The subtleties of explicitly correlated Z-averaged perturbation theory: Choosing an R12 method for high-spin open-shell molecules

Explicitly correlated MP2-R12 and coupled cluster R12 methods have proven to be effective in achieving the basis set limit of correlated wave function methods. However, correlated methods for high-spin open-shell states are typically based on semicanonical orbitals, leading to an unrestricted formalism, which for double excitations requires three independent sets of amplitudes. In contrast, Z-averaged perturbation theory redefines the Hamiltonian with a symmetric exchange operator, thereby allowing a spin-restricted formulation with equivalent alpha and beta subspaces. In the current work, we present a preliminary study of explicitly correlated ZAPT for second-order perturbation theory. The superior basis set convergence of R12 methods is demonstrated for a set of atomization energies, showing the R12 results to be competitive with common basis set extrapolation techniques, albeit at a fraction of the cost. Given the efficiency gains associated with the symmetric exchange operator, we suggest ZAPT as a candidate for reducing the cost of current open-shell MP2-R12 and CCSD(T)-R12 computations.