Fixing the catastrophic breakdown of single reference coupled cluster theory for strongly correlated systems: Two paradigms toward the implicit inclusion of high-rank correlation with low-spin channels.

The dual exponential coupled cluster theory proposed by Tribedi et al.[J. Chem. Theory Comput. 16, 10, 6317-6328 (2020)] performs significantly better for a wide range of weakly correlated systems than the coupled cluster theory with singles and doubles excitations due to the implicit inclusion of high-rank excitations. The high-rank excitations are included through the action of a set of vacuum annihilating scattering operators that act non-trivially on certain correlated wavefunctions and are determined via a set of local denominators involving the energy difference between certain excited states. This often leads the theory to be prone to instabilities. In this paper, we show that restricting the correlated wavefunction, on which the scattering operators act, to be spanned by only the singlet-paired determinants can avoid catastrophic breakdown. For the first time, we present two nonequivalent approaches to arrive at the working equations, viz., the projective approach with sufficiency conditions and the amplitude form with many-body expansion. Although the effect of the triple excitation is quite small around molecular equilibrium geometry, this scheme leads to a better qualitative description of the energetics in the regions of strong correlation. With many pilot numerical applications, we have demonstrated the performance of the dual-exponential scheme with both the proposed solution strategies while restricting the excitation subspaces coupled to the corresponding lowest spin channels.