Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry

Section I: Exponential Type Basis Quantum Chemistry

Chapter One: A Sturmian Approach to Photoionization of Molecules

• Abstract
• 1 Introduction
• 2 Generalities
• 3 Examples Taken from the Literature
• 4 Survey of Theoretical Methods
• 5 Sturmian Approach
• 6 Conclusions
• Acknowledgments
• Appendix List of Photoionization Calculations for Different Molecules

Chapter Two: General Coalescence Conditions for the Exact Wave Functions: Higher-Order Relations for Coulombic and Non-Coulombic Systems

• Abstract
• 1 Introduction
• 2 Basic Formulation
• 3 Primitive General Coalescence Conditions
• 4 General Coalescence Conditions
• 5 Verification of GCCs
• 6 Solving the SE with GCCs
• 7 Conclusions
• Acknowledgment

Chapter Three: Exponentially Correlated Wave Functions for Four-Body Systems

• Abstract
• 1 Introduction and History
• 2 Relative Coordinates
• 3 Four-Body Wave Functions
• 4 Potential and Kinetic Energy Operators
• 5 Matrix Elements
• 6 Angular Integration
• 7 Shape Integration
• 8 Applications
• Acknowledgments
• Appendix Boundary Integrals

Chapter Four: Analytic Formulas for Two-Center Two-Electron Integrals with Exponential Functions

• Abstract
• 1 Introduction
• 2 Integral Representation for the Master Integral
• 3 Recurrence Relations for the General Integral with σ₀₀ ≠ 0
• 4 Recurrence Relations at σ₀₀ = 0
• 5 James-Coolidge Integrals σ₂₀ = 0
• 6 Conclusion
• Acknowledgment
• Appendix A Master Integral
• Appendix B Inhomogeneous Terms

Chapter Five: Singlet and Triplet Bound State Spectra in the Four-Electron Be-Like Atomic Systems

• Abstract
• 1 Introduction
• 2 Hamiltonian and Bound State Wave Functions in the CI Method
• 3 General Structure of the Bound State Spectra
• 4 Spectral Diagram of the Four-Electron Be-Like Atoms
• 5 Conclusion
• Acknowledgments

Chapter Six: An Application of the Gaussian Transform for Approximating Some Bessel Functions and Multicenter Integrals Involving 1s Slater-Type Orbitals

• Abstract
• 1 Introduction
• 2 Methodology
• 3 Results for the Coulomb Potential
• 4 Concluding Remarks
• Appendix

Chapter Seven: Size-Extensivity Corrections in Single- and Multireference Configuration Interaction Calculations

• Abstract
• 1 Introduction
• 2 Theoretical Background
• 3 Results and Discussion
• 4 Conclusion
• Acknowledgments

Chapter Eight: Introducing a Polynomial Expression of Molecular Integrals for Algebraic the Molecular Orbital (MO) Equation

• Abstract
• 1 Introduction
• 2 Method
• 3 Results and Discussion
• 4 Conclusion
• Acknowledgments
• Appendix Taylor Expansion of Overlap Integral of × 16 about a₀ and b₀

Chapter Nine: Analytic Calculation of Momentum Distribution and Compton Profiles of Atoms Using Hartree–Fock–Roothaan Method: Applications to Atoms 2 ≤ Z ≤ 10

• Abstract
• 1 Introduction
• 2 Analytical Expression for Momentum Density and Atomic Compton Profiles
• 3 Auxiliary Functions B_mn^l(α, β; q)
• 4 Compton Profile of Atoms 2 ≤ Z ≤ 10
• 5 Results and Discussions
• Acknowledgment

Chapter Ten: Evaluation of One-Electron Basic Integrals of Irregular Solid Harmonics and Slater-Type Orbitals Using Fourier Transforms

• Abstract
• 1 Introduction
• 2 Properties of Solid Spherical Harmonics
• 3 One-Electron Integrals Between ISHs and STOs with Equal Screening Parameters
• 4 Numerical Results and Discussion

Section II: Electron Correlation in Molecules and Solids

Chapter Eleven: Excitation Energies of Molecules from Ensemble Density Functional Theory: Multiconfiguration Approaches

• Abstract
• 1 Ensemble Variation Principle and Its Descendants
• 2 Multiconfiguration Wavefunction-Based Methods for Ensembles
• 3 State-Averaged Spin-Restricted KS Method
• 4 Range-Separated Approaches
• 5 Summary and Outlook
• Acknowledgments

Chapter Twelve: Application of the Space-Pseudo-Time Method to Density Functional Theory

• Abstract
• 1 Introduction
• 2 Kohn–Sham Equations
• 3 Radial Equations
• 4 Numerical Results and Conclusions
• Acknowledgments

Chapter Thirteen: Potential Energy Curves of NaK Molecule from All-Electron Multireference-Coupled Cluster Calculations

• Abstract
• 1 Introduction
• 2 Synopsis of the Theory
• 3 Results and Discussion
• 4 Conclusions
• Acknowledgment

Chapter Fourteen: The Correlation Effects in Density Functional Theory Along the Dissociation Path

• Abstract
• 1 Introduction
• 2 Theory
• 3 Computational Details
• 4 Numerical Results and Discussion
• 5 Final Remarks
• Acknowledgments
• Conflict of Interest
• Appendix Analysis of the Behavior of the Investigated GGA Potentials near the Middle of the Bond

Chapter Fifteen: Introduction to the Variational and Diffusion Monte Carlo Methods

• Abstract
• 1 Variational Monte Carlo
• 2 Diffusion Monte Carlo
• Acknowledgments
• Appendix Statistical Estimator of Nonlinear Functions of Expectation Values

Chapter Sixteen: Configuration Interaction Monte Carlo with Coupled Clusters Wave Functions

• Abstract
• 1 Introduction
• 2 Method
• 3 Results in Homogeneous Systems
• 4 First Row Atoms
• 5 Conclusions

Chapter Seventeen: X-Ray Constrained Wave Functions: Fundamentals and Effects of the Molecular Orbitals Localization

• Abstract
• 1 Introduction
• 2 Theory
• 3 Computational Results
• 4 Conclusions and Perspectives
• Acknowledgments

Chapter Eighteen: Electron Impact Atomic and Ionic Ionization: Analytical, Semiempirical, and Semiclassical Methods

• Abstract
• 1 Introduction
• 2 Outline of the Models
• 3 Experimental Data Sources
• 4 Discussion
• 5 Conclusions
• Acknowledgments