Many-Electron Densities and Reduced Density Matrices

  • Jerzy Cioslowski

Part of the Mathematical and Computational Chemistry book series (MACC)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Properties of Reduced Density Matrices

  3. The Contracted Schrődinger Equation

    1. Hiroshi Nakatsuji
      Pages 85-116
    2. Carmela Valdemoro, L. M. Tel, E. Pérez-Romero
      Pages 117-137
    3. David A. Mazziotti
      Pages 139-163
  4. Density Matrix Functional Theory

    1. S. Goedecker, C. J. Umrigar
      Pages 165-181
    2. Neepa T. Maitra, Kieron Burke
      Pages 183-208
  5. Electron Intracule and Extracule Densities

    1. Elmer Valderrama, Jesus M. Ugalde, Russell J. Boyd
      Pages 231-248
    2. Jerzy Cioslowski
      Pages 249-265
    3. Toshikatsu Koga
      Pages 267-298
  6. Back Matter
    Pages 299-301

About this book


Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil­ iary yet essential N-representability conditions turned quite bleak. How­ ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv­ ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al­ lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her­ alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven­ tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry.


Atom Schrödinger equation chemical physics density density functional theory development electron illustration physics simulation structure topology

Editors and affiliations

  • Jerzy Cioslowski
    • 1
  1. 1.Florida State UniversityTallahasseeUSA

Bibliographic information

  • DOI
  • Copyright Information Kluwer Academic/Plenum Publishers, New York 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-6890-8
  • Online ISBN 978-1-4615-4211-7
  • Series Print ISSN 1568-217X
  • Buy this book on publisher's site