Heavy atom location by Patterson interpretation
The algorithm used to interpret the Patterson to find the heavier atoms
is totally different to that used in SHELXS-86; it may be summarized as
One peak is selected from the sharpened Patterson (or input by means of
a VECT instruction) to be used as a superposition vector. This must
correspond to a correct heavy-atom to heavy-atom vector otherwise the method
will fail. The entire procedure may be repeated any number of times with
different superposition vectors by specifying 'PATT nv', with |nv| > 1, or by
including more than one VECT instruction in the same job.
The Patterson function is calculated twice, displaced from the origin by
+U and -U, where U is the superposition vector. At each grid point the lower
of the two values is taken, and the resulting 'superposition minimum function'
is interpolated to find the peak positions. This is a much cleaner map than
the original Patterson and contains only 2N (or 4N etc. if the superposition
vector was multiple) peaks rather than N**2. The superposition map should
ideally consist of one image of the structure and its inverse; it has an
effective 'space group' of P-1 (or C-1 for a centred lattice etc.).
Possible origin shifts are found which place one of the images correctly
with respect to the cell origin, i.e. most of the symmetry equivalents can be
found in the peak-list. The SYMFOM figure of merit (normalized so that the
largest value for a given superposition vector is 99.9) indicates how well the
space group symmetry is satisfied for this image.
For each acceptable origin shift, atomic numbers are assigned to the
potential atoms based on average peak heights, and a 'crossword table' is
generated. This gives the minimum distance and Patterson minimum function for
each possible pair of unique atoms, taking symmetry into account. This table
should be interpreted by hand to find a subset of the atoms making chemically
sensible minimum interatomic distances linked by consistently large Patterson
minimum function values. The PATFOM figure of merit measures the internal
consistency of these minimum function values and is also normalised to a
maximum of 99.9 for a given superposition vector. The Patterson values
are recalculated from the original F(obs) data, not from the peak-list.
For high symmetry space groups the minimum function is calculated as an
average of the two (or more) smallest Patterson densities.
For each set of potential atoms a 'correlation coefficient' (Fujinaga and
Read, J. Appl. Cryst., 20 (1987) 517-521) is calculated as a measure of the
agreement between E(obs) and E(calc), and expressed as a percentage. This
figure of merit may be used to compare solutions from different superposition
PATT nv [#] dmin [#] resl [#] Nsup [#] Zmin [#] maxat [#]
VECT X Y Z
In the unlikely event of a routine PATT run failing to give an acceptable
solution, the best approach - after checking the data reduction diagnostics
carefully as explained above - is to select several potential heavy-atom to
heavy-atom vectors by hand from the Patterson peak-list and specify them on
VECT instructions (either in the same job or different jobs according to local
circumstances) for use as superposition vectors. The exhaustiveness of the
search can also be increased - at a significant cost in computer time - by
making the first PATT parameter negative and/or by increasing the value of
resl a little. The sign of the second PATT parameter (a negative sign
excludes atoms on special positions) and the list of elements which might be
present (SFAC/UNIT) should perhaps also be reconsidered.