Front Cover -- Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems -- Copyright -- Contents -- Contributors -- Preface -- Section I: Molecular Electronic Structure Methodology and Reviews -- Chapter One: Present Status of Selected Configuration Interaction With Truncation Energy Error -- 1. Introduction -- 2. Atomic Self-Consistent Fields -- 3. Molecular Self-Consistent Fields -- 4. CI and General Tools -- 4.1. Projection Operators -- 4.2. Subclasses -- 4.3. Partition of Degenerate Spaces: Interacting Spaces -- 4.4. Fast-Converging CI Expansions: NOs and Ergonals -- 4.5. Multireference CI -- 4.6. Atomic Orbital Bases With Prescribed Completeness Error -- 5. Energy Contribution of a Single Configuration -- 5.1. Dick Brown´s Original Formula -- 5.2. A Priori Brown´s Formulae -- 6. Summary of SCI -- 6.1. Preselection of Configurations Without TEE -- 6.2. Selection of Configurations With TEE -- 6.3. SCI by Parts -- 6.4. Truncation Energy Error -- 6.5. Valence SCI and Related Models -- 7. Mechanics of the Selection Process -- 8. SCI on Large Systems -- 9. Final Remarks -- Acknowledgments -- References -- Chapter Two: Recent Developments in Asymptotic Expansions From Numerical Analysis and Approximation Theory -- 1. Introduction -- 2. Trapezoidal Rule Approximations and Generalizations of the E-M Expansion -- 2.1. Classical E-M Expansion -- 2.2. Navot´s Generalizations of Classical E-M Expansion -- 2.3. Recent Generalizations of E-M Expansions -- 2.4. Applications to Computation of Singular Integrals -- 2.5. Further Remarks on E-M Expansion and Generalizations -- 3. Error Expansions for Gauss-Legendre Quadrature -- 4. Asymptotics of Legendre Polynomials and Legendre Series Coefficients -- 4.1. Asymptotics of Legendre Polynomials and Related Integrals -- 4.2. Asymptotics of Legendre Series Coefficients.

4.2.1. Asymptotics of en[f] in Presence of Endpoint Singularities -- 4.2.2. Asymptotics of en[f] in Presence of Interior and Endpoint Singularities -- References -- Chapter Three: The Kinetic Energy Pauli Enhancement Factor and Its Role in Determining the Shell Structure of Atoms and M ... -- 1. Introduction -- 2. The Concepts of Shell Structure and the Pauli Potential -- 2.1. Shell Structure -- 2.2. The Pauli Potential -- 3. The Pauli Enhancement Factor and Shell Structure -- 3.1. Representation in Terms of One-Particle Orbitals -- 3.1.1. Application to the Al Atom -- 3.2. Representation by Means of Local-Scaling Transformations -- 3.3. The Explicit Functional Representation for Tp in Terms of the Liu-Parr Expansion -- 4. Discussion -- Acknowledgments -- References -- Chapter Four: On the Laguerre Representation of Coulomb Functions and the Relation to Orthogonal Polynomials -- 1. Introduction -- 2. Definitions and Notations of Coulomb Wave Functions -- 3. Series Representation of Coulomb Wave Functions in Terms of Laguerre-Type Functions -- 3.1. The Regular Coulomb Function -- 3.2. The Irregular Coulomb Functions -- 4. Connection With Orthogonal Polynomials -- 4.1. Generalized Pollaczek Polynomials -- 4.2. Meixner-Pollaczek Polynomials -- 5. Summary -- Appendix: Integral Involving Whittaker Function WÏ,μ2(z) -- A.1. Case 2+1N{0} -- A.2. Case 2+1N{0} -- References -- Chapter Five: Numerical Hartree-Fock and Many-Body Calculations for Diatomic Molecules -- 1. Introduction -- 1.1. The Hartree-Fock Equations for Atoms -- 1.2. The Hartree-Fock Equations for Diatomic Molecule -- 2. The Domain Decomposition Algorithm -- 3. A Model Problem -- 4. Many-Body Calculations of the Correlation Energy -- 5. Numerical Solutions of the Orbital and Pair Equations -- 5.1. The Single-Electron Equation -- 5.2. The Pair Equation for Two Noninteracting Electrons.

