Theoretical and applicative properties of the correlation and G-particle-hole matrices
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 th...
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2009
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paper:paper_00207608_v109_n11_p2622_Valdemoro2023-06-08T14:41:30Z Theoretical and applicative properties of the correlation and G-particle-hole matrices Chemical physics Constructing algorithms Construction algorithms Correlation matrix Dinger equation Electron systems Hermitian International society Second-order reduced density Color Correlation methods Presses (machine tools) Mathematical operators 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v109_n11_p2622_Valdemoro http://hdl.handle.net/20.500.12110/paper_00207608_v109_n11_p2622_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 |
Chemical physics Constructing algorithms Construction algorithms Correlation matrix Dinger equation Electron systems Hermitian International society Second-order reduced density Color Correlation methods Presses (machine tools) Mathematical operators |
| spellingShingle |
Chemical physics Constructing algorithms Construction algorithms Correlation matrix Dinger equation Electron systems Hermitian International society Second-order reduced density Color Correlation methods Presses (machine tools) Mathematical operators Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| topic_facet |
Chemical physics Constructing algorithms Construction algorithms Correlation matrix Dinger equation Electron systems Hermitian International society Second-order reduced density Color Correlation methods Presses (machine tools) Mathematical operators |
| description |
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. |
| title |
Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| title_short |
Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| title_full |
Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| title_fullStr |
Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| title_full_unstemmed |
Theoretical and applicative properties of the correlation and G-particle-hole matrices |
| title_sort |
theoretical and applicative properties of the correlation and g-particle-hole matrices |
| publishDate |
2009 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v109_n11_p2622_Valdemoro http://hdl.handle.net/20.500.12110/paper_00207608_v109_n11_p2622_Valdemoro |
| _version_ |
1768543879633567744 |