The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial

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 R...

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Detalles Bibliográficos
Publicado:	2009
Materias:	Anti-hermitian contracted schrödinger equation Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Beryllium Correlation detectors Correlation methods Schrodinger equation Mathematical operators
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v109_n14_p3178_Alcoba http://hdl.handle.net/20.500.12110/paper_00207608_v109_n14_p3178_Alcoba
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00207608_v109_n14_p3178_Alcoba
record_format	dspace
spelling	paper:paper_00207608_v109_n14_p3178_Alcoba2023-06-08T14:41:31Z The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial Anti-hermitian contracted schrödinger equation Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Beryllium Correlation detectors Correlation methods Schrodinger equation Mathematical operators 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 Li2 and BeH2 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v109_n14_p3178_Alcoba http://hdl.handle.net/20.500.12110/paper_00207608_v109_n14_p3178_Alcoba
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Anti-hermitian contracted schrödinger equation Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Beryllium Correlation detectors Correlation methods Schrodinger equation Mathematical operators
spellingShingle	Anti-hermitian contracted schrödinger equation Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Beryllium Correlation detectors Correlation methods Schrodinger equation Mathematical operators The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
topic_facet	Anti-hermitian contracted schrödinger equation Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Contracted schrodinger equation Correlation matrix Electronic correlation effects G-matrix Reduced density matrix Beryllium Correlation detectors Correlation methods Schrodinger equation Mathematical operators
description	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 Li2 and BeH2 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.
title	The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
title_short	The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
title_full	The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
title_fullStr	The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
title_full_unstemmed	The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial
title_sort	correlation contracted schrodinger equation: an accurate solution of the g-particle-hole hypervirial
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v109_n14_p3178_Alcoba http://hdl.handle.net/20.500.12110/paper_00207608_v109_n14_p3178_Alcoba
_version_	1768542300926902272

The correlation contracted schrodinger equation: An accurate solution of the G-particle-hole hypervirial

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