Fundamental World of Quantum Chemistry: A Tribute to the Memory of Per-Olov Löwdin, Volume 1Erkki 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. |
Contents
H Shull | 1 |
Notes 662 | 2 |
Macroscopic Quantum Tunneling a Natural OrbitalOccupation | 5 |
The Kind and Personal Influence of PerOlov Löwdin | 14 |
section measurements | 19 |
Notes 690 | 22 |
Hermitian quantum mechanics | 26 |
Löwdins Definition of a Molecule | 27 |
Discussion | 379 |
The Generalized Multistructural Wave Function GMS | 390 |
Conclusions | 393 |
Extending the Concept of Chemical Bond | 399 |
Hubac and S Wilson | 407 |
Reactions of Nitrous Oxide with Lithium and Copper | 408 |
B Roos P Å Malmqvist and L Cagliardi | 425 |
BrillouinWigner Perturbation Theory and the ManyBody Problem | 426 |
References | 32 |
E R Scerri | 34 |
Conclusions 177 | 36 |
The Born Oppenheimer Approximation and the Potential Energy | 52 |
Linear JahnTeller Systems | 54 |
References 692 | 63 |
Stuber and J Paldus | 67 |
Löwdins Remarks on the Aufbau Principle and a Philosophers | 68 |
HF Equations and Thouless Stability Conditions | 75 |
Index 695 | 81 |
Classification of BrokenSymmetry Solutions | 85 |
Symmetry Restricted HF Equations and Stability Conditions | 92 |
Applications | 106 |
O E Alon and L S Cederbaum | 117 |
Concluding Remarks | 123 |
B SpinIndependent Matrix Elements | 130 |
SymmetryBased Factorization of the OSGF | 132 |
F A Matsen | 141 |
Triplet States | 145 |
Analytical Continuation of the OSGF | 147 |
What do the terms Ab Initio and First Principles Really Mean | 151 |
Multichannel QuantumClassical Diffusion Equations 181 | 155 |
Catalysis | 161 |
The Spin Projection Operator | 171 |
The Crossed Beam Experiment | 174 |
The Pauli Exclusive Principle SpinStatistics Connection | 183 |
QuantumClassical Reduction of the Dynamical Operator | 184 |
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 |
TwoChannel Diffusion Equations in the Adiabatic Case | 201 |
Some Contradictions with the Concept of Particle Identity and Their | 204 |
Conclusion | 207 |
Field Energy Density | 213 |
Concluding Remarks | 215 |
Srivastava | 221 |
Computations | 228 |
Conclusion | 235 |
J P Dahl | 237 |
P Fulde | 241 |
PhaseSpace Dynamics | 244 |
Generalized PositionSpace Densities | 246 |
Examples | 247 |
A Nicolaides | 253 |
Gaussian Wave Packet in Two Dimensions | 254 |
Cuprate Layers Electrons and OffDiagonal LongRange Order | 260 |
Harmonic Polynomials Hyperspherical Harmonics and Sturmians | 261 |
Generalized angular momentum | 267 |
The standard tree | 273 |
Gegenbauer polynomials | 280 |
Essentials of the SSA for the Calculation and Use of Correlated | 282 |
The manycenter oneelectron problem | 286 |
References | 294 |
Intermediate Exciton Theory for the Electronic Spectra | 297 |
Sturmian Basis Sets for Atomic and Molecular Calculations | 300 |
W P Reinhardt and H Perry | 305 |
Further Remarks and Conclusions | 313 |
coherent states and natural orbitals | 319 |
Discontinuous Derivative Problem | 327 |
The Tunneling Problem | 331 |
Number Analysis | 341 |
Molecular Structure and Matrix Manipulation | 349 |
Acknowledgment | 367 |
Discussion | 369 |
Independent Particle Models | 372 |
Mühlhäuser and S D Peyerimhoff | 377 |
S R Gwaltney G J O Beran and M HeadGordon | 433 |
Summary | 438 |
Examples | 441 |
Excited States? | 449 |
Potential Energy Surfaces | 452 |
105 | 456 |
R McWeeny | 459 |
G Berthier M Defranceschi and C Le Bris | 467 |
Symmetry Considerations | 470 |
Acknowledgments | 480 |
References | 484 |
Geometric Formulation | 490 |
Reduction and Invariant Subspaces | 504 |
Method Evaluation | 505 |
Spin Labels | 515 |
R Lefebvre and B Stern | 516 |
Densities | 519 |
O Dolgounitcheva V G Zakrzewski and J V Ortiz | 525 |
Summary | 535 |
Results | 548 |
Conclusions | 552 |
Ionization of WatsonCrick Base Pairs | 559 |
The Multichannel Wave Function of the Hydrogen Atom | 560 |
Kth Order Approximations for States | 563 |
Cationization of WatsonCrick Base Pairs | 567 |
Conclusions | 576 |
The Fundamental Optimization Theorem | 579 |
Concluding Remarks | 582 |
584 | |
A J Thakkar and T Koga Analytical HartreeFock Wave Functions for Atoms and Ions | 587 |
Singlezeta Wave Functions | 588 |
First the Elementary Approach 680 | 589 |
Doublezeta Wave Functions | 590 |
Near HartreeFock Wave Functions | 591 |
Heavy Atoms | 595 |
Other Recent Work | 596 |
Summary | 597 |
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 |
Comparison of Analytic Perturbative Results and Numerical | 607 |
The Scaling Factor for Atomic Systems | 608 |
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 |
Validation of the Decomposition Ec Za Eca +4Ec | 616 |
Van der Waals Interactions | 617 |
A Final Word | 618 |
Conclusions | 619 |
Acknowledgment | 620 |
627 | |
P Politzer Some Exact Energy Relationships | 631 |
Molecular Energies | 632 |
Interaction Energies | 635 |
Discussion and Summary | 636 |
Classical Orbits of Valence Electrons in Atoms | 640 |
Effective OneElectron Potential in Atoms | 647 |
Conclusion | 651 |
Dedication | 653 |
Conclusion | 660 |
Contour Integration | 665 |
675 | |
Common terms and phrases
angular momentum antisymmetric approximation atoms basis set boson calculations coefficients complex components computed considered coordinates correlation energy corresponding Coulomb Hamiltonian defined density matrix diagonal diagrams Dirac e.g. Ref eigenfunctions eigenstates eigenvalues eigenvectors electrons expression fermion Fock matrix follows formulation Fukutome Gel'fand GHF solutions given Hamiltonian Hartree-Fock HF equations HF-CC identical particles integrals interaction Kryachko linear matrix elements method molecular orbitals molecule MSOS nuclear nuclei obtained one-electron operator orthogonal orthonormal overlap pairing theorem Paldus parameters Pauli Per-Olov Löwdin permutation symmetry perturbation theory Phys physical polynomial properties Quantum Chem quantum chemistry quantum mechanics quantum numbers quasiparticles reduced density representation respectively ROHF Sanibel Schrödinger equation singlet space spectrum spin orbitals stability conditions structure Sturmian subgroup subspace Table tion transformation translationally invariant unitary variation vectors wave function wavefunction Wigner zero