Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

Abstract

The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as for instance their inability to account for dispersion forces. First results for atoms, however, indicate that the RPA overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the KS Hamiltonian. In this contribution, three simple extensions of the RPA are examined, (a) its augmentation by an LDA for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed sub-shell atoms are clearly superior to those obtained with the unmodified RPA. Quite some effort is made to ensure highly converged RPA data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular for the inherent frequency integration, should also be useful for applications of RPA-type functionals to more complex systems.

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

“…1 and 2 EXXRPA methods with a N 6 scaling with the system size N were developed on the basis of Eq. (16). Starting from Eqs.…”

“…11,15,17,49,50 RPA methods considering only the Coulomb kernel shall be denoted direct RPA (dRPA) methods here. Some dRPA approaches are corrected such that the correlation energy is exact to second-order perturbation theory 16,19,51 or are augmented with additional first-order singles terms. 32 Other DFT based RPA methods employ range-separation approaches in order to treat only parts of the correlation energy via the RPA, while other parts of the correlation energy are treated by approximate semilocal functionals of the density.…”

Third-order corrections to random-phase approximation correlation energies

“…[63][64][65][66][67][68][69][70][71][72][73][74][75][76] The use of the Kohn-Sham determinant instead of the Hartree-Fock determinant as the reference determinant in RPA methods might be advantageous in order to account implicitly for single excitations that are commonly absent in Hartree-Fock based RPA methods. It has been shown for some small molecules that, depending however on the underlying exchange-correlation potential, Kohn-Sham orbitals are closer to Brueckner orbitals than Hartree-Fock orbitals 77 (see, however, Ref.…”

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

“…Studies which have explored this aspect for RPA + EXX total-energy calculations have usually focused on the differences between LDA and GGA or on the effect of including Hartree-Fock exchange [22,[34][35][36][37][38]. In most cases, the initial choice of XC potential has been found to play only a minor role; a notable exception is the study of cerium in Ref.…”