  The dual exponential coupled cluster (CC) theory proposed by Tribedi et
al.[J. Chem. Theory Comput. 2020, 16, 10, 6317-6328] performs significantly
better than the coupled cluster theory with singles and doubles excitations
(CCSD) 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 intruders. In this manuscript, we show that restricting the correlated
wavefunction, on which the scattering operators act upon, to be spanned by only
the singlet paired determinants can avoid the 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. While 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 a number of 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.
