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The correlation contracted Schrödinger equation: An accurate solution of the G ‐particle‐hole hypervirial
Author(s) -
Alcoba D. R.,
Valdemoro C.,
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.21943
Subject(s) - hermitian matrix , schrödinger equation , operator (biology) , mathematical physics , physics , matrix (chemical analysis) , quantum mechanics , mathematics , chemistry , biochemistry , repressor , chromatography , transcription factor , gene
The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2nd‐order correlation transition matrix elements into the 2‐body space is the so called correlation contracted Schrödinger equation (CCSE) (Alcoba, Phys Rev A 2002, 65, 032519). As shown by Alcoba (Phys Rev A 2002, 65, 032519) the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the correlation operator (GHV), which can be identified with the anti‐Hermitian part of the CCSE. A comparative analysis of the GHV and the anti‐Hermitian part of the contracted Schrödinger equation (ACSE) indicates that the former is a stronger stationarity condition than the latter. By applying a Heisenberg‐like unitary transformation to the G ‐particle‐hole operator (Valdemoro et al., Phys Rev A 2000, 61, 032507), a good approximation of the expectation value of this operator as well as of the GHV is obtained. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li 2 and BeH 2 molecules. The correlation energies obtained are within 98.80–100.09% of the full‐configuration interaction ones. The convergence of these calculations was faster when using the GHV than with the ACSE. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009