Conceptual Perspectives in Quantum Chemistry

edited by

Jean-Louis Calaisf

and

Eugene Kryachko Bogoliubov Institute for Theoretical Physics,

Kiev, Ukraine

KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

CONTENTS

Foreword xv

Recent Developments In Multiple Scattering Theory And Density Functional Theory For Molecules And Solids

R. K. Nesbet

1. Introduction 1 2. Multiple Scattering Theory 3

2.1. Full-Potential Theory 4 2.2. Angular Momentum Representation 6 2.3. Surface Matching Theorem 8 2.4. Surface Integral Formalism 10 2.5. Atomic Cell Orbitals 14

3. Variational Principles 14 3.1. Kohn-Rostoker Variational Principle 15 3.2. Schlosser-Marcus Variational Principle 16

4. Wave Functions at Cell Boundaries 19 4.1. Wave Functions in the Near-Field Region 20 4.2. Convergence of Internal Sums 22

5. Green Functions 26 5.1. Definitions 26 5.2. Properties of the Green Function 29 5.3. Construction of the Green Function 30 Computational Theory 34 6.1. Basis Functions 34 6.2. Linearized Methods 36 6.3. Canonical Scaling 40 6.4. Poisson Equation 42 Density Functional Theory 44 7.1. Reference-State Density Functional Theory 45 7.2. Variation of Occupation Numbers 49 7.3. Self-Interaction Corrections 52

Acknowledgments 55 References 55

Localized Atomic Hybrids: A General Theory

G. G. Hall and D. Rees

1. Introduction 2. Use of Symmetry

2.1. Tetrahedral Example 2.2. Use of Group Theory

3. Basis Space 4. Sample Space 5. Alias Functions

5.1. Operator Alias Functions 5.1.1. Square hybrids 5.2. Basis Alias Functions

6. Example of Hybrids 6.1. Octahedral Hybrids 6.2. The Cubic Hybrids 6.3. Other Hybrids

7. Localization 7.1. Properties of Localized Hybrids

8. Several Equivalent Sets 8.1. Radial Eigenfunctions 8.1.1. Five function example 8.1.2. Eleven function example 8.2. General Comments

9. Quadrature lO.Calculation of Molecular Properties References

Quantum Electrodynamics And Molecular Structure Molecular Electrodynamics

R. G. Woolley

1. Introduction

CONTENTS vu

2. Quantum Mechanics of the Spectroscopic Experiment 3. The Electrodynamics of Molecules

3.1. Gauge Transformations 3.2. The General Hamiltonian 3.3. The Coulomb Gauge Theory 3.4. Polarization Fields 3.5. Scattering at High Energies

4. Electron-Molecule Scattering 5. Photon-Molecule Scattering; the Kramers-Heisenberg Formula 6. Discussion 7. References

94 97 97

100 103 105 108 109 115 119 123

Aspects Of The Chemical Bond 1996

J. F. Ogilvie 127

1. Introduction 127 2. Ionic Materials 127 3. Application of an Alternative Approach to Inorganic Structures 133 4. Mechanisms of Reactions 138 5. Conclusion 141 References 142

Lie Symmetries In Quantum Mechanics

D. R. Truax 145

1. Introduction 145 2. Lie Symmetries 147

2.1. Real Schrödinger Algebras, (SA)N 147 2.2. Complexification of (SA)N 151 Solutions to the Time-Dependent Schrödinger Equation 155 3.1. Systems in One Dimension 155 3.2. Systems in Two Dimensions 159 3.3. Comments 165

4. Coherent States 166

vm

5. Examples 5.1. Harmonie Oscillator 5.1.1. One dimension 5.1.2. Two dimensions 5.2. Driven Harmonie Oscillator 5.2.1. One dimension 5.2.2. Two dimensions

6. Transformation of the Schrödinger Equation 6.1. A Velocity Dependent Potential 6.2. Spinless Particle in an Electromagnetic Field

Acknowledgement Appendix I References

The Interplay Between Quantum Chemistry And Molecular Dynamics Simulations

S. M. Kost, J. Brickmann, and R. S. Berry

1. Introduction 2. Molecular Dynamics Simulations

2.1. Principles 2.2. Constant Temperature Simulations 2.2.1. General outline 2.2.2. Finite-mass stochastic collision dynamics 2.3. Constant Pressure Stimulations 2.4. Forces by Electronic Structure Theory 2.4.1. Ab initio molecular dynamics 2.4.2. Hybrid QM/MM methods

