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 B Atomic Molecular and Optical Physics

Peculiar property of conditional electron densities

Toshikatsu Koga

Published Sep 7, 2012• 4 citations
Publisher

Abstract

The pth-order conditional electron density C(p)N(r1, ..., rp − 1|rp) of an N-electron system is shown to have a peculiar property that when the radius rp = |rp| of the pth electron approaches ∞, it reduces to the (p−1)th-order reduced density Γ(p − 1)N − 1(r1, ..., rp − 1) divided by p of the (N−1)-electron system arising from the removal of an electron from the original system, where both systems are considered to be in their ground states.

DOI
10.1088/0953-4075/45/18/185003

Related papers

Construction of explicitly correlated one-electron reduced density matrices

Jerzy Ciosłowski

A general construction of an ensemble N-representable one-electron reduced density matrix Γ1(r1→′;r→1) is presented. Unlike the conventional spectral representation, it explicitly incorporates the recently derived discontinuity in the fifth derivative of Γ1(r1→′;r→1) with respect to |r1→′−r→1|. Its practical relevance in the context of the density-matrix functional theory is discussed.

The Journal of Chemical Physics•Dec 9, 2020•5 citations

Traces of spin-adapted reduced density matrices

E. P�rez-Romero, Luis M. Tel, C. Valdemoro

The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1997•20 citations

Expansion of the Density Matrix of an N-Fermion System in Terms of the Correlation Densities of Fermion Clusters

Tai‐ichi Shibuya, Oktay Si̇nanoğlu

The N-fermion density operator D = |Ψ〈〉Ψ| is decomposed into the densities of clusters of correlating fermions. The m-body cluster densities γ̂(m) are ``orthogonal'' to the one-body ``Fock-Dirac''-type densities ρ1, i.e., Γr1(ρ1γ̂1,2,(m)…,m)=0. The reduced-correlation-density matrices obtained differ from the conventional reduced-density-matrices and are particularly convenient for the treatment of fermion-fermion correlations.

Journal of Mathematical Physics•Jun 1, 1969•4 citations

Approach to N representability

Hong Guo, Auchin Tang

Abstract In this paper, some operator endomorphisms which give rise to conditions for N representability of pth order density matrices are presented.

International Journal of Quantum Chemistry•Feb 1, 1983•3 citations

Traces of spin‐adapted reduced density matrices

Encarnación Pérez-Romero, Luis M. Tel, C. Valdemoro

The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1997•5 citations

Spin-adapted reduced Hamiltonian. I. Elementary excitations

Carmela Valdemoro

The spin-adapted pth-order reduced Hamiltonians (SRH) are obtained for an m-electron system, within the formalism of second quantization. This transformation is applied to the usual many-body Hamiltonian and involves an augmenting mapping, a spin projection, and a reducing mapping into the p-body reduced space. These three operations are combined into a single algorithm, allowing the work to be carried out within the two-body space. The SRH matrices thus obtained (1) have the same trace as that of the corresponding full configuration-interaction (CI) matrix, and (2) can be written as expansions involving the p eigenvalues and the corresponding pth-order reduced density matrices (RDM) of the m-body system in the chosen spin symmetry. Both of these properties guarantee that all and only the relevant information about our system is contained in the SRH matrices (and the SRH operators). The excitations of the eigenstates of the 1-SRH and the 2-SRH can be interpreted as the normal modes (or elementary excitations) of our electronic system in a given symmetry. A preliminary calculation on the Be atom yields encouraging results when compared with experiment. In the following paper (paper II of this series) the theory is applied to obtain the total energy and the reduced density matrices.

Physical Review A•Apr 1, 1985•69 citations
The pth-order conditional electron density C(p)N(r1, ..., rp − 1|rp) of an N-electron system is shown to have a peculiar property that when the radius rp = |rp| of the pth electron approaches ∞, it reduces to the (p−1)th-order reduced density Γ(p − 1)N − 1(r1, ..., rp − 1) divided by p of the (N−1)-electron system arising from the removal of an electron from the original system, where both systems are considered to be in their ground states.
The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.
The traces of the p-order reduced density matrices (p-RDM) split into independent contributions associated to the subsets of p-electron eigenstates of the Ŝ2 and Ŝz operators. Here, we report the partial traces for the blocks of the low-order RDMs corresponding to pure spin states of an N-electron system. A systematic method for calculating those of higher order RDMs is described and some useful relations are also given. All these relations which must be fulfilled independently by a RDM can be considered as N- and S-representability conditions © 1997 John Wiley & Sons, Inc.
The spin-adapted pth-order reduced Hamiltonians (SRH) are obtained for an m-electron system, within the formalism of second quantization. This transformation is applied to the usual many-body Hamiltonian and involves an augmenting mapping, a spin projection, and a reducing mapping into the p-body reduced space. These three operations are combined into a single algorithm, allowing the work to be carried out within the two-body space. The SRH matrices thus obtained (1) have the same trace as that of the corresponding full configuration-interaction (CI) matrix, and (2) can be written as expansions involving the p eigenvalues and the corresponding pth-order reduced density matrices (RDM) of the m-body system in the chosen spin symmetry. Both of these properties guarantee that all and only the relevant information about our system is contained in the SRH matrices (and the SRH operators). The excitations of the eigenstates of the 1-SRH and the 2-SRH can be interpreted as the normal modes (or elementary excitations) of our electronic system in a given symmetry. A preliminary calculation on the Be atom yields encouraging results when compared with experiment. In the following paper (paper II of this series) the theory is applied to obtain the total energy and the reduced density matrices.