The Many-Body Expansion for Metals: II. Nonadditive Terms in Clusters Composed of Metals with ns1, ns2, and ns2p1 Configurations

The many-body expansion (MBE) was applied to homometallic and heterometallic trimers of metals with ns¹, ns², and ns²p¹ configurations to investigate its convergence, the magnitude and nature (stabilizing/destabilizing) of the individual terms and seek an understanding of their variation across the different families of clusters. In particular, we examined the series of alkali metals (Li₃, Na₃, K₃, Li₂Na, LiNa₂), alkali metal borides (Li₂B and LiB₂), and alkaline earth metals (Be₃, Be₂Mg, BeMg₃, and Mg₃) trimers, as well as sodium clusters Na_n, n = 2–5. We found that there is no uniform contribution (stabilizing or destabilizing) across the series in the different families of trimers. For instance, the 2-B term stabilizes the ground states of the Na₃ (doublet), Na₄ (singlet), and Na₅ (doublet) clusters, and the 3-B term destabilizes them; however, the opposite holds for the quartet state of the Li₃, Li₂Na, LiNa₂, and Na₃ clusters (destabilizing 2-B, stabilizing 3-B). Substituting Li with B in the quartet state of Li₃ results in a significant reduction of the 3-B term amounting to 16% (Li₂B) and 5% (LiB₃) of the binding energy. On the contrary, the ground states of the alkaline earth metal clusters (Be₃, Be₂Mg, BeMg₃, and Mg₃) are stabilized by the 3-B term, while the 2-B term destabilizes them. Overall, we find that the 3-B terms significantly stabilize the high-spin multiplicity states of the ns¹ configurations and the low-spin states of the ns² configurations. Finally, as the size of the metal increases, the contribution of the 3-B term to the binding energy decreases due to the longer metal–metal bond distances.