The main modules of the program are:
EXPO, LIST, DATA, NTREOR, EXTRACTION, NORMAL, INVARIANTS, PHASE, FOURIER/LEAST-SQUARES, DIRECT, PATTERSON.
EXPO module
It interprets commands and calls desired routines.
LIST module
It is the software interface between EXPO2013 and the direct access file on which data and results are stored.
DATA module
This routine reads the basic crystallographic informations like cell parameters, space group symbol (it may be also found by the program, using “findspace” directive), wavelength, unit cell content and the counts (or reflections). It includes a modified version of the subroutine SYMM Burzlaff & Hountas (1982). Symmetry operators are directly derived from the space group symbol.
An external file (containing counts or reflections) is supplied by the user. If an external reflection file is supplied (avoiding the extraction step), diffraction data are checked in order to find out equivalent reflections or systematically absent reflections (which are then excluded from the data set).
N-TREOR module
This routine performs the indexing step (a peak search procedure is automatically carried out by the program before the indexing step). If available, an external peak positions file can be supplied to the program and the automatic peak search procedure will be skipped by EXPO2014. The indexing procedure retains the basic search algorithm of TREOR90, (Werner et al., 1985) and has been strengthened in the last version of N-TREOR09 (Altomare et al., 2009).
EXTRACTION module
In this module diffraction integrated intensities are extracted from the powder diffraction pattern. To calculate the integrated intensities, the program uses the Le Bail algorithm (Le Bail, Duroy & Fourquet, 1988) and combines it with a least squares procedure minimizing the quantity:
|
∑wi (yoi – yci) 2 |
(1) |
NORMAL module
In this module diffraction intensities are normalized using the Wilson method (Wilson, 1942). Statistical analysis of the intensities is made in order to suggest the presence or absence of the inversion centre, to identify the possible presence and type of pseudotranslational symmetry (Cascarano et al., 1988 a,b; Fan, Yao & Qian, 1988) and to detect preferred orientation effects (Altomare et al., 1994; Altomare et al., 1996). Possible deviations (of displacive type) from ideal pseudotranslational symmetry are also detected. All the above information is used as prior information in the integrated intensities extraction process, unless the directive NOPSEUDO is given to the program. When some additional prior information, besides positivity and atomicity of electron density, is available, then a suitable renormalization of structure factors is made.
INVARIANTS module
Up to 10000 triplets relating reflections with normalized E values greater than a given threshold (strong triplets) are stored for active use in the phasing process. Also triplets (PSI-ZERO triplets) relating two reflections with large E and one with E close to zero are generated: they are used to define a special figure of merit (PSCOMB). Special types of triplets (PSI-E triplets) based on two strong and one intermediate reflections (just below the threshold of strong reflections) are calculated and used in the FOURIER/LEAST-SQUARES module in order to extend phase information (Altomare et al., 1991). Negative quartets are generated by combining the psi-zero triplets in pairs, and those with cross-magnitudes smaller than a given threshold are estimated by means of their first representation, as described by Giacovazzo (1976). These quartets are used to provide an important contribution to the CPHASE FOM.
PHASE module
In the EXPO2014 program the most reliable one-phase s.s. are treated as known phases. Besides triplets, also the most reliable negative quartets and two-phase s.s. may be actively used. Each relationship is used with its proper weight: the concentration parameter of the first representation for quartets and two-phase s.s., and C or G for triplets.
– CONVERGENCE/DIVERGENCE PROCEDURE –
The convergence procedure (Germain et al., 1970) is a convenient way of defining an optimum starting set of phases to be expanded by the tangent formula or by any other algorithm. When the P10 formula is used, as a default, a special convergence process is devised which chooses the starting set.
Once the starting set has been defined, a good pathway for phase expansion is determined by a divergence procedure. In the divergence map, starting from the reflections in the starting set, each new reflection is linked to the preceding ones with the highest value of < α >.
– PHASE EXTENSION AND REFINEMENT –
The starting set defined by the preceding step is usually formed by the origin (and enantiomorph) fixing reflections, a few one phase s.s. and a number of other phases which may be obtained:
a) by magic integer permutation (White & Woolfson, 1975; Main, 1978),
b) by a random approach (Baggio et al., 1978; Burla et al., 1992).
The option a) is the default, b) runs if the directive RANDOM is used. In this last case a large number (depending on the available computer time) of trials can be requested.
