Highly accurate results for the homogeneous electron gas (HEG) have only been achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we introduce a recently developed stochastic technique, full configuration interaction quantum Monte Carlo (FCIQMC), which samples the exact wave function expanded in plane-wave Slater determinants. Despite the introduction of a basis-set incompleteness error, we obtain a finite-basis energy, which is significantly and variationally lower than any previously published work for the 54-electron HEG at
rs = 0.5 a.u., in a Hilbert space of
10108 Slater determinants. At this value of
rs, as well as of 1.0 a.u., we remove the remaining basis-set incompleteness error by extrapolation, yielding results comparable to state-of-the-art DMC backflow energies. In doing so, we demonstrate that it is possible to yield highly accurate results with the FCIQMC method in periodic systems.
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
O(M−1) to
O(M−5/3), where
M is the total number of orbital basis functions.
We suggest an efficient method to resolve electronic cusps in electronic structure calculations through the use of 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 [Formula: see text] to [Formula: see text], where M is the total number of orbital basis functions.