Perturbation calculation of the uniform electron gas with a transcorrelated Hamiltonian

With a transcorrelated Hamiltonian, we perform a many body perturbation calculation on the uniform electron gas in the high density regime. By using a correlation factor optimized for a single determinant Jastrow ansatz, the second order correlation energy is calculated as 1-ln2/pi 2ln(r(s))-0.05075. This already reproduces the exact logarithmic term of the random phase approximation (RPA) result, while the constant term is roughly 7% larger than the RPA one. The close agreement with the RPA method demonstrates that the transcorrelated method offers a viable and potentially efficient method for treating metallic systems. (C) 2022 Author(s).