Self-consistent many-body perturbation theory in range-separated density-functional theory: A one-electron reduced-density-matrix-based formulation

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schrödinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this “self-consistency problem” and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order Møller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid Görling-Levy-type MBPT-DFT model.