SF-[2]R12: a spin-adapted explicitly correlated method applicable to arbitrary electronic states

The 2](R12) method M. Torheyden and E. F. Valeev, J. Chem. Phys. 131, 171103 (2009)] is an explicitly correlated perturbative correction that can greatly reduce the basis set error of an arbitrary electronic structure method for which the two-electron density matrix is available. Here we present a spin-adapted variant (denoted as SF-2](R12)) that is formulated completely in terms of spin-free quantities. A spin-free cumulant decomposition and multi-reference generalized Brillouin condition are used to avoid three-particle reduced density matrix completely. The computational complexity of SF-2](R12) is proportional to the sixth power of the system size and is comparable to the cost of the single-reference MP2-R12 method. The SF-2](R12) method is shown to decrease greatly the basis set error of multi-configurational wave functions.