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Journal of Physics A Mathematical and General

Spectral density distribution moments ofN-electron Hamiltonians in the low-density limit

Josep Planelles, Fernando Rajadell, Jacek Karwowski

Published Mar 21, 1997• 7 citations
Publisher

Abstract

Previously derived expressions for moments of spectral density distribution of an N-electron Hamiltonian defined in a finite-dimensional model space spanned by a set of spin-adapted antisymmetrized products of orthonormal orbitals (full configuration interaction space) are reduced to the low electron density limit, i.e. to the case when the number of electrons is much smaller than the number of orbitals. The limit of a very large number of electrons is also considered.

DOI
10.1088/0305-4470/30/6/037

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Previously derived expressions for moments of spectral density distribution of an N-electron Hamiltonian defined in a finite-dimensional model space spanned by a set of spin-adapted antisymmetrized products of orthonormal orbitals (full configuration interaction space) are reduced to the low electron density limit, i.e. to the case when the number of electrons is much smaller than the number of orbitals. The limit of a very large number of electrons is also considered.
An N-electron Hamiltonian projected onto a K-orbital, antisymmetric and spin-adapted model space (in quantum chemistry known as the full configuration interaction space) may be expressed as a linear combination of products of generators of the unitary group . Consequently, spectral density distribution moments and other quantities which characterize global properties of the Hamiltonian spectra in are defined by the averages over the model space of products of the generators. This paper presents a set of new recurrent formulae for the averages and describes a simple graphical method of their evaluation.
Abstract Expressions for moments of spectral density distributions of a many‐electron Hamiltonian defined in a finite‐dimensional, antisymmetric, and spin‐adapted model space (as, e.g., a full configuration interaction space) are derived. The moments are expressed in terms of combinations of two‐electron integrals corresponding to a symmetric (a two‐electron singlet) and antisymmetric (two‐electron triplet) two‐electron wave functions. A diagrammatic approach based on Hugenholtz‐type diagrams and leading to a simple and universal classification scheme of the terms appearing in the expression for a specific moment is proposed. © 1995 John Wiley & Sons, Inc.