Application of the Method of Steepest Descents to X-Ray Structure Analysis

Abstract

Although the Fourier method of synthesis has enjoyed a long and justified supremacy in the armoury of techniques for X-ray structure analysis, the time is rapidly approaching when its use will be limited by the complexity of the structures investigated. In the absence of any universally applicable method of obtaining phase angles, Fourier refinement can be applied only to those structures which are sufficiently simple for an accurate estimate of their parameters to be made. It is an unfortunate fact that the Fourier refinement process converges only if the trial parameters are reasonably close to the true ones, and the region of convergence is roughly that of the differential method¹.