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Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part A

Book Description

This volume presents a series of articles concerning current important topics in quantum chemistry.

  • Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology
  • Features detailed reviews written by leading international researchers

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
  6. Contributors
  7. Chapter One: Frank Harris, a Master of Mountains
    1. Abstract
  8. Chapter Two: System-Size Dependence in Grand Canonical and Canonical Ensembles
    1. Abstract
    2. 1 Introduction and Motivation
    3. 2 Canonical and Grand Canonical Ensembles and Their Thermodynamics
    4. 3 Thermodynamic Equivalence for Large Systems
    5. 4 Non-interacting, Homogeneous Systems at Finite System Size
    6. 5 Relationship to Density Functional Theory
    7. Acknowledgments
    8. A Appendix
  9. Chapter Three: The Mean Excitation Energy of Atomic Ions
    1. Abstract
    2. 1 Introduction
    3. 2 The Polarization Propagator and Mean Excitation Energy
    4. 3 Computational Details
    5. 4 Results
    6. 5 Discussion
    7. Acknowledgment
  10. Chapter Four: Hybrid Functionals with Variationally Fitted Exact Exchange
    1. Abstract
    2. 1 Introduction
    3. 2 Auxiliary Density Functional Theory
    4. 3 Variationally Fitted Exact Exchange
    5. 4 Computational Details
    6. 5 Validation
    7. 6 Timings
    8. 7 Conclusion
    9. Acknowledgments
  11. Chapter Five: The Hydrogen H2+ and HeH2 + Molecular Ions Confined in Dihedral Angles
    1. Abstract
    2. 1 Introduction
    3. 2 The Schrödinger Equation and its Exact Solutions Within the Born–Oppenheimer Approximation
    4. 3 The Hydrogen H2+ Molecular Ion
    5. 4 The HeH2 + Molecular Ion
    6. 5 Discussion and Conclusions
    7. Appendices
  12. Chapter Six: Angular Momentum Theory in Bases of Lamé Spheroconal Harmonics
    1. Abstract
    2. 1 Introduction
    3. 2 Symmetries in the Rotations of Asymmetric Molecules
    4. 3 Actions of Operators of Angular Momentum and Linear Momentum on Rotational Eigenstates
    5. 4 Discussion
    6. Acknowledgments
    7. Appendix
  13. Chapter Seven: The Fourier Space Restricted Hartree–Fock Method for the Electronic Structure Calculation of One-Dimensionally Periodic Systems
    1. Abstract
    2. 1 Introduction
    3. 2 Theoretical Background
    4. 3 Spatial Symmetry in Linear Chains
    5. 4 Computational Details
    6. 5 A Numerical Example
    7. 6 Conclusion
    8. Acknowledgments
  14. Chapter Eight: Generalized Response Theory for a Photoexcited Many-Atom System
    1. Abstract
    2. 1 Introduction
    3. 2 Equations of Motion for a Dissipative Dynamics
    4. 3 Optical and Photoconductivity Responses
    5. 4 Model Calculations of Steady States and Relaxing States at a Photoexcited Semiconductor Surface
    6. 5 Conclusions
    7. Acknowledgments
  15. Chapter Nine: Frank Discussion of the Status of Ground-State Orbital-Free DFT
    1. Abstract
    2. 1 Introduction
    3. 2 Qualitative Distinctions Among GGAs for torb
    4. 3 Positivity and Near-Origin Conditions
    5. 4 Empirical Exploration of the Limits of GGA KE
    6. 5 Summary Discussion
    7. Acknowledgments
  16. Chapter Ten: Statistical Inference with Minimum Relative Entropy: A Robust Numerical Algorithm Employing Sinc Quadrature
    1. Abstract
    2. 1 Introduction
    3. 2 Maximum Entropy Principle
    4. 3 Minimum Relative Entropy
    5. 4 Solving for the MRE Distribution
    6. 5 Sinc Quadrature
    7. 6 Employing Sinc Quadrature to Find MRE
    8. 7 Computation Results
    9. 8 Conclusion
    10. Acknowledgments
  17. Chapter Eleven: Computational Methods for Chemistry and Physics, and Schrödinger in 3 + 1
    1. Abstract
    2. 1 Introduction and Summary
    3. 2 Computational Methods in 1 D
    4. 3 Solving Partial Differential Equations
    5. 4 Space–Time Schrödinger's PDE in 3 + 1
    6. 5 Examples of Computations
  18. Chapter Twelve: Approximate Coherent States for Nonlinear Systems
    1. Abstract
    2. 1 Introduction
    3. 2 Harmonic Oscillator or Field Coherent States
    4. 3 Deformed Oscillators
    5. 4 Nonlinear Coherent States
    6. 5 Numerical Results
    7. 6 Discussion
    8. Acknowledgments
  19. Chapter Thirteen: Electronic Properties in Supercritical Fluids: The Absorption Spectrum of p-Nitroaniline in Supercritical Water
    1. Abstract
    2. 1 Introduction
    3. 2 Methodology
    4. 3 Results and Discussion
    5. 4 Summary and Conclusions
    6. Acknowledgment
  20. Chapter Fourteen: On a Hyperbolic Solution to the Nonlinear Schrödinger Equation for a Square Well Potential Coupled to a Contact Impurity at the Delocalization Threshold
    1. Abstract
    2. 1 Introduction
    3. 2 Ground State Analytic Solution
    4. 3 Full Width Half Maximum
    5. 4 Conclusions
    6. Acknowledgments
  21. Chapter Fifteen: Multiresolution Approach for Laser-Modified Collisions of Atoms and Ions
    1. Abstract
    2. 1 Introduction
    3. 2 Theory
    4. 3 Results
    5. 4 Concluding Remarks
    6. Acknowledgments
  22. Index