Advances in Quantum Chemistry: Lowdin Volume

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Advances in Quantum Chemistry: Lowdin Volume presents a series of articles exploring aspects of the application of quantum mechanics to atoms, molecules, and solids.

Celebrates Per-Olov Lowdin, who would have been 100 in 2016
Contains papers by many who use his ideas in theoretical chemistry and physics today

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Front Cover 2
Löwdin Volume 5
Copyright 6
Contents 7
Contributors 13
Preface 15
Chapter One: Per-Olov Löwdin 17
- Acknowledgments 23
- References 23
Chapter Two: From Numerical Orbitals to Analytical Ones and Back 25
- 1. Introduction 25
- 2. Exponentials 27
- 3. General Bases on One-Dimensional Domains 30
- 4. Momentum Space Representations 33
- 5. Mixed Representations 39

Front Cover 2
Löwdin Volume 5
Copyright 6
Contents 7
Contributors 13
Preface 15
Chapter One: Per-Olov Löwdin 17
- Acknowledgments 23
- References 23
Chapter Two: From Numerical Orbitals to Analytical Ones and Back 25
- 1. Introduction 25
- 2. Exponentials 27
- 3. General Bases on One-Dimensional Domains 30
- 4. Momentum Space Representations 33
- 5. Mixed Representations 39
- 6. Four-Component Spinorbitals 42
- 7. Epitome 44
- References 46
Chapter Three: The Time-Dependent Variational Principal in Quantum Mechanics and Its Application 49
- 1. Basic Equations 49
- 2. Coherent States 53
  - 2.1. Gaussian Wave Packet as a Coherent State 54
    - 2.1.1. Gaussian Wave Packet with Evolving Width 58
  - 2.2. The Determinant Coherent State for N Electrons 64
- References 67
Chapter Four: Specifics on the Scientific Legacy of Per-Olov Löwdin 69
- 1. Introduction 70
  - 1.1. Two Educational Systems: Summer and Winter Institutes 70
  - 1.2. Quantum Chemistry Would Come of Age Within Ten Years' Notice 71
  - 1.3. Preview of Present Status of Some of Löwdin´s Themes and Thoughts 72
- 2. At the Early QTP 74
  - 2.1. Lost with Lower Bounds 75
  - 2.2. Further Lost with Projected Hartree–Fock 75
  - 2.3. CI at QTP 76
- 3. Projection Operators 78
  - 3.1. Partitioning of Degenerate Spaces 79
- 4. Fast-Converging CI Expansions 80
  - 4.1. Natural Orbitals 80
  - 4.2. Ergonals 81
- 5. Nearing Full CI with Truncation Energy Errors 82
  - 5.1. Dick Brown´s Formula for Configurational Energy Contributions 83
  - 5.2. SCI with Truncation Energy Error 84
  - 5.3. Role of Projectors and NOs in SCI with Truncation Energy Error 84
- 6. Unambiguous Dirac-Type Calculations 85
  - 6.1. Ambiguity of Perturbative Quantum Electrodynamics for Bound States 85
  - 6.3. Variational Theorem for Relativistic Bound States 87
  - 6.2. Variational Theorem for Nonrelativistic Bound States 87
  - 6.4. What Is Wrong with the Brown–Ravenhall Paper? 90
  - 6.5. Joe Sucher´s Folk Theorem Is Wrong 90
  - 6.6. Optimal Decoupling of Positive- and Negative-Energy Orbitals 91
- 7. Final Remarks 92
- References 93
- Acknowledgments 93
Chapter Five: Time-Dependent Perturbation Theory with Application to Atomic Systems 99
- 1. Introduction 100
- 2. Standard Time-Independent Perturbation Theory 100
  - 2.1. Nondegenerate and Degenerate Theory 100
  - 2.2. Quasi-Degenerate Theory 102
  - 2.3. Linked-Diagram Theorem 103
- 3. Relativistic and QED Effects 104
- 4. Time-Dependent Perturbation Theory 105
  - 4.1. The Time-Evolution Operator 105
  - 4.2. The Electron Propagator 106
  - 4.3. The S-Matrix 107
  - 4.4. The Green´s Function 107
  - 4.5. The Covariant Evolution Operator 108
  - 4.6. Single-Photon Exchange 109
  - 4.8. Green´s Operator 112
  - 4.7. Gell-Mann–Low Theorem 112
  - 4.9. Time Dependence of the Green´s Operator 114
- 5. QED and Electron Correlation 116
  - 5.1. Nonradiative QED in Combination with Electron Correlation 116
  - 5.2. Radiative QED Effects in Combination with Electron Correlation 117
