Translation Search

X-PLOR performs a translation search by computing the target function

$$1 - E_{XREF}/W_A$$ (19.6)

where the target is specified by TARGet in the xrefin statement . (The various targets are described in section 13.3.) In particular, translation searches can be carried out with correlation coefficients between $F$s, $E$s, $F^2$s, and $E^2$s, with the standard residual, with the vector (A,B) residual, or with the packing function. The search is carried out over a 3-dimensional grid that can be specified in fractional (“MODE=FRACtional") or orthogonal Å (“MODE=ORTHogonal") coordinates. The search routine computes the structure factors $F_{calc}$ of the translated primary molecule and the symmetry-related molecules by applying appropriate phase-shift operators in reciprocal space to the calculated structure factors of the original (not translated) molecule and its symmetry mates (except for the packing function). In this way, the computation is very fast, and it is also highly vectorized. The symmetry mates are defined by the space-group operators in the xrefin statement. The partial structure factors $F_{part}$ are kept constant during the translation search. This feature can be used if one wants to translate only a part of the molecule (see also the example file in section 19.5.8).

The asymmetric unit of a translation function is in general larger than the asymmetric unit of the unit cell. For example, in space group $P6_522$, the asymmetric unit for the translation function is $x=0 \dots 1$, $y=0 \dots 1$, $z=0 \dots 0.5$, whereas the crystallographic asymmetric unit is $x=0 \dots 1$, $y=0 \dots 1$, $z=0 \dots 1/12$. Hirshfeld (1968) has defined the “Cheshire groups" for the 230 crystallographic space groups. The unit cell of a particular Cheshire group corresponds to an asymmetric unit of X-PLOR's translation function (see Table 2 of the Hirshfeld paper). It is sometimes quite useful to run a translation search on a very coarse lattice that covers the complete unit cell (i.e., XGRId= 0 0.1 1, YGRId= 0. 0.1 1, ZGRId=0 0.1 1). Based on the observed redundancies, one can then deduce other choices for the asymmetric unit of the translation function not listed in the Hirshfeld paper.

The output of the routine provides a complete listing of the computed translation function, which is written to the specified file. The format of this file is suitable for Mathematica. In addition, a sorted list of a specified number of highest peaks is written to the standard output. A packing analysis is carried out for each listed peak. The packing value consists of the ratio of the molecular volume to the unit-cell volume; it is expressed as a percentage. The value of the translation function for the highest peak is stored in the symbol $RESULT; the corresponding packing function value is stored in the symbol $PACKING. The main coordinate set is translated according to the highest translation function value.