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Density Matrices and Density Functionals: Proceedings of the A. John Coleman Symposium PDF

717 Pages·1987·14.962 MB·English
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Density Matrices and Density Functionals A. JOHN COLEMAN Density Matrices and Density Functionals Proceedings o/the A. John Coleman Symposium Edited by Robert Erdahl and Vedene H. Smith, Jr. Queen's University, Kingston, Canada D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER ,. ACADEMIC PUBLISHERS GROUP DORDRECHT/BOSTON/LANCASTER/TOKYO Library of Congress Cataloging in Publication Data Density matrices and density functionals. Includes index. I. Density matrices-Congresses. 2. Density functionals-Congresses. 3. Coleman, A. John (Albert John), 1918- I. Coleman, A. John (Albert John), 1918- II. Erdahl, Robert. III. Smith, Vedene H. OCI74.17.D44D47 1987 530.1'529434 87-4718 ISBN-13: 978-94-010-8214-3 E-ISBN-13: 978-94-009-3855-7 DOl: 10.107/978-94-009-3855-7 Published by D. Reidel Publishing Company, P.O. Box 17,3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. All Rights Reserved © 1987 by D. Reidel Publishing Company, Dordrecht, Holland No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner CONTENTS PREFACE .......•.........................•....................•. i x The publications of A. John Coleman ...•...•........•.•......... xiii A Tribute to A. John Coleman - The "Tame" Mathematician ....... . P. O. Lowdi n Reduced Density Matrices: 1929-1989 ......•........•........... 5 A.J. Coleman Some Aspects on the Development of the Theory of Reduced Density Matrices and the Representability Problem .......•...... 21 P.O. Lowdin Representability Conditions 51 Robert Erdahl On the Diagonal N-Representability Problem .............•....•.. 77 M.M. Mestechkin Fermion N-Representability Conditions Generated by a Decomposition of the 1-Particle Identity Operator onto Mutually Orthogonal Proj ection Operators ..•........•........... 89 Hubert Grudzinski The Unitarily Invariant Decomposition of Hermitian Operators ... 115 Zong-Hao Zeng and Chi a-Chung Sun Building Up N-Electron States with Symplectic Symmetry......... 141 Z.H. Zeng, C.C. Sun and A.J. Coleman Time Dependent Antisymmetrized Geminal Power Theory Using a Coherent State Formulation .....•......•...........•.... 167 E. Deumens, B. Weiner and Y. Ohrn Griffiths Inequalities for Fermion Systems 193 J.K. Percus Entropy of Reduced Density Matrices ....................•....... 213 Mary Beth Ruskai A Lower Bound to the Ground State Energy of a Boson System Wi th Fermion Source .•...•...•......•.........................•. 231 M. Rosina, B. Golli and R. M. Erdahl vi CONTENTS Reduced Density Operators, Their Related von Neumann Density Operators, Close Cousins of These, and Their Physical Interpretation •.•.•.••..•..•..•......•.....................••.. 249 Everett G. Larson Theory and Practice of the Spin-Adapted Reduced Hamiltonians (SRHY .•....••..•.....•..•.........•..•...•........ 275 C. Valdemoro Variational Principle with Built-In Pure State N-Representability Cgnditions. The N-Electron Case •..........• 289 Eduardo V. Ludena Wigner Distributions as Representations of the Density Matrix .. 305 Leon Cohen Inter-Relationships Between Various Representations of One-Matrices and Related Densities: A Road Map and an Exampl e •.•.....•.....•.......•..•.............................. 327 Ajit J. Thakkar, Anthony C. Tanner and Vedene H. Smith, Jr. Current Problems in Density Functional Theory.................. 339 E. Zaremba The Interface Between Reduced Density Matrices and Density Functional Theory...................................... 359 John E. Harriman The Physics Underlying the Langreth-Mehl Scheme for Non-Uniform Systems .•.•..•.•.••...•......•...•..•.......•.• 375 David C. Langreth Understanding Energy Differences in Density Functional Theory.. 391 S.H. Vosko and Jolanta B. Lagowski Density Functional Calculations of Molecular Bond Energies ..•.. 443 A.D. Becke Non-Local Effects on Atomic and Molecular Correlation Energies Studied with a Gradient-Corrected Density Functional ••..........•.•.•...........•..•.•.••..•..••..•...... 457 A. Savin, H. Preuss and H. Stoll An Evaluation of Local Electron Correlation Corrections and Non-Local Exchange Corrections to the Hartree-Fock-Slater Method from Calculations on Bond Energies and Electronic Spectra of Molecular Systems ••.••.•...•......••...•.••.••...••• 467 Vincenzo Tschinke and Tom Ziegler Correlation Energy Functionals of One-Matrices and Hartree-Fock Densi ties ..•..••.•...•...•..•..•...•.....••.••.••. 479 Mel Levy CONTENTS vii Some Remarks on Scaling Relations in Density Functional Theory .....••.•.........•...•..•........•....•................. 499 Wei tao Yang Deduction of Semiempirical MO Methods from Density Functional Theory .............................................. 507 Einar Lindholm and Stig Lundqvist Charge and Spin Densities in Molecular Solids: Local Density Functional Calculations Versus Experiment .•..•......... 517 Pierre J. Becker A Functional of the Two-Particle Density Matrix for the Approximate Calculation of the Electronic Correlation Energy 545 Renato Colle and Oriano Salvetti Extracules, Intracules, Correlation Holes, Potentials, Coefficients and All That •.......•............................. 553 Ajit J. Thakkar The Exact Schr~dinger Equation for the Electron Density........ 583 Geoffrey Hunter Adiabatic Separation, Broken Symmetries and Geometry Optimization................................................... 597 Osvaldo Goscinski and Vladimiro Mujica Asymptotic Results for Density Matrices and Electron Density in Atoms and Nearly Spherical Molecules .......••....•.. 613 N.H. March and R. Pucci An Algorithm for Calculating Isoelectronic Changes in Energies, Densi ties, and One-Matrices....................... 629 Jean E. Osburn and Mel Levy Atoms and Ions in the Limit of Large Nuclear Charge ....•......• 643 Jose L. Gazquez, Marcelo Galvan, Elba Ortiz and Alberto Vela Improved Thomas-Fermi Theory for Atoms •...•......•....•......•. 