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

Journal of Physics A Mathematical and General

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

Alicia Torre, Luis Laín

Published Jan 21, 1995• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/28/2/005

Related papers

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

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

Fernando Rajadell, Josep Planelles, Jacek Karwowski +1 more

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.

International Journal of Quantum Chemistry•Oct 15, 1995•3 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 traces ofp-order replacement operators overN-electron spin-adapted spaces

Alicia Torre, Luis Laín, Judith Millán

We present here a simple method for the direct evaluation of traces of p-order replacement operators (p-RO's) calculated in a finite-dimensional, antisymmetric, and spin-adapted N-electron space. The procedure is based on the reduction of the operator order together with a performance of the summations through Slater determinants. Very useful and general formulas, which can be applied to RO's of any order p\ensuremath{\le}N, are then derived.

Physical Review A•Feb 1, 1993•18 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

Traces of powers of the Hamiltonian operator in finite-dimensional antisymmetric model spaces

Fernando Rajadell, Josep Planelles, Jacek Karwowski

A general method of evaluation of traces of arbitrary powers of Hermitian operators containing one- and two-body interactions and defined in a finite-dimensional model space is presented. The model space is taken as the antisymmetric and spin-adapted part of an N-fold Cartesian product of a one-electron space. The method is based on the symmetric group approach to the theory of many-electron systems.

Journal of Physics A Mathematical and General•Aug 7, 1993•11 citations
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.
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.