Toward a Stochastic Complete Active Space Second-Order Perturbation Theory

In this work, an
internally contracted stochastic complete active
space second-order perturbation theory, stochastic−CASPT2,
is reported. The method relies on stochastically sampled reduced density
matrices (RDMs) up to rank four and contractions thereof with the
generalized Fock matrix. A new protocol for calculating higher-order
RDMs in full configuration interaction quantum Monte Carlo (FCIQMC)
has been designed based on (1) restricting sampling of the corresponding
excitations to a deterministic subspace, (2) averaging the RDMs from
independent dynamics and (3) projecting them onto the closest positive
semi-definite matrix. Our protocol avoids previously encountered numerical
conditioning problems in the orthogonalization of the perturber overlap
matrix stemming from numerical noise. The chromium dimer CASSCF(12,12)/CASPT2
binding curve is computed as a proof of concept.