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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2011
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v111_n2_p245_Valdemoro http://hdl.handle.net/20.500.12110/paper_00207608_v111_n2_p245_Valdemoro |
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paper:paper_00207608_v111_n2_p245_Valdemoro2023-06-08T14:41:32Z Some theoretical questions about the G-particle-hole hypervirial equation 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v111_n2_p245_Valdemoro 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 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. |
| 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 |
| publishDate |
2011 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v111_n2_p245_Valdemoro http://hdl.handle.net/20.500.12110/paper_00207608_v111_n2_p245_Valdemoro |
| _version_ |
1768546428441853952 |