Effective one-body potential fitted for many-body interactions associated with a Jastrow function: application to the quantum Monte Carlo calculations

An efficient method of optimizing a Slater determinant, $D$, in the Jastrow-Slater-type wave function, $FD$, is suggested. Here, the so-called transcorrelated Hamiltonian, $\frac{1}{F}{\cal H} F$, which is a similarity transformation of the usual Hamiltonian of an electronic system with respect to a Jastrow function $F$, is fitted to an effective Hamiltonian, ${\cal H}_{\rm eff} = \sum_{i}^{N} \left( -\frac{1}{2} \nabla^2_i + v({\mathbf r_i}) \right)$, in which all the electron-electron and electron-neucleus interactions are represented by a one-body potential, $v({\mathbf r})$. A single-particle Schr\"odinger equation is then solved by using $v({\mathbf r})$ to determine the orbitals, of which the Slater determinant consists. The obtained orbitals improve the atomic total energies in the variational Monte Carlo calculations compared to those given by the density-functional-based orbitals. Advantages of using the optimized orbitals in the diffusion Monte Carlo calculations are also discussed.