Patterson Interpretation Algorithm

1. One peak is selected from the sharpened Patterson (or input by means of a VECT instruction) and used as a superposition vector. This peak 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.
2. 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 N2. The superposition map should ideally consist of one image of the structure and its inverse; it has an effective 'space group' of P (or C for a centered lattice etc.).
3. 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.
4. 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 Fo 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.
5. For each set of potential atoms a 'correlation coefficient' (Fujinaga and Read, 1987) is calculated as a measure of the agreement between Eo and Ec, and expressed as a percentage. This figure of merit may be used to compare solutions from different superposition vectors.