Ebook: Crystal Structure Determination: The Role of the Cosine Seminvariants
Author: Herbert A. Hauptman (auth.)
- Tags: Crystallography
- Year: 1972
- Publisher: Springer US
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-2
The Phase Problem....Pages 3-65
Explicit Formulas for the Cosine Seminvariants: The Algebraic Approach....Pages 67-124
The Joint Probability Distribution of Two Structure Factors and Related Conditional Distributions and Expectation Values....Pages 125-157
Probability Distribution of Three Structure Factors and Applications....Pages 159-183
Front Matter....Pages 185-186
The Calculation of the Cosine Seminvariants....Pages 187-209
Using Calculated Cosines to Determine Values of Initial Phases....Pages 211-225
The Tangent Techniques....Pages 227-249
Front Matter....Pages 251-251
Two Androstane Derivatives; Least-Squares Analysis of the Cosine Invariants....Pages 253-282
The Estradiol·Urea Complex and 6?-Fluorocortisol; Two-Dimensional Invariants....Pages 283-306
Hexestrol; Quadruples....Pages 307-326
9?-Fluorocortisol; Pairs....Pages 327-359
Valinomycin; Strong Enantiomorph Discrimination....Pages 361-384
9-t-Butyl-9,10-Dihydroanthracene; Modified Tangent Procedure....Pages 385-395
Back Matter....Pages 397-407
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-2
The Phase Problem....Pages 3-65
Explicit Formulas for the Cosine Seminvariants: The Algebraic Approach....Pages 67-124
The Joint Probability Distribution of Two Structure Factors and Related Conditional Distributions and Expectation Values....Pages 125-157
Probability Distribution of Three Structure Factors and Applications....Pages 159-183
Front Matter....Pages 185-186
The Calculation of the Cosine Seminvariants....Pages 187-209
Using Calculated Cosines to Determine Values of Initial Phases....Pages 211-225
The Tangent Techniques....Pages 227-249
Front Matter....Pages 251-251
Two Androstane Derivatives; Least-Squares Analysis of the Cosine Invariants....Pages 253-282
The Estradiol·Urea Complex and 6?-Fluorocortisol; Two-Dimensional Invariants....Pages 283-306
Hexestrol; Quadruples....Pages 307-326
9?-Fluorocortisol; Pairs....Pages 327-359
Valinomycin; Strong Enantiomorph Discrimination....Pages 361-384
9-t-Butyl-9,10-Dihydroanthracene; Modified Tangent Procedure....Pages 385-395
Back Matter....Pages 397-407
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