LOCALIZATION AND DELOCALIZATION IN QUANTUM CHEMISTRY VOLUME I ATOMS AND MOLECULES IN THE GROUND STATE

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1 LOCALIZATION AND DELOCALIZATION IN QUANTUM CHEMISTRY VOLUME I ATOMS AND MOLECULES IN THE GROUND STATE

2 LOCALIZATION AND DELOCALIZATION IN QUANTUM CHEMISTRY VOLUME I Atoms and Molecules in the Ground State Edited by ODILON CHALVET and RAYMOND DAUDEL Centre de Mecanique Ondulatoire Appliquee du G.N.R.S., 23, rue du Maroc, Paris 1geme and SIMON DINER and JEAN PAUL MALRIEU 1nstitut de Bi%gie Physico-Chimique, 13, rue Pierre et Marie Curie, Paris 5eme D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND / BOSTON-U.S.A.

3 Library of Congress Cataloging in Publication Data Main entry under title: Atoms and molecules in the ground state. (Localization and delocalization in quantum chemistry; v. 1) "Papers presented during the academic year at an international seminar organized by some members of the Centre de mecanique ondulatoire appliquee du C.N.R.S. and some members of the Laboratoire de chimie quantique de I'Institut de biologie physico-chimique." Includes bibliographical references and index. 1. Atomic theory-congresses. 2. Molecular theory-congresses. I. Chalvet, Odilon, ed. II. Series. QD461.A86 541' ISBN-\3: e-isbn-\3: DOl: / 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 , U.S.A. All Rights Reserved Copyright 1975 by D. Reidel Publishing Company, Dordrecht-Holland 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

4 TABLE OF CONTENTS PREFACE VII PART I / STATISTICAL ANALYSIS OF THE SPATIAL LOCALIZABILITY OF MOLECULAR ELECTRONS R. DAUDEL / Introduction to the Loge Theory 3 J. P. MALRIEU / Discussion of Daudel Contribution 9 R. F. W. BADER / Comparison of Loge and Virial Methods of Partitioning Molecular Charge Distributions 15 R. DAUDEL and J. P. MALRIEU / Summary of the Discussion of Professor Bader's Paper 39 PART II / SEPARABILITY AND ANALYSIS OF WAVE FUNCTIONS IN LOCAL ELEMENTS R. CONSTA NCIEL / Group Density Analysis of Molecular Wave Functions Into Separated Elements 43 PIERRE CLA VERIE, JEAN-PAUL MALRIEU, and SIMON DINER / Discussion of Constanciel Contribution: The Relationship Between Functional Localization and the Operator 'Number of Particles in a One-Particle Functional Subspace' 53 PH. MILLIE, B. LEVY, and G. BERTHIER / Localization and Relocalization in Orbital Theories 59 J. M. CARPENTER and DAVID PETERS / The Direct S.C.F. Computation of the Localised Molecular Orbitals of the Formaldehyde Molecule 99 R. DA UDEL / Summary of the Discussion of Professor Peters' Paper 107 J. P. DAUDEY / Comments About the Communication of Professor Peters 109 R. DA UDEL / Relation Between Localizability of Orbitals and Localizability of Electrons 111 PART III / EXPRESSION OF THE ENERGY IN TERMS OF LOCAL CONTRIBUTIONS N. H. MARCH / Localizability of Energy and Electronic Density in Molecules and Crystals 115 R. F. PRAT / Localization and Symmetry Breaking of Molecular Hartree-Fock Orbitals 131

5 VI TABLE OF CONTENTS WERNER KUTZELNIGG / Localization and Correlation 143 J. P. DAUDEY, J. P. MALRIEU, and o. ROJAS / Empirical and Theoretical Partitions of the Molecular Energy Into Local Contributions: Additive Systematic and Conformational Problems 155 G. LEROY and D. PEETERS / The Transferable Properties of Localized Orbitals 207 KLAUS RUED ENBERG / The Nature of the Chemical Bond, an Energetic View 223 PART IV / MOLECULES IN AN ELECTROMAGNETIC FIELD, ADDITIVE SYSTEMATICS J. P. MALRIEU / The Localized Interpretation of the Observables of the Ground State (Introduction to Part IV) 249 HENRI LUMBROSO and CHANTAL LIEGEOIS / A Discussion Upon the Additivity Concept of Dipole Moments 251 J. P. MALRIEU / Remark on the Theoretical Foundation of the Vectorial Additive Systematics for the Molecular Dipole Moments 263 J. HOARAU / Diamagnetic Susceptibilities and Electronic Delocalization 265 Y. ELLINGER, B. LEVY, PH. MILLIE, and R. SUBRA I Analysis of NMR and EPR Coupling Constants Using Localized Orbitals 283 CONCLUSIONS R. DAUDEL / Nature and Classification of Chemical Bonds (Final Discussion) 329 J. P. MALRIEU I The Degree of Delocalization and Its Relation with the Ground State Energy. The Problem of Aromaticity (Contribution to the Final Discussion) 335 L. SALEM / How Delocalized Molecular Orbitals are built by the Interaction of Localized Group Orbitals 345 L. SALEM / Lone Pairs in Organic Molecules and How They Determine Conformations 347 I. G. CSIZMADIA / Sizes and Shapes of Electron Pairs 349 INDEX OF NAMES 355 INDEX OF SUBJECTS 361

6 PREFACE This book is devoted to a general discussion about localization and delocalization in quantum chemistry. The first volume is concerned with molecules in their ground state. It is made of papers presented during the academic year at an international seminar organized by some members of the 'Centre de Mecanique Ondulatoire Appliquee du C.N.R.S.' and some members of the 'Laboratoire de Chimie Quantique de l'institut de Biologie Physico-Chimique'. It contains also reports of discussions which followed the presentation of invited papers. It is a 'forum' in which each expert gives his opinion on a work in progress. The volume is divided into four parts. The first one is a statistical analysis of the localizability of molecular electrons in the three-dimensional space. It contains an exposition of the basic ideas of the loge theory which provides a framework to do such an analysis. The second part is concerned with the separability of a molecular wave function and its expression in terms of localized elements. An exploration is made of the relationship between the localizability of electrons and the possibility of expressing the wave function in terms of localized orbitals. The third part is devoted to the partition of the energy in local contributions. The last part of the volume contains a set of papers related with molecular properties which appear when a molecule interacts with an electromagnetic field. Such properties are analyzed in local contributions and the theoretical bases of additive systematics are described. A concluding section shows the impact of the theory of electronic localizability on the mathematical and physical nature of the chemical bond and therefore on the classification of chemical bonds. The second volume will be devoted to ionized and excited states, phenomenon depending on the time and therefore exciton theory. R. DAUDEL