Combining the Transcorrelated method with Full Configuration Interaction Quantum Monte Carlo: application to the homogeneous electron gas

We suggest an efficient method to resolve electronic cusps in electronic structure calculations by using an effective transcorrelated Hamiltonian. This effective Hamiltonian takes a simple form for plane wave bases, containing up to two-body operators only, and its use incurs almost no additional computational overhead compared to that of the original Hamiltonian. We apply this method in combination with the full configuration interaction quantum Monte Carlo (FCIQMC) method to the homogeneous electron gas. As a projection technique, the non-Hermitian nature of the transcorrelated Hamiltonian does not cause complications or numerical difficulties for FCIQMC. The rate of convergence of the total energy to the complete basis set limit is improved from ${\cal O}(M^{-1})$ to ${\cal O}\left({M^{-5/3}}\right)$, where $M$ is the total number of orbital basis functions.