title: Detailed differential coefficients of anomalous dispersion terms to derivatives in least-squares refinement for X-ray crystallography
abstract: In X-ray crystallographic analysis, correct trial structures are refined by least-squares method. The detailed differential coefficients for the parameters of the calculated structure factor Fc(h) can not be found in any papers, textbooks, nor user's manual of several crystallographic computer systems. We describe, firstly, the basic expression of the structure factors, Fo(h) and Fc(h), anomalous dispersion terms of the structure factor, and then least-squares refining of magnitude of Fo(h) and Fo(h)2 for use in teaching, education and computer programming. Secondly we derive the differential terms of the structure factors, solve the normal equation by diagonal, block and full-matrix approximations, and apply these to the revised computer program LSBF in DS*SYSTEM. Several practical tests are performed for these differentiations.
authors.affiliation: Faculty of Engineering, Science University of Tokyo, Japan.
authors.initials: S
authors.lastname: Okada
authors.initials: K
authors.lastname: Okada