Section 25.2.10.3. Heavy-atom location using SHELXS and SHELXD

Space-group-general automatic Patterson map interpretation was introduced in the program SHELXS86 (Sheldrick, 1985); completely different algorithms are employed in the current version of SHELXS, based on the Patterson superposition minimum function (Buerger, 1959, 1964; Richardson & Jacobson, 1987; Sheldrick, 1991, 1998a; Sheldrick et al., 1993). The algorithm used in SHELXS is as follows:

The program SHELXD (Sheldrick & Gould, 1995; Sheldrick, 1997, 1998b) is now part of the SHELX system. It is designed both for the ab initio solution of macromolecular structures from atomic resolution native data alone and for the location of heavy-atom sites from ΔF or F_A values at much lower resolution, in particular for the location of larger numbers of anomalous scatterers from MAD data. The dual-space approach of SHELXD was inspired by the Shake and Bake philosophy of Miller et al. (1993, 1994) but differs in many details, in particular in the extensive use it makes of the Patterson function that proves very effective in applications involving ΔF or F_A data. The ab initio applications of SHELXD have been described in Chapter 16.1 , so only the location of heavy atoms will be described here. An advantage of the Patterson function is that it provides a good noise filter for the ΔF or F_A data: negative regions of the Patterson function can simply be ignored. On the other hand, the direct-methods approach is efficient at handling a large number of sites, whereas the number of Patterson peaks to analyse increases with the square of the number of atoms. Thus, for reasons of efficiency, the Patterson function is employed at two stages in SHELXD: at the beginning to obtain starting atom positions (otherwise random starting atoms would be employed) and at the end, in the form of the triangular table described above, to recognize which atoms are correct. In between, several cycles of real/reciprocal space alternation are employed as in the ab initio structure solution, alternating between tangent refinement, E-map calculation and peak search, and possibly random omit maps, in which a specified fraction of the potential atoms are left out at random.

Since the input files for the direct and Patterson methods in SHELXS and the integrated method in SHELXD are almost identical (usually only one instruction needs to be changed), it is easy to try all three methods for difficult problems. The Patterson map interpretation in SHELXS is a good choice if the heavy atoms have variable occupancies and it is not known how many heavy-atom sites need to be found; the direct-methods approaches work best with equal atoms. In general, the conventional direct methods in SHELXS will tend to perform best in a non-polar space group that does not possess special positions; however, for more than about a dozen sites, only the integrated approach in SHELXD is likely to prove effective; the SHELXD algorithm works best when the number of sites is known. Especially for the MAD method, the quality of the data is decisive; it is essential to collect data with a high redundancy to optimize the signal-to-noise ratio and eliminate outliers. In general, a resolution of 3.5 Å is adequate for the location of heavy-atom sites. At the time of writing, SHELXD does not include facilities for the further calculations necessary to obtain maps. Experience indicates that it is only necessary to refine the B values of the heavy atoms using other programs; their coordinates are already rather precise.

Excellent accounts of the theory of direct and Patterson methods with extensive literature references have been presented in IT B Chapter 2.2 by Giacovazzo (2001) and Chapter 2.3 by Rossmann & Arnold (2001).