Crystal Structure Determination: The Role of the Cosine Seminvariants

A. The Theoretical Basis.- I. The Phase Problem.- II. Explicit Formulas for the Cosine Seminvariants: The Algebraic Approach.- III. The Joint Probability Distribution of Two Structure Factors and Related Conditional Distributions and Expectation Values.- IV. Probability Distribution of Three Structure Factors and Applications.- B. Techniques of Implementation.- V. The Calculation of the Cosine Seminvariants.- VI. Using Calculated Cosines to Determine Values of Initial Phases.- VII. The Tangent Techniques.- C. The Applications.- VIII. Two Androstane Derivatives; Least-Squares Analysis of the Cosine Invariants.- IX. The Estradiol · Urea Complex and 6?-Fluorocortisol; Two-Dimensional Invariants.- X. Hexestrol; Quadruples.- XI. 9?-Fluorocortisol; Pairs.- XII. Valinomycin; Strong Enantiomorph Discrimination.- XIII. 9-t-Butyl 9,10-Dihydroanthracene; Modified Tangent Procedure.