Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree–Fock Theory

Journal Article · Thu Mar 22 00:00:00 EDT 2018 · Journal of Chemical Theory and Computation

DOI:https://doi.org/10.1021/acs.jctc.7b01288· OSTI ID:1539138

Nascimento, Daniel R. ^[1]; DePrince, A. Eugene ^[1]

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1. Florida State Univ., Tallahassee, FL (United States)

The Hartree–Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014, 89, 010502(R)]. This formulation of the problem transfers the nonconvexity of the Hartree–Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree–Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin (Ŝ² and Ŝ₃) symmetry breaking properties. When imposing Ŝ² and Ŝ₃ symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be–H₂ insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ² and Ŝ₃ symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree–Fock theory.

• Research Organization: Energy Frontier Research Centers (EFRC) (United States). Center for Actinide Science & Technology (CAST); Florida State Univ., Tallahassee, FL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0016568
• OSTI ID: 1539138
• Journal Information: Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 5 Vol. 14; ISSN 1549-9618
• Publisher: American Chemical Society
• Country of Publication: United States
• Language: English

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