X-PLOR performs a translation search by computing the target function
where the target is specified by TARGet in the
xrefin statement .
(The various targets are described in section 12.3.) In
particular, translation searches can be carried out with
correlation coefficients between Fs, Es, 
s, and 
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 
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 
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 17.5.8).
The asymmetric unit of a translation function
is in general larger than the asymmetric unit of the unit cell.
For example,
in space group 
, the asymmetric unit for the translation function
is 
, 
, 
, whereas the crystallographic
asymmetric unit is 
, 
, 
.
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.