Orbital invariant single-reference coupled electron pair approximation with extensive renormalized triples correction

A single-reference coupled electron pair approximation is proposed that is exact for two-electron systems, rigorously size-extensive, and invariant under rotations of the occupied and virtual orbitals amongst themselves. In addition, an alternative framework is presented to derive renormalized perturbative corrections to single and double excitation approaches, which are likewise rigorously extensive and invariant under rotations of occupied and virtual orbitals. The new methodology, which is still in a prototype phase at the time of writing this paper, is baptised eXtensive Configuration Interaction with renormalized connected triples corrections, p-RXCISD〈T〉, where 'p' indicates the preliminary, prototype stage of its development. A few variations on the theme are discussed, notably the completely renormalized p-RXCISD〈M3〉 and the Brueckner orbital based p-RBXCISD〈T〉. The methodology is applied to obtain potential energy curves and low lying vibrational energy levels (up to v=8) for a variety of closed-shell and open-shell diatomics that exhibit a range of chemical bonding patterns (HF, BF, F2, N2, BeO, BN, CN, O2, and Be2). Low-order Dunham expansions of the vibrational data are compared between reference CCSDT, CCSD(T), and the newly developed p-RXCISD〈T〉, p-RXCISD〈M3〉 and p-RBXCISD〈T〉 methods. In addition, for the HF molecule the complete set of J=0 vibrational levels, obtained from p-RBXCISD〈T〉 and p-RBXCISD〈M3〉 calculations using basis set extrapolation based on the aug-cc-pVTZ/aug-cc-pVQZ basis sets, are compared to experiment.