****************** * LATEST RELEASE * ****************** SEXIE 3.0 - an updated computer program for the calculation of ---------------------------------------------------------------- coordination shells and geometries ---------------------------------- Anne E. Tabor-Morris Physics Department University of Notre Dame Notre Dame, IN. 46556 Bernhard Rupp*) Lawrence Livermore National Laboratory University of California, P.O.Box 808, Livermore, CA 94551 *) To whom correspondence should be addressed ABSTRACT ======== We report a new version of our FORTRAN program SEXIE (ACBV). New features permit interfacing to related programs for EXAFS calculations (FEFF by J. J. Rehr et al.) and structure visualization (SCHAKAL by E. Keller). The code has been refined and the basis transformation matrix from fractional to cartesian coordinates has been corrected and made compatible with IUCr (International Union for Crystallography) standards. We discuss how to determine the correct space group setting and atom position input. New examples for Unix script files are provided. NEW VERSION SUMMARY =================== Title of program: SEXIE 3.0 Catalogue number: Program available from: CPC Program Library, Queens University of Belfast, N.Ireland (see application form in this issue) Reference to original program: Comp. Phys. Commun. 67 (1992) 543 Authors of original Program: B. Rupp, B. Smith and J. Wong Does the new version supersede the original program? yes Licensing Provisions: none Computer: VAX, PC, Sun Sparc, SGI Indigo R4000 tested Operating system: independent, DOS, VMS, UNIX, IRIX tested Programming language: FORTRAN 77 (ANSI X3.9-1978) Memory required: 320 kBytes, dimension dependent No. of bits in a word: 16 No. of processors used: 1 Has the code been vectorized: no No. of lines in combined program and test deck: 6500 Keywords: X-ray Absorption Spectroscopy, EXAFS, coordination shells, coordination geometries, bond distance, bond angles, cartesian atomic coordinates Nature of physical problem: calculation of coordination shells and geometries around a central atom in a crystal structure and presentation in a form suitable for EXAFS data interpretation and refinement. Method of solution: based on the input of space group, unit cell parameters and fractional coordinates of nonequivalent atoms in the unit cell, we expand the cluster of atoms and calculate the distances from each symmetry- generated atom to the central atom, sort the distances into shells and attempt to identify shell geometries. Restrictions on the complexity of the problem: Per default, the unit cell is limited to twenty nonequivalent atoms. This parameter is easily changed at the cost of about 10 kB memory per additional atom. Typical running time: few seconds on Intel iAP80486DX processors. LONG WRITE UP ============= 1. Introduction --------------- We recently introduced a simple FORTRAN program [1] which calculates the atomic environment around a central atom of a crystal structure in a shell by shell fashion, as needed for EXAFS (Extended X-ray Absorption Fine Structure) modelling and interpretation. In addition, complete distance and bond angle information is provided and our program, SEXIE, can be easily adapted to interface to a variety of useful programs. Included in this version (SEXIE 3.0) are facilities for input generation to a high order multiple-scattering calculation [2] of X-ray absorption fine structure, FEFF5, based on an extended curved-wave formalism [3], and for a molecular structure presentation program, SCHAKAL [4] . The success of the program SEXIE (we estimate a user community of about a hundred regular users) results in part from the fact that it requires only a minimum crystallographic input, comprised of unit cell dimensions, the Hermann-Mauguin space group symbol, and the basis set of atoms in the asymmetric unit. The cumbersome input of space group symmetry operators can be completely avoided, which is of particular value for the high symmetry space groups frequently encountered in EXAFS analysis of inorganic solid materials [5]. Users of SEXIE have made various suggestions for improvements, and have pointed out some difficulties caused by idiosyncrasies not obvious from the initial program description. Many of the users' suggestions have been implemented and an error in the basis transformation from fractional to cartesian coordinates affecting oblique lattices [6] has been corrected. Shell grouping and distance information have not been affected by this error. 