FOURIER/LEAST-SQUARES module
The sets of phases generated by the tangent routine are first expanded through psi-E relationships and then passed to the fast fourier transform routine written by L.F.Ten Eick (1977) and subsequently modified by the MULTAN team (Main et al., 1980).
DIRECT module
In this module some “direct-space” approaches for solving crystal structures from powder diffraction data, can be used. The basic idea is to actively use structural and geometrical information, available a priori, during the structure solution process.
LABELLING procedure
The atomic species assigned to the peaks of an electron density map obtained at the end of a direct method procedure, can be modified using chemical information about the structure. The procedure (Altomare et al., 2002) requires: 1) the prior information on the number and coordination of the heavy atoms (the procedure can only handle tetrahedral and octohedral coordinations); 2) the range of the typical distances between heavy atoms; 3) the range of the typical distances between heavy and light atoms.
POLPO procedure
Using the “%polyhedra” command, two procedures can be activated. Both of them use a Monte Carlo approach and exploit the experimental information about the heavy – atom connectivity. The first one (POLPO1) (Altomare et al., 2000) is suggested when all the heavy atoms are rightly positioned and labelled. It is able to correctly locate the light atoms. The second one (POLPO2) (Giacovazzo et al., 2002) is able to position one or more missing cations and surrounding anions.
PATTERSON module
In the EXPO2014 program it is possible to compute a PATTERSON map using various coefficients. By using a special directive (INVERSION) it is possible to exploit the positivity of the electron density (in the direct space) in the extraction routine. The so-modified Patterson map is inverted providing a set of structure factor values to use in a new extraction process.
Altomare A., Burla M.C., Cascarano G., Giacovazzo C., Guagliardi A., Moliterni, A.G.G. & Polidori, G. (1996). J. Appl. Cryst. 29, 341-345.
Altomare A., Cascarano G., Giacovazzo C., Guagliardi A., Burla M.C., Polidori G. & Camalli M. (1994). J. Appl. Cryst. 27, 435 – 436.
Altomare A., Cascarano G., Giacovazzo C. & Viterbo D. (1991). Acta Cryst. A47, 744-748.
Altomare, A., Campi, G., Cuocci, C., Eriksson, L., Giacovazzo, C., Moliterni, A., Rizzi, R. & Werner, P.-E. (2009). J. Appl. Cryst. 42, 768-775.+
Altomare A., Giacovazzo C., Guagliardi A. Moliterni A.G.G., Rizzi R. (2000). J. Appl. Cryst. 33, 1305-1310.
Altomare A., Giacovazzo C., Ianigro M., Moliterni A.G.G., Rizzi R. (2002). J. Appl. Cryst. 35, 21-27.
Baggio R., Woolfson M.M., Declerq J.P. & Germain G. (1978). Acta Cryst. A34, 883-892.
Burla M.C., Cascarano G. & Giacovazzo C. (1992). Acta Cryst. A48, 906-912.
Burzlaff H. & Hountas A. (1982). J. Appl. Cryst. 15, 464-467.
Cascarano G., Giacovazzo C. & Luic’ M. (1988a). Acta Cryst. A44, 176-183.
Cascarano G., Giacovazzo C. & Luic’ M. (1988b). Acta Cryst. A44, 183-188.
Fan H., Yao J. & Qian J. (1988). Acta Cryst. A44, 688-691.
Germain G., Main P. & Woolfson M.M. (1970). Acta Cryst. B26, 274-285.
Giacovazzo C. (1976). Acta Cryst. A32, 958-966.
Giacovazzo C., Altomare A., Cuocci C., Moliterni A.G.G., Rizzi R. (2002). J. Appl. Cryst. 35, 422-429.
Le Bail A., Duroy H. & Fourquet J.L. (1988). Math. Res. Bull. 23, 447-452.
Main P. (1978). Acta Cryst. A34, 31-38.
Main P., Fiske S.J., Hull S.E., Lessinger L., Germain G., Declercq J.P. & Woolfson M.M. (1980) – MULTAN80, a system of computer programs for the automatic solution of crystal structures from x-ray diffraction data – Univ. of York, England.
Ten Eick L.F. (1977). Acta Cryst. A33, 486-496.
Werner P.-E., Eriksson L. & Westdahl M. (1985). J. Appl.Cryst. 18, 367-370.
White P.S. & Woolfson M.M. (1975). Acta Cryst. A31, 53-56.
Wilson, A. J. C. (1942). Nature, 152.