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Crystal Structure Determination The Role of the Cosine Seminvariants
Author
Title
Crystal Structure Determination [electronic resource] : The Role of the Cosine Seminvariants / by Herbert A. Hauptman.
ISBN
9781468499544
Publication
Boston, MA : Springer US : Imprint: Springer, 1972.
Physical Description
1 online resource (XII, 407 p.) 4 illus.
Local Notes
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Summary
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.
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Springer ENIN.
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Format
Books / Online
Language
English
Added to Catalog
January 11, 2019
Contents
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.
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