Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian

It has been well established that the Jastrow correlation factor can effectively capture the electron correlation effects, and thus, the efficient optimization of the many-body wave function including the Jastrow correlation factor is of great importance. For this purpose, the transcorrelated $+$ variational Monte Carlo (TC$+$VMC) method is one of the promising methods, where the one-electron orbitals in the Slater determinant and the Jastrow factor are self-consistently optimized in the TC and VMC methods, respectively. In particular, the TC method is based on similarity-transformation of the Hamitonian by the Jastrow factor, which enables the efficient optimization of the one-electron orbitals under the effective interaction. Through test calculations of some closed-shell atoms, He, Be, and Ne, we find that the total energy is in many cases systematically improved by using better Jastrow functions. We find that even a one-shot TC$+$VMC calculation, where the Jastrow parameters are optimized at the Hartree-Fock$+$VMC level, can yield partial benefits from orbital optimization. It is also suggested that one-shot TC$+$VMC can be a good alternative way for complex systems. Our study provides important insights for optimizing many-body wave function including the Jastrow correlation factor, which would be of great help for development of highly accurate electronic structure calculations.