Developing the random phase approximation into a practical post-Kohn–Sham correlation model

The random phase approximation (RPA) to the density functional correlation energy systematically improves upon many limitations of present semilocal functionals, but was considered too computationally expensive for widespread use in the past. Here a physically appealing reformulation of the RPA correlation model is developed that substantially reduces its computational complexity. The density functional RPA correlation energy is shown to equal one-half times the difference of all RPA electronic excitation energies computed at full and first order coupling. Thus, the RPA correlation energy may be considered as a difference of electronic zero point vibrational energies, where each eigenmode corresponds to an electronic excitation. This surprisingly simple result is intimately related to plasma theories of electron correlation. Differences to electron pair correlation models underlying popular correlated wave function methods are discussed. The RPA correlation energy is further transformed into an explicit functional of the Kohn-Sham orbitals. The only nontrivial ingredient to this functional is the sign function of the response operator. A stable iterative algorithm to evaluate this sign function based on the Newton-Schulz iteration is presented. Integral direct implementations scale as the fifth power of the system size, similar to second order Moller-Plesset calculations. With these improvements, RPA may become the long-sought robust and efficient zero order post-Kohn-Sham correlation model.