Post-Kohn-Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation

Using expectation-value coupled-cluster theory and many-body perturbation theory (MBPT), we formulate a series of corrections to the post-Kohn-Sham (post-KS) random-phase approximation (RPA) energy. The beyond-RPA terms are of two types: those accounting for the non-Hartree-Fock reference and those introducing the coupled-cluster doubles non-ring contractions. The contributions of the former type, introduced via the semicanonical orbital basis, drastically reduce the binding strength in noncovalent systems. The good accuracy is recovered by the attractive third-order doubles correction referred to as E_c^2g. The existing RPA approaches based on KS orbitals neglect most of the proposed corrections but can perform well thanks to error cancellation. The proposed method accounts for every contribution in the state-of-the-art renormalized second-order perturbation theory (rPT2) approach but adds additional terms which initially contribute in the third order of MBPT. The cost of energy evaluation scales as noniterative $O\left(N^4\right)$ in the implementation with low-rank tensor decomposition. The numerical tests of the proposed approach demonstrate accurate results for noncovalent dimers of polar molecules and for the challenging many-body noncovalent cluster of CH₄···(H₂O)₂₀.