3. Aspects of Parametrization 3.1. General Remarks 3.2. Optimal Simulated Annealing 3.3. Extended Systems Revisited 3.4. Examples 3.4.1. Lennard-Jones parameters from quantum chemical data 3.4.2. Ab initio data and thermal averages

4. Conclusions 5. Acknowledgements 6. References

CONTENTS ix

The Permutation Group In Many-Electron Theory

S. Rettrup 225

1. Introduction 225 2. The Electronic Schrödinger Equation 226

2.1. Permutation Symmetry 227 2.2. The Pauli Principle 228 2.3. N-Electron Spin Eigenfunctions 229 2.4. Spin-Free Quantum Chemistry 230

3. Approximate N-Electron Functions 232 3.1. Configuration State Functions 233 3.2. Matrix Elements 235

4. Concluding Remarks 236 5. Acknowledgment 237 References 237

New Developments In Many Body Perturbation Theory And Coupled Cluster Theory

D. Cremer and Z. He 239

1. Introduction 239 2. Moller-Plesset Perturbation Theory 243

2.1. Derivation of the Moller-Plesset Correlation Energy at Lower Orders 244 2.2. Derivation of M0ller-Plesset Correlation Energies in Terms of Two-Electron Integral Formulas 252 2.3. Correlation Effects Covered at Various Orders of M0ller-Plesset Perturbation Theory 260

3. M0ller-Plesset Perturbation Theory at Sixth Order 262 3.1. Derivation of a Sixth Order Energy Formula in Terms of Cluster Operators 264 3.2. Setting Up Two-Electron Integral Formulas 270 3.3. Implementation and Testing of a MP6 Computer Program 275

X CONTENTS

3.4. Comparison of MP6 and Füll CI Correlation Energies 277 4. Coupled Cluster Theory 278

4.1. The Projection Coupled Cluster Approach 279 4.2. The Quadratic CI Approach - an Approximate Coupled Cluster Method 283

5. Analysis of Coupled Cluster Methods in Terms of Perturbation Theory 285 5.1. Expansion of CC Methods to Higher Orders of Perturbation Theory 288 5.2. Comparison of CCSD and QCISD 290 5.3. Comparison of CCSD(T) and QCISD(T) 295

6. Coupled Cluster Methods with Triple Excitations 297 6.1. Implementation of a Coupled Cluster Singles, Doubles, and Triples Method: CCSDT 298 6.2. Development of a QCI Method With Single, Double, and Triple Excitation: QCISDT 301 6.3. Analysis of CCSDT and QCISDT 307 6.4. Implementation and Application of QCISDT 310

7. Conclusions and Outlook 313 8. Acknowledgements 314 9. References 315

A Philosopher's Perspective On The "Problem" Of Molecular Shape

J. L. Ramsey

1. Introduction 2. A Physical Account of Shape 3. Interlude: Exactly Which Concept of Shape is Being Challenged? 4. Reduction and Explanation 5. Realism, Physicalism and Materialism 6. Conclusion Acknowledgements Endnotes References

319

319 320 322 323 327 330 332 332 334

CONTENTS XI

Van Der Waals Interactions From Density Functional Theories: The He-CO System As A Case Study

F. A. Gianturco and F. Paesani 337

1. Introduction 337 2. An Outline of Interaction Contributions 339 3. The Density Functional Approach 342 4. An Overview of Earlier Studies on the He-CO Interaction 345

4.1. A Comparison of the Latest PES 348 5. DFT Calculations of the Interaction 350

5.1. The Effects of DFT Exchange and Correlation 352 5.2. The Post-Hartree-Fock Treatments 360 5.3. Comparing DFT and ab Initio TKD Results 364 5.4. DFT Results Versus a Multiproperty Potential 368 5.5. DFT Results Versus a Spectroscopic Potential 370

6. Summary and Conclusions 373 7. Acknowledgements 376 References 376

Different Legacies and Common Aims: Robert MuUiken, Linus Pauling And The Origins Of Quantum Chemistry

A. Simöes and K. Gavroglu 383

Part I 384 Part II 392 Notes 406