Many algebraic formulas for the evaluation of triplet phase invariants from isomorphous replacement and anomalous dispersion data

Abstract

An algebraic analysis is presented for the calculation of triplet phase invariants from isomorphous replacement and anomalous dispersion data. The analysis applies when there is one type or one predominant type of anomalously scattering atoms. The use of the formulas largely parallels a recent approach that is based on a General Rule for evaluating triplet phase invariants. It involves the mixing of terms from isomorphous replacement with various types of terms arising in anomalous dispersion or the mixing of various terms arising in anomalous dispersion alone. The mixing of terms gives rise to a myriad of formulas that can generate values anywhere in the range from -π to π. In the tests performed, it was found that the algebraic formulas offered an improvement in accuracy over that obtained from the General Rule. The accuracy is potentially high but depends ultimately on the reliability of the experimental data.