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In this article we report a stochastic evaluation of the recently proposedLCC multireference perturbation theory [Sharma S., and Alavi A., J. Chem. Phys.143, 102815, (2015)]. In this method both the zeroth order and first orderwavefunctions are sampled stochastically by propagating simultaneously twopopulations of signed walkers. The sampling of the zeroth order wavefunctionfollows a set of stochastic processes identical to the one used in the FCIQMCmethod. To sample the first order wavefunction, the usual FCIQMC algorithm isaugmented with a source term that spawns walkers in the sampled first orderwavefunction from the zeroth order wavefunction. The second order energy isalso computed stochastically but requires no additional overhead outside of theadded cost of sampling the first order wavefunction. This fully stochasticmethod opens up the possibility of simultaneously treating large active spacesto account for static correlation and recovering the dynamical correlationusing perturbation theory. This method is used to study a few benchmark systemsincluding the carbon dimer and aromatic molecules. We have computed thesinglet-triplet gaps of benzene and m-xylylene. For m-xylylene, which hasproved difficult for standard CASSCF+PT, we find the singlet-triplet gap to bein good agreement with the experimental values.

Stochastic multi-reference perturbation theory with application to linearized coupled cluster method