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The Unitary Group Adaptation (UGA) offers a very compact and efficient spin adaptation strategy for any spin-free Hamiltonian in a many body framework. Our use of UGA in the context of state-specific (SS) Jeziorski–Monkhorst Ansatz based multireference coupled cluster (MRCC) theory obviates the non-commutativity between the spin-free cluster operators via a normal ordered exponential parametrization in the wave operator. A previous formulation of UGA-SSMRCC by us [R. Maitra, D. Sinha, and D. Mukherjee, J. Chem. Phys. 137, 024105 (2012)], using the same ansatz, employed certain sufficiency conditions to reach the final working equations, which cannot be improved systematically. In this article, we will present a more rigorous formulation that follows from an exact factorization of the unlinked terms of the Bloch equation, resulting in equations on which a hierarchy of approximations can be systematically performed on the emergent additional terms. This derivation was shown in our recent article [D. Chakravarti, S. Sen, and D. Mukherjee, Mol. Phys. 119, e1979676 (2021)] in the context of a single open shell CC formalism and was applied to spectroscopic energy differences where the contribution of the new terms was found to be of the order of ∼0.001 eV for ionization potential, electron affinity, and excitation energy. In the current work, we will present a comparison between the earlier and current formulations via both a theoretical analysis and a numerical demonstration of the dramatic effect of the additional terms brought in by the factorization on potential energy curves. The contribution of such terms was found to gain importance with an increase in the number of singly occupied active orbitals in the model space functions. [ABSTRACT FROM AUTHOR]

The Unitary Group Adapted Open Shell Coupled Cluster (UGA-OSCC) theory, which is the single reference CSF limit of the UGA-State Universal Multireference CC (UGA-SUMRCC) formulation by Mukherjee et al. [Sen, Shee, and Mukherjee, J. Chem. Phys. 137, 074104 (2012)], was proposed and successfully applied via a normal ordered Jeziorski-Monkhorst (J-M)-like CC ansatz for the wave operator. This generates a spin-adapted, size extensive energy. The computed energy differences of spectroscopic interest such as IP, EA and EE were consequently size intensive. Here we revisit the formulation by suggesting a rigorous version which completely bypasses the use of a sufficiency condition posited in our earlier formulation via an exact factorisation of the wave operator in the Bloch equation. This brings in certain connected composites involving contractions among the cluster operators in the resultant equations. This formulation is flexible enough to accommodate truncation of these composites while remaining rigorously size-extensive for each such approximant. We test the effect of these new terms in the Bloch equation for this formulation by evaluating IP, EA and EE for a test set of molecules, which shifts the respective results closer in the order of 0.1 to 0.001 eV towards the benchmark EOM-CCSDt or FCI or experimental values. [ABSTRACT FROM AUTHOR]