The momentum expectation values 〈pt〉, t from −2 to 4, of 26 diatomic molecules have been calculated with the quality of HF wave functions expanded on Gaussian basis sets. The highest powers of the momenta are strongly dependent on the basis sets and specially on the number of primitive Gaussian functions which describe the basis sets. However, the negative powers have a slight dependence with the ... [Show full abstract] size of the basis set. Orbital contributions to the total molecular momentum values vary for the different powers. For 〈pt〉 with t = 3 and 4 the highest values correspond to the inner orbitals which are not strongly affected by the inclusion of polarization functions. In contrast, the valence molecular orbitals give the highest weight to the t = −2 and −1 powers. These values vary with the number of polarization functions, included in the description of the molecular wave function. The augmented-correlation-consistent valence-polarized quadruple-zeta is found to yield superior results to those obtained using the other four basis sets.