Density Functional Theory NATO ASI Series Advanced Science Institutes Series

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Volume 337 - Density Functional Theory edited by Eberhard K. U. Gross and Reiner M. Dreizler

~ Series B: Physics Density Functional Theory

Edited by Eberhard K. U. Gross Institute for Theoretical Physics Julius Maximilian University Wurzburg, Germany and Reiner M. Dreizler Institute for Theoretical Physics Johann Wolfgang Goethe University Frankfurt am Main, Germany

Springer Science+Business Media, LLC Proceedings of a NATO Advanced Study Institute on Density Functional Theory, held August 16-27, 1993, in II Ciocco, Italy

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Density functional theory / edited by Eberhard K.U. Gross and Reiner M. Drelzler. p. en. — (NATO ASI series. Series B, Physics : v. 337) "Published 1n cooperation with NATO Scientific Affairs Division." "Proceedings of a NATO Advanced Study Institute on Density Functional Theory, held August 16-27, 1993, In II Ciocco, Italy"- -T.p. verso. Includes bibliographical references and Index. ISBN 978-1-4757-9977-4 1. Density functlonals—Congresses. 2. Mathenatlea 1 physlcs- -Congresses. 3. Quantum theory—Congresses. I. Gross, E. K. U. (Eberhard K. U.), 1953- . II. Drelzler, Reiner M. III. North Atlantic Treaty Organization. Scientific Affairs Division. IV. NATO Advanced Study Institute on Density Functional Theory (1993 : II Ciocco, Italy) V. Series. QC20.7.D43D475 1994 530.4'1 —dc20 94-48908 CIP

ISBN 978-1-4757-9977-4 ISBN 978-1-4757-9975-0 (eBook) DOI 10.1007/978-1-4757-9975-0

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 SCIENTIFIC WORK OF MARK RASOLT

Mark Rasolt was a very talented and creative physicist. We will give a brief resume of his scientific contributions, the variety of his work, and attempt to capture the spirit of his personal qualities that made him so special as a scientist. Mark graduated from the Stevens Institute of Technology in 1965 with a B.S. in Electrical Engineering. On entering Cornell University, also in 1965, he joined the Department of Applied and Engineering Physics taking courses both there and in the Department of Physics. He became the first graduate student of Neil Ashcroft, graduating in 1971 with a Ph.D in Theoretical Physics. Mark then took a postdoctoral fellowship at the National Research Council of Canada, working with Roger Taylor (1971-1973). This was followed by a second postdoctoral fellowship, with Sy Vosko, at the University of Toronto (1973-75). In 1975, he joined the research staff at Battelle in Columbus, Ohio, where he also had a joint appointment at Ohio State University. From 1978, he was a member of the senior research staff at Oak Ridge National Laboratory. During his time at Oak Ridge, Mark held a variety of visiting professor appointments at a number of major universities and research laborat9ries in several countries. Mark was the author or co-author of more than one hundred scientific papers and review articles. He was a Fellow of the American Physical Society. Toward the end of his life Mark's general areas of expertise included the the• ory of highly correlated Bose and Fermi systems, quantum Hall effect, valley waves in semiconductors, electrons in high magnetic fields, superconductivity, and density functional theory. However, Mark's early work was on the nonlocal electron-ion in• teraction in metals and the resulting implications for ion-ion potentials. This led to a number of papers involving both bulk materials and surface properties, and it necessarily required the study of the effects of exchange and correlation on charge distributions in metals and led to the study of nonlocality on the Fermi surface of metals. His work on fundamental properties of density-density correlation functions led in a natural way to their implications for the density functional theory of inhomo• geneous many-electron systems, which had been developed by Hohenberg and Kohn, and Kohn and Sham. From the early 1970s, Mark made fundamental contributions to density func• tional theory. He understood very early on the fascinating consequences of corre• lations between electrons in inhomogeneous many-electron systems and how they differ in a quite fundamental way from the behaviour of their homogeneous single• component counterparts. He made basic contributions to an understanding of these nonuniform systems in a series of papers with Wally Geldart. For the density-fuctional

v Mark Rasolt in 1988 (Courtesy of G. Vignale)

