CCSD-PCM: improving upon the reference reaction field approximation at no cost.

The combination of the coupled cluster (CC) method with the polarizable continuum model (PCM) of solvation requires a much larger computational effort than gas phase CC calculations, since the PCM contribution depends nonlinearly on the CC reduced density: perturbation theory energy and density (PTED) scheme. An approximation can be introduced that neglects the "correlation" PCM contribution and only considers the "reference" PCM contribution to the free energy: PTE scheme. The PTE scheme is a computationally efficient strategy, since the cost is comparable to gas phase CC, but the difference in the free energy with respect to the PTED scheme can be significant. In this work, two intermediate approximations are presented, PTE(S) and PTES (where S stands for singles), which retain the computational efficiency of the PTE scheme while reducing the energy gap with the PTED scheme. PTE(S) only introduces an energy correction to the PTE free energy, while PTES introduces explicit PCM terms in the iterative solution of the CC equations. PTE(S) improves the PTE free energy, although such correction is small. PTES recovers 50%-80% of the PTE-PTED difference and represents a promising approach to perform calculations in solution of CC quality at a cost comparable to gas phase CC. The expressions for the CC-PTE(S) and -PTES wave functions, free energy, and free energy analytical gradients are presented, and the methods are tested with numerical examples.