Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Chemistry

Spectral density distribution of an N‐electron Hamiltonian in a finite‐dimensional and spin‐adapted model space

Fernando Rajadell, Josep Planelles, Jacek Karwowski, V. Mas

Published Oct 15, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1002/qua.560560202

Related papers

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

Josep Planelles, Fernando Rajadell, Jacek Karwowski

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.

Journal of Physics A Mathematical and General•Mar 21, 1997•7 citations

Operator averages in finite-dimensional N-electron model spaces: a diagrammatic approach

Jacek Karwowski

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.

Molecular Physics•Jun 10, 2004•0 citations

Calculation of moments of spectral density distributions in finite-dimensional N-electron spin-adapted spaces

Alicia Torre, Luis Laín

This paper reports a calculation of moments of spectral density distributions which are used in statistical theory of spectra of many-electron systems. The procedure lead to formulae which are fit for computer evaluations. The method is based on the determination of spin-adapted traces of powers of the Hamiltonian operator, represented in a finite-dimensional antisymmetric and spin-adapted Hilbert space. A whole study of the traces which appear in this problem is described.

Journal of Physics A Mathematical and General•Jan 21, 1995•4 citations

The first two moments of energy level distributions in N-electron spin-adapted model spaces

Jacek Karwowski, M. Bancewicz

Formulae are derived for the average value and for the dispersion of the spectrum of an electronic Hamiltonian in a finite-dimensional, antisymmetric and spin-adapted space. Both the moments are expressed in terms of the corresponding two-electron quantities. The derivation is based on the theory of spin-adapted reduced Hamiltonians.

Journal of Physics A Mathematical and General•Dec 21, 1987•31 citations

Eigenvalues of model Hamiltonian matrices from spectral density distribution moments: The Heisenberg spin Hamiltonian

Jacek Karwowski, Dorota Biel�nska-Wa, Jacek Jurkowski

An approach aimed at approximating the extreme (the lowest and/or the highest) eigenvalues of matrices representing many-electron model Hamiltonians from a knowledge of several spectral density distribution moments is proposed. A detailed discussion of the Heisenberg spin Hamiltonian spectrum is presented as an example of an application. © 1996 John Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1996•17 citations

Calculation of traces of Hamiltonian powers in finite-dimensional N-electron spin-adapted spaces: application to the determination of moments of spectral density distributions

Luis Laín, Alicia Torre

Explicit formulae for the calculation of traces of N-order replacement operators in finite-dimensional, antisymmetric and spin-adapted N-electron Hilbert spaces are derived. These formulae are useful in the calculation of traces of Hamiltonian powers and provide an easier determination of moments of spectral density distributions according to the general procedure reported recently.

Journal of Physics A Mathematical and General•Jun 21, 1995•2 citations
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.
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.