The Transcorrelated Method Combined with the Variational Monte Carlo Calculation: Application to Atoms

The transcorrelated (TC) method is a useful approach to optimize the Jastrow-Slater-type many-body wave function $FD$. The basic idea of the TC method [1] is based on the similarity transformation of a many-body Hamiltonian ${\cal H}$ with respect to the Jastrow factor $F$: ${\cal H}_{\rm TC}=frac{1}{F} {\cal H} F$ in order to incorporate the correlation effect into ${\cal H}_{\rm TC}$. Both the $F$ and $D$ are optimized by minimizing the variance $\sigma^2=\int |{\cal H}_{rm TC}D - E D |^2 d^{3N} x$. The optimization for $F$ is implemented by the variational Monte Carlo calculation, and $D$ is determined by the TC self-consistent-field equation for the one-body wave functions $\phi_{\mu}(x)$, which is derived from the functional derivative of $\sigma^2$ with respect to $\phi_{mu}(x)$. In this talk, we will present the results given by the transcorrelated variational Monte Carlo (TC-VMC) method for the ground state [2] and the excited states of atoms [3]. [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, {\bf 309}, 209; {\bf 310}, 43; {\bf 310}, 63; {\bf 311}, 309 (1969). [2]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. {\bf 119}, 10015 (2003). [3]N. Umezawa and S. Tsuneyuki, J. Chem. Phys. {\bf 121}, 7070 (2004).