- 6. Concluding Remarks 119
- Acknowledgments 120
- References 120
Chapter Six: Quantum Partitioning Methods for Few-Atom and Many-Atom Dynamics☆ 123
- 1. Introduction 124
- 2. Molecular Effective Potentials and Long-Lived States from Partitioning Methods 125
  - 2.1. Partitioning of the Functional Space of Molecular States 125
  - 2.2. Partitioning the Wave Operator 127
  - 2.3. Projection Operators for Molecular Effective Potentials 129
  - 2.4. Projection Operators for Long-Lived States 133
- 3. Dissipative Many-Atom Dynamics from Partitioning Methods 136
  - 3.1. Contracted Density Operator from a Partitioned Functional Space 137
  - 3.2. Reduced Density Operator from a Partitioned Physical Space 138
- 4. Conclusions 141
- Acknowledgments 142
- References 142
Chapter Seven: Vibrational Quantum Squeezing Induced by Inelastic Collisions 145
- 1. Introduction 146
- 2. Algebraic Form of the Landau–Teller Model 149
- 3. Squeezing Coherent States 152
- 4. Squeezing from an Initial Thermal Distribution 157
- 5. Discussion 161
- Acknowledgments 162
- References 162
Chapter Eight: Resonances in the Continuum, Field-Induced Nonstationary States, and the State- and Property-Specific Trea ... 165
- 1. Quantum Chemistry and Many-Electron Problems in the High-Lying Portions of the ``Excitation Axis´´ 167
- 3. State- and Property-Specific Quantum Chemistry 170
- 2. Topics 170
- 4. Backgrounds 172
  - 4.1. Topic I: Field-Free Resonance States and the MEP 173
  - 4.2. Topics II and III: Ground or Excited States Perturbed by Strong Static or Periodic or Pulsed Fields, and the Nonpert ... 174
    - 4.2.1. Topic II: Complex-Energy Variational Methods for Static and Periodic Strong Fields 175
    - 4.2.2. Topic III: ``Grid´´ Methods 177
  - 5. Overview and Elements of the SPS Theory on Topics I, II, and III 178
    - 5.1. Topic I 178
      - 5.1.1. Decaying-State Theory as Framework for the Description of N-Electron Resonance States 180
      - 5.1.2. Essentials of the SPS Approach 182
      - 5.1.3. The Complex Eigenvalue Schrödinger Equation 186
      - 5.1.4. Exterior Complex Scaling and Analytic Continuation Involving the Asymptotic Region 188
    - 5.2. Topic II 189
      - 5.2.1. Field-Induced Resonances from Analytic Continuation of Large-Order Perturbation Series 189
    - 5.3. Topic III 190
  - 6. Epilogue 191
  - Acknowledgments 192
  - References 192
- Chapter Nine: High-Temperature Superconductivity in Strongly Correlated Electronic Systems 199
  - 1. Per Olov Löwdin 200
  - 2. Introduction to Superconductivity 200
  - 3. The Pairing Instability in Classical and High-Temperature Superconductors 202
  - 4. ODLRO in Superconductors 205
  - 5. The Bohm-Pines Hamiltonian 209
    - 5.1. The Short-Range Hamiltonian Hsr 211
    - 5.2. Long-Range Hamiltonian and Plasma Oscillations 212
  - 6. Total Hamiltonian 212
  - 7. Choice of Localized Basis Functions and Summary of Group Theoretical Analysis of Cuprate Superconductor Real-Space Con ... 213
  - 8. The Superconducting Ground State 215
  - 9. Condensate Wave Functions 219
  - 10. Role of Electron Correlation 221
  - References 222
- Chapter Ten: Quantum Chemistry and Superconductors 225
  - 1. Introduction 226
  - 2. Coupling and Localization 228
  - 3. The Hubbard Gap and the Absorption Spectrum of Transition Metal Oxides 230
  - 4. Wave Functions and Conductivity in the Local State 235
  - 5. Organic SC 236
  - 6. Tungsten and Molybdenum Bronzes 238
  - 7. Conclusion 239
  - Acknowledgments 240
  - References 240
- Chapter Eleven: State-Quantum-Chemistry Set in a Photonic Framework 243
  - 1. Photon q-States: Fock Space 246
  - 2. Basic Photonic Scheme 247
    - 2.1. Reading q-States 248
  - 3. Abstract and Laboratory Spaces: Linking/Relating Systems 249
    - 3.1. Role of Configuration Space 249
    - 3.2. Frequency–Time Regime 250
