Crystal structure completion and refinement

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Crystal structure completion and refinement ('%fourier' command)

       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, 1978; Main et al. 1980).

Several additional features have been introduced in the present version:
a) From the solution with the highest CFOM value a Fourier map may be calculated by involving a supplemental number of reflections which are phased through the so-called psi-E triplets (Altomare et al. 1991)
b) Special positions are handled, peaks very close to symmetry elements are moved onto symmetry elements, the site symmetry is defined and the atomic occupancy factor is calculated; key numbers for designating free, coupled or fixed positional parameters for least-squares subroutines are also calculated together with symmetry conditions on the thermal ellipsoid.
c) Cycles of structure factor calculation -least squares- (2Fo -Fc) Fourier synthesis are automatically performed in order to provide a more complete and refined crystal structure. Due to reflection overlapping the results of the refinement must carefully be considered by the user who will take always into account the ratio 'number of parameters to refine/number of independent observations'.
The program provides the following R-factors which can be used as reliability parameters:

(8)

(9)

(10)

An alternative approach, based on real space techniques (Altomare et al. 2002) originally used for phase extension and refinement of proteins (Giacovazzo & Siliqi, 1997; Burla et al. 2000), has been introduced in EXPO and modified to improve the phasing process from powder data. It combines an Electron Density Modification procedure with Fourier map calculations.

Directives in fourier command

The following directives must be added after the command '%fourier' in the input file to activate some specific features of the procedure

COORDINATION El dmin dmax n

The minimum and maximum value of the bond distance are assigned to element El. n is the coordination type.

Allowed values for bond angles are:

n = 1

55 - 180 Degrees

n = 2

85 - 145 Degrees

EDMO

This directive is used to enable a direct space procedure consisting of an Electron Density Modification (EDM) process followed by successive Fourier maps using (2Fobs -Fcalc) coefficients. Except for the Fourier directive 'set', all the rest of Fourier recycling directives are not valid for EDM procedure.

2EOEC

This directive enables to use (2Eobs-Ecalc) as Fourier coefficients in the Fourier step (if EDM procedure is applied).

EOBS

This directive enables to use the observed normalised structure factors (Eobs) as Fourier coefficient in the Fourier step (if EDM procedure is applied).

FRAGMENT string

Used to supply a known fragment to be completed. String is the name of the file in which, for each atom, are stored: Element X, Y, Z, isotropic thermal factor.

FWHM D

This directive is used in order to change the value of D that is the parameter for the condition 2θ1 - 2θ2 < D*FWHM.
Default value is approximately 0.9 depending on the ratio between the number of observations and the number of parameters to refine.

GRID x

The grid on which the Fourier-map is evaluated will have a spacing of approximately x angstroms. The default spacing is computed by the program (1/3 Å).

INTEGRATION x n

x is the radius of integration in the peak search routine. (Default value 0.5). n may be 1 to use the gaussian fitting of the fourier peak in the map or 2 to use the peak average density. (Default value 2).

LAYX

This directive can be used only if MAP directive is given. The Fourier-map will be printed in section of constant x.

LAYY

This directive can be used only if MAP directive is given. The Fourier-map will be printed in section of constant y.

LAYZ

This directive can be used only if MAP directive is given. The Fourier-map will be printed in section of constant z.

LEVEL n

All numerical values in the E-map greater than n will be underlined with **** in the lineprinter output to facilitate contouring.

The default is 100. The map is automatically scaled between ± 999 (approximately) at the grid points at which it is calculated.

Note, however, that it is printed between ± 99. (This directive can be used only if associated to MAP directive).

LIMITS x1 x2 x3

The E-map will be printed from 0 to x1 along x, from 0 to x2 along y, from 0 to x3 along z. (This directive can be used only if associated to MAP directive).

MAP

If MAP is specified, the E-map will be printed on the lineprinter. The printing of the E-map is rarely used.

The output is in sections of constant y with x across the page and z running down it on a grid of about three points per angstrom.

The maximum number of grid points across the page is 36 ( i.e. about 12 angstroms in length). If more are needed, a new page is started.

PEAKS n

The number of peaks to be searched for in the map. The default is the number of peaks which

(occ(i)*m) = 1.3 * n

where occ is the crystallographic site occupancy factor, m is the number of symmetry operators, n is the number of non-hydrogen atoms in the unit cell.

PSE

To actively use PSI-E triplets in these procedures (Default doesn't use them). (This directive can be used only if associated to YPSIE directive of INVARIANTS routine).

RADIUS El x

The value x of the radius used to compute the connectivity is assigned to element El.

RECYCLE n

Used to stop the recycling procedure after cycle number n. If n is equal to zero only the E-map will be calculated.

SET n

The serial number of the set from which to calculate the E-map. If 'SET n' is not specified, the set with the highest combined figure of merit will be used, and then if FOURIER routine is re-run, the set with the next highest combined FOM will be used.

SOGF x

The percentage of the largest |F| value reflections actively used in the Fourier recycling routine.

The reflections with the smallest |F| values corresponding to the rejected percentage have a zero weight value in the refinement process. (Default value 100.0).

SOGI x

The percentage of the most intense groups of overlapping reflections actively used in the Fourier recycling routine. (Default value 91.0).

STOPF x

This directive enables to stop the Fourier step at the cycle number x (if EDM procedure is applied). The default value of x is 10 (the maximum allowed value).

