Convergence behavior of the random phase approximation renormalized correlation energy

Article

关键词: DENSITY-FUNCTIONAL THEORY;    EXCHANGE-CORRELATION ENERGY;    TRANSITION-METAL CHEMISTRY;    ADIABATIC CONNECTION;    ELECTRON CORRELATION;    PERTURBATION-THEORY;    HARTREE-FOCK;    CORRELATION KERNEL;    FORCES;    GAS;   

DOI  :  10.1103/PhysRevB.95.195158

来源: SCIE

【 摘 要 】

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 theKohn-Sham gap approaches zero. Additionally, RPArenormalization enables the simultaneous calculation ofRPAand beyond-RPAcorrelation 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 beyondRPA 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.

【 授权许可】

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