  In this work, we report potential energy surfaces (PESs) of the sodium dimer
calculated by variational (VMC) and lattice regularized diffusion Monte Carlo
(LRDMC). The VMC calculation is accurate for determining the equilibrium
distance and the qualitative shape of the experimental PES. Remarkably, after
the application of the LRDMC projection to this single determinant ansatz,
namely the Jastrow Antisymmetrized Geminal Product (JAGP), chemical accuracy (~
1kcal/mol) is reached, and the obtained dissociation energy, equilibrium
internuclear distance, and harmonic vibrational frequency are in very good
agreement with the experimental ones. This outcome crucially depends on the
quality of the optimization used to determine the best possible trial function
within the chosen ansatz. The strategy adopted in this work is to minimize the
variational energy by initializing the trial function with the DFT single
determinant ansatz expanded exactly in the same atomic basis used for the
corresponding VMC and LRDMC calculations. This atomic basis is ad-hoc reshaped
for QMC calculations. Indeed, we multiply the standard Gaussian type atomic
orbitals by a one-body Jastrow factor, satisfying in this way the electron-ion
cusp conditions. This allows us to use a very small basis almost converged in
the complete basis set limit, by reducing the computational effort as well as
the statistical fluctuations on the total energy. In order to achieve these
important advantages, we have defined a very efficient DFT algorithm in the
mentioned basis, by estimating the corresponding matrix elements on a mesh, and
by using a much finer mesh grid in the vicinity of nuclei.
