Stochastic perturbation theory to correct non-linearly parametrized wavefunctions

We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the variational method gaurantees that the VMC energy can be systematically improved the cost of doing so in practice is often prohibitive. The sPT algorithm presented in this work represents an efficient way to improve the VMC energies with a relatively small computational overhead. We demonstrate that for the carbon dimer and Fe-porphyrin the sPT algorithm is able to capture $>97\%$ and $>60\%$ respectively of the correlation energy missing from the zeroth order wavefunction. Further, the sPT algorithm is also ideally suited for massively parallel computations because it delivers super-linear speedup with an increasing number of processors.