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.