETRY will be executed automatically ( see command documentation for symmetry ). The information generated by SYMMETRY can be saved to a file using the PRINT ATOM command.

 

Atoms are labelled with their chemical symbol, provided ATOM variables as well the atom types T are defined. By default, the label also includes the shell numbers, but by selecting GSET LINE SYMBOL, the numbers generated by the SYMMETRY command are used. GSET LABEL LARGE affects the size of the labels. GSET LABEL OFF removes them. GSET AXES OFF removes the axes.

 

The appearance of the plot is controlled by the variables BOND, SIZE, VX, VY, VZ. These can be viewed with LIST and changed with CHANGE. A line representing the bond between two atoms is drawn if the distance between those two atoms is less than BOND. If BOND has its default value of 0, then a distance slightly greater than R1 is assumed. The atoms are represented by circles of radius SIZE*MTRn where MTRn is the muffin-tin radius for that atom type. If SIZE is given a value of 0 then a predefined minimum is assumed.

 

The structure is drawn as seen looking from a viewing position specified by three cartesian coordinates towards the origin of the coordinates. If the SET option VIEW is set to AUTO, the projection position is calculated automatically so as to give a minimum overlap. If VIEW is set to current, then three variables, VX, VY and VZ are updated using the last viewing position and are then used by DRAW. VX, VY and VZ may thereafter be changed manually if required. The default positions of 3.5, 2.5, 1.5 usually gives a useful view. VX, VY, and VZ must be positive and the sum of their squares must exceed 1.1. If VX+VY+VZ=0, then a minimum overlap position will be generated even though CURRENT has been selected.

 

In addition to bonds drawn due to the value of BOND, specific bonds may be included by setting the variables Bn:m

to a non-zero value. n and m here are atom numbers as generated by SYMMETRY not shell numbers. n must exceed m. m is zero for the central atom.

 

With DRAW UNIT and DRAW PATH, if automatic viewing is in use, the viewing position will be selected for the whole cluster. Although this means that it is not optimised for a particular unit, it allows additional units to be added one by one using, for example:

 

                DR NOC 2

 

To add unit 2 to the picture. NOCLEAR assumes the CLUSTER, PATH or UNIT option is in accord with previous usage.

 

If a cluster was drawn at the last call, the new cluster will be overlaid. This makes it possible to see how a cluster has changed during refinement.

 

                DR CL; ( ... refine the structure ... ) ; DR NOC

 

POSITIVE is the same as CLUSTER, but the minimum overlap projection always has VX, VY and VZ > 0.

 

END

 

 

Terminates the program.

 

Syntax:                    END

 

Abbreviations:         none

 

Notes:

 

The program saves parameter values. Use RECOVER the next time the program is used in order to restore them, before, using the command CHANGE, which will overwrite the saved values.

 

  

EXPAND

 

 

EXPAND creates a parameter table containing 1 atom per shell, of c1 symmetry, from a table of higher symmetry. It can be used when it is necessary to reduce the symmetry of an idealised model of the structure. It can also be used when it is necessary to include some inter-ligand as well as intra-ligand MS paths when using the MS UNIT rather than MS ALL option.

 

 

Syntax:                    EXPAND

 

Abbreviations:         EXP

 

Notes:

 

The cluster will be truncated if the total number of atoms exceeds the number of shells allowed by the program ( see LIST DIMENSION ).

  

EXTRACT

 

 

EXTRACT creates a file containing either the whole sum or a partial sum of multiple scattering paths. In addition it generates a table of scattering paths, including their lengths, multiplicities and magnitudes. The latter function is likely to be used more often than the former, which was the original purpose of the command.

 

 

Syntax:                    EXTRACT [PAUSE/NOPAUSE/QUIET]

 

Abbreviations:         EXT

 

Notes:

 

The command provides information on MS paths that have already been calculated (subject to filter conditions). A list of all the paths calculated will be displayed. The effect of additional filter conditions on both the number of paths, and the resultant spectrum, may then be evaluated. The path sum defined by the current filter conditions, as well as the path information, is written to a file whose name is requested.

