Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134)

597 Pages·2007·2.803 MB·English

by  David A. Mazziotti

REDUCED-DENSITY-
MATRIX MECHANICS:
WITH APPLICATION TO
MANY-ELECTRON ATOMS
AND MOLECULES
ADVANCESINCHEMICALPHYSICS
VOLUME134
Edited by
DAVID A. MAZZIOTTI
Series Editor
STUARTA. RICE
DepartmentofChemistry
and
TheJamesFranckInstitute
TheUniversityofChicago
Chicago,Illinois
WILEY-INTERSCIENCE
A JOHN WILEY & SONS, INC., PUBLICATION

REDUCED-DENSITY-MATRIX MECHANICS:
WITH APPLICATION TO MANY-ELECTRON
ATOMS AND MOLECULES
A SPECIALVOLUMEOFADVANCES INCHEMICAL PHYSICS
VOLUME134
EDITORIALBOARD
BRUCE J.BERNE, Department of Chemistry, Columbia University, New York,New York,
U.S.A.
KURT BINDER, Institut fu¨r Physik, Johannes Gutenberg-Universita¨t Mainz, Mainz,
Germany
A. WELFORD CASTLEMENA, JR., Department of Chemistry, The Pennsylvania State
University,UniversityPark,Pennsylvania,U.S.A.
DAVID CHANDLER, Department of Chemistry, University of California, Berkeley,
California, U.S.A.
M.S.CHILD,Department ofTheoretical Chemistry,UniversityofOxford,Oxford,U.K.
WILLIAM T. COFFEY, Department of Microelectronics and Electrical Engineering, Trinity
College,UniversityofDublin,Dublin,Ireland
F.FLEMINGCRIM,DepartmentofChemistry,UniversityofWisconsin,Madison,Wisconsin,
U.S.A.
ERNESTR.DAVIDSON,DepartmentofChemistry,IndianaUniversity,Bloomington,Indiana
U.S.A.
GRAHAM R. FLEMING, Department of Chemistry, University of California, Berkeley,
California, U.S.A.
KARLF.FREED,TheJamesFranckInstitute,TheUniversityofChicago,Chicago,Illinois,
U.S.A.
PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems, Brussels,
Belgium
ERIC J. HELLER, Institute for Theoretical Atomic and Molecular Physics, Harvard-
SmithsonianCenter forAstrophysics,Cambridge,Massachusetts, U.S.A.
ROBIN M. HOCHSTRASSER, Department of Chemistry, The University of Pennsylvania,
Philadelphia,Pennsylvania,U.S.A.
R.KOSLOFF,TheFritzHaberResearchCenterforMolecularDynamicsandDepartmentof
PhysicalChemistry,The HebrewUniversityofJerusalem,Jerusalem,Israel
RUDOLPH A. MARCUS, Department of Chemistry, California Institute of Technology,
Pasadena, California,U.S.A.
G.NICOLIS,CenterforNonlinearPhenomenaandComplexSystems,Universite´ Librede
Bruxelles, Brussels,Belgium
THOMAS P. RUSSELL, Department of Polymer Science, University of Massachusetts,
Amherst,Massachusetts, U.S.A.
DONALD G. TRUHLAR, Department of Chemistry, University of Minnesota, Minneapolis,
Minnesota,U.S.A.
JOHN D. WEEKS, Institute for Physical Science and Technology and Department of
Chemistry,UniversityofMaryland,College Park, Maryland,U.S.A.
PETER G. WOLYNES, Department of Chemistry, University of California, San Diego,
California, U.S.A.
REDUCED-DENSITY-
MATRIX MECHANICS:
WITH APPLICATION TO
MANY-ELECTRON ATOMS
AND MOLECULES
ADVANCESINCHEMICALPHYSICS
VOLUME134
Edited by
DAVID A. MAZZIOTTI
Series Editor
STUARTA. RICE
DepartmentofChemistry
and
TheJamesFranckInstitute
TheUniversityofChicago
Chicago,Illinois
WILEY-INTERSCIENCE
A JOHN WILEY & SONS, INC., PUBLICATION
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CONTRIBUTORS TO VOLUME 134
D. R. ALCOBA Departamento de F´ısica, Facultad de Ciencias Exactas y
Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428,
Buenos Aires, Argentina
PAUL W. AYERS Department of Chemistry, McMaster University, Hamilton,
Ontario L8S 4M1, Canada
BASTIAANJ.BRAAMSDepartmentofMathematicsandComputerScience,Emory
University, 400 Dowman Drive #W401, Atlanta, GA 30322 USA
GARNETKIN-LICCHANDepartmentofChemistryandChemicalBiology,Cornell
University, Ithaca, New York 14853-1301 USA
A. JOHN COLEMAN Department of Mathematics and Statistics, Queen’s
University, Kingston, Ontario K7L 3N6, Canada
ERNEST R. DAVIDSON Department of Chemistry, University of Washington,
Bagley Hall 303C/Box 351700, Seattle, WA 98195-1700 USA
ROBERT M. ERDAHL Department of Mathematics and Statistics, Queen’s
University, Kingston, Ontario K7L 3N6, Canada
MITUHIROFUKUDADepartmentofMathematicalandComputingSciences,Tokyo
Institute of Technology, Japan
JOHNE.HARRIMANDepartmentofChemistry,UniversityofWisconsin,Madison,
WI 53706 USA
JOHN M. HERBERT Department of Chemistry, The Ohio State University,
Columbus, OH 43210 USA
