Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle de...
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todo:paper_15499618_v11_n9_p4064_Poelmans2023-10-03T16:23:16Z Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function Poelmans, W. Van Raemdonck, M. Verstichel, B. De Baerdemacker, S. Torre, A. Lain, L. Massaccesi, G.E. Alcoba, D.R. Bultinck, P. Van Neck, D. We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N<inf>2</inf>, and CN-). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L3, where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework. © 2015 American Chemical Society. Fil:Massaccesi, G.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15499618_v11_n9_p4064_Poelmans |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N<inf>2</inf>, and CN-). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L3, where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework. © 2015 American Chemical Society. |
| format |
JOUR |
| author |
Poelmans, W. Van Raemdonck, M. Verstichel, B. De Baerdemacker, S. Torre, A. Lain, L. Massaccesi, G.E. Alcoba, D.R. Bultinck, P. Van Neck, D. |
| spellingShingle |
Poelmans, W. Van Raemdonck, M. Verstichel, B. De Baerdemacker, S. Torre, A. Lain, L. Massaccesi, G.E. Alcoba, D.R. Bultinck, P. Van Neck, D. Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| author_facet |
Poelmans, W. Van Raemdonck, M. Verstichel, B. De Baerdemacker, S. Torre, A. Lain, L. Massaccesi, G.E. Alcoba, D.R. Bultinck, P. Van Neck, D. |
| author_sort |
Poelmans, W. |
| title |
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| title_short |
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| title_full |
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| title_fullStr |
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| title_full_unstemmed |
Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function |
| title_sort |
variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function |
| url |
http://hdl.handle.net/20.500.12110/paper_15499618_v11_n9_p4064_Poelmans |
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