 

QUIET disables terminal output, writing path information only to the disc file.

PAUSE pauses between each line of output.

NOPAUSE is the default option.

 

This command does not automatically update the theory. It uses the last set of paths calculated, further reduced in number by any change in filter conditions.

 

 

 

FFILTER

 

 

Isolate contributions of specific shells to the experimental EXAFS spectrum using Fourier filtering.

 

Syntax:                    FFILTER [SHORT/MEDIUM/LONG] [+/-spectrum_number]

 

Abbreviation:           FF

 

Notes:

 

This command allows parts of the Fourier transform of the experimental data to be back-transformed. In this way it is possible to see which shells in the structure caused which parts of the EXAFS spectrum. After receiving this command the program displays the current experimental spectrum and its Fourier transform.

The user is prompted:

 

                ENTER RMIN and ENTER RMAX

 

in order to determine which part of the displayed spectrum is to be back-transformed (the window). The program then prompts:

 

                 Enter MOVE, NEXT OR CONTINUE

 

MOVE allows the current window to be changed. NEXT allows a new window to be defined. CONTINUE goes on to the next stage. You can define up to three windows at a time. Lines indicating the extent of the windows appear on the Fourier transform plot. After a CONTINUE the back-transform of the last window is displayed.

The range in r-space is calculated automatically and depends on the point spacing Δk. This is dependent on the length of the spectrum in use, but may be altered using the option number described below.

 

The next prompt is:

 

                Enter shell radius or CONTINUE

 

If you enter a number which indicates the actual radius of the shell that this window is trying to isolate then a graph showing the backscattering magnitude and phase is displayed. CONTINUE will go to the next stage. NOTE: the last window entered is processed first.

 

The next prompt is:

 

                Enter PRINT, REPLACE, NEXT or END

 

PRINT will write the new spectrum to a file. You will be prompted for a filename. If the phase and backscattering magnitude have been calculated these are also written out. REPLACE will replace the current experimental spectrum with the new spectrum for all future plotting etc. NEXT will go on to the process another window, if there is one. END will exit from the FFILTER command.

 

SHORT, MEDIUM and LONG control how many points are used in the back-transformed spectrum ( and consequently how much R space is visible in the original spectrum ). SHORT (default) uses 200, LONG uses 500 points. If the range in r-space is initially too short, MEDIUM or LONG should be used as required.

 

For a multi-spectrum fit, the spectrum_number should be specified. If the spectrum number is -ve, each plot will be in full-page format, rather that 4 per page.

 

Note that the parameters RMIN and RMAX are not used by the FFILTER command. As no window function or phase correction is used in the Fourier transform, FTSET options referring to these are ignored. The weighting used by the Fourier transform is given by FTSET option FTWEIGHT. The GSET options are used to determine the format of the plots.

except for WEIGHTING, FFILTER uses a k**2 weighting at present. Previously a k**3 weighting has been used.

 

EF and EMIN are reset for the duration of the command, so the spectrum plotted will not be directly comparable with that displayed by the command PLOT.

 

 

FIT

 

 

Calculates and displays the updated fit-index.

 

Syntax:                    FIT BOND_VALENCE/EXAFS/FT/STATS/QUIET/ weighting

 

Abbreviations:         FI

 

Notes:

 

FIT Recalculates the theory (if required) and quantifies the fit between experiment and theory. The fit is described in terms of the fit-index, chi^2 and R-factor which are defined under refinement, in the theory section, chapter 1. The discrepancies between ideal and actual parameter values are also displayed if restrained refinement is in use. The relative weighting of theory, distance restraints, and angle restraints are given by WEX, WD and WA. If multiple spectra are being used, their relative contributions to the fit-index and R-factor are determined by WEX1, WEX2 etc. (multiplied by WEX). These weighting are displayed by the command.

