Ground-state correlation energy for the homogeneous electron gas calculated by the transcorrelated method

Abstract

We have investigated the correlation energy for the homogeneous electron gas given by the transcorrelated (TC) method. In the TC method, the energy is defined by an expectation value of an effective Hamiltonian constructed by similarity transformation of the original Hamiltonian with respect to a Jastrow factor. In our calculation, a two-body Jastrow factor, which is the simplest function representing the electronic correlation effects, was adopted. Two parameters in the Jastrow factor are determined by the cusp conditions, which restricts the short-range electronic interactions and the long-range asymptotic condition resulted from the random-phase approximation. The energy is expressed within three-body integrals using the two-body Jastrow factor and so it is easily applied to the homogeneous electron gas without Monte Carlo sampling. We found that the TC method yields a fairly good estimate of the correlation energy, and so that of the total energy, especially for near the region of metallic densities (2<r s <10) in spite of our simple formulation.