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Theoretical and applicative properties of the correlation and G ‐particle‐hole matrices
Author(s) -
Valdemoro C.,
Alcoba D. R.,
Tel L. M.,
PérezRomero E.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22042
Subject(s) - wave function , order (exchange) , schrödinger equation , hermitian matrix , convergence (economics) , operator (biology) , quantum mechanics , matrix (chemical analysis) , physics , mathematics , particle (ecology) , correlation function (quantum field theory) , density matrix , mathematical physics , quantum , chemistry , biochemistry , finance , repressor , chromatography , transcription factor , dielectric , economics , gene , economic growth , oceanography , geology
We have recently (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics, 2008; Alcoba et al., Int J Quantum Chem, in press) reported the form of the G ‐particle‐hole hypervirial equation, which can be identified with the anti‐Hermitian part of the correlation contracted Schrödinger equation (Alcoba, Phys Rev A, 2002, 65, 032519), as a tool to obtain the second‐order reduced density matrix of an N ‐electron system without previous knowledge of the wave‐function. The results which have been obtained when solving the G ‐particle‐hole hypervirial equation with an iterative method also described in (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics, 2008; Alcoba et al., Int J Quantum Chem, in press) have been highly accurate. The convergence of these test calculations has been very smooth, though rather slow. One of the factors which determines the performance of the method is the accuracy with which the 3‐order correlation matrices (3‐CM) involved in the calculations are approximated. It is, therefore, necessary to optimize to the utmost the construction algorithms of these 3‐order matrices in terms of the 2‐CM. In this article, the main theoretical features of the p ‐CM are described. Also, some aspects of the correlation contracted Schrödinger equation and of the G ‐particle‐hole hypervirial equation are revisited. A new theorem, concerning the sufficiency of the hypervirial of the 3‐order correlation operator to guarantee a correspondence between its solution and that of the Schrödinger equation, and some preliminary results concerning the constructing algorithms of the 3‐CM in terms of the 2‐CM, are reported in the second part of this article. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009