vi community, in particular, we might add at this point that from about 1987, together with Giovanni Vignale, Mark made a second important contribution to density func• tional theory by developing the theory of inhomogeneous many-electron systems in magnetic fields in terms of spin and current density functionals. This provided an important extension of the work of Hohenberg, Kohn and Sham. These two growing fields, correlations in inhomogeneous many-electron systems, and density functional theory of electrons in high magnetic fields can clearly be identified as areas where Mark has made lasting contributions to condensed matter physics. It is really remarkable that during this time, Mark was simultaneously pursu• ing with great vigour interests in a number of other fields, and we want to give a brief overview of this work as well. In the area of critical phenonmena, he studied dilute Bose gases, with applications to 4He on vycor, and collaborated with Michael Stephen and Michael Fisher. With Tony Haymet, Mark studied the critical properties of effective Hamiltonians described in terms of higher order tensor order parameters, with his most recent contribution being an application to C60 . Mark also made a number of contributions to surface physics, not only within density functional theory but also to dl:"ective potentials and chemisorption. Dating back from his very early days (when he almost became a plasma physicist at Cornell!), Mark also had a deep interest in semiconductors. He worked on electron-hole droplets, introduced the con• cept of valley waves in semiconductors and studied electron-hole lifetimes in plasmas in semiconducting systems. From very early on, Mark was also keenly interested in the properties of quan• tum systems in magnetic fields. He worked with Eric Fawcett on the interpretation of magnetoresistance in iron. He contributed to the modern theory of the quan• tum Hall effect, both integer and fractional, in papers with Allan MacDonald, Bert Halperin, Francois Perrot and others. He also contributed to the theory of high Tc superconductivity with a number of people, including Dennis Newns and Giovanni Vignale. One of Mark's most recent contrihutions was the remarkable prediction that low-density carrier systems in very high magnetic fields may be induced to go into a new superconducting state. This is very different from what is expected on the basis of COllllllon "garden variety" of quantum systems in magnetic fields. This new quantum state in very high magnetic fields is being actively searched for in ongoing experiments. In all of these areas, Mark made truly unique contributions. Very few people have contributed to so many areas in so short a time span. Very special personal characteristics and qualities as a scientist are required in order to do this. To choose but a few words to describe him, Mark was truly original and intensely creative. His work involved new ideas, not just doing something a bit better or a bit different. He also had a masterful understanding of the principles which should guide physicists, and scientists in general in their approach to research, together with a very deep respect and feeling for physics itself. He had extremely high standards and was never one to he satisfied with a quick fix. He was always willing to work hard and to think about a problem as long as was necessary in order to solve it, and to understand it fully to his satisfaction. He liked to think about physical problems in terms of symmetries and basic principles of physics, and he was able to express his ideas very clearly to his colleagues, both experimentalists and theoreticians alike. In all of his endeavours, Mark was an extremely dedicated and intense person. He was well aware of the importance of making enduring contributions to physics and he derived great joy from discovery and creation. He was just as unique and original in his personal life as he was in his physics. Knowing him and being in his company

vii was always stimulating and rewarding. Mark Rasolt shared a great deal of physics and insight with us to our lasting benefit. His contributions were very valuable and we very much admire and appreciate the work that he did. He will be missed by his many friends and colleagues.

D.J.W. Geldart N.W. Ashcroft Department of Physics Department of Physics Dalhousie University Cornell University Halifax, Nova Scotia Ithaca, NY, 14853-2501 Canada B3H 3J 5 U.S.A.

viii PREFACE

The first Nato Advanced Studies Institute entirely devoted to density functional theory was held in Portugal in September 1983. The proceedings of this School, publis• hed in early 1985, is still used as a standard reference covering the basic development of the theory and applications in atomic, molecular, solid state and nuclear physics. Ho• wever, astonishing progress has been achieved in the intervening years: The foundations of the theory have been extended to cover excited states and time dependent problems more fully, density functional theory of classical liquids and superconducting systems has been addressed and extensions to relativistic, that is, field theoretical systems, as well as a more thorough discussion of magnetic field problems have been presented. In addition, new functionals have been devised, for instance under the heading of ge• neralised gradient expansions, and the number of applications in the traditional fields has steadily increased, in particular in chemistry. Applications in new fields, as for instance the structure of atomic clusters and the marriage of density functional theory with molecular dynamics and simulated annealing, have provided additional impetus to the field of density functional theory. In view of this development, the time seemed just right to organise a sequel to the 1983 meeting, this time in sunny Italy. Our hope, that we would thus provide a forum where reports on the progress made and on the problems still unsolved could be sampled, proved to be correct. The 15 main lectures addressed the topics fundamental aspects atoms, molecules and clusters plasmas, liquids and solids. In addition there were short contributions covering either new developments or more controversial issues. The format of the School was thus quite similar to the format adopted in 1983. There was, however, increased emphasis on topics from solid state physics, that is, from one of the canonical fields for both the development and the application of density functional theory. Thanks are due to a number of people: first of all to the lecturers of the School, who worked hard to offer spirited as well as lucid presentations and to the participants, mainly of the younger generation, who were fully receptive and critical. The necessary secretarial support was given by Annette Jung, who carried the major burden in the preparatory phase and the local organisation. The staff of the Conference venue, II Ciocco, helped to make our School a memorable experience.

