Investigation of the Correlation Potential from Kohn-Sham Perturbation Theory

112

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.

Section: Introductionmentioning

confidence: 99%

“…The lowest order correlation contribution resulting from perturbation theory, E (2) c , has been extensively studied for atoms and small molecules. 31,32,35,36,37,38 E…”

Section: Introductionmentioning

confidence: 99%

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

Jiang

Engel²

2007

112

“…48,49 There have been also numerous applications of OEP within RPA or MP2 energy functionals to atoms or molecules. 38,[50][51][52][53][54][55][56][57][58][59] In some of the publications, different derivations of the OEP equation were given thatunlike the one of Sham and Schlüter -do not involve the electronic self-energy but rather rely on total energy expressions 50,59 or expressions for the electron density. 58 One of the fundamental questions concerning the OEP KS scheme is the magnitude of the true KS gap.…”

Section: Introductionmentioning

confidence: 99%

Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation

Klimeš

Kresse

2014

We present an implementation of the optimised effective potential (OEP) scheme for the exactexchange (EXX) and random phase approximation (RPA) energy functionals and apply these methods to a range of bulk materials. We calculate the Kohn-Sham (KS) potentials and the corresponding band gaps and compare them to the potentials obtained by standard local density approximation (LDA) calculations. The KS gaps increase upon going from the LDA to the OEP in the RPA and finally to the OEP for EXX. This can be explained by the different depth of the potentials in the bonding and interstitial regions. To obtain the true quasi-particle gaps the derivative discontinuities or G0W0 corrections need to be added to the RPA-OEP KS gaps. The predicted G0W0@RPA-OEP quasi-particle gaps are about 5% too large compared to the experimental values. However, compared to G0W0 calculations based on local or semi-local functionals, where the errors vary between different materials, we obtain a rather consistent description among all the materials.

“…We note that, when continuum states are included, the GL2 potential actually diverges at infinity for finite systems [43][44][45][46][47]. Nevertheless, this problem is avoided when using a discrete basis set with functions vanishing at infinity (such as the basis set used in this work) [46][47][48].…”

Section: B Self-consistent Oep Double-hybrid Approximationsmentioning

confidence: 99%

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

Śmiga

Franck

Mussard

et al. 2016

We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effectivepotential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset (MP2) correlation contribution. We have implemented a one-parameter version of this OEP-based selfconsistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchangecorrelation potentials and correlated densities.