Search for lowest-energy structure of Zintl dianion Si12 2-, Ge12 2-, and Sn12 2-

We perform an unbiased search for the lowest-energy structures of Zintl dianions (Si12 2-, Ge12 2-, and Sn12 2-), by using the basin-hopping (BH) global optimization method combined with density functional theory geometric optimization. High-level ab initio calculation at the coupled-cluster level is used to determine relative stabilities and energy ranking among competitive low-lying isomers of the dianions obtained from the BH search. For Si12 2-, all BH searches (based on independent initial structures) lead to the same lowest-energy structure Si 12a 2-, a tricapped trigonal prism (TTP) with Cs group symmetry. Coupled-cluster calculation, however, suggests that another TTP isomer of Si 12c 2- is nearly isoenergetic with Si 12a 2-. For Sn12 2-, all BH searches lead to the icosahedral structure Ih - Sn 12a 2-, i.e., the stannaspherene. For Ge12 2-, however, most BH searches lead to the TTP-containing Ge 12b 2-, while a few BH searches lead to the empty-cage icosahedral structure Ih - Ge 12a 2- (named as germaniaspherene). High-level ab initio calculation indicates that Ih - Ge 12a 2- and TTP-containing Ge 12b 2- are almost isoenergetic and, thus, both may be considered as candidates for the lowest-energy structure at 0 K. Ge 12a 2- has a much larger energy gap (2.04 eV) between highest occupied molecular orbital and lowest unoccupied molecular orbital than Ge 12b 2- (1.29 eV), while Ge 12b 2- has a lower free energy than Ih - Ge 12a 2- at elevated temperature (>980 K). The TTP-containing Si 12a 2- and Ge 12b 2- exhibit large negative nuclear independent chemical shift (NICS) value (∼-44) at the center of TTP, indicating aromatic character. In contrast, germaniaspherene Ih - Ge 12a 2- and stannaspherene Ih - Sn 12a 2- exhibit modest positive NICS values, ∼12 and 3, respectively, at the center of the empty cage, indicating weakly antiaromatic character.