In this study, a one-dimensional adaptive computational method and a quantum optimization approach were used to evaluate the energy state and adsorption properties of clusters consisting of metal atoms. During the calculation, an external potential based on the nuclear charge, number of valence electrons, and gravitational properties of atoms was determined, and the total energy was calculated by the adaptive electron density. Based on the results obtained, a multi-criteria selection method was developed based on the energy limit, atomic composition, and electronic properties. A simplified quantum mechanical operator was constructed for the selected clusters, and its lowest energy state was determined by quantum optimization. The results of the study show that the adsorption processes of metal clusters can be quickly and reliably assessed at the initial stage and provide an effective computational basis for the selection of catalytic materials.