Degenerate coupled-cluster theory

TL;DR

This paper introduces a size-extensive, converging, black-box coupled-cluster method for computing energies and wave functions of stationary states across various reference states, including degenerate and nondegenerate cases.

Contribution

It develops a new degenerate coupled-cluster theory and a state-universal multireference coupled-cluster theory for strong correlation, with implementations and performance comparisons.

Findings

The $ riangle$CC and QCC theories are size-extensive and convergent.

QCC and $ riangle$CC outperform EOM-CC, CI, $ riangle$MP, and MBGF in transition energy calculations.

The theories are compared up to high excitation orders, demonstrating their effectiveness.

Abstract

A size-extensive, converging, black-box, ab initio coupled-cluster ($\Delta$CC) ansatz is introduced that computes the energies and wave functions of stationary 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 Rayleigh-Schr\"{o}dinger perturbation ($\Delta$MP) theory. For ionized and electron-attached references, it can be viewed as 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. Additionally, a new state-universal multireference coupled-cluster theory for general model spaces is developed by slightly modifying the $\Delta$CC ansatz. This quasidegenerate coupled-cluster (QCC) theory is size-extensive, converging, but not black-box, which is expected to be well suited for strong correlation. Determinant-based, general-order algorithms of $\Delta$CC and QCC theories are implemented, which are 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. For transition energies, the order of performance is: QCC $\approx$ $\Delta$CC $>$ EOM-CC $>$ CI at the same excitation order or QCC $\approx$ $\Delta$CC $>$ $\Delta$MP $>$ MBGF at the same cost scaling.