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• W2085173407 abstract "Variational minimization of the ground-state energy as a function of the two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions, provides a polynomial-scaling approach to studying strongly correlated molecules without computing the many-electron wave function. Here we introduce a route to enhancing necessary conditions for $N$ representability through rank restriction of the 2-RDM. Rather than adding computationally more expensive $N$-representability conditions, we directly enhance the accuracy of two-particle (2-positivity) conditions through rank restriction, which removes degrees of freedom in the 2-RDM that are not sufficiently constrained. We select the rank of the particle-hole 2-RDM by deriving the ranks associated with model wave functions, including both mean-field and antisymmetrized geminal power (AGP) wave functions. Because the 2-positivity conditions are exact for quantum systems with AGP ground states, the rank of the particle-hole 2-RDM from the AGP ansatz provides a minimum for its value in variational 2-RDM calculations of general quantum systems. To implement the rank-restricted conditions, we extend a first-order algorithm for large-scale semidefinite programming. The rank-restricted conditions significantly improve the accuracy of the energies; for example, the percentages of correlation energies recovered for HF, CO, and N${}_{2}$ improve from 115.2%, 121.7%, and 121.5% without rank restriction to 97.8%, 101.1%, and 100.0% with rank restriction. Similar results are found at both equilibrium and nonequilibrium geometries. While more accurate, the rank-restricted $N$-representability conditions are less expensive computationally than the full-rank conditions." @default.
• W2085173407 created "2016-06-24" @default.
• W2085173407 creator A5002674961 @default.
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• W2085173407 date "2011-11-08" @default.
• W2085173407 modified "2023-09-27" @default.
• W2085173407 title "Rank restriction for the variational calculation of two-electron reduced density matrices of many-electron atoms and molecules" @default.
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• W2085173407 doi "https://doi.org/10.1103/physreva.84.052506" @default.
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