If the keyword FT is specified, then the Fourier transforms are also recalculated. If weight is specified then it is used as the k-weighting in the calculations rather than the value currently specified by SET WEIGHTING, which is the default.

 

Keyword STATS gives statistics referring to specific shells.

 

The calculation of chi2 relies on the number of independent points in the spectrum which is normally calculated automatically by the program using 1/2πΔkΔr, but may alternatively be specified using the parameter NIND. It also uses Np, the number of refined parameters. This must be set by the user, using the parameter NPARS, to the total number of parameters refined at any time during the analysis.

 

The fit-index includes a term due to the soft constraints used by he program, especially that due to A parameter values which fall beyond DWMIN or DWMAX. The term is given by:

 

                Σi constant x ((DWMIN-Ai)2 + (Ai-DWMAX)2 )          for all terms A < DWMIN or A > DWMAX

 

There are no such terms in the R-factor or chi2.

 

With keyword BOND\-VALENCE the bond valence sum for each cluster is displayed, using the parameter BOND to define the number of bonded atoms. A default value of atomic valence is assumed, which may be overwritten using ION parameters for each atom type. Note however that these should be reset before further potential calculations are performed.

 

FTSET

 

 

Controls options concerned with Fourier transforms.

 

Syntax:                    FTSET keyword value

                                FTSET LIST

                                FTSET

 

Abbreviations:         FT

 

Notes:

 

The options which control the way Fourier transforms are calculated are set by this command.

The first format changes the setting of keyword to option and returns to the normal EXCURVE command level.

 

The second lists the current values of all the options and stays within the FTSET environment.

 

The third format enters the FTSET environment.

 

For historical reasons these parameters also control some features of radial distribution calculations.

 

The keywords are:

 

 

                FTPHASE


This determines how the phase of the Fourier transform is calculated.

First shell                 : the phase is calculated from the first shell backscattering factor.

Second                    : the phase is calculated from the second shell

None                       : no phase correction

 


                FTWEIGHT


Controls the weighting applied to the spectrum before it is transformed.

None                       : no weighting

K                              : k-weighting

K2                            : k2 weighting

K3                            : k3 weighting

K/fpim                      : weighted by k/back-scattering magnitude

 


                FTWIND


Controls the type of window.

 

Hanning

Gaussian

Kaiser/Bessel

Blackmann/Harris

 

The parameter WP determines the characteristics of the window, in a manner depending on the choice of window function.

 

 


FTMULT


One                                                                                  : no multiplication of transform

R-squared                                                                        : transform is multiplied by R**2

 


FTCENT


Controls the position of the centre of the window which is Fourier

transformed. Note that the window type is controlled using the

parameters WIND and WP. The default window is a Gaussian with

width 0.1

 

Auto                         : centre of window is midpoint of spectrum

K                              : centre uses the parameter CENT (in wave numbers)

Energy                     : centre uses the parameter CENT (in energy)

 

 


                RDF


Controls the type of radial distribution function calculated and displayed by PLOT RDF.

Atomic                     : atomic radial distribution function

Electron                   : electron radial distribution function (requires that ATOM parameters are defined).

Atomic/r2                 : 1/R2 times atomic rdf.


                TRANSFORM


Determines whether the imaginary part of the Fourier transform is displayed as well as its modulus.

 

Modulus                  : only the modulus of the complex FT is displayed.

Sine+modulus         : both the modulus and the imaginary part are displayed, revealing errors in the phase as well as the magnitude of the EXAFS function.

 

 


                QUIT


Leave FTRANS command.


                LIST

 


Display option table.

 


                RESET


sets all options to 1

 


 

The values of WP are set using the CHANGE command. The values

allowed depend on the setting of FTWIND and are:

 

                WI


1 uses a Blackmann-Harris window, there are two sets of pre-defined coefficients defining a narrow or wide window. If WP = 1.0 the narrow window is used, if WP = 1.5 the wide window is used.

of window )

 

2 (default) uses a Gaussian window, the exponential power is -WP * ( square of K - K of centre of window )

 

3 uses a Hanning window, weight is ( cos( (K-Centre) * PI / (Kmax-Kmin)) ) ** WP

 

4 uses a Kaiser-Bessel window (no parameters).


