Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function

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• 作者：Ward Poelmans ; Mario Van Raemdonck ; Brecht Verstichel ; Stijn De Baerdemacker ; Alicia Torre ; Luis Lain ; Gustavo E. Massaccesi ; Diego R. Alcoba ; Patrick Bultinck ; Dimitri Van Neck
• 刊名：Journal of Chemical Theory and Computation
• 出版年：2015
• 出版时间：September 8, 2015
• 年：2015
• 卷：11
• 期：9
• 页码：4064-4076
• 全文大小：743K
• ISSN：1549-9626

文摘

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 -, -, and -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, N₂, and CN^{鈥?/sup>). 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.}