The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State PDF
Preview The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State
THE FUNDAMENTALS OF ELECTRON DENSITY, DENSITY MATRIX AND DENSITY FUNCTIONAL THEORY IN ATOMS, MOLECULES AND THE SOLID STATE Progress in Theoretical Chemistry and Physics VOLUME 14 Honorary Editor: W,N. Lipscomb (Harvard University, Cambridge, MA, U.S.A.) Editors-in-Chief' J. Maruani (Laboratoire de Chimie Physique, Paris, France) S. Wilson (Rutherford Appleton Laboratory, Oxfordshire, U.K.) Editorial Board: H. Agren (Royal Institute of Technology, Stockholm, Sweden) D. Avnir (Hebrew University ofJ erusalem, Israel) J. Cioslowski (Florida State University, Tallahassee, FL, U.S.A.) R Daudel (European Academy of Sciences, Arts and Humanities, Paris, France) G. Delgado-Barrio (Instituto de Matematicas y Fisica Fundamental, Madrid, Spain) E.K.U. Gross (Freie Universitiit, Berlin, Germany) W.E van Gunsteren (ETH-Zentrum, Zurich, Switzerland) K. Hirao (University of Tokyo, Japan) I. Hubac (Komensky University, Bratislava, Slovakia) M.P. Levy (Tulane University, New Orleans, LA, U.S.A.) R McW eeny (Universita di Pisa, Italy) P.G. Mezey (University of Saskatchewan, Saskatoon, SK, Canada) M.A.C. Nascimento (Instituto de Quimica, Rio de Janeiro, Brazil) N. Rahman (Dipartimento di Scienze Chimiche, Trieste, Italy) S.D. Schwartz (Yeshiva University, Bronx, NY, U.S.A.) S. Suhai (Cancer Research Center, Heidelberg, Germany) O. Tapia (University ofUppsala, Sweden) P.R Taylor (University ofW arwick, Coventry, U.K.) RG. Woolley (Nottingham Trent University, Nottingham, U.K.) Former Editors and Editorial Board Members: I. Prigogine (deceased) J. Rychlewski (deceased) Y.G. Smeyers (deceased) G.L. Malli (resigned) The titles published in this series are listed at the end of this volume. The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State Edited by N.!. Gidopoulos ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, England and S. Wilson Computational Science and Engineering Department, Atlas Centre, RutherfordAppleton Laboratory, Chilton, Oxfordshire, England , ~. Springer-Science+Business Media, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. Printed on acid-free paper ISBN 978-90-481-6508-7 ISBN 978-94-017-0409-0 (eBook) DOl 10.1007/978-94-017-0409-0 All Rights Reserved © 2003 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2003. Softcover reprint of the hardcover 1st edition 2003 No part of this work 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, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Progress in Theoretical Chemistry and Physics A series reporting advances in theoretical molecular and material sciences, including theoretical, mathematical and computational chemistry, physical chemistry and chemical physics Aim and Scope Science progresses by a symbiotic interaction between theory and experiment: theory is used to interpret experimental results and may suggest new experiments; experiment helps to test theoretical predictions and may lead to improved theories. Theoretical Chemistry (including Physical Chemistry and Chemical Physics) provides the concep tual and technical background and apparatus for the rationalisation of phenomena in the chemical sciences. It is, therefore, a wide ranging subject, reflecting the diversity of molecular and related species and processes arising in chemical systems. The book series Progress in Theoretical Chemistry and Physics aims to report advances in methods and applications in this extended domain. It will comprise monographs as well as collections of papers on particular themes, which may arise from proceedings of symposia or invited papers on specific topics as well as initiatives from authors or translations. The basic theories of physics - classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics - support the theoretical apparatus which is used in molecular sciences. Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns. Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry: it will, therefore, constitute a major part of this book series. However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions); molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals; surface, interface, solvent and solid-state effects; excited-state dynamics, reactive collisions, and chemical reactions. Recent decades have seen the emergence of a novel approach to scientific research, based on the exploitation of fast electronic digital computers. Computation provides a method of investigation which transcends the traditional division between theory and experiment. Computer-assisted simulation and design may afford a solution to complex problems which would otherwise be intractable to theoretical analysis, and may also provide a viable alternative to difficult or costly laboratory experiments. Though stemming from Theoretical Chemistry, Computational Chemistry is a field of research v Progress in Theoretical Chemistry and Physics in its own right, which can help to test theoretical predictions and may also suggest improved theories. The field of theoretical molecular sciences ranges from fundamental physical questions relevant to the molecular concept, through the statics and dynamics of isolated molecules, aggregates and materials, molecular properties and interactions, and the role of molecules in the biological sciences. Therefore, it involves the physical basis for geometric and electronic structure, states of aggregation, physical and chemical transformations, thermodynamic and kinetic properties, as well as unusual properties such as extreme flexibility or strong relativistic or quantum-field effects, extreme conditions such as