Produktbild: Theory and Practice of Direct Methods in Crystallography

Theory and Practice of Direct Methods in Crystallography

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

05.10.2011

Verlag

Springer Us

Seitenzahl

436

Maße (L/B/H)

23.5/15.5/2.4 cm

Gewicht

657 g

Auflage

1980

Sprache

Englisch

ISBN

978-1-4613-2981-7

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

05.10.2011

Verlag

Springer Us

Seitenzahl

436

Maße (L/B/H)

23.5/15.5/2.4 cm

Gewicht

657 g

Auflage

1980

Sprache

Englisch

ISBN

978-1-4613-2981-7

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Theory and Practice of Direct Methods in Crystallography
  • 1. Principles of Direct Methods of Phase Determination in Crystal Structure Analysis.- 1.1. Introduction.- 1.2. Spherical Symmetry of Atoms: Sayre’s Equation.- 1.3. Unitary and Normalized Structure Factors.- 1.4. Karle-Hauptman Determinants.- 1.5. Structure Invariants and Seminvariants.- 1.6. Probability Theory.- 1.7. Solving the Phase Problem for a Real Structure.- 1.8. Refinement of Phases.- 1.9. Possible Future Developments of Direct Methods.- References.- 2. Definition of Origin and Enantiomorph and Calculation of |E| Values.- I: Definition of Origin and Enantiomorph.- 2.1. Introduction.- 2.2. Some Preliminaries.- 2.3. Invariance.- 2.4. Variation of Phase among the Laue-Related Reflections.- 2.5. Defining the Origin.- 2.5.1. Primitive Centrosymmetric Space Groups.- 2.5.2. Nonprimitive Centrosymmetric Space Groups.- 2.5.3. Noncentrosymmetric Space Groups.- 2.5.4. Primitive Noncentrosymmetric Space Groups.- 2.5.5. Nonprimitive Noncentrosymmetric Space Groups.- 2.6. Some Unusual Requirements of S/I Selectors.- 2.7. In Conclusion.- Appendix 2A.1.- Appendix 2A.2.- II: Calculation of |E| Values.- References.- 3. Symbolic Addition and Multisolution Methods.- 3.1. Introduction.- 3.2. Symbolic Addition: Centrosymmetric Case.- 3.2.1. Phase Determination in Space Group $$P\mathop 1\limits^ - $$: Pyridoxal Phosphate Oxime Dihydrate.- 3.3. Symbolic Addition: Noncentrosymmetric Case.- 3.3.1. Phase Determination in Space Group P21: Tubercidin.- 3.4. Advantages and Disadvantages of Symbolic Addition.- 3.5. Multisolution Methods.- 3.5.1. Introduction: Multisolution Philosophy and Brief Description of the Program MULTAN.- 3.5.2. Centrosymmetric Case: Papaverine Hydrochloride.- 3.5.3. Noncentrosymmetric Case: Methyl Warifteine and Dimethyl Warifteine.- 3.5.4. Experience with Large Structures: Ribonuclease-Potassium Hexachloroplatinate.- 3.6. Success Is Not Guaranteed.- 3.6.1. Some Prerequisites for Success in Using Direct Methods.- 3.6.2. Figures of Merit: a Practical Guide.- 3.6.3. Signs of Trouble, and Past Remedies When the Structure Failed to Solve.- 3.6.4. Comments on Molecular Scattering Factors.- 3.7. More Recent Developments of the Multisolution Method: Magic Integers.- References.- 4. Probabilistic Theory of the Structure Seminvariants.- 4.1. Major Goal.- 4.2. Introduction.- 4.3. Structure Invariants.- 4.4. Structure Seminvariants.- 4.5. The Structure Seminvariants Link the Observed Magnitudes |E| with the Desired Phases ?.- 4.6. Probabilistic Background.- 4.7. Three-Phase Structure Invariant.- 4.7.1. Space Group P1.- 4.7.2. Space Group $$P\mathop 1\limits^ - $$.- 4.8. Four-Phase Structure Invariant (Quartet).- 4.8.1. Space Group P1.- 4.8.2.Space Group $$P\mathop 1\limits^ - $$.- 4.9. The Neighborhood Principle.- 4.10. More on Quartets: Higher Neighborhoods.- 4.10.1. Third Neighborhoods of the Structure Invariant $${\phi _4} = {\phi _h} + {\phi _k} + {\phi _l} + {\phi _m}$$.- 4.10.2.Higher Neighborhoods.- 4.10.3. Probability Distributions in PI Derived from the Third (Thirteen-Magnitude) Neighborhoods.- 4.10.4. Probability Distributions in $$P\mathop 1\limits^ - $$ Derived from the Third (Thirteen-Magnitude) Neighborhoods.- 4.11. Two-Phase Structure Seminvariants (Pairs).- 4.11.1. Space Group $$P\mathop 1\limits^ - $$.- 4.11.2. Space Group P21.- 4.11.3. Space Group P212121.- 4.12. Concluding Remarks.- References.- 5. Application of Calculated Cosine Invariants in Phase Determination.- 5.1. Introduction.- 5.2. Accuracy of Cosine Calculations.- 5.3. Quartets, Quintets, and Triplets.- 5.4. ?1 Cosines.- 5.5. Pair Relationships.- 5.6. Strong Enantiomorph Selection.