Spectral finite-element formulation of the optimized effective potential method for atomic structure in the random phase approximation

Abstract

We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs a polynomial mesh with element nodes placed according to the Chebyshev–Gauss–Lobatto scheme, high-order C0-continuous Lagrange polynomial basis functions, and Gauss–Legendre quadrature for spatial integration. We employ distinct polynomial degrees for the orbitals, Hartree potential, and RPA–OEP exchange–correlation potential. Through representative examples, we verify the accuracy of the developed framework, assess the fidelity of one-parameter double-hybrid functionals constructed with RPA correlation, and develop a machine-learned model for the RPA–OEP exchange–correlation potential at the level of the generalized gradient approximation, based on the kernel method and linear regression.