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