Basis-Set-Error-Free Random-Phase Approximation Correlation Energies for Atoms Based on the Sternheimer Equation.

Abstract

The finite basis set errors for all-electron random-phase approximation (RPA) correlation energy calculations are analyzed for isolated atomic systems. We show that, within the resolution-of-identity (RI) RPA framework, the major source of the basis set errors is the incompleteness of the single-particle atomic orbitals used to expand the Kohn-Sham eigenstates, instead of the auxiliary basis set (ABS) to represent the density response function χ0 and the bare Coulomb operator v. By solving the Sternheimer equation for the first-order wave function on a dense radial grid, we are able to eliminate the major error─the incompleteness error of the single-particle atomic basis set─for atomic RPA calculations. The error stemming from a finite ABS can be readily rendered vanishingly small by increasing the size of the ABS, or by iteratively determining the eigenmodes of the χ0v operator. The variational property of the RI-RPA correlation energy can be further exploited to optimize the ABS in order to achieve fast convergence of the RI-RPA correlation energy. These numerical techniques enable us to obtain basis-set-error-free RPA correlation energies for atoms, and in this work, such energies for atoms from H to Kr are presented. The implications of the numerical techniques developed in the present work for addressing the basis set issue for molecules and solids are discussed.