The Electronic Structure of Complex Systems PDF
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The Electronic Structure of Complex Systems NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical D. Reidel Publishing Company and Physical Sciences Dordrecht, Boston, and Lancaster o Behavioral and Social Sciences Martinus Nijhoff Publishers E Engineering and The Hague, Boston, and Lancaster Materials Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, and Tokyo Recent Volumes in this Series Volume 111-Monopole '83 edited by James L. Stone Volume 112-Condensed Matter Research Using Neutrons: Today and Tomorrow edited by Stephen W. Lovesey and Reinhard Scherm Volume 113-The Electronic Structure of Complex Systems edited by P. Phariseau and W. M. Temmerman Volume 114-Energy Transfer Processes in Condensed Matter edited by Baldassare Di Bartolo Volume 115-Progress in Gauge Field Theory edited by G. t'Hooft, A. Jaffe, G. Lehman, P. K. Mitter, I. Singer and R. Storra Volume 116-Nonequilibrium Cooperative Phenomena in Physics and Related Fields edited by Manuel G. Velarde Volume 117-Moment Formation in Solids edited by W. J. L. Buyers Series B: Physics The Electronic Structure of Complex Systems Edited by P. Phariseau Rijksuniversiteit Ghent, Belgium and w. M. Temmerman SERe Daresbury Laboratory Daresbury, United Kingdom Plenum Press New York and London Published in cooperation with NATO Scientific Affairs ·Division Proceedings of a NATO Advanced Study Institute on Electronic Structure of Complex Systems, held July 12-23, 1982, at the State University of Ghent, Belgium Library of Congress Cataloging in Publication Data NATO Advanced Study Institute on Electronic Structure of Complex Systems (1982: State University of Ghent) The electronic structure of complex systems. (NATO ASI series. Series B, Physics; v. 113) "Published in cooperation with NATO Scientific Affairs Division." "Proceedings of a NATO Advanced Study Institute on Electronic Structure of Complex Systems, held July 12-23, 1982, at the State University of Ghent, Belgium"-Verso t.p. Includes bibliographical references and index. 1. Electronic structure-Congresses. 2. Free electron theory of metals-Con gresses. I. Phariseau, P. II. Temmerman, W. M. III. Title. IV. Series. QC176.8.E4N336 1982 530.4'1 84-17856 ISBN-13: 978-1-4612-9466-5 e-ISBN-13: 978-1-4613-2405-8 001: 10.1007/978-1-4613-2405-8 © 1984 Plenum Press, New York Softcover reprint of the hardcover 1s t edition 1984 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved. 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 PREFACE We present here the transcripts of lectures and talks which were delivered at the NATO ADVANCED STUDY INSTITUTE "Electronic Structure of Complex Systems" held at the State University of Ghent, Belgium during the period July 12-23, 1982. The aim of these lectures was to highlight some of the current progress in our understanding of the electronic structure of com plex systems. A massive leap forward is obtained in bandstructure calculations with the advent of linear methods. The bandtheory also profitted tremendously from the recent developments in the density functional theories for the properties of the interacting electron gas in the presence of an external field of ions. The means of per forming fast bandstructure calculations and the confidence in the underlying potential functions have led in the past five years or so to a wealth of investigations into the electronic properties of elemental solids and compounds. The study of the trends of the electronic structure through families of materials provided invalu able insights for the prediction of new materials. The detailed study of the electronic structure of specific solids was not neglected and our present knowledge of d- and f-metals and metal hydrides was reviewed. For those systems we also investi gated the accuracy of the one electron potentials in fine detail and we complemented this with the study of small clusters of atoms where our calculations are amenable to comparison with the frontiers of quantum chemistry calculations. The band theory of random solids based on KKR-CPA calculations has also seen a rapid developement over the past years. Those methods have not only led to the study of the electronic structure of random substitutional alloys but the technique can also be used to study metallic magnetism at finite temperature. We also devoted some time to the techniques of first principles lattice dynamics which has seen steady progress and where the pre- v vi PREFACE sent techniques will lead to first principles calculations of phonon spectra in the near future. Fermi surface studies were crucial to the development of bandtheory in the 1960's and 1970's and is now complemented by spectroscopy calculations which can probe the occupied and unoccu pied bands and is developing as an invaluable way of analyzing the calculated bands. We set aside some time to the study of materials which demand more theoretical investigations and where in the near future the bandstructure calculations should contribute. In short, this institute was dedicated to the coming-of-age of band theory techniques in the study of the electronic properties of metals and this will lead in the 1980's to the prediction of new materials and the understanding from first principles of such outstanding issues in solid state physics as metallic magnetism at finite temperature and electron-ion interactions. This institute was timely both in the presentation of the methods developed and to give the flavor of new things to corne. While the individual contributions are self-contained accounts of the relevant topics, and no effort has been made to standardize the notations all through the text, cross references are frequent and each is written with evident awareness of the unity of the subject. The Advanced Study Institute was financially sponsored by the tIATO Scientific Affairs Division (Brussels, Belgium). Co-sponsors were the National Science Foundation (Washington, D.C., U.S.A.) and the State University of Ghent. In particular we are indebted to Prof. Dr. Ir. A. Cottenie, Rector of the University of Ghent, who made it possible that the institute took place in ideal circumstances. We are grateful to all lecturers for their most valuable con tribution and their collaboration in preparing the manuscripts. The Institute itself could not have been realized without the enormous enthusiasm of all participants and lecturers and without the unti ring efforts of our co-workers at the "Seminarie voor Theoretische Vaste Stof- en Lage Energie Kernfysica". Also Hrs. A. Goossens- De Paepe's help in typing the manuscripts is gratefully acknowledged. P. Phariseau W. Ternrnerman Ghent and Daresbury, December 1983 CONTENTS The Role of Electronic Structure Computations in the the Advancement of Solid State Physics • • . . • • . 