Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation
The G-particle-hole hypervirial (GHV) equation has been recently reported (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics Vancouver: Canada, 2008. Alcoba et al., Int J Quantum Chem 2009, 109, 3178; Valdemoro et al., Int J Quantum Chem 200...
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paper:paper_00207608_v111_n5_p937_Alcoba2023-06-08T14:41:33Z Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation contracted Schrödinger equation correlation matrix electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix reduced density matrix correlation matrix Dinger equation electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix Reduced-density matrix Computational efficiency Correlation detectors Quantum theory Matrix algebra The G-particle-hole hypervirial (GHV) equation has been recently reported (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics Vancouver: Canada, 2008. Alcoba et al., Int J Quantum Chem 2009, 109, 3178; Valdemoro et al., Int J Quantum Chem 2009, 109, 2622). This equation is the newest member of the family of equations which can be obtained by applying a matrix-contracting mapping (Valdemoro, An R Soc Esp Fís 1983, 79, 106; Valdemoro, Phys Rev A 1985, 31, 2114; Valdemoro, in Density Matrices and Density Functionals, Reidel: Dordrecht, 1987; p 275.) to the matrix representation in the N-electron space of the Schrödinger, Liouville and hypervirial equations. The procedure that we have applied in order to solve the GHV equation exploits the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Hirschfelder and Epstein, Phys Rev 1961, 123, 1495) and follows the general lines of Mazziotti's variational approach for solving the anti-Hermitian contracted Schrödinger equation (ACSE) (Mazziotti, Phys Rev Lett 2006, 97, 143002; Mazziotti, Phys Rev A 2007, 75, 022505; Mazziotti, J Chem Phys 2007, 126, 184101). In this article, we report how the method's convergence has been significantly enhanced and how its computational scaling has been considerably reduced (in both floating-point operations and storage). The results for a variety of atomic and molecular calculations confirming these methodological improvements are reported here. Copyright © 2010 Wiley Periodicals, Inc. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v111_n5_p937_Alcoba http://hdl.handle.net/20.500.12110/paper_00207608_v111_n5_p937_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 |
contracted Schrödinger equation correlation matrix electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix reduced density matrix correlation matrix Dinger equation electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix Reduced-density matrix Computational efficiency Correlation detectors Quantum theory Matrix algebra |
spellingShingle |
contracted Schrödinger equation correlation matrix electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix reduced density matrix correlation matrix Dinger equation electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix Reduced-density matrix Computational efficiency Correlation detectors Quantum theory Matrix algebra Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
topic_facet |
contracted Schrödinger equation correlation matrix electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix reduced density matrix correlation matrix Dinger equation electronic correlation effects G-matrix hypervirial of the G-particle-hole matrix Reduced-density matrix Computational efficiency Correlation detectors Quantum theory Matrix algebra |
description |
The G-particle-hole hypervirial (GHV) equation has been recently reported (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics Vancouver: Canada, 2008. Alcoba et al., Int J Quantum Chem 2009, 109, 3178; Valdemoro et al., Int J Quantum Chem 2009, 109, 2622). This equation is the newest member of the family of equations which can be obtained by applying a matrix-contracting mapping (Valdemoro, An R Soc Esp Fís 1983, 79, 106; Valdemoro, Phys Rev A 1985, 31, 2114; Valdemoro, in Density Matrices and Density Functionals, Reidel: Dordrecht, 1987; p 275.) to the matrix representation in the N-electron space of the Schrödinger, Liouville and hypervirial equations. The procedure that we have applied in order to solve the GHV equation exploits the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Hirschfelder and Epstein, Phys Rev 1961, 123, 1495) and follows the general lines of Mazziotti's variational approach for solving the anti-Hermitian contracted Schrödinger equation (ACSE) (Mazziotti, Phys Rev Lett 2006, 97, 143002; Mazziotti, Phys Rev A 2007, 75, 022505; Mazziotti, J Chem Phys 2007, 126, 184101). In this article, we report how the method's convergence has been significantly enhanced and how its computational scaling has been considerably reduced (in both floating-point operations and storage). The results for a variety of atomic and molecular calculations confirming these methodological improvements are reported here. Copyright © 2010 Wiley Periodicals, Inc. |
title |
Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
title_short |
Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
title_full |
Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
title_fullStr |
Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
title_full_unstemmed |
Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation |
title_sort |
convergence and computational efficiency enhancements in the iterative solution of the g-particle-hole hypervirial equation |
publishDate |
2011 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v111_n5_p937_Alcoba http://hdl.handle.net/20.500.12110/paper_00207608_v111_n5_p937_Alcoba |
_version_ |
1768545449160998912 |