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Foreword; Preface; Contents; Part I: Fundamentals; Chapter 1: The DV-Xα Molecular Orbital Calculation Method and Recent Development; 1.1 Introduction; 1.2 Total Energy Calculation; 1.3 Relativistic DVME Method; 1.4 Recent Application of the DV-Xα Method; 1.4.1 Electronic State of Mobile Li Ions in Super-Ionic Conductors; 1.4.1.1 Introduction; 1.4.1.2 Li3N Crystal; 1.4.1.3 Model Cluster of Mobile Li Ion in Li3N Crystal; 1.4.1.4 Local Cluster Energy of Mobile Li Ion; 1.4.1.5 Bonding Nature and Li Ion Movement; 1.4.1.6 Conclusion; 1.4.2 Electronic States of Lanthanide Ions in Phosphate Glasses
1.4.2.1 Introduction1.4.2.2 Fluorescence Spectra of Pr3+ Ion in Phosphate Glass; 1.4.2.3 Fluorescence Spectra of Tb3+ Ion in Phosphate Glass; 1.4 Conclusion; References; Part II: Recent Theoretical Progress; Chapter 2: Algebraic Molecular Orbital Theory; 2.1 Introduction; 2.1.1 Multivariable Problem; 2.1.2 Variational Principle; 2.1.3 Trial Functions and Molecular Integrals; 2.1.4 SCF Method; 2.1.5 Nonadiabatic Process; 2.1.6 Aim of Our Study; 2.2 Theory; 2.2.1 Polynomial Expression of Molecular Integrals; 2.2.2 Total Electronic Energy; 2.2.3 Extension in the Variational Principle
2.3 Discussion2.3.1 Multivariable Theory for Chemistry; 2.3.2 Polynomial Expression of Molecular Integrals over STFs; 2.3.3 Advantage of Extension of the Variational Principle; 2.3.4 Advantage in Calculation of Electron Correlation; 2.3.5 Integer Variables in Quantum Chemistry; 2.3.6 Advantage of Polynomial Equation; 2.3.7 Advantage in the Born-Oppenheimer Approximation; 2.3 Conclusion; References; Chapter 3: Analytical Expression of Molecular Integrals over Slater-Type Functions for Generating Their Polynomial Expressions; 3.1 Introduction; 3.2 General Formulation; 3.2.1 Preliminaries
3.2.1.1 The Coordinate System3.2.1.2 Slater-Type Function; 3.2.1.3 Molecular Integrals Discussed in This Article; 3.2.1.4 Coordinate System of Integration; 3.2.1.5 Change of Variable for Two Center Integration; 3.2.1.6 Domain of Integration; 3.2.1.7 One-Center Charge Density Centered on A; 3.2.1.8 Transfer of Origin of Spherical Harmonics from B to A; 3.2.1.9 Two-Center Charge Density Centered on A and B; 3.2.1.10 One-Center Charge Density Centered on B; 3.2.1.11 Two-Center Integration; 3.2.1.12 Two-Center Charge Density with Jacobian; 3.2.1.13 Short Summary
3.2.1.14 Formulas Frequently Used for the Calculation of Molecular Integrals3.2.2 One-Electron Integral; 3.2.2.1 One-Center Integral; Overlap Integral; Kinetic Energy Integral; Nuclear Attraction Energy Integral; 3.2.2.2 Two-Center Integral; Overlap Integral; Kinetic Energy Integral; Nuclear Attraction Energy Integral; Electron Repulsion Integral; Potential by the Second Electron; One-Center Electron Repulsion Integral; Two-Center Electron Repulsion Integral; Partial Potential Integral of Order l and m; Integration over phi
1.4.2.1 Introduction1.4.2.2 Fluorescence Spectra of Pr3+ Ion in Phosphate Glass; 1.4.2.3 Fluorescence Spectra of Tb3+ Ion in Phosphate Glass; 1.4 Conclusion; References; Part II: Recent Theoretical Progress; Chapter 2: Algebraic Molecular Orbital Theory; 2.1 Introduction; 2.1.1 Multivariable Problem; 2.1.2 Variational Principle; 2.1.3 Trial Functions and Molecular Integrals; 2.1.4 SCF Method; 2.1.5 Nonadiabatic Process; 2.1.6 Aim of Our Study; 2.2 Theory; 2.2.1 Polynomial Expression of Molecular Integrals; 2.2.2 Total Electronic Energy; 2.2.3 Extension in the Variational Principle
2.3 Discussion2.3.1 Multivariable Theory for Chemistry; 2.3.2 Polynomial Expression of Molecular Integrals over STFs; 2.3.3 Advantage of Extension of the Variational Principle; 2.3.4 Advantage in Calculation of Electron Correlation; 2.3.5 Integer Variables in Quantum Chemistry; 2.3.6 Advantage of Polynomial Equation; 2.3.7 Advantage in the Born-Oppenheimer Approximation; 2.3 Conclusion; References; Chapter 3: Analytical Expression of Molecular Integrals over Slater-Type Functions for Generating Their Polynomial Expressions; 3.1 Introduction; 3.2 General Formulation; 3.2.1 Preliminaries
3.2.1.1 The Coordinate System3.2.1.2 Slater-Type Function; 3.2.1.3 Molecular Integrals Discussed in This Article; 3.2.1.4 Coordinate System of Integration; 3.2.1.5 Change of Variable for Two Center Integration; 3.2.1.6 Domain of Integration; 3.2.1.7 One-Center Charge Density Centered on A; 3.2.1.8 Transfer of Origin of Spherical Harmonics from B to A; 3.2.1.9 Two-Center Charge Density Centered on A and B; 3.2.1.10 One-Center Charge Density Centered on B; 3.2.1.11 Two-Center Integration; 3.2.1.12 Two-Center Charge Density with Jacobian; 3.2.1.13 Short Summary
3.2.1.14 Formulas Frequently Used for the Calculation of Molecular Integrals3.2.2 One-Electron Integral; 3.2.2.1 One-Center Integral; Overlap Integral; Kinetic Energy Integral; Nuclear Attraction Energy Integral; 3.2.2.2 Two-Center Integral; Overlap Integral; Kinetic Energy Integral; Nuclear Attraction Energy Integral; Electron Repulsion Integral; Potential by the Second Electron; One-Center Electron Repulsion Integral; Two-Center Electron Repulsion Integral; Partial Potential Integral of Order l and m; Integration over phi