Convergence behavior of the random phase approximation renormalized correlation energy

Bates, Jefferson E.; Sensenig, Jonathon; Ruzsinszky, Adrienn

doi:10.1103/physrevb.95.195158

Convergence behavior of the random phase approximation renormalized correlation energy

Journal Article · Fri May 26 00:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.95.195158· OSTI ID:1469907

Bates, Jefferson E. ^[1]; Sensenig, Jonathon ^[1]; Ruzsinszky, Adrienn ^[1]

Temple Univ., Philadelphia, PA (United States)

Based on the random phase approximation (RPA), RPA renormalization is a robust many-body perturbation theory that works for molecules and materials because it does not diverge as the Kohn-Sham gap approaches zero. Additionally, RPA renormalization enables the simultaneous calculation of RPA and beyond-RPA correlation energies since the total correlation energy is the sum of a series of independent contributions. The first-order approximation (RPAr1) yields the dominant beyond-RPA contribution to the correlation energy for a given exchange-correlation kernel, but systematically underestimates the total beyond-RPA correction. For both the homogeneous electron gas model and real systems, we demonstrate numerically that RPA renormalization beyond first order converges monotonically to the infinite-order beyond-RPA correlation energy for several model exchange-correlation kernels and that the rate of convergence is principally determined by the choice of the kernel and spin polarization of the ground state. The monotonic convergence is rationalized from an analysis of the RPA renormalized correlation energy corrections, assuming the exchange-correlation kernel and response functions satisfy some reasonable conditions. In this work, for spin-unpolarized atoms, molecules, and bulk solids, we find that RPA renormalization is typically converged to 1 meV error or less by fourth order regardless of the band gap or dimensionality. Most spin-polarized systems converge at a slightly slower rate, with errors on the order of 10 meV at fourth order and typically requiring up to sixth order to reach 1 meV error or less. Slowest to converge, however, open-shell atoms present the most challenging case and require many higher orders to converge.

View Accepted Manuscript (DOE)

Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)

Sponsoring Organization:: American Chemical Society Petroleum Research Fund; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012575

OSTI ID:: 1469907

Alternate ID(s):: OSTI ID: 1372517

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 19 Vol. 95; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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