ix There is, however, also a sad note. During the last year we have lost. two of the researchers, still in the prime of their lives, who have contributed in a very substantial way to the development of our field: Mark Rasolt and Michael Schliiter. The contri• butions of Michael Schliiter are honoured at the Conference on Electronic Structure of Solids, held in Greece on Septemher 19-23, 1993. We dedicate this School and this volume to the memory of Mark Rasolt. The idea for this dedication originated with John Perdew. We asked Wally Geldart and Neil Ashcroft to provide a resume of Mark's scientific work. We also thank John Perdew, Giovanni Vigna.le and all the friends and colleagues of Mark for their contributions.

R.M. Dreizler

E.K.U. Gross

x CONTENTS

I. FUNDAMENTAL ASPECTS AND APPROXIMATE FUNCTIONALS

General Reviews

Overview of Density Functional Theory 3 W. Kohn

Coordinate Scaling Requirements for Approximating Exchange and Correlation ...... 11 M. Levy

Energy Functionals: Gradient Expansions and Beyond ...... 33 D.J.W. Geldart

Density Gradient Expansion of the Electronic Exchange- Correlation Energy, and its Generalization ...... 51 J.P. Perdew

Density Functional Aspects of Relativistic Field Theories 65 E. Engel, H. Muller, C. Speicher and R.M. Dreizler

Excited States and Electron-Atom Scattering ...... 119 L. Fritsche

Density Functional Theory of Time-Dependent Systems 149 E.K.U. Gross, C.A. Ullrich and U.J. Gossmann

xi Special Topics

Density Functional Formalism in Relativistic Nuclear Mean Field Theory ...... 173 M. Centelles

Recent Developments in Kohn-Sham Theory for Orbital Dependent Exchange-Correlation Energy Functionals 191 J.B. Krieger, Y. Li and G.J.Iafrate

Physical Interpretation of Electron Correlation in the Local-Density Approximation ...... 217 V. Sahni

II. ATOMS, MOLECULES AND CLUSTERS

General Reviews

Topology of Electron Density and Open Quantum Systems ...... 237 R.F.W. Bader

Molecules and Molecular Dynamics 273 R.O. Jones

Applications of Density Functional Theory in Chemistry ...... 299 N.H. March

Simple Views of Metallic Clusters 323 J.P. Perdew

Special Topics

Charge Sensitivity Analysis as Diagnostic Tool for Predicting Trends in Chemical Reactivity ...... 339 R.F. Nalewajski

III. SOLIDS: BULK AND SURFACE PROPERTIES

General Reviews

Metallic Surfaces and Density Functional Theory 393 J.F. Dobson

xii Density Functional Theory of the Superconducting State 431 E.K. U. Gross, S. Kurth, K. Capelle and M. Liiders

Fluctuations in Density Functional Theory: Random Metallic Alloys and Itinerant Paramagnets ...... 461 B.L. Gyorffy, J.B.Saunton and G.M. Stocks

Current Density Functional Theory and Orbital Magnetism 485 G. Vignale

Special Topics

Valence Density Functionals 513 J.F. Annett

Local Density Functional and Strong On-Site Correlations: The Electronic Structure of La 2Cu04 ...... 525 M.T. Czyzyk and G.A. Sawatzky

Mixed-Basis Scheme for DFT Calculations 549 H. Eschrig

Energetics of Solid Surfaces: Clusters and Anticlusters, Generalized Liquid-Drop Model, Energy Density, Stress Field, and Rigorous Theorems ...... 559 P. Ziesche

IV. LIQUIDS AND PLASMAS

General Reviews

Inhomogeneous Fluids and the Freezing Transition 581 N.W. Ashcroft

Density Functional Methods for Plasmas and Liquid Metals 625 C. Dharma-wardana and F. Perrot

Special Topics

Density Functional Approach to Vortex Matter 651

D.J.C. Jackson and M.P. Das

xiii Participants ... . 663

Index ...... 671

xiv