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A General SCF Theory

We live in a molecular world, almost closed shell in nature, and for this reason Chemistry has been a science dealing with closed shell mol­ ecules. However, the high degree of experimental sophistication reached in the past decade has made more apparent the role of open shell structures in chemical...

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Bibliographic Details
Main Authors: Carbo, Ramon, Riera, Joseph M. (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1978, 1978
Edition:1st ed. 1978
Series:Lecture Notes in Chemistry
Subjects:
Physical Chemistry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Historical Review
  • 1. The Open Shell Development
  • 2. The Multiconfigurational Scheme
  • II. Electronic Energy, Fock Operators and Coupling Operators
  • 1. Introduction
  • 2. General Energy Expression
  • 3. General Coulomb and Exchange Operators
  • 4. Energy and Lagrangian Variation: Fock Operators and Euler Equations
  • 5. Coupling Operator
  • 6. Null Gradient Coupling Operator Part
  • 7. Lagrange multipliers Hermitean Condition Coupling Operator Part
  • 8. LCAO Form of Coupling Operator
  • 9. Simplified Energy Forms. Monoconfigurational Open Shell
  • 10. Closed Shell
  • 11. Corollary
  • III. Eigenspace Manipulations
  • 1. Introduction
  • 2. General Formalism
  • 3. Unconditional Convergence in SCF Procedures: Level Shift Techniques
  • IV. Multiconfigurational Structure of Monoconfigurational SCF Procedures
  • 1. Monoconfigurational Energy and Euler Equations
  • 2. Results
  • 3. Final Remarks
  • V. Paired Excitation Multiconfigurational SCF
  • X. The Problem of the Helium Atom First Excited Singlet State
  • 1. A Possible Solution
  • 2. The “Triplet Catastrophe”
  • 3. Further Analysis of the “The Triplet Catastrophe”
  • 4. Some Results on Monoconfigurational He SCF
  • XI. Applications
  • 1. Introduction
  • 2. SCF Study of Water: Ground and Excited States
  • 3. Paired Excitation Calculation on Water
  • 4. Formaldehyde
  • 5. Magnesium Oxyde
  • 6. Nitrogen Dioxyde
  • 7. Methanol
  • 8. Diimine
  • 9. Methylenimine
  • 10. Glycine
  • 11. Excited States of Some Molecules with C=O and C=N Bonds: INDO Procedure
  • Appendix A: Monoconfigurational State Parameters
  • Appendix B: Slater Rules
  • Appendix C: Multiconfigurational Fock Operators
  • Suggested Reading
  • Bibliographical Survey
  • A. Open Shell SCF Theory
  • B. Multiconfigurational SCF Theory
  • 1. Closed Shell MCPESCF Theory
  • 2. Complete MCPE Energy Expression
  • 3. Two Electron Systems
  • 4. MCPESCF Theory with an Invariant Closed Shell
  • 5. Open Shell PEMCSCF
  • 6. Special Cases
  • VI. SCF Perturbation Theory
  • 1. Perturbation Theory
  • 2. Open Shell SCF Theory
  • 3. Interaction of Two Molecules as an Application Example
  • VII. General Theory for Two and Three Electron Systems
  • 1. Two Electron Systems
  • 2. Three Electron Systems
  • VIII. Approximate SCF Theories
  • 1. Atomic Orbital Representation
  • 2. Decomposition of the Electronic Repulsion Matrix
  • 3. Empirical Approximate Methods
  • 4. Model Potentials: Huzinaga’s Approach
  • IX. Miscellaneous Remarks
  • 1. A Synthetic Approach
  • 2. The Concept of Shell
  • 3. Symmetry
  • 4. Optimization of Non-Linear Parameters
  • 5. Generalized Brillouin’s Theorem and Off-Diagonal Hermitean Conditions onLagrange Multipliers
  • 6. Error Analysis
  • 7. Mathematical Structure of SCF

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