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 B₆²⁻ cluster prefers the planar D_2h geometry, whereas Al₆²⁻ favours the O_h structure. In this work, we analyse the origin of the relative stability of D_2h and O_h 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 (Al₆²⁻ and Ga₆²⁻) or do not (B₆²⁻) compensate the higher Pauli repulsion of the O_h form. Analysing the orbital interaction term in more detail, we find that the preference of B₆²⁻ 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 B₆²⁻. [ABSTRACT FROM AUTHOR]