Development and applications of a unitary group adapted state specific multi-reference coupled cluster theory with internally contracted treatment of inactive double excitations

Any multi-reference coupled cluster (MRCC) development based on the Jeziorski-Monkhorst (JM) multi-exponential ansatz for the wave-operator Ω suffers from spin-contamination problem for non-singlet states. We have very recently proposed a spin-free unitary group adapted (UGA) analogue of the JM ansatz, where the cluster operators are defined in terms of spin-free unitary generators and a normal ordered, rather than ordinary, exponential parametrization of Ω is used. A consequence of the latter choice is the emergence of the "direct?term" of the MRCC equations that terminates at exactly the quartic power of the cluster amplitudes. Our UGA-MRCC ansatz has been utilized to generate both the spin-free state specific (SS) and the state universal MRCC formalisms. It is well-known that the SSMRCC theory requires suitable sufficiency conditions to resolve the redundancy of the cluster amplitudes. In this paper, we propose an alternative variant of the UGA-SSMRCC theory, where the sufficiency conditions are used for all cluster operators containing active orbitals and the single excitations with inactive orbitals, while the inactive double excitations are assumed to be independent of the model functions they act upon. The working equations for the inactive double excitations are thus derived in an internally contracted (IC) manner in the sense that the matrix elements entering the MRCC equations involve excitations from an entire combination of the model functions. We call this theory as UGA-ICID-MRCC, where ICID is the acronym for "Internally Contracted treatment of Inactive Double excitations." Since the number of such excitations are the most numerous, choosing them to be independent of the model functions will lead to very significant reduction in the number of cluster amplitudes for large active spaces, and is worth exploring. Moreover, unlike for the excitations involving active orbitals, where there is inadequate coupling between the model and the virtual functions in the SSMRCC equations generated from sufficiency conditions, our internally contracted treatment of inactive double excitations involves much more complete couplings. Numerical implementation of our formalism amply demonstrates the efficacy of the formalism.