All-metal aromatic clusters M4(2-) (M = B, Al, and Ga). Are π-electrons distortive or not?

The π-electrons in benzene, the quintessential aromatic molecule, were previously shown to be distortive, i.e., they prefer localized double bonds alternating with single bonds. It is the σ-electrons that force the double bonds to delocalize, leading to a regular, D(6h) geometry. Herein, we computationally investigate the double-bond localizing or delocalizing propensities of σ- and π-electrons in the archetypal all-metal aromatic cluster Al(4)(2-) and its second- and fourth-period analogs B(4)(2-) and Ga(4)(2-), using Kohn-Sham molecular orbital (MO) theory at BP86/TZ2P in combination with quantitative bond energy decomposition analyses (EDA). We compare the three all-metal aromatic clusters with the structurally related organic species C(4)H(4)(2+), C(4)H(4), and C(4)H(4)(2-). Our analyses reveal that the π-electrons in the group-13 M(4)(2-) molecules have a weak preference for localizing the double bonds. Instead, the σ-electrons enforce the regular D(4h) equilibrium geometry with delocalized double bonds.