2. Correct structural input data -------------------------------- Our program performs a variety of consistency checks for the plausibility of the crystallographic information. However, incorrect results from SEXIE were occasionally obtained as a consequence of improper input data. Structural information derived from compilations such as Wyckoff [7], Pearson/Villars [8] or from older original literature should always be checked for consistency of the equipoint positions for each atom in the asymmetric unit cell with the positions listed in the International Tables for Crystallography [9] (abbreviated ITC). In the subsequent sections we discuss typical cases where subtle input mistakes lead to hard-to-detect errors in the output data. 2.1. Choice of space group origin --------------------------------- A common source of input errors stems from the fact that some centrosymmetric space groups are listed in the ITC with two choices of origin, either located at the site of highest point group symmetry (origin choice 1) or at the symmetry (inversion) centre (origin choice 2). SEXIE accepts only the standard settings of these space groups, with the lattice origin at the centre (denoted as 'origin at centre' or 'origin at 1(bar)' in the ITC). Problems occur when fractional coordinates from non-standard settings are to be transformed into the setting used by SEXIE. This appears to be a common problem, which occasional users of crystal data encounter from time to time. We therefore feel that it may be of use to outline examples of such transformations and how to avoid pitfalls. TiO2 (Anatase), was reported in Wyckoff in space group I41/amd (No. 141) with atom coordinates of Ti in 4a (0, 0, 0) and O in 8e (0, 0, z'), z'=0.2066. Entered into SEXIE, his data results in erroneous multiplicities, an x-ray density twice as high as expected, and incorrect nearest neighbour distances. These observations can be considered strong hints for incorrect input data (severe blunders, like incompatibility between space group and crystal system decoded from unit cell dimensions, or colliding atoms, are recognized by the program and flagged). A closer look at the ITC (space group No. 141) reveals that (0, 0, 0) is a special position for the setting with origin (0, 1/4, -1/8) from the centre, whereas the standard setting (origin choice 2) places the origin at the centre as listed on the subsequent page(s) of the ITC. To obtain the correct coordinates one must shift the origin by (0, -1/4, 1/8) yielding (4a) (0, 3/4, 1/8) for Ti, and (8e) (0, -1/4, z'+1/8) or (0, 3/4, 0.3314) for oxygen, which is consistent with the corresponding equipoint positions in the second origin choice. These values can be entered directly into the program, and deliver the correct results. The z'' for this origin setting can be determined from the fact that (0, 3/4,0 .3314) is compatible with either the second or third coordinate triple listed in the ITC for (8e), namely (0, 3/4, 1/4+z'') or (0, 3/4, z(bar)''), with z(bar)'' = -z''. We obtain thus for z'' the values of 0.0814 or -0.3314 (or 0.6686). All are equivalent and for example, O (8e) at (0, 1/4, 0.0814) delivers the desired result. Another typical case subject to different choices of origin is the diamond structure (Ge, Si) in space group Fd3m (No. 227) which yields correct results with the (8a) atoms in the second choice position (1/8, 1/8, 1/8) only. We have chosen the example of TiO2 because it also shows how to make use of the control variables to define the tolerance in the definition of a shell. With a small permitted shell 'thickness' (CONV = 0.001 A~) the shell interpretation program finds a fourfold geometry at a distance of 1.934 A~ plus a nearly perpendicular linear arrangement at 1.964 A~. The actual structure is a rather distorted octahedron, and by reducing the control parameter CONV to 0.05, the program groups the atoms in a sixfold coordination, although the actual octahedron is too distorted to be recognized as such by SEXIE. In cases where high accuracy for shell distances is desired and the geometry search is of no interest (see section 3, FEFF input), the control variable CONV should be set to 0.001 or lower. 2.2. Incomplete transformation of structural information -------------------------------------------------------- Standard settings for space groups and structural data were only adopted after a considerable number of structures had already been reported. As a result, non-standard settings or structures which have been incompletely transformed into standard settings, are sometimes encountered. We found, for example, cases where hexagonal cell dimensions were reported, but the fractional atom coordinates were left in the rhombohedral setting of the corresponding space group (R3(bar)c for alpha-Fe2O3 in Pearson/Villars). SEXIE provides a conversion routine in INSHELL for such cases**) We have added a MathCad file describing atom coordinate transformation to the machine readable documentation. **)The program explicitly asks in the input description for the first coordinate