SABRE KAIS Department of Chemistry, Purdue University, West Lafayette, IN
47907 USA
WERNER KUTZELNIGG Lehrstuhl fu¨r Theoretische Chemie Ruhr-Universita¨t
Bochum, D-44780 Bochum, Germany
DAVID A. MAZZIOTTI Department of Chemistry and The James Franck Institute,
The University of Chicago, Chicago, IL 60637 USA
DEBASHIS MUKHERJEE Department of Physical Chemistry, Indian Association for
the Cultivation of Science, Calcutta 700 032, India and Jawaharlal Center
for Advanced Scientific Research, Bangalore, India
v
vi contributors to volume 134
MAHO NAKATA Department of Applied Chemistry, The University of Tokyo,
Japan
JEROME K. PERCUS Courant Institute and Department of Physics, New York
University, 251 Mercer Street, New York, NY 10012 USA
MARIO PIRIS Kimika Fakultatea, Euskal Herriko Unibertsitatea, and Donostia
International Physics Center (DIPC) P.K. 1072, 20080 Donostia, Euskadi,
Spain
B. C. RINDERSPACHER Department of Chemistry, The University of Georgia,
Athens, GA 30602 USA
MITJA ROSINA Faculty of Mathematics and Physics, University of Ljubljana,
Jadranska 19, P.O. Box 2964, 1001 Ljubljana, Slovenia and Jozˇef Stefan
Institute, Ljubljana, Slovenia
C.VALDEMOROInstitutodeMatema´ticasyF´ısicaFundamental,ConsejoSuperior
de Investigaciones Cient´ıficas, Serrano 123, 28006 Madrid, Madrid, Spain
MAKOTO YAMASHITA Department of Information System Creation, Kanagawa
University, Japan
TAKESHI YANAI Department of Chemistry and Chemical Biology, Cornell
University, Ithaca, New York 14853-1301 USA
ZHENGJI ZHAO High Performance Computing Research Department, Lawrence
Berkeley National Laboratory, 1 Cyclotron Road, Mail Stop 15F1650,
Berkeley, CA 94720 USA
PREFACE
Inthe1950sseveralscientistsincludingJosephMayer,JohnColeman,Per-Olov
Lowdin, and Charles Coulson expounded on the possibilities for using the two-
electronreduceddensitymatrixtocomputetheenergiesandpropertiesofatomic
and molecular systems without the many-electron wavefunction. AnN-electron
densitymatrixmaybeassembledfromanN-electronwavefunctionbymultiply-
ingthewavefunctioncbyitsadjointc(cid:2) toobtaincc(cid:2).IntegratingtheN-electron
density matrix over all save two electrons yields the two-electron reduced den-
sity matrix (2-RDM). Because electrons interact with each other in pairs by
Coulomb repulsion, the energies and other electronic properties of atoms and
molecules can be computed directly from a knowledge of the 2-RDM. The
factthatthe2-RDMistherepositoryofallthephysicallyandchemicallyimpor-
tantinformationinthemany-particlewavefunctionsuggeststhetantalizingpos-
sibility that for a given molecular system the 2-RDM can be computed directly
withoutconstructingthemany-electronwavefunction.Forfiftyyearsbothscien-
tists and mathematicians have pursued the goal of a 2-RDM approach to mole-
cular electronic structure. Efforts, however, were stymied because the 2-RDM
must be constrained by nontrivial conditions to ensure that the 2-RDM derives
from an N-electron wavefunction. These restrictions on RDMs were given the
appellation N-representability conditions by John Coleman. Ten years ago the
calculation of the 2-RDM without the wavefunction seemed an impossibility.
Dramatic progress, however, has been made since then, and today two comple-
mentary approaches to the direct calculation of the 2-RDM have emerged. The
presentbook,withchaptersfrommanyofthescientistswhocontributedtothese
advances,providesadetailedyetpedagogicaltourofmodern2-RDMtheoryand
its present and potential applications to many-electron atoms and molecules.
Ifirstbecameinterestedin2-RDMtheorywhenreadingarticlesbyColeman
and ter Haar in the chemistry library at Princeton University in the summer of
1995. For someone who had just graduated college, reading Coleman and ter
Haar was rather ‘‘heady’’ material. However, despite some of the difficulties
from N-representability it seemed apparent that a 2-RDM theory would offer
a powerful bridge between the density functional methods, which were rapidly
gainingpopularityaftermanyyearsofdevelopment,andtheabinitiowavefunc-
tion methods. At Harvard under the splendid guidance of Dudley Herschbach I
began to think about computing the 2-RDM without the wavefunction. In the
vii