663 Swapan K. Ghosh and Robert G. Parr A Bond Energy from Quantum Mechanics 677 R.F.W. Bader and K.B. Wiberg Measured Electron Densities and Band Structure Calculations ..•. 693 John Avery and Peter Sommer-Larsen X-ray Orthonormal Orbital Model for Crystallography 707 L.J. Massa Index ....................•..•.........•.•.......••....•........ 717 PREFACE THE COLEMAN SYMPOSIUM This collection of papers is dedicated to Albert John Coleman for his enthusiastic devotion to teaching and research and his many scientific accomplishments. John was born in Toronto on May 20, 1918 and 21 years later graduated from the University of Toronto in mathematics. Along the way he teamed up with Irving Kaplansky and Nathan Mendelson to win the first William Lowell Putnam Mathematical Competition in 1938. He earned his M.A. at Princeton in 1942 and then his Ph.D. at Toronto in 1943 in relativistic quantum mechanics under the direction of Leopold Infeld. During this period he was secretary of the Student Christian Movement in Toronto. Later, in 1945, he became traveling secretary of the World's Student Christian Federation in Geneva and in this capacity visited some 100 universities in 20 countries in the next four years. He spent the 50's as a member of the faculty at the University of Toronto and for 20 years, starting in 1960, he served as Dupuis Professor of Mathematics and Head of the Department at Queen's University. Since 1983 he has been Professor Emeritus at Queen's. His 1963 paper in the Reviews of Modern Physics on the "Structure of Fermion Density Matrices" was a landmark and served as an inspiration to many. In that paper many of the difficult mathematical and practical problems associated with density matrix theory were isolated and the potential usefulness of density ix x PREFACE matrices was brought before a wide audience. In the 60's John became a fixture at LOwdin's International Symposium at Sanibel and at the Summer Institutes in Uppsala. During this period he lectured and wrote about reduced density matrix theory. He found a substantial audience, and as is evidenced by this volume, he had a profound effect on many careers. The AGP wave function has proved to be a flexible and useful tool in nuclear, molecular and solid state physics, and in this period, John was exploring its fascinating mathematical and physical properties. A great expositor of mathematics, John was thoroughly appreciated by the theoretical chemists and physicists at Sanibel and Uppsala. In him they found a mathematician whom they could understand - even enjoy. It was the interdisciplinary flavor of these meetings - the chemists, physicists and mathematicians learning from each other - which proved so fruitful. His articles "Induced and Subduced Representations" (1968) and "The Symmetric Group Made Easy" (1968) are remarkable in their crystal clarity and accessibility. His treatment of the representations of the symmetric group is widely regarded as the best current one. John is fond of quoting Alfred North Whitehead. The following passage from Chapter 2 of "Science and the Modern World" vividly reflects - as all of his friends well know - his attitude that mathematics plays a far-reaching role in human affairs: "The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact". He had a passionate concern for his students, and tilis is the message that he brought them. An undergraduate once remarked that "Regardless of what he taught, he got you thinking". Another noted that only a portion of his lectures on Calculus were devoted to the subject. They contradicted every known text book on teaching techniques. "I don't think he actually taught me calculus, but I did learn it and I think he taught me how to learn it." He has interacted with students in a wide variety of ways: in the classroom and in study groups at his home. He has spent hours with students on a one-to-one basis. He stimulated the creation of, and served for fifteen years as Chairman of, The International Student Centre at Queen's. PREFACE XI from 1960 through 1964 he chaired the Ontario Mathematics Commission which brought the "new mathematics" to Canada and has recently been commended for bringing "an infectious and unrelenting enthusiasm" to this body. During this period he edited a widely used series of mathematical texts for Grades 4 through 13 for the Canadian system, and co-authored several in the series. From 1972 to 1974 he served as president of the Canadian Mathematical Society. He served as chairman and then treasurer of the Development and Exchange Commission of the International Mathematical Union in the period 1974-1982, taking special interest in improving mathematics teaching in Africa. John is a man of many parts. He was active in the National Committee of World University Service of Canada, 1949-1960, organizing a seminar in Mysore, India in 1952 which included many future world leaders. He spoke in 1973 at a conference in Pont-a-Mousson, France, organized by the World Council of Churches on the Future of Technological Man. He was a member of the Science Council of Canada for four years and directed a study of the "Mathematical Sciences of Canada". His report, published in 1977, contains a number of far-reaching recommendations for Canadian schools and was hailed by the "users" of mathematics. He was the sole layman from Canada invited to participate in the Lambeth Conference in 1978, which brought together 350 bishops of the World Anglican Communion. In 1980-1981 John worked for Marc Lalonde, Minister cf Energy, Mines and Resources, acting as liaison between this department and the Parliamentary Committee on Alternative Energy and Oil Substitution. Everyone who has visited John in Kingston has met Marie-Jeanne, whom he married in 1953. She is a graduate in theology of the University of Geneva. A much beloved and respected woman, her powers extend far beyond theological matters. However we must remark that she was unable to stop John from entering federal politics which he did in 1980. He was narrowly defeated by the Conservative incumbent, Flora MacDonald, in the riding of Kingston and the Islands.

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