## Fundamental World of Quantum Chemistry: A Tribute to the Memory of Per-Olov Löwdin, Volume 3Erkki J. Brändas, Eugene S. Kryachko Per-Olov Löwdin's stature has been a symbol of the world of quantum theory during the past five decades, through his basic contributions to the development of the conceptual framework of Quantum Chemistry and introduction of the fundamental concepts; through a staggering number of regular summer schools, winter institutes, innumerable lectures at Uppsala, Gainesville and elsewhere, and Sanibel Symposia; by founding the International Journal of Quantum Chemistry and Advances in Quantum Chemistry; and through his vision of the possible and his optimism for the future, which has inspired generations of physicists, chemists, mathematicians, and biologists to devote their lives to molecular electronic theory and dynamics, solid state, and quantum biology. Fundamental World of Quantum Chemistry: Volumes I, II and III form a collection of papers dedicated to the memory of Per-Olov Löwdin. These volumes are of interest to a broad audience of quantum, theoretical, physical, biological, and computational chemists; atomic, molecular, and condensed matter physicists; biophysicists; mathematicians working in many-body theory; and historians and philosophers of natural science. The volumes will be accessible to all levels, from students, PhD students, and postdocs to their supervisors. |

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### Contents

G G Hall | 1 |

Independent Particle Models 372 | 3 |

Macroscopic Quantum Tunneling a Natural OrbitalOccupation | 5 |

Hermitian quantum mechanics 26 | 7 |

The Swedish Doorman Poem by W Shull | 14 |

Conclusions | 16 |

R G Woolley and B T Sutclife | 21 |

Lowdins Definition of a Molecule | 27 |

Acknowledgements | 320 |

Malli | 323 |

Discontinuous Derivative Problem | 327 |

The Tunneling Problem | 331 |

SgBr and SgBr | 337 |

Number Analysis | 341 |

Molecular Structure and Matrix Manipulation | 349 |

RfCl4 | 352 |

One and Two Particle States | 30 |

Conclusions | 31 |

Symmetry in the Coulomb Hamiltonian | 36 |

Conclusions | 41 |

The Born Oppenheimer Approximation and the Potential Energy | 52 |

Problems in Two Space Variables | 54 |

Complex Extensions of Some Real Lie Algebras | 61 |

Dedication | 62 |

Lie Symmetry and the Geometric Phase effect in JahnTeller Systems | 63 |

R Kibler and M Daoud | 67 |

HF Equations and Thouless Stability Conditions | 75 |

A General Supersymmetric Hamiltonian | 77 |

Excited States? 449 | 81 |

A Fractional Supersymmetric Oscillator | 83 |

Classification of BrokenSymmetry Solutions | 85 |

Differential Realizations | 86 |

Symmetry Restricted HF Equations and Stability Conditions | 92 |

A Nicolaides | 93 |

Definition of the Atomic SpectralProduct Basis | 99 |

The Interaction of the ElectroMagnetic Field with HighN Rydberg | 100 |

Applications | 106 |

R Lefebvre and B Stern | 107 |

Concluding Remarks | 113 |

Conclusion | 114 |

E Alon and L S Cederbaum | 117 |

Concluding Remarks | 123 |

The OneParticle OpenShell Green Function | 124 |

Acknowledgments | 126 |

P R Surjdn and A Szabados | 129 |

B SpinIndependent Matrix Elements | 130 |

SymmetryBased Factorization of the OSGF | 132 |

Scattering from OpenShell ManyBody Targets | 139 |

F A Matsen | 141 |

Triplet States | 145 |

Analytical Continuation of the OSGF | 147 |

Using Noncanonical Orbital Energies in MBPT | 149 |

References | 153 |

Lindgren | 154 |

Catalysis | 161 |

Perturbation Corrections to Ionization Energies | 168 |

The Spin Projection Operator | 171 |

The Crossed Beam Experiment | 174 |

References 114 | 175 |

Conclusions | 177 |

G Kaplan | 183 |

QuantumClassical Reduction of the Dynamical Operator | 184 |

Mayer and A Hamza | 187 |

Parastatistics and Statistics of Quasiparticles in a Periodical Lattice | 190 |

QuantumClassical Reduction of the Relaxation Operator | 192 |

Indistinguishability of Identical Particles and the Symmetry Postulate | 198 |

The Expectation Value of the Electric Field at the Nuclei of a Molecule | 201 |

