Conceptual Foundations of Materials A Standard Model for Ground- and Excited-State Properties i This page intentionally left blank ii Series: Contemporary Concepts of Condensed Matter Science Series Editors: E. Burstein, M.L. Cohen, D.L. Mills and P.J. Stiles Conceptual Foundations of Materials A Standard Model for Ground- and Excited-State Properties Steven G. Louie and Marvin L. Cohen Department of Physics University of California Berkeley, CA, USA Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo iii Elsevier Radarweg29,POBox211,1000AEAmsterdam,TheNetherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Firstedition2006 Copyrightr2006ElsevierB.V. Allrightsreserved Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeanselectronic,mechanical,photocopying, recordingorotherwisewithoutthepriorwrittenpermissionofthepublisher PermissionsmaybesoughtdirectlyfromElsevier’sScience&TechnologyRights DepartmentinOxford,UK:phone(+44)(0)1865843830;fax(+44)(0)1865853333; email:permissions@elsevier.com.Alternativelyyoucansubmityourrequestonlineby visitingtheElsevierwebsiteathttp://elsevier.com/locate/permissions,andselecting ObtainingpermissiontouseElseviermaterial Notice Noresponsibilityisassumedbythepublisherforanyinjuryand/ordamagetopersons orpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuse oroperationofanymethods,products,instructionsorideascontainedinthematerial herein.Becauseofrapidadvancesinthemedicalsciences,inparticular,independent verificationofdiagnosesanddrugdosagesshouldbemade LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN-13:978-0-444-50976-5 ISBN-10:0-444-50976-3 ISSN: 1572-0934 ForinformationonallElsevierpublications visitourwebsiteatbooks.elsevier.com PrintedandboundinTheNetherlands 06 07 08 09 10 10 9 8 7 6 5 4 3 2 1 iv CONTENTS LIST OF CONTRIBUTORS vii PREFACE ix 1. OVERVIEW: A STANDARD MODEL OF SOLIDS M. L. Cohen 1 2. PREDICTING MATERIALS AND PROPERTIES: THEORY OF THE GROUND AND EXCITED STATE S. G. Louie 9 3. AB INITIO MOLECULAR DYNAMICS: DYNAMICS AND THERMODYNAMIC PROPERTIES R. Car 55 4. STRUCTURE AND ELECTRONIC PROPERTIES OF COMPLEX MATERIALS: CLUSTERS, LIQUIDS AND NANOCRYSTALS J. R. Chelikowsky 97 5. QUANTUM ELECTROSTATICS OF INSULATORS: POLARIZATION, WANNIER FUNCTIONS, AND ELECTRIC FIELDS D. Vanderbilt and R. Resta 139 6. ELECTRON TRANSPORT P. B. Allen 165 AUTHOR INDEX 219 SUBJECT INDEX 229 v This page intentionally left blank vi LIST OF CONTRIBUTORS P. B. Allen DepartmentofPhysicsandAstronomy,StateUniversityof New York, Stony Brook, NY 11794-3800, USA R. Car Department of Chemistry, Princeton University, Princeton, NJ 08544, USA J. R. Chelikowsky Departments of Physics and Chemical Engineering, Insti- tute for Computational Engineering and Sciences, Univer- sity of Texas, Austin, TX 78712, USA M. L. Cohen Department of Physics, University of California at Berkeley and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA S. G. Louie Department of Physics, University of California at Berkeley and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA R. Resta INFM-DEMOCRITOS National Simulation Center, Via Beirut 4, I-34014 Trieste, Italy and Dipartimento di Fisica Teorica, Universita` di Trieste, Strada Costiera 11, I-34014 Trieste, Italy D. Vanderbilt Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019, USA vii This page intentionally left blank viii PREFACE Thefundamentalinteractionsofimportance incondensedmatter aretheCoulomb attraction between the electrons and the nuclei and the Coulomb repulsion among the electrons and among the nuclei. The effects of many electrons under these interactions, obeying the laws of quantum mechanics, ultimately determine all the observed phenomenaandpropertiesofcondensedmattersystems. Thus,electronic structuretheoryhasplayedacentralroleinourunderstandingofatoms,molecules, andsolidssincethedawnofquantummechanics.Electronicstructuretheoryisnow a pillar of condensed matter science and is perhaps the largest theoretical sub-area in condensed matter physics. The goal of this volume in the series on ‘‘Conceptual Foundations of Material Properties: A Standard Model for Ground- and Excited-state Properties’’ is to present the fundamentals of electronic structure theory that are central to the un- derstanding and prediction of materials phenomena and properties. The emphasis willbeonfoundationsandconcepts.Thechaptersaredesignedtoofferabroadand comprehensive perspective of the field. They cover the basic aspects of modern electronic structure approaches and highlight their applications to the structural (ground state,vibrational,dynamicandthermodynamic,etc.)andelectronic(spec- troscopic,dielectric,magnetic,transport,etc.)propertiesofrealmaterialsincluding solids, clusters, liquids, and nanostructure materials. This framework also forms a basis for studies of emergent properties arising from low-energy electron correla- tions and interactions such as the quantum Hall effects, superconductivity, and other cooperative phenomena. Although some of the basics and models for solids were developed in the early partofthelastcenturybyfiguressuchasBloch,Pauli,FermiandSlater,thefieldof electronicstructuretheorywentthroughaphenomenalgrowthduringthepasttwo decades, leading to new concepts, understandings and predictive capabilities for determining the ground- and excited-state properties of real, complex materials from first principles. For example, theory can now be used to predict the existence and properties of materials not previously realized in nature or in the laboratory. Computer experiments can be performed to examine the behavior of individual atomsinaparticularprocess,toanalyzetheimportanceofdifferentmechanisms,or just to see what happens if one varies the interactions and parameters in the sim- ulation. Also, with ab initio calculations, one can determine from first principles important interaction parameters which are needed in model studies of complex processesorhighlycorrelatedsystems.Eachtimeanewmaterialoranovelformof a material is discovered, electronic structure theory inevitably plays a fundamental role in unraveling its properties. ix