  Recent developments in selected configuration interaction methods have led to
increased interest in using multi-Slater trial wave functions in various
quantum Monte Carlo (QMC) methods. Here we present an algorithm for calculating
the local energy of a multi-Slater wave function in orbital space QMC. For an
ab initio Hamiltonian, our algorithm has a cost scaling of $O(n^5 + n_c)$, as
opposed to the $O(n^4n_c)$ scaling of existing orbital space algorithms, where
$n$ is the system size, and $n_c$ is the number of configurations in the wave
function. We present our method using variational Monte Carlo calculations with
the Jastrow multi-Slater wave function, although the formalism should be
applicable for auxiliary field quantum Monte Carlo. We apply it to
polyacetylene and demonstrate the possibility of using a much larger number of
configurations than possible using existing methods.
