Traditional direct phasing procedures

Which phasing methods can be included in the category direct methods, and which require a different appellation? Originally, direct phasing was associated with those approaches which were able to derive phases directly from the diffraction moduli, without passing through deconvolution of the Patterson function. Since a Patterson map provides interatomic distances, and therefore lies in ‘direct space’, direct methods were also referred to as reciprocal space methods, and Patterson techniques as real-space methods. Historically, direct methods use 3-,4-, . . . , n-phase invariants and 1-2-, . . . phase seminvariants via the tangent formula or its modified algorithms. Since the 1950s, about a half a century of scientific effort has fallen under the above definition. Such approaches are classified here as traditional direct methods. Today, the situation is more ambiguous, because: (i) modern direct methods programs involve steps operating both in reciprocal space and in direct space, the latter mainly devoted to phase extension and refinement (see Chapter 8); (ii) in the past decade, new phasing methods for crystal structure solution (see Chapter 9) have been developed, based on the properties of Fourier transforms, which again work both in direct and in reciprocal space. Should they therefore be considered to be outside the direct methods category or not? Our choice is as follows. Direct methods are all of the approaches which allow us to derive phases from diffraction amplitudes, without passing through a Patterson function deconvolution. Thus, we also include in this category, charge flipping and VLD (vive la difference), here classified as non-traditional direct methods; their description is postponed to Chapter 9. In accordance with the above assumptions, in this chapter we will shortly illustrate traditional direct phasing procedures, with particular reference to those which are current and in regular use today: mainly the tangent procedures (see Section 6.2) and the cosine least squares technique, which is the basic tool of the shake and Bake method (see Section 6.4).