Computational Techniques in Quantum Chemistry and Molecular Physics: Proceedings of the NATO Advanced Study Institute held at Ramsau, Germany, 4–21 September, 1974 PDF
Preview Computational Techniques in Quantum Chemistry and Molecular Physics: Proceedings of the NATO Advanced Study Institute held at Ramsau, Germany, 4–21 September, 1974
Computational Techniques in Quantum Chemistry and Molecular Physics NATO ADVANCED STUDY INSTITUTES SERIES Proceedings of the Advanced Study Institute Programme, which aims at the dissemination of advanced knowledge and the formation of contacts among scientists from different countries The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht and Boston D Behavioral and Sijthoff International Publishing Company Social Sciences Leiden E Applied Sciences Noordhoff International Publishing Leiden Series C - Mathernaticaland Physical Sciences Volume 15 - Computational Techniques in Quantum Chemistry and Molecular Physics Computational Techniques in Quantum Chemistry and Molecular Physics Proceedings of the NATO Advanced Study Institute held at Ramsau, Germany, 4-21 September, 1974 edited by G. H. F. DIERCKSEN, Munich B. T. SUTCLIFFE, York A. VEILLARD, Strasbourg D. Reidel Publishing Company Dordrecht-Holland / Boston-U.S.A. Published in cooperation with NATO Scientific Affairs Division Library of Congress Cataloging in Publication Data NATO Advanced Study Institute on Computational Techniques in Quantum Chemistry and Molecular Physics, Ramsau bei Berchtesgaden, Ger., 1974. Computational techniques in quantum chemistry and molecular physics : [lectures] (NATO advanced study institutes series: Series C, mathematical and physical sciences; v. 15) Bibliography: p. 1. Electronic data processing-Molecules-Congresses. 2. Electronic data processing-Quantum chemistry Congresses. I. Diercksen, G. H. F. II. Title. III. Series. [DNLM: 1. Chemistry-Congresses. 2. Computers-Congresses. 3. Physics-Congresses. 4. Quantum theory-Congresses. QD462Al N279c 1974] QCI75.16.M6N2 1974 514'.28'02854 75-9913 ISBN-13: 978-94-010-1817-3 e-ISBN-13: 978-94-010-1815-9 001: 10.1007/978-94-010-1815-9 Published by D. Reidel Publishing Company P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. 306 Dartmouth Street. Boston, Mass. 02116, U.S.A. All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht Softcover reprint of the hardcover 1st edition 1975 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher CONTENTS PREFACE VII B. T. Sutcliffe FUNDAMENTALS OF COMPUTATIONAL QUANTUM CHEMISTRY G. H. F. Diercksen and W. P. Kraemer FUNDAMENTALS OF COMPUTER HARD- AND SOFTWARE IN RELATION TO QUANTUM CHEMICAL CALCULATIONS 107 A. Vei llard THE LOGIC OF SELF-CONSISTENT-FIELD PROCEDURES 201 B. Roos THE CONFIGURATION INTERACTION METHOD 251 P. Swanstr~m and F. Hegelund MOLECULAR PROPERTIES 299 V. R. Saunders AN INTRODUCTION TO MOLECULAR INTEGRAL EVALUATION 347 N. C. Handy CORRELATED WAVEFUNCTIONS 425 M. A. Robb PAIR FUNCTIONS AND DIAGRAMMATIC PERTURBATION THEORY 435 R. McWeeny SOME APPLICATIONS OF PROJECTION OPERATORS 505 G. Winnewisser MOLECULES IN ASTROPHYSICS 529 PREFACE This book contains the transcripts of the lectures presented at the NATO Advanced study Institute on "Computational Techniques in Quantum Chemistry and Molecular Physics", held at Ramsau, Germany, 4th - 21st Sept. 1974. Quantum theory was developed in the early decades of this century and was first applied to problems in chemistry and molecular physics as early as 1927. It soon emerged however, that it was impossible to con sider any but the simplest systems in any quantita tive detail because of the complexity of Schrodinger's equation which is the basic equation for chemical and molecular physics applications. This remained the si tuation until the development, after 1950, of elec tronic digital computers. It then became possible to attempt approximate solutions of Schrodinger's equa tion for fairly complicated systems, to yield results which were sufficiently accurate to make comparison with experiment meaningful. Starting in the early nineteen sixties in the United States at a few centres with access to good computers an enormous amount of work went into the development and implementation of schemes for approximate solu tions of Schrodinger's equation, particularly the de velopment of the Hartree-Fock self-consistent-field scheme. But it was soon found that the integrals needed for application of the methods to molecular problems are far from trivial to evaluate and cannot be easily approximated. In the past five or so years however big steps have been made in solving the inte gral evaluation problem and the field has progressed to such a stage that it is generally accepted that the results of quantum mechanical calculations are now sufficiently good to leqd to a better understand ing of experimental results in chemistry and molecular VIII PREFACE physics, and often to provide impetus for fresh ex perimental work. The aim of the Institute was to familiarize young pro fessionals in the field with the current state of the art and to indicate to them likely areas of advance in the near future. Basically the Institute had three di visions: detailed instructional lectures given for the whole period of the course, review lectures given in the last week of the course, and problem solving and instructional sessions which again were given through out the course. The Advanced Study Institute was financially spon sored by the NATO Scientific Affairs Division. The installation of a computer terminal system was made possible by a generous grant of IBM