Quantum Science: Methods and Structure. A Tribute to Per-Olov Löwdin PDF
Preview Quantum Science: Methods and Structure. A Tribute to Per-Olov Löwdin
QUANTUM SCIENCE METHODS AND STRUCTURE A Tribute to Per-Olov Lowdin PER-OLOV LOWDIN QUANTUM SCIENCE METHODS AND STRUCTURE A Tribute to Per-Olov Lowdin Edited by Jean-Louis Calais and Osvaldo Goscinski University of Uppsala Uppsala, Sweden Jan Underberg Aarhus University Aarhus, Denmark and Yngve Ohrn University of Florida Gainesville, Florida SPRINGER SCIENCE+BUSINESS MEDIA, LLC Library of Congress Cataloging in Publication Data Main entry under title: Quantum science. Includes index. 1. Quantum theory-Addresses, essays, lectures. 2. Lowdin, Per-Olov, 1916- 1. Lowdin, Per-Olov, 1916- II. Calais, Jean-Louis. QCI74.125.Q37 530.1'2 76-21354 ISBN 978-1-4757-1661-0 ISBN 978-1-4757-1659-7 (eBook) DOI 10.1007/978-1-4757-1659-7 © 1976 SpringerScience+Business Media New York Originally published by Plenum Press, New York in 1976 Softcover reprint of the hardcover 1s t edition 1976 AII rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface A "Festschrift" volume fulfils a more far-reaching purpose than the laudatory one. It shows how science develops as a result of the activities - scientific and organizational - of an individual person. Scientific achievement cannot be subjected to the very refined measurement techniques of science itself, but there is a continuous mutual evaluation among scientists which manifests itself through refereeing, literature citation and dedicatory volumes like the present one. Near and distant associates of Per-Olov Lowdin were enthusiastic about the idea of a tribute to him in the form of a collection of scientific papers on the occasion of his sixtieth birthday. Monographs and journals have fairly well-defined readerships. This book is directed to a wider group of scientists. It presents reviews of areas where Lowdin's work has influenced the development as well as research papers with original results. We feel that it can serve as a source on the current status of the quantum theory of matter for scientists in neighbouring fields. It might also provide stimulus for renewed scientific efforts among scientists turned administrators and will certainly be relevant for teachers and students of quantum theory. The organization of the contributions attempts to delineate the present frontiers in the research areas where students and associat es of Lowdin are working to implement his ideas or to develop new concepts in the re·ference frame he has provided. The first contri but ion is an appraisal and personal account of Per-Olov Lowdin from a close associate, and it is followed by a list of publications, and an analysis of the impact in the scientific literature. We have also found it appropriate to present here some previously unpublish ed material from the Summer Institute in Valadalen, where Lowdin and others made remarks of definite significance also some twenty years later. This is an example of the scientific climate which Lowdin creates twice a year in his unprecedented schools, workshops and symposia. There are some six contributions that are concerned with the overlap problem as it appears in molecules and solids. v vi PREFACE Related to these are three contributions to the theory of cohesion in crystals. Lowdin's unique contributions in the development of numerical procedures is stressed by Professor Slater and other contributors, while several formal aspects have been treated by others. Perturbation theory has' been a long time interest with Lowdin and is represented here by four papers, which in turn lead to the section on the electronic structure of atoms and molecules where both general and specific approaches to the correlation problem appear. The six contributions that end the volume are centered around biological applications of the theory and particular ly hydrogen bonds. The editors have been fortunate to be able to draw assistance from many interested parties and thanks are due to them. Anders Froman and Kimio Ohno have offered invaluable help and advice to us. The preparation of the photoready copy was in the hands of the indefatigable Mra Hanne Kirkegaard. Her fast and competent typing secured the completion of the volume in a minimum of time. The publishers have also supported the project beyond the pure business aspects. The emphasis on clear concepts, "decent" manipulations and the stubbornness not to have the easy way out are trademarks of Per Olov Lowdin. This has been and will be a continuous source of inspiration to very many. It is a privilege to express our warmest wishes to him on behalf of all his students, friends and colleagues. The Editors Contents Per-Olov Lowdin - Conqueror of Scientific, Educational and Rocky Mountains Kimio Ohno .•...•.......•.•......••.....•.........•... 1 Publications of Per-Olov Lowdin 1939-1976.................. 13 Per-Olov Lowdin in the Scientific Literature 1965-1974 Rolf Manne 25 Acta Valadalensia Revisited: Per-Olov Lowdin in Scientific Discussion Anders Froman and Osvaldo Goscinski................... 33 The Non-Orthogonality Problem and Orthogonalization Procedures Giuseppe del Re....................................... 53 Biorthonormal Bases in Hilbert Space Luc Lathouwers........................................ 77 Energy Weighted Maximum Overlap (EWMO) Jan Linderberg, Yngve Ohrn and Poui W. Thulstrup...... 93 The Calculation of the Exchange Parameter J = ~ (E. 1 t- E slng e triplet) for Two Equivalent Electrons using Canonical Molecular orbitals R.D. Harcourt......................................... 105 Importance of Overlap in the Analysis of Weak Exchange Inter actions by Perturbation Methods R. Block and L. Jansen................................ 123 Inelastic Scattering of Photons from Ionic Crystals and Effects of Overlap K. -F. Berggren........................................ 141 Some Comments on the Quantum-Mechanical Treatment of Defects ln Ionic Crystals Jean-Louis Calais..................................... 