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Physical review. B./Physical review. B

Publisher's Note: Convergence behavior of the random phase approximation renormalized correlation energy [Phys. Rev. B 95 , 195158 (2017)]

Jefferson E. Bates, J. Sensenig, Adrienn Ruzsinszky

Published Jan 31, 2018• 1 citation
Publisher

Abstract

Received 24 January 2018DOI:https://doi.org/10.1103/PhysRevB.97.039905©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structureTechniquesDensity functional theoryMany-body techniquesCondensed Matter, Materials & Applied Physics

DOI
10.1103/physrevb.97.039905

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Convergence behavior of the random phase approximation renormalized correlation energy

Jefferson E. Bates, J. Sensenig, Adrienn Ruzsinszky

Based on the random phase approximation (RPA), RPA renormalization [J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013)] 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. 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.

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Physical review. B./Physical review. B•Jan 10, 2018•0 citations
Received 24 January 2018DOI:https://doi.org/10.1103/PhysRevB.97.039905©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structureTechniquesDensity functional theoryMany-body techniquesCondensed Matter, Materials & Applied Physics
Based on the random phase approximation (RPA), RPA renormalization [J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013)] 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. 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.