triple as listed in the International Tables. This is important. Example: One wants to transform rhombohedral alpha-Fe2O3 data taken from Wyckoff into the hexagonal setting. The oxygen position one needs to enter is (6e), which is (x, 1/2-x, 1/4) with x = 0.553. Using this value for x yields (0.553, -0.053, 1/4). Also, the rhombohedral angle alpha is often listed in degrees and minutes. Our program requires the input in degrees and decimals. A related and quite subtle confusion in literature data exists for the example of SiO2, alpha-Quartz. Pearson lists Si (3a) at (0.4699,0,2/3) and O at the (6c) general position (x,y,z) with (0.4141, 0.2681, 0.1188), which apparently indicates the correct hexagonal setting for the trigonal space group P 32 2 1 (No. 154). This input however delivers no reasonable answer, as the first coordination shell in Quartz must form an oxygen tetrahedron. Hyde and Andersson [11] describe a nonstandard setting, placing Si (3a) into (0.4697, 0, 0) and O (6c) into (0.4135, 0.2669, 0.1158). From the obvious discrepancy in the z-position for Si atoms but not for the O atoms, we suspect a coordinate shift in the z-direction (a polar spacegroup, like P 32 2 1, has no set origin along z), and we conclude that the z-coordinate for oxygen was not properly shifted by 2/3 in Pearson's compilation. Adding 2/3 yields 0.7825 for the oxygen coordinate. By use of the standard setting and coordinates as reported in Pearson (oxygen z corrected), SEXIE properly detects a tetrahedral coordination of oxygen around Si. The corresponding input data can be found in the structural data base distributed with SEXIE. 3. Coordinate transformation ---------------------------- SEXIE derives the positions for atoms in coordination shells in fractional (i.e., unit cell specific) coordinates. Correct cartesian coordinates, though, are essential for the FEFF program input, and we wish to make sure that users have a clear understanding of how these coordinates are derived. The conversion from fractional atom coordinates to cartesian coordinates employs a basis transformation matrix which is not unique per se. Here we define the standard or default projection (based on their suitability for monoclinic systems as defined by the IUCr [12] ) now used in SEXIE: Let a,b,c be the unit cell vectors (basis) of any oblique lattice with a = |a|, b = |b|, c = |c|, and A,B,C a set of orthogonal axes (all in A~). Let us further define that (a) a,b,c and A,B,C are right handed and share the same origin (b) A be parallel to a (c) B be parallel to C x A (d) C be parallel to a x c . The basis transformation matrix M for X = xM takes the form | | | a b.cosg~ c.cosb~ | | | | | M = | 0 b.sing~ c.(cosa~-cosb~.cosg~)/sing~ | | | | | | 0 0 V/(a.b.sing~) | | | with V the unit cell volume V = a.b.c.(1 - cos^2a~ -cos^2b~ -cos^2g~ + 2.cosa~.cosb~.cosg~)^1/2 . x represents the fractional coordinate triple vector (x.y.z) and X the corresponding cartesian coordinate vector (X,Y,Z) in units of A~. The SEXIE documentation includes a MathCad file of this transformation for further reference. Older versions of SEXIE (below 2.1) failed to expand the matrix with the cell constants before the coordinate transformation took place and so delivered incorrect results for (infrequently used) oblique lattices. The shell grouping and the distances are not derived from cartesian coordinates and were therefore correct in all calculations. 4. FEFF5 input preparation -------------------------- The FORTRAN program INFEFF has been added to the utilities provided with SEXIE. INFEFF translates SEXIE output listings into FEFF readable input data. Based on an extended curved-wave formalism [3], the high order multiple-scattering program FEFF [2] calculates theoretical EXAFS spectra from model structures. The experimental data can be fitted against the calculated spectra and actual radial distances and occupation of nearest neighbour sites can be deduced. SEXIE outputs the absolute cartesian coordinates in A~ of atoms in the crystal lattice. If necessary, the cell origin is shifted so that the central atom rests at (0, 0, 0). Subshells, which were previously combined to enable the geometry search in SEXIE, are separated into individual shells again. FEFF reads the atomic coordinates and atom types for each shell and calculates EXAFS data with respect the X-ray ionized central atom. A maximum radial distance (or, alternatively, the number of coordination shells) to be included in the FEFF calculation is queried. Cartesian coordinates are listed under under ATOMS in the FEFF input, and crystallographically equivalent atoms are assigned a similar POTENTIAL flag. In the strictest sense, even crystallographically equivalent atoms in different shells have a different potential due to the