Rayleigh-Schrodinger many-body perturbation theory for density functionals: A unified treatment of one- and two-electron perturbations

摘要

A time-independent many-body Rayleigh-Schrodinger perturbation theory is developed for total energy functionals, which depend simultaneously on a wave function and on the associated electron density. The most prominent example of such functionals is the Kohn-Sham energy functional, but similar situations occur as well in quantum chemical solvent effect theories. In contrast to previous density-functional perturbation theories, formulated in terms of one-electron orbitals, the present approach provides energy and eigenvector corrections for a many-electron wave function that satisfies a nonlinear effective Schrodinger equation. While the perturbed eigenvalues of order n depend on the eigenvector corrections up to the nth order, perturbational corrections of the total energy functional satisfy Wigner's (2n+1) rule by virtue of nontrivial cancelations between eigenvalue and double count corrections up to order n. As a direct consequence of the nonlinearity of the effective Schrodinger equation, the wave-function corrections of any order are obtained by the solution of a self-consistent equation involving the second functional derivative of the density functional. Explicit total energy corrections are elaborated up to the fourth order. It is shown that the present approach reproduces standard results of the density-functional perturbation theory for static one-electron perturbations. Furthermore, two variants of the long-range Moller-Plesset correlation energy corrections in the range-separated hybrid density-functional framework are derived and discussed.