Explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12)

In this work, explicitly correlated second order N-electron valence state perturbation theory (NEVPT2-F12) has been derived and implemented for the first time. The NEVPT2-F12 algorithm presented here is based on a fully internally contracted wave function and includes the correction of semi-internal excitation subspaces. The algorithm exploits the resolution of identity (RI) approximation to improve the computational efficiency. The overall O(N5) scaling of the computational effort is documented. In Sec. III, the dissociation processes of diatomic molecules and the singlet-triplet gap of several systems are studied. For all relative energies studied in this work, the errors with respect to the complete basis set (CBS) limit for the NEVPT2-F12 method are within 1 kcal/mol. For moderately sized active spaces, the computational cost of a RI-NEVPT2-F12 correlation energy calculation for each root is comparable to a closed-shell RI-MP2-F12 calculation on the same system.