1 V. Heine Linear Methods in Band Theory. • . . . . . . . . . . . • . .. 11 O.K. Andersen Den~ity Functional Theory for Solids • . . . . . . . . . . . . 67 U. von Barth Density Functional Calculations for Atomic Clusters . • • • • 141 J. Harris The Band 110del for d- and f- Metals • . . . . . . . . • . • . 183 D.D. Koelling Electronic Structure of Hydrogen in Metals. . . . . . . . • • 243 M. Gupta First Principles Lattice Dynamics of Transition Metals ...• 345 W. Weber A First Principles Approach to the Band Theory of Random Metallic Alloys . . . . • . • • . . . . . . . . . . . . . 463 G.M. Stocks and H. Winter Alloy Phase Diagrams from First Principles 581 J.W.D. Connolly and A.R. Williams On the Theory of Ferro-magnetism of Transition Metals at Finite Temperatures . • • • . • • . . . . . • . • . . 593 B.L. Gyorffy, J. Kollar, A.J. Pindor, G.M. Stocks, J. Staunton and H. Winter Relating Electron Configuration, Crystal Structure and Bandstructure. ••..•••..•..••.•.•• 657 J.A. Wilson vii viii CONTENTS Electron Spectroscopy of Metallic Systems . . . • . . . . . . 709 P.J. Durham Features and Applications of the Haydock Recursion Hethod . . 761 V. Heine The Recursion Method and the Estimation of Local Densities of States . . . • . • . . . . . . . • . . . . . . . . . .. 769 N. Beer and D.G. Pettifor Computer Experiments on Amorphous Transition Hetals . . . . . 779 G.P. Weir and G.J. Morgan Index . • . . . • . . . . . . . . . . . 791 THE ROLE OF ELECTRONIC STRUCTURE COMPUTATIONS IN THE ADVANCEMENT OF SOLID STATE PHYSICS Volker Heine Cavendish Laboratory Madingley Road Cambridge CB3 OHE England ABSTRACT The present state of electronic structure computations is reviewed, and the contribution it can make to the main stream of solid state physics is analysed with examples. At the opening of this Nato Advanced Study Institute I would like to thank the University of Gent and Prof. Phariseau and Dr. Ternrnermann for bringing it about : I know from recent personal experience what a lot of work is required. The subject of electro nic structure calculations is a very timely one. We are often re minded how the power of computers is growing exponentially. Is our subject of electronic structure calculations also growing exponen tially in its contribution to the advancement of main-stream solid state physics ? What is its role? Much of the following two weeks will be devoted to the tech nical intricacies of making such calculations, and before we get wholly immersed in those I want to set the work in the wider con text : what do we hope to achieve? In all of science, achieving a real advance in understanding often depends on selecting just the right experiment or calculation to shed light on a phenomenon and not merely in heaping up more facts. Before answering those questions we need to focus on what are the present-day challenges in solid state physics. After all, superconductivity and semiconductors have been around a long time. Broadly speaking I see three main frontiers. 1. There is what one could call solid state chemistry understan- 2 v. HEINE ding the differences between similar elements or compounds. Why are Cu, Ag and Au different in various respects ? Why do Nb com pounds or certain crystal structures figure prominently among high Tc superconductors ? 2. Complex materials. Amorphous metals, metal cluster compounds, layer compounds, one-dimensional materials etc. etc. with their fascinating and unexpected variety of properties. 3. Complex phenomena : such as defects with their surrounding ato mic displacements and their interactions, and our old friends corrosion and catalysis. I want to emphasize that in all these fields there are inte resting principles to be discovered and understood. It is not just a matter of dotting detailed its or crossing tIS. But coming to grips with the details is an essential part of the process : we cannot say that we fully understand invar alloys until we under stand why a few alloys show the phenomenon and others do not. Clearly such understanding is not going to come without intel ligent computation, which establishes an essential role for our subject at the core of modern solid state research. But our analy sis also shows a difficulty of the computational approach. I believe Rutherford warned that the occupational hazard of experimental phy sics is to degenerate into what he called mere "stamp collecting". Similarly a computation can easily boil down to mere retesting of the Schrodinger equation. If one computes the conductivity or mag netic susceptibility of some material and gets agreement with expe riment, one has achieved two things. Firstly one has shown that one's approximations (and all electronic structure calculations involve approximations) are valid, but in most cases this will al ready have been established by similar calculations of related ma terials or properties. Secondly one has demonstrated that God be lieves in the same Schrodinger equation governing the real material on the laboratory bench as one has programmed into the computer. I exaggerate slightly. Nevertheless the truth remains that the essential difficulty of research lies in getting beyond this point. Analogous comments apply to experimental work, as already indica ted, and of course to theoretical physics too. So I do not make my remarks in order to denigrate computational physics, but as a spur to formulating its proper positive role. There is a further difficulty : having invested several man-years in developping a computational method, one cannot toss it aside and develop a dif ferent one just to respond to a fashionable hot discovery or con troversy. One is tied to one's soft-ware, and in order to parti cipate in the most active research front one has to sift literally hundreds or thousands of experimental what-is-going-on in order to see what is most significant and where one can best jump in. But again the same applies to experimentalists and theorists.
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