Efficient self-consistent treatment of electron correlation within the random phase approximation

Abstract

A self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipation-fluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchangecorrelation kernel in the calculation of the Kohn-Sham correlation energy and potential. The method, denoted self-consistent dRPA method, furthermore treats exactly the exchange energy and the local multiplicative KS exchange potential. It uses Gaussian basis sets, is reasonably efficient, exhibiting a scaling of the computational effort with the forth power of the system size, and thus is generally applicable to molecules. The resulting dRPA correlation potentials in contrast to common approximate correlation potentials are in good agreement with exact reference potentials. The negatives of the eigenvalues of the highest occupied molecular orbitals are found to be in good agreement with experimental ionization potentials. Total energies from self-consistent dRPA calculations, as expected, are even poorer than non-self-consistent dRPA total energies and dRPA reaction and non-covalent binding energies do not significantly benefit from self-consistency. On the other hand, energies obtained with a recently introduced adiabatic-connection dissipation-fluctuation approach (EXXRPA+, exact-exchange random phase approximation) that takes into account, besides the Coulomb kernel, also the exact frequency-dependent exchange kernel are significantly improved if evaluated with orbitals obtained from a self-consistent dRPA calculation instead of an exact exchange-only calculation. Total energies, reaction energies, and noncovalent binding energies obtained in this way are of the same quality as those of high-level quantum chemistry methods, like the coupled cluster singles doubles method which is computationally more demanding. © 2013 AIP Publishing LLC.

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

“…These coupled evolution equations have unique solutions (J,A) for the above initial conditions (12) and (13). Therefore, we can, instead of solving for the many-body wave function, solve these nonlinear coupled evolution equations for a given initial state and external pair (a ext ,j ext ), and determine the current and the potential of the combined matter-photon system from which all observables could be computed.…”

“…For instance, we can assume a perfect cubic cavity (zero-boundary conditions) of length L. 12 Then, with the allowed wave vectors k n = n(π/L) and the corresponding dimensionless creation and annihilation operatorsâ † n,λ andâ n,λ (see Appendix E for more details) we find…”

“…Especially density-functional theories, which are based on the simplest of those (functional) variables, the one-particle density (current), have proven to be exceptionally successful [11]. Their success can be attributed to the unprecedented balance between accuracy and numerical feasibility [12], which allows us at present to treat several thousands of atoms [13]. Although the different flavors of density-functional theories cover most of the traditional problems of physics and chemistry (including approaches that combine classical Maxwell dynamics with the quantum particles [14][15][16][17][18]), by construction these theories can not treat problems involving the quantum nature of light.…”

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

“…In fact, the Hellman−Feynman theorem shows that it is this charge polarization induced by the long-range correlation of quantum electron fluctuations that acts as the origin of the vdW forces on the nuclei. 39,313 Self-consistent implementations have been recently provided for several vdW methods discussed throughout Section 4, including RPA, 314 nonlocal density functionals, 163−165 as well as the TS 15 and XDM 315 pairwise methods. In many of these works, the effects of self-consistency on the binding energies are reported as negligible and, in general, the electron density is polarized in such a way that it shifts slightly away from the atoms toward the intermolecular regions.…”

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

“…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.…”