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In this work, we report potential energy surfaces (PESs) of the sodium dimercalculated by variational (VMC) and lattice regularized diffusion Monte Carlo(LRDMC). The VMC calculation is accurate for determining the equilibriumdistance and the qualitative shape of the experimental PES. Remarkably, afterthe 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, equilibriuminternuclear distance, and harmonic vibrational frequency are in very goodagreement with the experimental ones. This outcome crucially depends on thequality of the optimization used to determine the best possible trial functionwithin the chosen ansatz. The strategy adopted in this work is to minimize thevariational energy by initializing the trial function with the DFT singledeterminant ansatz expanded exactly in the same atomic basis used for thecorresponding VMC and LRDMC calculations. This atomic basis is ad-hoc reshapedfor QMC calculations. Indeed, we multiply the standard Gaussian type atomicorbitals by a one-body Jastrow factor, satisfying in this way the electron-ioncusp conditions. This allows us to use a very small basis almost converged inthe complete basis set limit, by reducing the computational effort as well asthe statistical fluctuations on the total energy. In order to achieve theseimportant advantages, we have defined a very efficient DFT algorithm in thementioned basis, by estimating the corresponding matrix elements on a mesh, andby using a much finer mesh grid in the vicinity of nuclei.

All-electron quantum Monte Carlo with Jastrow single determinant Ansatz: application to the sodium dimer