Degenerate coupled-cluster theory

Abstract

A size-extensive, converging, black-box, ab initio coupled-cluster ($\Delta$CC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of $\alpha$- and $\beta$-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Moeller-Plesset perturbation ($\Delta$MP) theory. For ionized and electron-attached references, it is a coupled-cluster Green's function, although the present theory is convergent toward the full-configuration-interaction (FCI) limits, while Feynman-Dyson many-body Green's function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree-Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. A new multireference coupled-cluster theory for a general model space is also developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of $\Delta$CC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with $\Delta$MP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of $\Delta$CC theory is computer-synthesized at the levels of single excitations ($\Delta$CCS) and of single and double excitations ($\Delta$CCSD). The order of performance is: QCC $\approx$ $\Delta$CC > EOM-CC > CI at the same order or QCC $\approx$ $\Delta$CC > $\Delta$MP > MBGF at the same cost scaling.