Systematically convergent method for accurate total energy calculations with localized atomic orbitals

We introduce a method for solving a self-consistent electronic calculation within localized atomic orbitals that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our results with the ones obtained with a standard quantum chemistry package for the simple benzene molecule. We find perfect agreement for small basis set and show that, within our scheme, it is possible to work with a very large basis in an efficient and stable way. Therefore we can avoid to introduce any extrapolation to reach the CBS limit. In our study we have also carried out variational Monte Carlo and lattice regularized diffusion Monte Carlo with a standard many-body wave function defined by the product of a Slater determinant and a Jastrow factor. Once the Jastrow factor is optimized by keeping fixed the Slater determinant provided by our scheme, we obtain a very good description of the atomization energy of the benzene molecule only when the basis of atomic orbitals is large enough and close to the CBS limit, yielding the lowest variational energies.