Efficient multireference perturbation theory without high-order reduced density matrices

We present a stochastic approach to perform strongly contracted n-electron valence state perturbation theory (SC-NEVPT), which only requires one- and two-body reduced density matrices, without introducing approximations. We use this method to perform SC-NEVPT2 for complete active space self-consistent field wave functions obtained from selected configuration interaction, although the approach is applicable to a larger class of wave functions, including those from orbital-space variational Monte Carlo. The accuracy of this approach is demonstrated for small test systems, and the scaling is investigated with the number of virtual orbitals and the molecule size. We also find the SC-NEVPT2 energy to be relatively insensitive to the quality of the reference wave function. Finally, the method is applied to the Fe(II)-porphyrin system with a (32e, 29o) active space and to the isomerization of [Cu₂O₂]²⁺ in a (28e, 32o) active space.