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Variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function

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Abstract
We perform a direct variational determination of the secondorder (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 manyelectron 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-2, 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 L-3, 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.
Keywords
RENORMALIZATION-GROUP, ANTISYMMETRIC PRODUCTS, SPACE SCF METHOD, COUPLED-CLUSTER THEORY, INITIO QUANTUM-CHEMISTRY, NONORTHOGONAL GEMINALS, HARTREE-FOCK, MOLECULES, STATES, ALGORITHM

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MLA
Poelmans, Ward, et al. “Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.” JOURNAL OF CHEMICAL THEORY AND COMPUTATION, vol. 11, no. 9, 2015, pp. 4064–76, doi:10.1021/acs.jctc.5b00378.
APA
Poelmans, W., Van Raemdonck, M., Verstichel, B., De Baerdemacker, S., Torre, A., Lain, L., … Van Neck, D. (2015). Variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function. JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 11(9), 4064–4076. https://doi.org/10.1021/acs.jctc.5b00378
Chicago author-date
Poelmans, Ward, Mario Van Raemdonck, Brecht Verstichel, Stijn De Baerdemacker, Alicia Torre, Luis Lain, Gustavo E Massaccesi, Diego R Alcoba, Patrick Bultinck, and Dimitri Van Neck. 2015. “Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.” JOURNAL OF CHEMICAL THEORY AND COMPUTATION 11 (9): 4064–76. https://doi.org/10.1021/acs.jctc.5b00378.
Chicago author-date (all authors)
Poelmans, Ward, Mario Van Raemdonck, Brecht Verstichel, Stijn De Baerdemacker, Alicia Torre, Luis Lain, Gustavo E Massaccesi, Diego R Alcoba, Patrick Bultinck, and Dimitri Van Neck. 2015. “Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.” JOURNAL OF CHEMICAL THEORY AND COMPUTATION 11 (9): 4064–4076. doi:10.1021/acs.jctc.5b00378.
Vancouver
1.
Poelmans W, Van Raemdonck M, Verstichel B, De Baerdemacker S, Torre A, Lain L, et al. Variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 2015;11(9):4064–76.
IEEE
[1]
W. Poelmans et al., “Variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function,” JOURNAL OF CHEMICAL THEORY AND COMPUTATION, vol. 11, no. 9, pp. 4064–4076, 2015.
@article{6953981,
  abstract     = {{We perform a direct variational determination of the secondorder (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 manyelectron 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-2, 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 L-3, 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.}},
  author       = {{Poelmans, Ward and Van Raemdonck, Mario and Verstichel, Brecht and De Baerdemacker, Stijn and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E and Alcoba, Diego R and Bultinck, Patrick and Van Neck, Dimitri}},
  issn         = {{1549-9618}},
  journal      = {{JOURNAL OF CHEMICAL THEORY AND COMPUTATION}},
  keywords     = {{RENORMALIZATION-GROUP,ANTISYMMETRIC PRODUCTS,SPACE SCF METHOD,COUPLED-CLUSTER THEORY,INITIO QUANTUM-CHEMISTRY,NONORTHOGONAL GEMINALS,HARTREE-FOCK,MOLECULES,STATES,ALGORITHM}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{4064--4076}},
  title        = {{Variational optimization of the second-order density matrix corresponding to a seniority-zero configuration interaction wave function}},
  url          = {{http://doi.org/10.1021/acs.jctc.5b00378}},
  volume       = {{11}},
  year         = {{2015}},
}

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