GENERATE

 

Generates additional clusters from an atom in an existing cluster.

 

Syntax:                    GENERATE {LINKED/UNLINKED} new_cluster_number

 

                                The program will prompt for an atom in an existing structure, to be used as the centre of the new one.

 

Abbreviations:         GE

 

Notes:

 

Given an existing cluster, the program generates a new cluster centred upon one of the atoms in the first cluster. The clusters may be linked or unlinked. With a linked cluster, any changes in one of the clusters results in changes in the others. This case is used when two central atoms (of either similar or different type) are within close proximity (say, 5 to 6 Angstroms). Unlinked cluster are used when the clusters are far apart, or else when they are near, but the inter-cluster distance itself is the variable of interest. GENERATE simplifies the task of setting up variables for a new cluster, but does not do all the work. Normally the atom types (Tn) must be changed for the new central atom (in general a scattering atom in the original cluster) and for the old central atom (now a scattering atom). The occupation numbers N may also need to be changed. Indeed, the command is not reliable except in the case that all the occupation numbers are 0 (point group C1). A minimum requirement is that the point group of the central atoms is the same. Even then, it will be necessary to adjust the occupation numbers if they are not equal to one. The only occasion when the occupation numbers will be correct with higher point symmetries is when the central atom of the first cluster is also the central atom of the second. This may arise when the command is used as a starting point for generating unlinked clusters about different atoms in a close-packed lattice. Note however, that this may often be done by using mixed sites for both absorbing and scattering atoms.

 

The default value of LINK variables is 0, and it is not possible to link a shell to shell 0 (the central atom of the first cluster). Shell 0 may however itself be changed, and the other clusters will be updated accordingly. This restriction may be removed in later versions.

 

If linked clusters are used, the links may be inspected using LIST LINKS. In recent versions links may also me inspected or CHANGEd individually, by means of the variables LINKn which specify the shell which will be updated when shell n is changed. Note that it is normal to change the first cluster which will then update the others, but in later versions any cyclical change may be performed ( i.e., in a 3 cluster structure, changing cluster 2 will update cluster 3 which will in turn update

cluster 1).

Note that link information is lost when NS is reduced, so it may not be reduced temporarily if links are in use. This was done in recent versions to avoid unwanted changes due to 'hidden' links.

 

GSET

 

 

Controls the options which affect the appearance of graphical output.

 

Syntax:                    GSET keyword option

                                GSET LIST

                                GSET

 

Abbreviations:         G, GS

 

Notes:

 

This command selects options which control the appearance of graphical output. If GSET alone is entered on the command line the command issues prompts for further input. At this stage you can enter a keyword and a new option, LIST (to list current options), RESET to change all options to the first on the list or QUIT to leave the GSET command. GSET LIST displays the current values and remains within the command. GSET keyword option changes the option associated with keyword and returns immediately to the EXCURVE command prompt. The keywords and options are as follows (all keywords and options may be abbreviated so long as they uniquely define the entry required.

A number corresponding to the list position may be also be entered ( e.g. G LA 1 will select the first option, which is ON).

                AXES


ON 

OFF

BOTTOM_ONLY


graphs have axes (default)

graphs have no axes

x-axes are only displayed on the lower graph of each column.

 


                DEVICE


TERMINAL

PLOTTER

 


(default)

hard copy only


                FRAMES


FIXED

 

SELECT

 


graphics output uses the whole screen, for single frame plots, and frames in sequential order for multi-frame plots (coplot, plot spectra etc.) (default)

allows the position of frames to be selected by the user. You will be prompted for a frame number for each plot. Frame 0 is the whole screen, 1,2,3 and 4 are for quarter screen, 5-19 for 5x3 frames.


                LABELS