171 vii viii CONTENTS Properties of Compressed Atoms from a Spherical Cellular Model Anders Froman......................................... 179 Static and Dynamic Correlations in Many-Electron Systems Stig Lund<lvist........................................ 201 Power Series Method for Cellular Calculations on Atoms, Molecules and Solids J. C. Slater........................................... 215 Test of Conventional Quantum Chemistry Methods on the Hydro gen Atom T.L. Bailey and J.L. Kinsey........................... 249 Numerical Aspects of Weyl's Theory Michael Hehenberger................................... 265 Quantization and a Green's Function for Systems of Linear Ordinary Differential E<luations Harold V. McIntosh.................................... 277 On Resonant Potential Scattering M. Berrondo and G. Garcla-Calderon.................... 295 Laguerre Polynomials, Reminiscences from Uppsala L.B. Redei............................................ 305 Partitioning Techni<lue for Determinantal E<luations Frank Weinhold................. . . . • . • . . • • . • . . . . . . . . . . • 307 Lower Bounds to Energy Eigenvalues Charles E. Reid....................................... 315 Bounds to the Sum-rule Function from Inner-Projections Ragnar Ahlberg. . . . . . • . . . . . . . . . . . . . • . . . • • . . • . . . . . • • . • . . 349 Investigations into the Properties of Pro3ected Spin Functions Ruben Paunc z. . . • • . . . • . . . . • . . . . . • . . . . . • . • . . . . . . . . . . . . . . 357 Many-Body Theory of Molecular Collisions David A. Micha........................................ 367 On the Lowdin Bracketing Function Erkki Brandas.......................................... 381 Numerical Infinite-Order Perturbation Theory Rodney J. Bartlett and David M. Silver................ 393 Calculation of the Bromine Nuclear Pseudo<luadrupole Coupling Constant in the LiBr Molecule Using a Density-of-States Function Deduced from Overlap Integrals H.B. Jansen and P. Pyykko............................. 409 CONTENTS ix On Inversion Symmetry in Momentum Space Per Kaijser and Vedene H. Smith Jr ••••••.••••••••••••• 417 Bonding Character o~ Inner-Shell Orbitals in Diatomic Molecules Osvaldo Goscinski ••••••..•.•••••..••••••••••.••••.•••• 427 A New Formulation o~ the Correlation Problem G.G. Hall............................................. 433 The Chemical Bond as a Many-Electron Problem Raymond Daudel. • ••• •••• . • •.• •• • ••• • ••• •••• •• •• •••• ••• • 445 Orbital Methods and Correlation Errors in Expectation Values S. Larsson and R.E. Brown............................. 459 Lon~range Interaction in some Two-Electron Systems W. Kolos.............................................. 465 The Generator Coordinate Method Illustrated on the Hydrogen Molecule Bernard Laskowski.. •.• • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • 479 Projected Hartree-Fock Calculations on the Ground and First Excited lE+ States o~ the Hydrogen Molecule g G. Howat and Sten Lunell.............................. 491 De~ormed Atoms and the Projected Hartree-Fock Method P. van Leuven......................................... 499 MCSCF Studies Chemical Reactions: Natural Reaction o~ Orbitals and Localized Reaction Orbitals Klaus Ruedenberg and Kenneth R. Sundberg.............. 505 The Phosphate Group in Quantum Biochemistry Alberte Pullman and Bernard Pullman................... 517 Towards the Theoretical Determination o~ the Con~ormation o~ Biological Macromolecules Janos J. Ladik........................................ 539 Energetics and Mechanism o~ 2-Aminopurine Induced Mutations Robert Rein and Ramon Garduno......................... 549 External Electrical Field and Proton Trans~er H. Choj nacki. • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • 561 Proton Tunnelling in DNA Base Pairs and Mutagenesis Suheil F. Abdulnur.................................... 567 On Proton Mobilities in Individual Hydrogen Bonds Mark A. Ratner and J.R. Sabin......................... 577 Index. • • • • • • • • • • • • • • • • • • • • . • • • • • • • •. • • • • • • • • • • • • • • • • • • • • • • • • 589 PER-OLOV LOWDIN - CONQUEROR OF SCIENTIFIC, EDUCATIONAL AND ROCKY MOUNTAINS Kimio Ohno Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan FOREWORD I happened to be the first Japanese scientist to meet Per Lowdin on Japanese soil. In September 1953, an international conference on theoretical physics was held in Japan. Professor Kotani gave me the responsibility of meeting some foreign guests at the Tokyo airport. Thus on one hot summer day, I met Per as well as Professor Waller and Professor Mulliken at the airport. At that time, I did not realize that this was to be the beginning of a long and happy association with Per and his groups. Four years later, in the summer of 1957, I was working with Roy McWeeny at Keele. Professor Daudel organized an international colloquium on quantum chemistry in Paris in October of that year. I took advantage of attending this colloquium by extending the trip to Uppsala in late September. The quantum chemistry group was busy in preparation for its move from Kemikum to a new building at Rundelsgrand 2A, but Per took very good care of us. I had been able to meet Professor Kotani at the Stockholm station, and we spent five nights in the group's apartment at Luthagesplanaden. The weather was miserable and it even sleeted on one day. Never theless I enjoyed my first visit to Uppsala immensely. The group members I remember having met on this occasion include Anders Froman, Klaus and Marianne Appel and Jean-Louis Calais. Although tickets were bought quite independently in England and Sweden, Per and I were ln the same compartment in the continental train from Copenhagen to Paris. We had plenty of time for discussion and when we arrived at Paris, I must confess that I was quite exhausted from
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