Two Androstane Derivatives; Least-Squares Analysis of the Cosine Invariants

  • Herbert A. Hauptman


The structures of 5α-androstan-3β-ol-17-one (C19H30O2) and 5β-androstane-3α, l7β-diol (C19H32O2) were solved via the least-squares analysis of the calculated cosine invariants, cos (ø123). Both these substances crystallize in space group P21 with two molecules in the unit cell. The computational procedure whereby phases were derived from the invariants is discussed in detail. The computed cosine invariants were compared with the observed values, and it was found that invariants for which the true value is relatively large are computed more accurately than invariants having smaller values.


Phase Determination Structure Invariant Chapter VIII Chapter Versus Spurious Peak 
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  1. Hauptman, H.; Fisher, J. and Weeks, C. (1971). Phase Determination by Least-Squares Analysis of Structure Invariants: Discussion of This Method as Applied to Two Androstane Derivatives. Acta Cryst. B27, 1550–1561.Google Scholar
  2. Fisher, J.; Hancock, H. and Hauptman, H. (1970). The Conditional Probability Distribution of Crystal Structure Invariants. Naval Research Laboratory Report 7132.Google Scholar
  3. Fisher, J.; Hancock, H. and Hauptman, H. (1970). Computer Program for the Calculation of the Crystal Structure Invariants Based on Certain Conditional Distributions. Naval Research Laboratory Report 7157.Google Scholar
  4. Hancock, H.; Fisher, J. and Hauptman, H. (1970). Computer Program for the Least-Squares Determination of the Phases of the Crystal Structure Factors. Naval Research Laboratory Report 7167.Google Scholar

Copyright information

© Springer Science+Business Media New York 1972

Authors and Affiliations

  • Herbert A. Hauptman
    • 1
  1. 1.Mathematical Biophysics DepartmentMedical Foundation of BuffaloBuffaloUSA

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