Ab initio direct methods: practical advice for getting beyond the first 300 atoms

Abstract

Not all crystallographic structural investigations are amenable to a phasing solution by direct methods alone. Guideline procedures are outlined which are intended to help the evaluation of whether directmethods procedures may be expected to phase diffraction data for large molecular structures. This analysis is directed at three separate levels of inquiry:(1) How good are the primary data and can E values be derived to represent a point-atom structure. (2) How well do the data interact through phase relationships and may they be expected to produce a stable phasing solution. (3) What is the prognosis for finding recognizable solutions. Data are presented from the post-mortem analyses of a number of large, difficult-to-solve, structures to illustrate each of these points. Direct-methods practitioners are to be encouraged that crystal structures having more than 300 atoms per asymmetric unit may occasionally be determined utilizing present methodologies provided that an a priori prognosis for obtaining a solution is favorably high, adequate computational resources are available, and sufficient persistent effort is applied.

Use of the minimal function for partial structure development in direct methods

“…Firstly, the 1.5/~ resolution restricts us to fewer E magnitudes from which to generate triples. Secondly, the point-atom approximation upon which direct methods are based tends to break down when the atoms of the structure have a wide distribution of thermal motion as is the case when many solvent molecules and amino-acid side chains are thermally disordered (Langs, 1993). The result is that the average values of the phase-invariant triples are less than their expected values and the tangent formula tends to drive the refinement to higher than average phaseinvariant values since the ratio of triples to phases is much lower than for higher-resolution data.…”

Frequency statistical method for evaluating cosine invariants of three-phase relationships

“…These 33 phases together with 9 additional unrestricted phases, expressed as magic integers, were actually used to solve this structure (Langs, 1988), which contains more than 300 independent atoms in the unit cell. It sould be cautioned that results such as these are sensitive to the accuracy with which the data have been measured and scaled, as well as to the degree to which the scaled [El values model the ideal pointatom structures upon which probabilistic direct methods have been derived (Langs, 1993). …”