13. Discussion and Conclusion -- References -- Section II: Electron Correlation in Atomic Systems -- Chapter Ten: Atomic Electronic Structure Computations With Hylleraas-CI Wave Functions -- 1. Introduction -- 2. Wave Functions and Potential-Energy Matrix Elements -- 2.1. One-Electron Integrals -- 2.2. Hylleraas Two-Electron Integrals -- 2.3. Exponentially Correlated Two-Electron Integrals -- 3. General Methods for Exponential Correlation -- 4. Hylleraas Integrals -- 5. Unlinked Three- and Four-Electron Integrals -- 6. The Auxiliary Two-Body Integrals gi -- 7. Check of K2 -- 8. Kinetic Energy -- 9. Kinetic Energy in Hylleraas-CI -- Appendix. Angular Momentum Formulas -- References -- Chapter Eleven: One-Particle Effective Potential for Helium Atom -- 1. Introduction -- 2. Preliminary -- 3. Construction of Basis Set -- 4. Eigen Equation and the Iterative Scheme -- 5. Results and Discussion -- 6. Conclusion -- Acknowledgments -- References -- Chapter Twelve: Configuration Interaction Study of the 3P Ground State of the Carbon Atom -- 1. Introduction -- 2. Configuration Interaction -- 3. Selection of Configurations -- 4. Calculations -- 5. Conclusions and Perspectives -- Acknowledgments -- References -- Further Reading -- Section III: Strong Correlation in Electronic Systems -- Chapter Thirteen: Extension of the Configuration Interaction Monte Carlo Method to Atoms and Molecules -- 1. Introduction -- 2. Method -- 2.1. CIMC Method -- 2.2. Importance Functions and Recursion Relations -- 2.3. Construction of the Single-Particle States -- 3. Results -- 3.1. Atoms -- 3.2. Molecules -- 4. Conclusions -- Acknowledgment -- References -- Chapter Fourteen: Time-Dependent Linear-Response Variational Monte Carlo -- 1. Introduction -- 2. Theory -- 2.1. Wave Function Parametrization -- 2.2. Linear Optimization Method -- 2.3. Linear-Response Theory.

2.4. Realization in VMC -- 2.5. Computational Details -- 3. Results -- 4. Conclusions and Perspectives -- Acknowledgments -- References -- Chapter Fifteen: Quantum Monte Carlo Calculations for Industrial Catalysts: Accurately Evaluating the H2 Dissociation Rea ... -- 1. Introduction -- 2. Setting Up the Model Geometries -- 3. QMC Methods -- 3.1. Complex Jastrow Factors: Testing Against Real Factors -- 3.2. Time-Step Bias, Other DMC Error Sources, and Specifications -- 4. Perspectives and Conclusions -- Acknowledgments -- References -- Chapter Sixteen: Density-Based Analysis of Spin-Resolved MP2 Method -- 1. Introduction -- 2. Computational Details -- 3. Methodology and Results -- 3.1. Proportionality of the Spin-Resolved MP2 Densities -- 3.2. Two-Dimensional Scan -- 3.3. Dipole Moments -- 4. Final Remarks -- Acknowledgments -- References -- Chapter Seventeen: Time-Dependent Configuration Interaction Using the Graphical Unitary Group Approach: Nonlinear Electri ... -- 1. Introduction -- 2. Theory -- 2.1. Configuration Interaction -- 2.2. Time-Dependent CI -- 2.3. Dynamic (Hyper)Polarizabilities -- 3. Results -- 4. Conclusions -- Acknowledgments -- References -- Chapter Eighteen: Hybrid Treatments Based on Determinant Seniority Numbers and Spatial Excitation Levels in the Configura ... -- 1. Introduction -- 2. Theory -- 2.1. Commutation Relations -- 2.2. Spin-Adapted Hybrid Methods -- 3. Results and Discussion -- 4. Concluding Remarks -- Acknowledgments -- References -- Chapter Nineteen: Potential Energy Curves for the LiK+ and NaK+ Molecular Ions With the Coupled Cluster Method -- 1. Introduction -- 2. Synopsis of the Theory -- 3. Results and Discussion -- 3.1. Atomic Calculations -- 3.2. LiK+ Molecular Ion -- 3.3. NaK+ Molecular Ion -- 4. Conclusions -- Acknowledgment -- References -- Index -- Back Cover.