The peak search algorithm involves a layer by layer
search of the map. In the discussion which follows,
reference is made to the form of the Fourier map as it
would be output by the program FOURR. The first summation
direction produces layers, referred to as pages. The second
summation direction produces lines down the page, while the
third summation direction produces the lines across the
page (see
FOURR
). The (x,y) referred to here are not necessarily
the crystallographic x,y. As each layer is searched, the
value of the function at every grid point is compared to
each adjacent grid point within the layer. When the value
of the function at a particular grid point, e.g. (x,y), is
found to be larger than at any of the grid points
surrounding it, an interpolation may be done to determine
the exact coordinates of the maximum within the layer and
the maximum value of the function within the layer. If
(x,y) lies at a corner of the layer (i.e. the first or last
grid point on the first or last line of the layer) no
interpolation is done and the maximum is taken to be on the
grid point. If (x,y) is a point on the first or last line,
but not at a corner, a one-dimensional interpolation is
done in the third sum direction (across the page). If (x,y)
is the first or last point on any line but the first or
last line, a one-dimensional interpolation is done in the
second sum direction (down the page). For any other point,
a two-dimensional interpolation is done.
After a layer has been completely searched, the peaks
from that layer are saved temporarily in the layer-to-layer
storage table. As the next layer is being searched, each
new peak is compared to those from the previous layer. If
two peaks are within the resolution and if the peak is
larger in the current layer, both the old and the new
coordinates are saved. When a peak has been found in three
successive layers, with the density going through a maximum
in the second layer, an interpolation is done in the first
sum direction (page to page) to find the most exact
coordinates and density for the peak. No interpolation can
be done in the first sum direction for peaks which occur
within half a grid point of the first or last layer or
which are not above the cutoff in three successive
layers.
Before a peak is saved in the permanent list, a check
is made to determine whether or not it is symmetrically
related to any of the peaks which have already been saved.
This insures that the final list will contain a unique set
of peaks. If the map is a Patterson map, the Laue symmetry,
rather than the space group symmetry, is used.
If a new peak is found to be symmetrically related to
a peak which has already been saved, only one of the two
will be saved. The more reliable of the two peaks will be
saved. The reliability of a peak depends on its position in
the map. The most reliable peaks are those at interior
points of the map. Their high reliability is a result of
the three-dimensional interpolation. Less reliable are
peaks on a face of the map (two-dimensional interpolation),
followed by peaks on an edge (one-dimensional
interpolation). The least reliable peaks are those at
corners of the map. For these, no interpolation can be
done.
After the map has been searched completely, the
coordinates of any atoms that may be present in the bdf are
compared with the coordinates of all the peaks which have
been saved. A list of the atoms which do not coincide with
any peaks is produced. Finally, the highest peaks are
listed in order of decreasing density. Each peak is labeled
with either the name of the atom which occupies the same
position or, if it coincides with no atom, a sequence
number. The peaks are listed and, optionally, output in
atom line images on the
file
pekand the punch file.
The number of highest peaks listed may be specified by the
user. If a peak has been identified with an atom name, that
name will appear in the first field of the atom line.
Otherwise, the the atom name will be
C
followed by the sequence number assigned to
the peak.
The program may also be used to search for holes.
When this option is chosen the map is read in with every
point being changed from plus to minus. This means that the
peaks listed at the end of the run are actually holes in
the entering map. It is necessary to do two separate runs
to find both peaks and holes in a map.
The three fields on the
plimit line are as
follows:
-
Minimum point density used in
peak search: Reasonable default values are
assumed according to the map type. This cutoff is
checked after the first layer. If more than one third
of all grid points in the first layer have density
values exceeding the cutoff, the cutoff is
incremented by one quarter of the average density in
that layer. The adjusted value is printed.
-
Resolution (in
Angstroms): This value sets the separation
of the maxima in the map which will establish two
discrete peaks. This parameter should be set to no
less than
/(2sin
). For example, if all the reflections
within the copper sphere of reflection were measured,
the resolution might be set to 0.75 Angstroms.
-
Total number of unique peaks to
be saved, sorted, and listed: The
coordinates and value of the function at the maximum
will be stored on file
pekin order of
decreasing peak density. If the number of peaks
specified is too large for the available memory, the
number of peaks will be adjusted to accomodate as
many peaks as possible for the memory available. The
default value for this parameter is twice the number
of non-hydrogen atoms in the asymmetric unit.
