Crystal Structure Determination: The Role of the Cosine Seminvariants

ISBN-13: 9781468499568 / Angielski / Miękka / 2012 / 407 str.

Herbert A. Hauptman; H. Hauptman

Opis

The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the so-called structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there- fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the E-map (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role.

Spis treści

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.