The cross-correlation function: main properties and first applications

Abstract

When a model structure, and more generally a model electron density ρM(r), is available, its cross-correlation functionC(u) with the unknown true structure ρ(r) cannot be exactly calculated. A useful approximation ofC(u) is obtained by replacing exp[i(φh − φMh)] by its expected value. In this caseC′(u), a potentially useful approximation of the functionC(u), is obtained. In this paper the main crystallographic properties of the functionsC(u) andC′(u) are established. It is also shown that such functions may be useful for the success of the phasing process.