- 5.7. NQEST.- 5.8. Automated Procedures.- 5.9. Exercises.- References.- 6. Phase Correlation with Calculated Cosine Invariants for Routine Structure Analysis.- 6.1. Phase Correlation Procedure.- 6.1.1. Definitions.- 6.1.2. Selection of the Starting Set.- 6.1.3. Phase Generation.- 6.1.4. Correlation Equations.- 6.1.5. End of the Phase Correlation Procedure.- 6.1.6. Quadruples and Quartets in Relation to the Phase Correlation Procedure.- 6.1.7. Dinaphtho [1,2-a; 1’,2’-h]anthracene.- 6.2. Simple Cosine-Invariant Calculations.- 6.2.1. Aminomalonic Acid.- 6.2.2. Scaling of Calculated Triple Invariants.- 6.2.3. Definition of KABhk Values.- 6.3. Phase Correlation with Calculated Triple Invariants.- 6.3.1. Centrosymmetric Space Groups.- 6.3.2. Noncentrosymmetric Space Groups with Three Centric Projections.- 6.3.3. Noncentrosymmetric Space Groups with One Centric Projection.- References.- 7. Application of Direct Methods to Difference Structure Factors.- 7.1. Introduction.- 7.1.1. Some Applications of DIRDIF Procedures.- 7.1.2. Two-Dimensional Wilson Plot.- 7.2. Difference Structure Factors.- 7.2.1. Probability Considerations.- 7.2.2. Classification of Reflections.- 7.3. Description of the Procedure.- 7.3.1. Tangent Refinement.- 7.3.2. Origin Specification.- 7.3.3. Trichloro-bis(triethylphosphine)cobalt(III).- 7.3.4. Heptahelicene.- 7.4. Some Observations.- References.- 8. Phase Extension and Refinement Using Convolutional and Related Equation Systems.- 8.1. Introduction.- 8.2. Outline of the Convolutional Equation Systems.- 8.3. Outlines of the Phasing Methods Based on the Convolutional Equation Systems.- 8.3.1. Tangent-Formula Refinement.- 8.3.2. Density Modification Methods.- 8.3.3. Least-Squares Phase Refinement.- 8.3.4. Davies-Rollett Technique.- 8.4. Comments on the Phasing Methods Based on the Convolutional Equation Systems.- 8.5. Computational and Practical Aspects.- 8.6. Summary.- References.- 9. Maximum Determinant Method.- 9.1. Introduction.- 9.2. Inequalities and Algebraic Properties of Determinants.- 9.2.1. Unitary and Normalized Structure Factors.- 9.2.2. Karle-Hauptman Determinants (1950).- 9.2.3. Determinants as a Function of Structure Invariants.- 9.2.4. The Ellipsoid Representation of Inequalities, and Efficiency in Phase Determination.- 9.3. Maximum Determinant Rule.- 9.3.1. Definition.- 9.3.2. Proof.- 9.3.3. Eigenvectors and the Ellipsoid Representation.- 9.3.4. Regression Equation.- 9.4. Practical Applications.- 9.4.1. Low-Order Determinants, and Determination of Structure Invariants.- 9.4.2. Medium-Order Determinants, and Their Use in ab initio Structure Determination.- 9.4.3. High-Order Determinants, and Their Use in Protein Structure Determination.- 9.5. New Gram Determinants.- 9.5.1. Use of Stereochemical Information—Known Fragments.- 9.5.2. The “Moduli-Model-Phase” Determinant.- 9.5.3. The Equiprobability Function in Direct Space.- Appendix 9A.1. Expression of the Hermitian Form Qm for m = 1,2.- Appendix 9A.2. Joint Probability for All Structure Factors: Compound Probability Law.- Appendix 9A.3. Negative Triplet Determination.- Appendix 9A.4. Determination of the Sign Invariants of the Last Row of.- Appendix 9A.5. Hilbert Space and Gram Determinants.- References.- 10. Molecular Replacement Method.- 10.1. Introduction.- 10.2. Preliminary Theoretical Considerations.- 10.3. Rotation Function.- 10.3.1. Fundamentals.- 10.3.2. Reciprocal-Space Expression.- 10.3.3. Matrix Algebra.- 10.3.4. Symmetry.- 10.3.5. Sampling and Background.- 10.3.6. Locked Rotation Function and Klug Peaks.- 10.3.7. Recognizing Known Fragments.- 10.3.8. Fast Rotation Function.- 10.4. Translation Problem.- 10.4.1. Introduction.- 10.4.2. Neither Structure is Known.- 10.4.3. Positioning of a Known Molecular Structure.- 10.4.4. Both Structures are Known.- 10.4.5. Use of Heavy Atoms to Determine a Molecular Center.- 10.4.6. Use of Packing Considerations.- 10.5. Phase Determination.- 10.5.1. Introduction.- 10.5.2. Reciprocal-Space Equations.- 10.5.3. Real-Space Molecular Replacement.- 10.5.4. Equivalence of Real- and Reciprocal-Space Molecular Replacement.- 10.6. Noncrystallographic Symmetry and Heavy-Atom Searches.- 10.7. Applications of Molecular Replacement.- 10.8. Conclusions.- References.