Full Matrix Refinement as a Tool to Discover the Quality of a Refined Structure

Abstract

This chapter discusses the foundations of optimization. The methods described are applicable to both least-squares and maximum-likelihood refinement protocols. These methods are also useful for studying the effects of different parameterizations of the models, including anisotropic atomic displacement parameters, rigid substructures, internal versus Cartesian coordinates, and restraints versus constraints. Full-matrix optimization methods coupled with the examination of the eigenvalues and eigenvectors of the curvature matrices provide powerful tools for the automatic identification of problematic regions in a refined structure. It provides a theoretically sound means of determining the precision of parameters at low resolution. The process can be reasonably automated. The memory requirements for full-matrix methods are proportional to the square of the number of parameters, which for macromolecular problems have been prohibitively large. Full-matrix methods retain all the correlation information. The most popular full-matrix program in crystallography is SHELXL, which has a conjugate gradients mode as well, especially designed for macromolecular refinement.