Some Contradictions with the Concept of Particle Identity and Their | 204 |

Conclusion | 207 |

Field Energy Density | 213 |

Comparison Between the ManyBody Perturbative and GreensFunction | 215 |

Srivastava | 221 |

MBPT Treatment of a Single Electron Outside Closed Shells | 225 |

Computations | 228 |

The Propagator or GreensFunction Method | 235 |

Summary and Conclusion | 241 |

S Larsson | 247 |

Conclusions | 253 |

Conclusion | 254 |

Earlier and More Recent Formulations | 258 |

Cuprate Layers Electrons and OffDiagonal LongRange Order | 260 |

Avery | 261 |

Illustration to Some of the Latest Achievements | 266 |

Generalized angular momentum | 267 |

R Krems and A Dalgarno | 273 |

Gegenbauer polynomials | 280 |

Collisions of SMolecules and 2SAtoms Without Hyperfine Interaction | 282 |

The manycenter oneelectron problem | 286 |

base stacks | 288 |

Summary | 290 |

References | 294 |

Preliminaries | 297 |

Sturmian Basis Sets for Atomic and Molecular Calculations | 300 |

The TwoState Model of SIN | 303 |

W P Reinhardt and H Perry | 305 |

Further Remarks and Conclusions | 313 |

The ManyState Model of SAI | 314 |

coherent states and natural orbitals | 319 |

Conclusions | 359 |

Acknowledgment | 367 |

Discussion | 369 |

The Intermediate Hamiltonian Method | 372 |

IPM Wavefunctions with the Correct Symmetries | 377 |

Superheavy Elements | 389 |

The Generalized Multistructural Wave Function GMS | 390 |

Tishchenko E S Kryachko and M T Nguyen | 393 |

Extending the Concept of Chemical Bond | 399 |

Summary and Conclusion | 400 |

Goidenko and L Labzowsky | 406 |

Hubac and S Wilson | 407 |

Reactions of Nitrous Oxide with Lithium and Copper | 408 |

Conclusion | 419 |

B Roos P A Malmqvist and L Cagliardi | 425 |

BrillouinWigner Perturbation Theory and the ManyBody Problem | 426 |

R Gwaltney G J O Beran and M HeadGordon | 433 |

De Facto Apparently Irreversible Molecular Dynamics | 434 |

Summary | 438 |

Examples | 441 |

Molecular Chirality and de lege Parity Violation Space Reflection | 448 |

Conclusions | 451 |

Potential Energy Surfaces | 452 |

R McWeeny | 459 |

A Personal Recollection | 464 |

G Berthier M Defranceschi and C Le Bris | 467 |

Symmetry Considerations | 470 |

Acknowledgement 391 | 471 |

J P Dahl | 474 |

F J Luque A BidonChanal J MunozMuriedas I Soteras C Curutchet | 475 |

Acknowledgments | 480 |

References | 484 |

Application of Fractional Models in Drug Design | 489 |

Geometric Formulation | 491 |

Integral Equations for Functions Amt and BmT | 504 |

Method Evaluation | 505 |

Spin Labels | 515 |

Acknowledgments | 518 |

Densities | 519 |

O Dolgounitcheva V G Zakrzewski and J V Ortiz | 525 |

The Method | 531 |

Details of Calculations | 535 |

Appendix | 537 |

S Mahalakshmi and D L Yeager | 547 |

Conclusion | 550 |

Results and Discussion 529 | 551 |

J Bertran M Noguera and M Sodupe | 557 |

Summary and Conclusions | 559 |

K1 Order Approximations for States | 563 |

Theoretical Procedures | 565 |

Cationization of WatsonCrick Base Pairs | 567 |

Trends in RX Bond Dissociation Energies in ClosedShell Systems | 571 |

Conclusions | 576 |

Conclusions | 578 |

The Fundamental Optimization Theorem | 579 |

Microsolvation | 584 |

A J Thakkar and T Koga | 587 |

Sequential Monte | 591 |

Heavy Atoms | 595 |

E dementi and G Corongiu | 601 |

The WeylWigner Representation 240 | 606 |

Hydrogen Bonding Detour to DNArt | 607 |

The Scaling Factor for Atomic Systems | 608 |

Aziridine Isotope Effects | 609 |

The Correlation Energy from HFCC and HF Computations | 614 |

Acknowledgments | 619 |

Acknowledgment | 620 |

Results and Discussion | 622 |

References | 627 |

N Ostrovsky | 631 |

Interaction Energies | 635 |

Discussion and Summary | 636 |

The role of the olefin on the catalytic activity and regioselectivity | 637 |

Classical Orbits of Valence Electrons in Atoms | 640 |

Effective OneElectron Potential in Atoms | 647 |

Conclusion | 651 |

Some Pertinent Problems Solved Long Ago or Just Recently | 653 |

Conclusion | 660 |

Notes | 662 |

665 | |

671 | |