Search for lowest-energy structure of Zintl dianion Si(12)(2-), Ge(12)(2-), and Sn(12)(2-)

We perform an unbiased search for the lowest-energy structures of Zintl dianions (Si(12)(2-), Ge(12)(2-), and Sn(12)(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 Si(12)(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 C(s) group symmetry. Coupled-cluster calculation, however, suggests that another TTP isomer of Si(12c)(2-) is nearly isoenergetic with Si(12a)(2-). For Sn(12)(2-), all BH searches lead to the icosahedral structure I(h)-Sn(12a)(2-), i.e., the stannaspherene. For Ge(12)(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 I(h)-Ge(12a)(2-) (named as germaniaspherene). High-level ab initio calculation indicates that I(h)-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 I(h)-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 (approximately -44) at the center of TTP, indicating aromatic character. In contrast, germaniaspherene I(h)-Ge(12a)(2-) and stannaspherene I(h)-Sn(12a)(2-) exhibit modest positive NICS values, approximately 12 and 3, respectively, at the center of the empty cage, indicating weakly antiaromatic character.