Many-Electron Densities and Reduced Density Matrices

1. Front Matter

   Pages i-xiv

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2. Properties of Reduced Density Matrices

   1. RDMs: How did we get here?

      • A. John Coleman

      Pages 1-17

   2. Some Theorems on Uniqueness and Reconstruction of Higher-Order Density Matrices

      • Mitja Rosina

      Pages 19-32

   3. Cumulant Expansions of Reduced Densities, Reduced Density Matrices, and Green’s Functions

      • Paul Ziesche

      Pages 33-56

   4. On Calculating Approximate and Exact Density Matrices

      • Robert Erdahl, Beiyan Jin

      Pages 57-84

3. The Contracted Schrődinger Equation

   1. Density Equation Theory in Chemical Physics

      • Hiroshi Nakatsuji

      Pages 85-116

   2. Critical Questions Concerning Iterative Solution of the Contracted Schrödinger Equation

      • Carmela Valdemoro, L. M. Tel, E. Pérez-Romero

      Pages 117-137

   3. Cumulants and the Contracted Schrödinger Equation

      • David A. Mazziotti

      Pages 139-163

4. Density Matrix Functional Theory

   1. Natural Orbital Functional Theory

      • S. Goedecker, C. J. Umrigar

      Pages 165-181

   2. The Pair Density in Approximate Density Functionals: The Hidden Agent

      • Neepa T. Maitra, Kieron Burke

      Pages 183-208

   3. Functional N-representability in Density Matrix and Density Functional Theory: An Illustration for Hooke’s Atom

      • E. V. Ludeña, V. Karasiev, A. Artemiev, D. Gómez

      Pages 209-230

5. Electron Intracule and Extracule Densities

   1. Intracule and Extracule Densities: Historical Perspectives and Future Prospects

      • Elmer Valderrama, Jesus M. Ugalde, Russell J. Boyd

      Pages 231-248

   2. Topology of Electron Correlation

      • Jerzy Cioslowski

      Pages 249-265

   3. Electron-Pair Densities of Atoms

      • Toshikatsu Koga

      Pages 267-298

6. Back Matter

   Pages 299-301

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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

• Florida State University, Tallahassee, USA

  Jerzy Cioslowski

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