Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

Abstract

A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle—hole (ph) and particle—particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

Variational generalized Kohn-Sham approach combining the random-phase-approximation and Green's-function methods

“…The off-diagonal (λ = λ ′ ) blocks of V C,1 reduce to the gradient of the RPA energy with respect to orbital rotations, thus establishing a link to orbital-optimized RPA approaches [19]. The diagonal (λ = λ ′ ) blocks, on the other hand, result from variations corresponding to changes in the occupation numbers and cannot be obtained in an orbital optimization framework.…”

“…While the rSE approach also improves considerably upon SL-RPA for noble-gas dimers, it spuriously overbinds in cases such as Ne 2 [32], whereas GKS-spRPA remains accurate, reflecting the additional stability resulting from variational optimization. Similar to orbital optimized RPA [19], GKS-spRPA thus implicitly accounts for singles corrections to all orders. A comparison of equilibrium properties for Ar 2 and Kr 2 and mean average errors for binding energies of S22 dataset shows that the GKS-spRPA improves upon both SL-RPA and OEP-RPA, see Table. IV.…”

“…However, while OEP-RPA produces accurate KS orbital energies, OEP-RPA results for bond energies and noncovalent interactions are less accurate than their SL-RPA counterparts [16]. This result is puzzling, because the OEP-RPA KS potentials are considerably more accurate than SL ones [18], and recent orbital-optimized RPA approaches improve upon SL RPA energetics [19].…”

“…Semicanonical approaches have successfully been used to devise perturbative corrections to SL-RPA in the past [32]. The present variational GKS spRPA method is designed to (i) recover SL-RPA for SL densities; (ii) reduce density-driven error by determining the density from the stationary point of the RPA rather than a SL energy functional; (iii) systematically improve SL-RPA energetics; (iv) approximate FSC RPA without sacrificing the variational principle; (v) yield a complete GKS effective one-particle Hamiltonian, unlike orbital optimized [19] or Brueckner [33] RPA, providing an intuitive one-electron picture and GKS orbital energies which accurately approximate quasiparticle spectra [34]; (vi) establish a straightforward connection to GFT and GW theory; (vii) eliminate the need for KS inversion or OEP approaches, which can be ill conditioned [35] and require cumbersome regularization [36][37][38].…”

Numerical methods for Kohn–Sham density functional theory

“…Most current strategies are to first obtain the effective Hamiltonian and corresponding Kohn-Sham orbitals based on a semi-local or hybrid functional, and then calculate the RPA correlation in a post-processing step. Self-consistency calculations have been performed using the optimized effective potential (OEP) framework (Godby, Schlüter and Sham 1986, Godby, Schlüter and Sham 1988, Fukazawa and Akai 2015 or more recently the generalized optimized effective potential approach (Jin et al 2017), but they come with considerable numerical effort. Finding an efficient approach for selfconsistent treatment of RPA functionals is an active research area, and in this review we will not discuss self-consistency for rung-5 functionals in detail.…”