International Tables for Crystallography (2010). Vol. B, ch. 2.2, pp. 215-243   | 1 | 2 |
doi: 10.1107/97809553602060000764

Chapter 2.2. Direct methods

Contents

  • 2.2. Direct methods  (pp. 215-243) | html | pdf | chapter contents |
    • 2.2.1. List of symbols and abbreviations  (p. 215) | html | pdf |
    • 2.2.2. Introduction  (p. 215) | html | pdf |
    • 2.2.3. Origin specification  (pp. 215-216) | html | pdf |
    • 2.2.4. Normalized structure factors  (pp. 216-221) | html | pdf |
      • 2.2.4.1. Definition of normalized structure factor  (pp. 216-218) | html | pdf |
      • 2.2.4.2. Definition of quasi-normalized structure factor  (pp. 218-219) | html | pdf |
      • 2.2.4.3. The calculation of normalized structure factors  (pp. 219-221) | html | pdf |
      • 2.2.4.4. Probability distributions of normalized structure factors  (p. 221) | html | pdf |
    • 2.2.5. Phase-determining formulae  (pp. 221-230) | html | pdf |
      • 2.2.5.1. Inequalities among structure factors  (pp. 221-222) | html | pdf |
      • 2.2.5.2. Probabilistic phase relationships for structure invariants  (pp. 222-223) | html | pdf |
      • 2.2.5.3. Triplet relationships  (pp. 223-224) | html | pdf |
      • 2.2.5.4. Triplet relationships using structural information  (pp. 224-225) | html | pdf |
      • 2.2.5.5. Quartet phase relationships  (pp. 225-227) | html | pdf |
      • 2.2.5.6. Quintet phase relationships  (p. 227) | html | pdf |
      • 2.2.5.7. Determinantal formulae  (pp. 227-228) | html | pdf |
      • 2.2.5.8. Algebraic relationships for structure seminvariants  (pp. 228-229) | html | pdf |
      • 2.2.5.9. Formulae estimating one-phase structure seminvariants of the first rank  (p. 229) | html | pdf |
      • 2.2.5.10. Formulae estimating two-phase structure seminvariants of the first rank  (pp. 229-230) | html | pdf |
    • 2.2.6. Direct methods in real and reciprocal space: Sayre's equation  (pp. 230-231) | html | pdf |
    • 2.2.7. Scheme of procedure for phase determination: the small-molecule case  (pp. 231-232) | html | pdf |
    • 2.2.8. Other multisolution methods applied to small molecules  (pp. 232-234) | html | pdf |
    • 2.2.9. Some references to direct-methods packages: the small-molecule case  (pp. 234-235) | html | pdf |
    • 2.2.10. Direct methods in macromolecular crystallography  (pp. 235-239) | html | pdf |
      • 2.2.10.1. Introduction  (p. 235) | html | pdf |
      • 2.2.10.2. Ab initio crystal structure solution of proteins  (pp. 235-236) | html | pdf |
      • 2.2.10.3. Integration of direct methods with isomorphous replacement techniques  (p. 236) | html | pdf |
      • 2.2.10.4. SIR–MIR case: one-step procedures  (pp. 236-237) | html | pdf |
      • 2.2.10.5. SIR–MIR case: the two-step procedure. Finding the heavy-atom substructure by direct methods  (p. 237) | html | pdf |
      • 2.2.10.6. SIR–MIR case: protein phasing by direct methods  (p. 237) | html | pdf |
      • 2.2.10.7. Integration of anomalous-dispersion techniques with direct methods  (pp. 237-238) | html | pdf |
      • 2.2.10.8. The SAD case: the one-step procedures  (p. 238) | html | pdf |
      • 2.2.10.9. SAD–MAD case: the two-step procedures. Finding the anomalous-scatterer substructure by direct methods  (pp. 238-239) | html | pdf |
      • 2.2.10.10. SAD–MAD case: protein phasing by direct methods  (p. 239) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 2.2.4.1. Probability density functions for cs. and ncs. crystals  (p. 221) | html | pdf |
      • Fig. 2.2.4.2. Cumulative distribution functions for cs. and ncs. crystals  (p. 222) | html | pdf |
      • Fig. 2.2.5.1. Curves of (2.2.5.6) for some values of [G =] [2\sigma_{3} \sigma_{2}^{-3/2} |E_{\bf h} E_{\bf k} E_{{\bf h} - {\bf k}}|]  (p. 223) | html | pdf |
      • Fig. 2.2.5.2. Variance (in square radians) as a function of α  (p. 223) | html | pdf |
      • Fig. 2.2.5.3. Distributions (2.2.5.18) (solid curve) and (2.2.5.20) (dashed curve) for the indicated [|E|] values in three typical cases  (p. 225) | html | pdf |
      • Fig. 2.2.7.1. The form of w as given by (2.2.7.2)  (p. 232) | html | pdf |
    • Tables
      • Table 2.2.3.1. Allowed origin translations, seminvariant moduli and phases for centrosymmetric primitive space groups  (p. 217) | html | pdf |
      • Table 2.2.3.2. Allowed origin translations, seminvariant moduli and phases for noncentrosymmetric primitive space groups  (pp. 218-219) | html | pdf |
      • Table 2.2.3.3. Allowed origin translations, seminvariant moduli and phases for centrosymmetric non-primitive space groups  (p. 220) | html | pdf |
      • Table 2.2.3.4. Allowed origin translations, seminvariant moduli and phases for noncentrosymmetric non-primitive space groups  (pp. 220-221) | html | pdf |
      • Table 2.2.4.1. Moments of the distributions (2.2.4.4) and (2.2.4.5)  (p. 222) | html | pdf |
      • Table 2.2.5.1. List of quartets symmetry equivalent to [\Phi = \Phi_{1}] in the class mmm   (p. 226) | html | pdf |
      • Table 2.2.8.1. Magic-integer sequences for small numbers of phases ( n ) together with the number of sets produced and the root-mean-square error in the phases  (p. 233) | html | pdf |