  In this article we report a stochastic evaluation of the recently proposed
LCC multireference perturbation theory [Sharma S., and Alavi A., J. Chem. Phys.
143, 102815, (2015)]. In this method both the zeroth order and first order
wavefunctions are sampled stochastically by propagating simultaneously two
populations of signed walkers. The sampling of the zeroth order wavefunction
follows a set of stochastic processes identical to the one used in the FCIQMC
method. To sample the first order wavefunction, the usual FCIQMC algorithm is
augmented with a source term that spawns walkers in the sampled first order
wavefunction from the zeroth order wavefunction. The second order energy is
also computed stochastically but requires no additional overhead outside of the
added cost of sampling the first order wavefunction. This fully stochastic
method opens up the possibility of simultaneously treating large active spaces
to account for static correlation and recovering the dynamical correlation
using perturbation theory. This method is used to study a few benchmark systems
including the carbon dimer and aromatic molecules. We have computed the
singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has
proved difficult for standard CASSCF+PT, we find the singlet-triplet gap to be
in good agreement with the experimental values.
