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 Ec2g. 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(N4) 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.