Abstract Central pairwise empirical interatomic potential functions have been extensively used to calculate various properties of metallic solids. Although enough useful information could be gathered from these calculations, they are inadequate to reflect the true behaviour of a metal. In the present work we have computed the binding energy using a first-principles quantum-mechanical interaction model under Ashcroft's local pseudopotential formalism. The binding energy contains non-central terms and the stability conditions have been accordingly worked out. A perfect lattice of fcc aluminium subjected to tensile and compressive stresses in the  direction, has been investigated for mechanical stability under the above model. Two phases of stable structure were found. A tensile strength of 0.405 GPa and a maximum strain of 5.18% were calculated which are a little lower compared to their experimental values.