  - 4. Quantum Physics of Tonomura Double-Slit Experiment 251
    - 4.1. A Century Later 252
  - 5. One-Photon Initiated Quantum Physical Processes 253
    - 5.1. Opening Access to Spin-Triplet States: Optically Assisted Way 254
    - 5.2. Photon Upconversion: Triplet–Triplet Two-Photon Interactions 256
  - 6. Probe Through X-Ray and Higher Frequency Photon States 257
  - 7. Chemistry from a Photonic Quantum Physical Perspective 259
    - 7.1. Dissociation Competition 262
  - 8. Information Transfers 262
  - 9. Discussion 264
  - Acknowledgments 266
  - References 266
- Chapter Twelve: Quantum Chemistry with Thermodynamic Condition. A Journey into the Supercritical Region and Approaching t ... 269
  - 1. Introduction 270
  - 2. Short Review of Some Molecular Studies in the Supercritical Region 271
  - 3. Supercritical Ar and the Vicinities of the Critical Point 273
  - 4. Summary and Conclusions 277
  - Acknowledgments 278
  - References 278
- Chapter Thirteen: Electron Propagator Theory: Foundations and Predictions 283
  - 1. Introduction 284
  - 2. Poles and Residues of the Electron Propagator 285
  - 3. Derivation of the Dyson Quasiparticle Equation 287
  - 4. Approximations in the Dyson Quasiparticle Equation 291
  - 5. Test Calculations 307
  - 6. Recent Applications and Extensions 309
  - 7. Conclusions and Prospects 310
  - References 311
- Chapter Fourteen: Cognition of Learning and Memory: What Have Löwdin´s Orthogonalizations Got to Do With That? 315
  - 1. Introduction 315
  - 2. Recapitulation of Orthogonalization Schemes 320
  - 3. Numerical Demonstration 323
  - 4. A Model for Neuronal Network 328
  - 5. Adaptation to Cognitive Memory 331
  - References 334
  - 6. In Sum 334
  - Acknowledgment 334
- Chapter Fifteen: Ab Initio Complex Potential Energy Surfaces From Standard Quantum Chemistry Packages 337
  - 1. Motivation and Difficulties in Calculating CPES 338
  - 2. Ab Initio CPES by Using Existing and Modified SQCPs—A Brief Overview 341
    - 2.1. Complex Absorbing Potentials 341
    - 2.2. Reflection-Free CAPs 343
    - 2.3. Uniform Complex Basis Functions 344
    - 2.4. Partial CBFs—Scaling Only the Diffuse Basis Functions 345
    - 2.5. Summary 346
  - 3. CPES From SQCPs—Recent Developments 346
    - 3.1. CPES by Removing (CAPs) via Padé43 346
    - 3.2. CPES From a Single Stabilization Graph 350
      - 3.2.1. The TCP Method 352
      - 3.2.2. The RVP Method 353
      - 3.2.3. Proof of Concept—Autoionization Feshbach Resonance of the Hydrogen Molecule by the RVP Method 354
      - 3.2.4. CPES for Cold Collisions 354
      - 3.2.5. Summary 356
    - 4. Concluding Remarks 356
    - Acknowledgments 358
    - References 359
  - Chapter Sixteen: High-Resolution Quantum-Mechanical Signal Processing for in vivo NMR Spectroscopy 363
    - 1. Introduction 365
      - 1.1. Why Are the Current Signal Processing Methods Within MRS of Limited Value? 368
      - 1.2. Advanced Signal Processing Method in MRS: Why Is the FPT Equivalent to Quantum-Mechanical Spectral Analysis? 369
    - 2. Methods 373
      - 2.1. Acquisition of MRS Time Signals 373
      - 2.2. Reconstructions 374
        
        2.2.1. Nonparametric Reconstructions Through the DFT and the FPT 374
        
        2.2.2. Parametric Signal Processing via the FPT(+) 375
      - 3. Results 378
        
        3.1. The Encoded MRS Time Signals 378
        
        3.3. Iterative Averaging of Envelopes Through the FPT 380
        
        3.2. Comparison of Total Shape Spectra Reconstructed by the DFT and Nonparametric FPT 380
        
        3.4. Parametric Reconstruction (Quantification) Through the FPT 388
      - 4. Discussion and Conclusions 391
      - Acknowledgments 394
      - References 394
    - Index 397
    - Back Cover 409

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