[en] A method for performing Hartree--Fock calculations on diatomic molecules using partial-wave expansions in spheroidal coordinates is presented. This method makes no use of conventional basis set techniques but, instead, relies heavily on numerical integration. The computational formalism is described, and results of partial-wave calculations are compared with results from the standard matrix method. The partial-wave method is expected to be particularly useful for those expectation values which are difficult to compute with the matrix method. Although it is limited to diatomic molecules, the partial wave method is not limited to the Hartree--Fock level of approximation