THRE x

x is the threshold for the E value of the reflections actively used in the Electron Density Modification step. The default value is 0.8.

THRM x

x is the fraction of the Fourier map points actively used in the Electron Density Modification step. The default value is 0.025.

THRW x

x is the threshold of the Bessel weight of the reflections actively used in the Fourier step (if EDM procedure is applied). The default value is 0.5.

 

ExampleS

Example 1

Only the E-map corresponding to the set number 7 and the complete FOURIER/LEAST-SQUARES procedure for set number 10 are requested by the user. The binary file "vfi.bin" must exist.

%structure nbpo

%fourier
   set 7
   recyc 0
%fourier
   set 10
%continue


Directives in label command

Direct methods applied to powder diffraction data often provide electron density maps of which the quality is usually affected by systematic and/or random phase errors, by amplitude truncation effects in the series representation of the electron density, etc. The frequent incorrect labelling of the peaks can strongly affect the efficiency of the procedures used for crystal structure refinement. An algorithm has been introduced in EXPO aiming at using the crystal chemical information that is usually available a priori to improve the peak labelling (Altomare et al., 2001)

The following directives must be added after the command '%label' in the input file to activate some specific features.

DLIGHT d tol

d is the expected heavy atom to light atom distance;

tol is the tolerance around the ideal distances. Default value = 0.5.

The program uses only one value of 'd' for all types of light atoms.

 

DWEIGHT d tol

d is the expected heavy atom to heavy atom distance;

tol defines the tolerance around the ideal distances. Default value = 0.5.

The program uses only one value of 'd' for all types of heavy atoms.

 

LABEL n1 El1 n2 El2

n is the number of peaks to relabel using El element;

El is the atomic species to assign to the peaks.

Only two combination (n, El) can be used.

 

COORD xi

x specifies the expected number of heavy atoms surrounding each i-th heavy atom (the coordination type) (i = 1,2).


Example

Example 1

Use of the label change procedure to relabel the peaks of an electron density map obtained by applying the FOURIER procedure. The binary file "vfi.bin" must exist.

% window

% structure vfi

% job VFI - Synchrotron data

% changelab

 

label 3 al 3 p

 

coord 4 4

 

dwei 3.1 0.5

 

dlig 1.9 0.5

% continue


Directives in polyhedra command

The following directives must be added after the command '%polyhedra' in the input file to activate some specific features of the polyhedra procedure

MISSING n1 n2 El tetrahedron (octahedron) d tol1 tol2

n1 and n2 are the two order numbers (taken from an external file or from a Fourier map) of the cations between which the missing cation must be located;
El is the missing cation label tetrahedron (octahedron): the type of coordination of the missing cation. (The procedure can only handle octahedron and tetrahedron);
d is the expected cation-anion distance;
tol1, tol2 are the tolerance parameters for the distance and the tetrahedron (octahedron) angle respectively. Default values are 0.3.

OCTAHEDRON El d tol1 tol2

d is the expected octahedral coordination distance around the El element;
tol1 and tol2 are the tolerance parameters for distances and angles respectively.

TETRAHEDRON El d tol1 tol2

d is the expected tetrahedral coordination distance around the El element;
tol1 and tol2 are the tolerance parameters for the distances and angles respectively.

ExampleS

Example 1

The POLPO1 procedure is applied to locate the light atoms around each specified heavy atoms. The crox.fra file contains the cations coordinates.
The binary file 'crox.bin' must exist.

% window

%structure crox

%job CROX - home diffractometer data

%polyhedra


fragment crox.fra

 

octahedron 1 1.92 0.2 0.2

 

tetrahedron 2 1.75 0.2 0.2


tetrahedron 3 1.75 0.2 0.2

 

tetrahedron 4 1.75 0.2 0.2

%continue


Example 2

The POLPO2 procedure is applied to locate one or more missing cations and surronding anions. The sapo.fra file contains the located cations coordinates.
The binary file 'sapo.bin' must exist.

% window

%structure sapo

%job SAPO - data from home diffractometer

%polyhedra

 

fragment sapo.fra

 

tetrahedron Si 1 1.6 0.2 0.2

 

tetrahedron Si 2 1.6 0.2 0.2

 

missing 1 2 Si tetrahedron 1.6 0.2 0.2

 

missing 1 2 Si tetrahedron 1.6 0.2 0.2

%continue

Directives in Patterson command

The following directives must be added after the command '%patterson' in the input file to activate some specific features of the patterson procedure.

E**2 (or E*E)

Coefficients to be used in the Patterson synthesis. This is the default.

E*F (or F*E)

Coefficients to be used in the Patterson synthesis.

F**2 (or F*F)

Coefficients to be used in the Patterson synthesis.

INVERSE

To activate the procedure of calculating the |F| values from an inverted suitably modified Patterson map to use as starting point for the Le Bail algorithm in the extraction routine.

MAP, LAYX, LAYY, LAYZ, PEAKS, LIMIT, GRID: See FOURIER directives.

NPAT n

The number of cycles of successive inversions of the Patterson map.( Default values: 6 for X-ray data, 5 for neutron data

References

Altomare A., Cascarano G., Giacovazzo C. & Viterbo D. (1991). Acta Cryst. A47, 744-748.

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, 977-979.


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