## 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 Sutcliffe | 21 |

One and Two Particle States | 30 |

A C Nascimento and A G H Barbosa | 371 |

IPM Wavefunctions with the Correct Symmetries | 377 |

method | 382 |

The Generalized Multistructural Wave Function GMS | 390 |

O Tishchenko E S Kryachko and M T Nguyen | 393 |

Extending the Concept of Chemical Bond | 399 |

Summary and conclusion | 400 |

QED Effects in Heavy Elements | 407 |

The Spectrum of the Coulomb Hamiltonian | 31 |

Conclusions | 41 |

The Born Oppenheimer Approximation and the Potential Energy | 52 |

Complex Extensions of Some Real Lie Algebras | 61 |

Dedication | 62 |

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

Stuber and J Paldus | 68 |

HF Equations and Thouless Stability Conditions | 75 |

A General Supersymmetric Hamiltonian | 77 |

Excited States? 449 | 81 |

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 |

O E Alon and L S Cederbaum | 117 |

Concluding Remarks | 123 |

Acknowledgments | 126 |

P R Surján and A Szabados | 129 |

A Transformation Properties of the Unitary Group Generators 128 | 130 |

SymmetryBased Factorization of the OSGF | 132 |

F A Matsen | 141 |

Triplet States | 145 |

Analytical Continuation of the OSGF | 147 |

Using Noncanonical Orbital Energies in MBPT | 149 |

Catalysis | 161 |

Perturbation Corrections to Ionization Energies | 168 |

The Spin Projection Operator | 171 |

The Crossed Beam Experiment | 174 |

References 114 | 175 |

Conclusions | 177 |

The Pauli Exclusive Principle SpinStatistics Connection | 183 |

QuantumClassical Reduction of the Dynamical Operator | 184 |

Mayer and A Hamza | 186 |

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 |

Computations | 228 |

The Propagator or GreensFunction Method | 235 |

J P Dahl | 237 |

P Fulde | 241 |

Generalized PositionSpace Densities | 246 |

Pairing | 249 |

Excitation Spectra | 250 |

References 63 | 254 |

J Dunne and E J Brändas | 257 |

Earlier and More Recent Formulations | 258 |

J Avery | 261 |

Te for Superconducting Cuprates | 264 |

Generalized angular momentum | 267 |

J J Ladik | 271 |

R Krems and A Dalgarno | 273 |

Gegenbauer polynomials | 280 |

Collisions of XMolecules and SAtoms with Hyperfine Interaction | 286 |

References | 294 |

Intermediate Exciton Theory for the Electronic Spectra | 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 |

Conclusions | 319 |

Malli | 322 |

Discontinuous Derivative Problem | 327 |

The Tunneling Problem | 331 |

SgBr and SgBr | 337 |

Number Analysis | 341 |

Molecular Structure and Matrix Manipulation | 349 |

Relativistic DirackFock SCF Calculations for Molecules | 352 |

Conclusions | 359 |

Discussion | 369 |

Reactions of Nitrous Oxide with Lithium and Copper | 408 |

Acknowledgements | 420 |

B Roos PA Malmqvist and L Cagliardi | 425 |

BrillouinWigner Perturbation Theory and the ManyBody Problem | 426 |

S 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 |

PhaseSpace Dynamics 244 | 474 |

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

Acknowledgments | 480 |

References | 484 |

Application of Fractional Models in Drug Design | 489 |

Geometric Formulation 496 | 491 |

Integral Equations for Functions At and Bt | 504 |

Method Evaluation | 505 |

Spin Labels | 515 |

Acknowledgments | 518 |

Densities | 519 |

e LiH 537 | 521 |

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

The Method | 531 |

Details of Calculations | 535 |

Appendix | 537 |

Summary and Future Work | 539 |

Results and Discussion 529 | 551 |

J Bertran M Noguera and M Sodupe | 557 |

R Erdahl | 559 |

References | 560 |

Cationization of WatsonCrick Base Pairs | 567 |

The KSpectrum | 573 |

Trends in RO 3Scission in OpenShell Systems | 575 |

Conclusions | 576 |

The Fundamental Optimization Theorem | 579 |

Concluding Remarks | 582 |

References | 584 |

A J Thakkar and T Koga Analytical HartreeFock Wave Functions for Atoms and Ions | 587 |

Singlezeta Wave Functions | 588 |

Doublezeta Wave Functions | 590 |

Sequential Monte | 591 |

Heavy Atoms | 595 |

Other Recent Work | 596 |

Summary | 597 |

References | 598 |

E Clementi and G Corongiu The Origin of the Molecular Atomization Energy Explained With the HF and HFCC Models | 601 |

Introduction | 602 |

Scaling the HartreeFock Energy | 603 |

Analyses of the Correlation Energy from Experiments and HF Computations | 604 |

The Scaling Factor for Atomic Systems | 608 |

Aziridine Isotope Effects | 609 |

Scaling Factor for an Atom in a Molecular System | 610 |

Validation of the Molecular Scaling Functional | 612 |

The Correlation Energy from HFCC and HF Computations | 614 |

616 | |

Van der Waals Interactions | 617 |

A Final Word | 618 |

Conclusions 619 | 620 |

References | 627 |

properties of the model catalysts | 628 |

P Politzer Some Exact Energy Relationships | 631 |

Molecular Energies | 632 |

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 | |