intense radiation fields or interaction with the continuum, and the specificity of biochemical reactions. Theoretical chemistry has an applied branch - a part of molecular engineering, which involves the investigation of structure-property relationships aiming at the design, synthesis and application of molecules and materials endowed with specific functions, now in demand in such areas as molecular electronics, drug design or genetic engineering. Relevant properties include conductivity (normal, semi- and supra-), magnetism (ferro- or ferri-), optoelectronic effects (involving nonlinear response), photochromism and photoreactivity, radiation and thermal resistance, molecular recog nition and information processing, and biological and pharmaceutical activities, as well as properties favouring self-assembling mechanisms and combination properties needed in multifunctional systems. Progress in Theoretical Chemistry and Physics is made at different rates in these various research fields. The aim of this book series is to provide timely and in-depth coverage of selected topics and broad-ranging yet detailed analysis of contemporary theories and their applications. The series will be of primary interest to those whose research is directly concerned with the development and application of theoretical approaches in the chemical sciences. It will provide up-to-date reports on theoretical methods for the chemist, thermodynamician or spectroscopist, the atomic, molecular or cluster physicist, and the biochemist or molecular biologist who wish to employ techniques developed in theoretical, mathematical or computational chemistry in their research programmes. It is also intended to provide the graduate student with a readily accessible documentation on various branches of theoretical chemistry, physical chem istry and chemical physics. vi Contents Preface xi Contributing Authors xiii Part I The Workshop The Fundamental of Electron Density, Density Matrix and Density Func- tional Theory for Atoms, Molecules and the Solid State 3 B. T. Sutcliffe 1 Introduction 3 2 Density Matrix Theory (DMT) 4 3 Density Functional Theory (DFT) 5 4 Concl usions 7 The Programme 9 Abstracts of Talks and Posters 15 List of Participants 33 Part II The Proceedings The Keldysh formalism applied to time-dependent current-density-functional theory 43 Robert van Leeuwen 1 Introduction 43 2 Keldysh action 45 3 Kohn-Sham equations and linear response 49 4 TDOPM equations 52 5 Integral equation for the xc-kernel 55 6 The exchange-only kernel for the electron gas 58 7 Conclusions 60 Appendix: A 61 Appendix: B 62 Vll viii ELECTRON DENSITY THEORY Appendix: C 63 Appendix: D 65 Towards time-dependent density-functional theory for molecules in strong laser pulses 69 T. Kreibich, N.J. Gidopoulos, R. van Leeuwen, and E.K. U. Gross 1 Introduction 69 2 Formulation of DFT approach, absence of e-n correlation func tional 71 3 Ansatz to describe e-n correlation 72 Pair density functional theory 79 A. Nagy 1 Introduction 79 2 Pair density functional theory 80 3 Discussion 86 The Kummer Variety for N-particles 89 A. J. Coleman 1 Introduction 89 2 Key Definitions 90 3 Results 92 4 Next Steps? 94 Some Unsolved Problems in Density Matrix Theory and Density Functional Theory 97 Roy McWeeny 1 Preliminaries: the density functions 98 2 Density matrices to density functionals 103 3 Examples: density functions for simple systems 105 4 A group theoretical approach 108 5 Conclusion 113 The new formulation of the density functional theory, the limitation of accuracy of the Kohn-Sham potential and its expression in terms of the external potential 115 Andreas K. Theophilou 1 Introduction 115 2 The New Formulation of DFT 116 3 The KS potential as a mapping of the external potential. 126 Functional N-representability in density matrix and density functional the- ory 129 E. V. Ludeiia, V. V. Karasiev , P. Nieto 1 Introduction 130 2 Functional N -represent ability 132 3 Functional N-representability through built-in pure-state N- represent ability conditions 134 Contents IX 4 Functional N-representability in DFT: Application to Hooke's atom 136 4.1 General considerations 136 4.2 Constructive approach based on local-scaling transfor- mations 137 4.3 Construction of exact functional for Hooke's atom 138 5 Conclusions 140 6 Acknowledgments 142 Density-functional theory for the Hubbard model 145 K. Capelle, N. A. Lima, M. F. Silva, and L. N. Oliveira 1 The Hubbard model and density-functional theory 146 2 Exchange-correlation energy of the Hubbard model 149 3 Applications 154 3.1 Luttinger liquids 154 3.2 Impurity models 156 3.3 Spin-density waves 160 3.4 Mott insulator 162 4 Summary and outlook 165 Demonstrating the effectiveness of a nonlocal density functional description of exchange and correlation 169 Philip P. Rushton and Stewart J. Clark 1 Introduction 169 2 WDA theory 171 3 Cosine-wave electron gas. 172 3.1 XC-energy density exc(r) 173 3.2 Total XC-energy 174 3.3 XC-potentials 175 3.4 XC-holes 175 3.5 Pair-correlation functions 177 4 Large amplitude perturbations 177 5 Conclusions 179 6 Acknowledgements 182 Incorporating the Virial Field into the Hartree-Fock Equations 185 R.F. W. Bader 1 Introduction 186 2 Incorporation of V(r) into the Hartree-Fock Equations 189 Hohenbere;-Kohn Theorem and Constrained Search Formulation for Diago- nal Spm Density Functional Theory 195 Nikitas 1. Gidopoulos 1 Introduction 195 2 Spin-Density-Fuctional Theory 196 3 Diagonal-Spin-Density-Functional theory 201 x ELECTRON DENSITY THEORY Part III The Forum The Forum - Questions 209 The Forum - Discussion 211 A Glossary 219 A Selected Bibliography 221 Index 223
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