Spin-Restriction in Explicitly Correlated Coupled Cluster Theory: The Z-Averaged CCSD(2)(R12)over-bar Approach

R12 methods have now been established to improve both the efficiency and accuracy of wave function-based theories. While closed-shell and spin-orbital methodologies for coupled cluster theory are well-studied, R12 corrections based on an open-shell, spin-restricted formalism have not been well developed. We present an efficient spin-restricted R12 method based on the symmetric exchange or Z-averaged approach that reduces the number of variational parameters. The current formalism reduces spin contamination relative to unrestricted methods but remains rigorously size consistent in contrast to other spin-adapted formulations. The theory is derived entirely in spin-orbital quantities, but Z-averaged symmetries are exploited to minimize the computational work in the residual equations. R12 corrections are formulated in a perturbative manner and are therefore obtained with little extra cost relative to the standard coupled cluster problem. R12 results with only a triple-zeta basis are competitive with conventional aug-cc-pVSZ and aug-cc-p V6Z results, demonstrating the utility of the method in thermochemical problems for high-spin open-shell systems.