Germany. Invalu able administrative assistance and the computer fa cilities were supplied by the Max-Planck-Institute for Physics and Astrophysics, MUnchen. The Organi zing Committee wishes to express its gratitude for this support. In particular we would like to thank Dr. T. Kester (NATO, BrUssel) Dr. G. HUbner (IBM, Sindelfingen), and Prof. Dr. L. Biermann (MPI, Munich) for their interest and constant incouragement. The editors would also like to thank the lecturers for their co-operation in preparing the material that made this publication possible. The institute itself was made possible by the enor mous enthusiasm of the students, lecturers and de monstrators on the course; and by the untiring efforts of the administrative and technical staff and of the service staff of the Alpenhotel Hochkater, Ramsau. December 1974 The Organizing Committee G.H.F. Diercksen, Munich B.T. Sutcliffe, York A. Veillard, StraBbourg FUNDAMENTALS OF COMPUTATIONAL QUANTUM CHEMISTRY B. T. Sutcliffe Dept. of Chemistry, University of York, England 1. THE BASIC PROBLEM The chief aim of this course is to describe practicable methods of solving the eigen-value problem: H'l' E'l' (1.1) and the realisation of these methods on electronic digital computers. Here E is one of a set of possible energies {E } n and ~ one of a set of associated state functions {'l' }. The n H Hamiltonian Operator we shall take to be N N 2 A ! H(l,2--N) L: h (i) + L: Ie / (1. 2a) 1=1 1J· = 1 41TE 0 r ~.J. h(i) (1. 2b) which describes (in conventional notation), the motion of N electrons, moving in the field provided by N nuclei each wi th n charge Z ,fixed in space, assuming only electrostatic interactions. n We shall generally quote this Hamiltonian in atomic units, by quoting all distances as multiples of the fundamental length a 41TE h2 /me2. o Diercksen et aL (eds.), Computational Techniques in Quantum Chemistry and Molecular Physics, 1-105. All Rights Reserved Copyright © 1975 by D. Reidel Publishing Company, Dordrecht-Holland. 2 B. T.SUTCLIFFE To a lesser extent we shall also be concerned with describ ing practicable methods of calculating expectation values of operators, between the calculated state functions. We shall not have much occasion in future to refer explicitly to why we want to know how to solve these problems, so it seems appropriate to describe the context at this stage, in the hope of forestalling possible puzzlement or exasperation later. We hope to be able to produce numbers from our calculations which, at very least, can be compared with experimental numbers. Better than this we hope to be able to anticipate numerically the outcome of as yet unperformed experiments, and best of all, we hope to have methods which will yield numbers so reliable as to be useful alternatives to experimental measurement. When we reflect on the fact that most experiments are done on huge assemblies of molecules, (a tube of gas in a spectroscope, a flask of liquid on a heating mantle and so on), and that these assemblies are open, (if only by virtue of the intervention of the measuring apparatus) and therefore developing in time, we may wonder what possible relevance our simple isolated molecule, time independant Hamiltonian, can have to an experimental situation. The answer is, I think, that so far as we know, the solution of the problem as we have stated it is a sine qu~non of any progress towards a complete description of the experimental situation. Essentially we believe that the experimental situation can be described by an equation of the form (1.3) where ~ here is a complicated Hamiltonian describing the whole system. We believe however that in systems where chemical reaction is not taking place H can usefully be written as sum of FUNDAMENTALS OF COMPUTATIONAL QUANTUM CHEMISTRY 3 isolated molecule Hamiltonians together with interaction terms. In systems where the interactions are weak then the assembly properties will be essentially those of the isolated molecules, suitably averaged according to statistical mechanical principles. Thus the solution of the isolated molecule problem here forms a natural starting point. In reacting systems and systems subject to strong time dependent interactions, the situation is by no means so clear. However it is perhaps not too much to assert that even in these situations, it is extremely likely that isolated molecule functions will play an important role in the explanation of the overall behaviour of the system. However the Hamiltonian that we have written down in (1.2) is not the full Hamiltonian even for the isolated molecule, and unfortunately we are not completely sure of what the full Hamiltonian in fact is. This is essentially because the Hc1assica1" Hamiltonian for the problem, though known, is inadequate, but we are not sure of how we should construct properly the relativistic one. We believe however that the classical Hamiltonian, represents the leading term (in most situations) of the full Hamiltonian. We further believe that most of the other terms can be taken care of by allowing every particle to have spin, and by associating with the spin a magnetic moment operator. A ll(n) g nremt S(n) (1. 4) n where S (n) is a spin operator appropriate to the n'th particle, and g is assigned from experiment. We then add to the n Hamiltonian all those extra terms which we would expect to arise classically from the presence of these extra magnetic moments. But (1.2) still does not fully represent the isolated molecule, even in the leading term approximation, since it lacks
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