Estimate of structure invariants

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Estimate of structure invariants ('%invariants' command)

       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.
Active triplets may be estimated according to Cochran's (1955) P3 distribution: the concentration parameter of the von Mises distribution is then:

                                       (3)

Triplets can also be estimated according to their second representation (i.e. P10 formula, as described by Cascarano et al., 1984). The concentration parameter of the new von Mises distribution is given by

G = C (1 + q)

(4)

where q is a function (positive or negative) of all the magnitudes in the second representation of the triplet. The G values are rescaled on the C values and the triplets are ranked in decreasing order of G. The top relationships represent a better selection of triplets with phase value close to zero than that obtained when ranking according to C. These triplets will be actively used in the phase determination process.
Triplets characterized by a negative G represent a sufficiently good selection of relationships close to 180 degrees, to be used for the calculation of a powerful FOM (CPHASE). Triplets with G close to zero are expected to have values widely dispersed around 90 or 270 degrees and are used to compute an enantiomorph sensitive FOM. A similar FOM is also computed using quartets estimated with a very small concentration parameter.
As a default, triplets are estimated according to P10 formula.
The parameter C of the Cochran distribution (say P3) is suitably modified when the pseudo information in the section 'NORMAL module' is available. Then triplet phases are no longer expected to be around zero (see quoted references) and may lie anywhere between 0 and 2π.
The method of the joint probability distribution functions (Cascarano et al., 1991; Carrozzini et al., 1997) can be applied to obtain an estimate of normalized structure factors, that will be used as a source of supplementary prior information in the extraction process (if directive ESTIMATION is used).

Directives in invariants command

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


GMIN x

Positive triplets with G < x are not actively used.

Default value x=0.6 (in any case 0.2 < x < / = 1.0 is accepted range of value.


COCHRAN

To use the P3 formula. (By default P10 formula is used).


CORRECTION x

If a PSEUDOTRANSLATION procedure is on, a correction factor depending on x is applied to the probabilistic argument of weak-weak-weak triplets when they are present. The default value is calculated by program.

x = -1 eliminates weak-weak-weak triplets,

x = 1 corresponds to the largest confidence in them.


EMAX x

Maximum value of E for the weak reflections for the psi-zero search (up to a maximum of NRPSIZERO reflections). x > 0.3 not accepted.

Minimum value for the normalized structure factors in the sigma2 search. x < 1.0 not accepted.

Default = minimum value of E for the strongest reflections selected by normalization routine.


ESTIMATION

To run the procedure which estimates the |E|'s for all the reflections and use them as a prior information in a new extraction process.

The procedure will not be applied if PSEUDOTRANSLATIONAL information has been recycled.


NPSI0

To not calculate PSI-0 triplets (Default uses them).


NRPSIZERO n

The number of weakest reflections for the psi-zero search.

Default = number computed by normalization routine.

The value will substitute the default one in the direct access file.


NRTRIPLETS n

The number of strongest reflections for the sigma2 search. ( Up to Emin = 1.0 )

Default = number computed by normalization routine (nstrong).

The value will substitute the default one in the direct access file.

Value less than nstrong/2 is not accepted.


NLARGE n

To supply the number of largest reflections for the psi-zero search ( default = number of strongest reflections used for sigma2 search).

nlarge > nrtriplets is not accepted.


NQUARTETS

To not calculate negative quartets (Default uses them).


NUMK n

The number of free-vectors used by P10 formula.

Default value is provided by EXPO according to the structural complexity:

n = min ( natom / msym + 30, 70 )

where natom is the number of atoms in the cell and msym is the number of symmetry operators of the space group.


YPSIE

To calculate PSI-E triplets (Default doesn't use them).
 

Example

Example 1

Use of the triplets estimation as prior information for a new extraction process.

%structure mes
%job MES - data from home diffractometer
%initialize
%data
   pattern mes.pow
   cell 8.588 9.931 11.105 90.0 93.754 90.0
   content C 24 N 4 O 20 S 4 H 52
   spacegroup p 21/c
   wavelength 1.5406
   filetype double
%extraction
%normal
   nopseudo
%invariants
   estimation
%continue


References

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

Carrozzini B., Giacovazzo C., Guagliardi A., Rizzi R., Burla M.C. & Polidori G. (1997). J. Appl. Cryst. 30, 92-97

Cascarano G., Giacovazzo C., Burla M.C., Nunzi A. & Polidori G. (1984). Acta Cryst. A40, 389-394.

Cascarano, G., Giacovazzo, C., Guagliardi, A. & Steadman, N. (1991). Acta Cryst. A47, 480-484.

Cochran W.(1955). Acta Cryst. 8, 473-478.

Giacovazzo C. (1976). Acta Cryst. A32, 958-966.

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