Some theoretical questions about the G-particle-hole hypervirial equation
By applying a matrix contracting mapping, involving the G-particle-hole operator, to the matrix representation of the N-electron density hypervirial equation, one obtains the G-particle-hole hypervirial (GHV) equation (Alcoba, et al., Int J Quant Chem 2009, 109, 3178). This equation may be solved by...
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todo:paper_00207608_v111_n2_p245_Valdemoro2023-10-03T14:18:41Z Some theoretical questions about the G-particle-hole hypervirial equation Valdemoro, C. Alcoba, D.R. Tel, L.M. Paérez-Romero, E. contracted Schrödinger equation correlation matrix electronic correlation effects G-particle-hole matrix reduced density matrix Correlation matrix Dinger equation Electronic correlation effects matrix Reduced-density matrix Correlation detectors Hamiltonians Mathematical operators Quantum theory Equations of state By applying a matrix contracting mapping, involving the G-particle-hole operator, to the matrix representation of the N-electron density hypervirial equation, one obtains the G-particle-hole hypervirial (GHV) equation (Alcoba, et al., Int J Quant Chem 2009, 109, 3178). This equation may be solved by exploiting the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Fernández and Castro, Hypervirial Theorems., Lecture Notes in Chemistry Series 43, 1987) and by following the general lines of Mazziotti's approach for solving the anti-Hermitian contracted Schrödinger equation (Mazziotti, Phys Rev Lett 2006, 97, 143002), which can be identified with the second-order density hypervirial equation. The accuracy of the results obtained with this method when studying the ground-state of a set of atoms and molecules was excellent when compared with the equivalent full configuration interaction (FCI) quantities. Here, we analyze two open questions: under what conditions the solution of the GHV equation corresponds to a Hamiltonian eigenstate, and the possibility of extending the field of application of this methodology to the study of excited and multiconfigurational states. A brief account of the main difficulties that arise when studying this type of states is described. © 2010 Wiley Periodicals, Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00207608_v111_n2_p245_Valdemoro |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
contracted Schrödinger equation correlation matrix electronic correlation effects G-particle-hole matrix reduced density matrix Correlation matrix Dinger equation Electronic correlation effects matrix Reduced-density matrix Correlation detectors Hamiltonians Mathematical operators Quantum theory Equations of state |
spellingShingle |
contracted Schrödinger equation correlation matrix electronic correlation effects G-particle-hole matrix reduced density matrix Correlation matrix Dinger equation Electronic correlation effects matrix Reduced-density matrix Correlation detectors Hamiltonians Mathematical operators Quantum theory Equations of state Valdemoro, C. Alcoba, D.R. Tel, L.M. Paérez-Romero, E. Some theoretical questions about the G-particle-hole hypervirial equation |
topic_facet |
contracted Schrödinger equation correlation matrix electronic correlation effects G-particle-hole matrix reduced density matrix Correlation matrix Dinger equation Electronic correlation effects matrix Reduced-density matrix Correlation detectors Hamiltonians Mathematical operators Quantum theory Equations of state |
description |
By applying a matrix contracting mapping, involving the G-particle-hole operator, to the matrix representation of the N-electron density hypervirial equation, one obtains the G-particle-hole hypervirial (GHV) equation (Alcoba, et al., Int J Quant Chem 2009, 109, 3178). This equation may be solved by exploiting the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Fernández and Castro, Hypervirial Theorems., Lecture Notes in Chemistry Series 43, 1987) and by following the general lines of Mazziotti's approach for solving the anti-Hermitian contracted Schrödinger equation (Mazziotti, Phys Rev Lett 2006, 97, 143002), which can be identified with the second-order density hypervirial equation. The accuracy of the results obtained with this method when studying the ground-state of a set of atoms and molecules was excellent when compared with the equivalent full configuration interaction (FCI) quantities. Here, we analyze two open questions: under what conditions the solution of the GHV equation corresponds to a Hamiltonian eigenstate, and the possibility of extending the field of application of this methodology to the study of excited and multiconfigurational states. A brief account of the main difficulties that arise when studying this type of states is described. © 2010 Wiley Periodicals, Inc. |
format |
JOUR |
author |
Valdemoro, C. Alcoba, D.R. Tel, L.M. Paérez-Romero, E. |
author_facet |
Valdemoro, C. Alcoba, D.R. Tel, L.M. Paérez-Romero, E. |
author_sort |
Valdemoro, C. |
title |
Some theoretical questions about the G-particle-hole hypervirial equation |
title_short |
Some theoretical questions about the G-particle-hole hypervirial equation |
title_full |
Some theoretical questions about the G-particle-hole hypervirial equation |
title_fullStr |
Some theoretical questions about the G-particle-hole hypervirial equation |
title_full_unstemmed |
Some theoretical questions about the G-particle-hole hypervirial equation |
title_sort |
some theoretical questions about the g-particle-hole hypervirial equation |
url |
http://hdl.handle.net/20.500.12110/paper_00207608_v111_n2_p245_Valdemoro |
work_keys_str_mv |
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