Planar vs. three-dimensional X62-, X2Y42-, and X3Y32- (X, Y = B, Al, Ga) metal clusters: an analysis of their relative energies through the turn-upside-down approach

Despite the fact that B and Al belong to the same group 13 elements, the B-6(2-) cluster prefers the planar D-2h geometry, whereas Al-6(2-) favours the Oh structure. In this work, we analyse the origin of the relative stability of D2h and Oh forms in these clusters by means of energy decomposition analysis based on the turn-upside-down approach. Our results show that what causes the different trends observed is the orbital interaction term, which combined with the electrostatic component do (Al-6(2-) and Ga-6(2-)) or do not (B-6(2-)) compensate the higher Pauli repulsion of the Oh form. Analysing the orbital interaction term in more detail, we find that the preference of B-6(2-) for the planar D-2h form has to be attributed to two particular molecular orbital interactions. Our results are in line with a dominant delocalisation force in Al clusters and the preference for more localised bonding in B metal clusters. For mixed clusters, we have found that those with more than two B atoms prefer the planar structure for the same reasons as for B-6(2-).