Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Abstract

We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is non-orthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian

“…While there have been attempts to merge a symmetry-projected mean-field reference with a symmetry-adapted cluster operator [17,18], practical attempts to projectively restore the symmetries of a broken-symmetry coupled cluster wave function have only been made in the past few years. Duguet [19,20] and Scuseria [21] have proposed independent ways to achieve this, and Tsuchimochi and Ten-no have provided a third approach [22], albeit so far at the linearized coupled cluster level.…”

Second-Order Perturbation Theory with Spin-Symmetry-Projected Hartree–Fock

“…In Table I the uncorrected and corrected second-order energies, E 2 and L (Eqs. (24) and (30)). The level-shift correction is essential to keep the qualitative results of rSUPT2.…”

“…Therefore, the DIIS convergence is somewhat slow with the present implementation. Nevertheless, other preconditioning schemes are available to improve the convergence behavior, 24 and we will test and report their performances in a separate paper.…”

Extending spin‐symmetry projected coupled‐cluster to large model spaces using an iterative null‐space projection technique

“…The estimated gaps of ECISD and ECISD+Q are 7.9 and 22.8 kcal mol -1 , which are somewhat smaller than the SC-LCTSD and RASPT2 results. We have also performed a variety of spin-extended linearized CC calculations [10] to capture size-consistent effects, but found that their correlation energies diverge for this system because of intruder states; the ECISD first excited state lies relatively close to the ground state. While EACCSD is stable in this respect, and is deemed to be a better approximation than ECISD, it gave a potential curve that is quite similar to ECISD+Q, with a gap of 23.1 kcal mol -1 .…”

“…With this form, SUHF became a versatile tool for studying degenerate systems with the same computational scaling as HF. [6][7][8][9] Spin-projection on broken-symmetry CC, which we call spinextended CC (ECC), [10,11] is therefore an attractive candidate for describing both static and dynamical correlation effects (we have to clarify that it is different from the extended coupled-cluster of Arponen, which was derived from the bivariational principle in 1983 [12] ) and many authors have explored its potential. [11,13,14] However, challenges remain in combining CC and spin-projection, with two particular difficulties.…”