presence of the core hole of the X-ray ionized atom. However, the effect of the core hole can usually be ignored beyond the first shells, and crystallographic equivalence can be used to distinguish unique potentials. In the example [5] of GaAs, with gallium as the central atom, the four nearest neighbour arsenic atoms (first shell) and the twelve arsenic atoms comprising the third coordination shell are given the same POTENTIAL. The assignment of different potentials for crystallographically equivalent inner shell atoms is left to the discretion of the FEFF user. Atoms of the same element, at different distances and different crystallographic symmetry, but with similar electronic environments, can also be assigned the same POTENTIAL. Such a simplification reduces FEFF runtime. Other FEFF parameters are written to the input file as comments (preceded by a *) and can be edited by the user. In EXAFS studies involving single crystals or samples where the nearest neighbours have some preferred orientation, use is made of the linear polarization of the X-ray beam. Future versions of FEFF (FEFF6) will take into account the preferential direction of the outgoing excited quantum-mechanical electron wave. Input must designate this preferred direction. Further revisions will be made in the INFEFF translation program to accommodate this development. 5. SCHAKAL input ---------------- A simple, nice feature of SEXIE Version 3.0 is the generation of an input file for the graphic presentation program SCHAKAL which is available for a variety of operating systems [4]. Figure 1 shows a computer drawing based on structural information [5] decoded by SEXIE. The associated input file SCHAKAL.DAT was created appending the SEXIE output file ATOM.XYZ to CELL.DAT. Figure 1: (Omitted) Crystal structure drawing of LiCaCrF6 created by SCHAKAL [4] from an input file prepared by SEXIE. 6. Testing and documentation ---------------------------- SEXIE has been tested extensively by our user community and we are confident that the program is reliable at this point. We provide 3 test runs, one for a high symmetry cubic case, one for a monoclinic system, and one which creates an input file for FEFF5 as described in its program documentation. The layout of all other output files is essentially unchanged from the previous version, and their listing is therefore omitted. A revised manual is included in the source deck as a PostScript file. Latest information on updates, installation dependent features (batch files and scripts), suggestions and error reports can be exchanged on Internet via anonymous ftp at host OEDIPUS.LLNL.GOV. 7. Acknowledgments ------------------ This work was supported in part by the U.S. Department of Energy at the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48. Parts of the code are property of Vienna Air (formerly PhysiSoft Corporation). Work on INFEFF was supported by ONR under contract # N00014-89-J-1108 and the GAANNP Scholarship, U.S. Dept. of Education. We are grateful to the user community for providing valuable feedback, in particular to Dr. Bruce Bunker, Dr. P. Bandyopadhyay, Dr. J. J. Rehr and Dr. B. Ravel for helpful pointers. 8. References ------------- 1) B.Rupp, B.Smith and J.Wong, Comp.Phys.Comm. 67, 543 (1992) 2) J.J.Rehr, R.C.Albers and S.I.Zabinsky, Phys.Rev.Lett. 69, 3397 (1992), for information e-mail to jjr@leonardo.phys.washington.edu 3) J.J.Rehr and R.C.Albers, Phys.Rev.B. 41, 8139 (1990) 4) E.Keller, J.Appl.Cryst. 22, 16 (1989), for information e-mail to kell@sun1.ruf-uni-freiburg.de 5) See for example, A.E. Tabor-Morris, K.M.Kemner, B.A.Bunker, K.A. Bertness, Jpn.J.Appl.Phys. 32, Suppl. 32-2, 404 (1993) and B.Rupp et al., J.Sol.State Chem. 107, 471 (1993) 6) This error has been pointed out to B.R. independently by Dr. B. Poumellec, Universite Paris Sud, Orsay, and Dr. Ch. Brouder through CPC. 7) Crystal Structures, R.W.G.Wyckoff, Wiley & Sons, N.Y. (1963) 8) Pearson's Handbook of Crystallographic Data for Intermetallic Phases, P.Villars and L.D.Calvert, eds., American Society for Metals, Metals Park, Ohio (1985) 9) International Tables for Crystallography, Vol. I, The Kynoch Press, Birmingham,England (1968); or International Tables for Crystallography, Vol. A, Theo Hahn, ed., D.Reidl Publishing Company (1988) 10) Dr.Joe Wong, Lawrence Livermore National Laboratory, has discovered this error in the published data and kindly brought it to our attention 11) B.G.Hyde and S.Andersson, Inorganic Crystal Structures, Wiley, New York (1989) 12) See, e.g., Protein Data Bank (PDB) Atomic Coordinate and Bibliographic Entry Format Description, Protein Data Bank, Brookhaven National Laboratory, Upton, NY 11973. Available via anonoymous ftp from pdb.pdb.bnl.gov. 13) J. J. Rehr, University of Washington, personal communication