CONTRIBUTORS TO THIS VOLUME S. M. BLINDER S. F. BOYS INGA FISCHER-HJALMARS LAURENS JANSEN HERBERT JEHLE PER-OLOV LOWDIN R. McWEENY P. RAJAGOPAL E. STEINER ADVANCES IN QUANTUM CHEMISTRY EDITED BY PER-OLOV LOWDIN DEPARTMENT OF QUANTUM CHEMISTRY UPPSALA UNIVERSITY UPPSALA, SWEDEN AND QUANTUM THEORY PROJECT UNIVERSITY OF FLORIDA OAINESVILLE, FLORIDA V O L U M E 2-1965 @ A C A D E M I C P R E S S New York London COPYRIGHT 0 1965, BY ACADEMIC PRESS INC. ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS. ACADEMIC PRESS INC. 111 Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House, London W.I LIBRARY OF CONGRESS CATALOG CARD NUMBER: 64-8029 PRINTED IN THE UNITED STATES OF AMERICA LIST OF CONTRIBUTORS Numbers in parentheses indicate the pages on which the authors' contributions begin. S. M. BLINDER(47),' Department of Chemistry, Harvard University, Cambridge, Massachusetts S. F. BOYS(l), Department of Theoretical Chemistry, University of Cambridge, Cambridge, England INCA FISCHER-HJALMARS (25), Institute of Theoretical Physics, University of Stockholm, Stockholm, Sweden LAURENS JANSEN(1 19). International Division, Battelle Memorial Institute, Geneva, Switzerland HERBERT JEHLE(195), Physics Department, The George Washington University, Washington, D.C. PER-OLOV LOWDIN(21 3), Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden, and Quantum Theory Project, University of Florida, Gainesville, Florida R. MCWEENY (93), Quantum Theory Group, University of Keele, Keele, Staffordshire, England P. RAJAGOPAL ( 1),2 Department of Theoretical Chemistry, University of Cambridge, Cambridge, England E. STEINER (93),3 Quantum Theory Group, University of Keele, Keele, Staffordshire, England Present address: Department of Chemistry, University of Michigan, Ann Arbor, Michigan. Present address: Max-Plank-Institut f ur Physik und Astrophysik, Munich, Germany. 3 Present address: Department of Chemistry, University of Exeter, England. V PREFACE In investigating the highly different phenomena in nature, scientists have always tried to find some fundamental principles that can explain the variety from a basic unity. Today they have not only shown that all the various kinds of matter are built up from a rather limited number of atoms, but also that these atoms are constituted of a few basic elements or building blocks. It seems possible to understand the innermost structure of matter and its behavior in terms of a few elementary particles: electrons, protons, neutrons, photons, etc., and their interactions. Since these particles obey not the laws of classical physics but the rules of modern quantum theory or wave mechanics established in 1925, there has developed a new field of “quantum science” which deals with the explanation of nature on this ground. Quantum chemistry deals particularly with the electronic structure of atoms, molecules, and crystalline matter and describes it in terms of electronic wave patterns. It uses physical and chemical insight, sophisticated mathematics, and high-speed computers to solve the wave equations and achieve its results. Its goals are great, but perhaps the new field can better boast of its conceptual framework than of its numerical accomplishments. It provides a unification of the natural sciences that was previously inconceivable, and the modern development of cellular biology shows that the life sciences are now, in turn, using the same basis. “Quantum biology” is a new field which describes the life processes and the functioning of the cell on a molecular and submolecular level. Qua