X-PLOR performs conventional rotation searches in Patterson space. The real-space Patterson search method of Huber and Steigemann (1985) is employed. The stationary Patterson map P2 is computed from the observed intensities by fast Fourier transformation on the specified grid. The Patterson map P1 to be rotated is computed from either the observed intensities (self-rotation search) or from a search model (cross-rotation search). Note that the rotation search routine takes the layout of the map P1 as it was written using the xrefin map statement (see Section 14.1). In most cases, the layout of P1 will look like this:
EXTEnd=BOX XMIN=-45.0 XMAX=45.0 YMIN=-45.0 YMAX=45.0 ZMIN=0.0 ZMAX=30.0where one makes use of the centrosymmetry and 30.0 is the maximum vector length. Patterson vectors are selected according to the value of the Patterson map at the particular grid point (THREshold) and according to the distance from the grid point to the origin (RANGe). Of this selected subset of Patterson vectors, only the strongest NPEAKs Patterson vectors are chosen for the rotation search.
The selected Patterson vectors are rotated using
Eulerian angles (
, 
, 
) as defined
by Rossmann and Blow (1962), pseudo-orthogonal Eulerian angles
as defined by Lattman (1972),
or spherical polar angles (
)
(see Section 2.4 for the conventions).
The
Lattman angles are related to
the Eulerian angles by
The 
angles are sampled at a constant interval 
.
Following Lattman (1972), the
variable interval for 
is given by 
,
and
the variable interval for 
is given by 
. For both Eulerian angles and spherical polar angles, the sampling
interval is constant (
) for the three angular variables.
The rotation search should be restricted to the asymmetric unit
of the rotation function (Rao, Jih, and Hartsuck 1980).
Using the convention in the Rao et al. paper, the
Patterson symmetry of the rotated map 
is ``1", and
that of 
is the Patterson symmetry of the space group.
The values of the Patterson map P2 at the positions of the rotated Patterson vectors of map P1 are computed by linear eight-point interpolation (Nordman 1980).
For each
sampled orientation 
the product function
between the rotated vectors of P1 and the interpolated values of the Patterson map P2 is computed.
Upon completion of the rotation function,
all sampled grid points are sorted with respect to their product
correlation value,
and a simple peak search is carried out using the matrix metric defined
in Brünger (1990). For two given rotation matrices
, the metric is defined as
where 
is the number of symmetry operators of the space
group of the crystal and 
is
the rotational part of the symmetry operator s. This
definition applies to the default option SELF=FALSE. If
SELF=TRUE is specified, the metric is defined as
i.e., the metric assumes the crystal symmetry for both
Patterson maps P1 and P2.
In the case of space group 
,
the metric m is related to a rotation angle 
,
which defines a rotation around
a certain axis a:
Application of this rotation around a
transforms the matrix 
into 
.
Two RF grid points are considered
as being in the same cluster
if the corresponding
rotation matrices yield 
. For
example, if 
is set to 0.25, matrices belong to the same
cluster if they can be transformed by a rotation of 10
or less around a certain axis.
The incorporation of crystallographic symmetry in Eq. 17.3
ensures that clusters of grid points at the boundaries of the asymmetric
unit of the RF are treated properly.
This peak search removes grid points
that are close to grid points
with larger RF values. It is not a true peak search, but rather
reduces the number of points to be checked by subsequent analysis.
The reduced set of the highest
grid points is written to a specified file. For example, if 
is set to 0.25, the file will contain grid points that are
mutually different by at least 10
.
This file will be read by the PC-refinement procedure described
below. The value for
should be chosen to be less than the
radius of convergence of the PC-refinement (around 10
).
It should be noted that the peak search procedure
maps the grid points into
an asymmetric unit of the rotation function.
