The algorithm evaluating the overlap integrals for the numerical atomic orbitals is presented. The general class of atomic orbitals is discussed, where the radial part of the atomic orbital is represented as a piecewise polynomial and the angular part is a complex spherical harmonic. The molecular problem is reduced to the diatomic case, which is solved in prolate spheroidal coordinate system. In the prolate spheroidal coordinates, the overlap integral is reduced to the integral over the polygon. The application of the piecewise polynomial representation of the radial part further reduces the complexity of the problem. Finally, it is shown that the integral can be obtained analytically for s, p, d orbitals.

PACS numbers: 31.25.--v, 31.15.--p, 71.15.--m