The relative stabilities of the unknown larger closo-borane dianions BnHn2- (n = 13-17), were evaluated at the B3LYP/6-31G* level of density functional theory by comparing the average energies, E/n, and also by the energies using the model equation: Bn-1Hn-12- + B6H10 --> BnHn2- + B5H9 (n = 6-17). Starting with the small closo-borane, B5H52-, the sequential addition of BH groups is represented by formal transfer from B6H10 to build up larger and larger clusters. Most of the energies for these sequential steps are exothermic, but not for the B12H122- to B13H132- and the B14H142- to B15H152- stages. The cumulative total energies (Delta H-add) Of these BH group additions, based on B5H52- as the reference zero, tend to increase with increasing cluster size. Delta H-add indicates that the larger unknown closo-boranes B13H132- to B17H172- are more stable than B9H92-, B10H102-, and B11H112-; this agrees with E/n and with Lipscomb's earlier conclusion based on the PRDDO average energies. B13H132-, B14H142-, and B15H152- are less stable than B12H122-, which has the lowest average energy on a per vertex basis among the closo-borane dianions. However, the total Delta H-add treatment indicates the larger B16H162- and B17H172- to be favorable relative to B12H122-, because of the larger number of vertexes. The formation of B13H132- from B12H122- is especially unfavorable. The further formation of B14H142- and B15H152- via BH transfer also is endothermic. These are not the only thermodynamic difficulties in building up large closo-borane dianions beyond B12H122-. The highly exothermic disproportionation of larger and smaller closo-borane dianions, e.g., B12+nH12+n2+ B12-nH12-n2- --> 2B(12)H(12)(2-) (n = 1-5), also indicate possible synthetic problems in preparing larger closo-boranes with more than 12 vertexes under condition where smaller boranes are present. All the larger closo- BnHn2- (n = 13-17) cluster exhibit "three-dimensional aromaticity", judging from the computed Nucleus Independent Chemical Shifts (NICS), which range from -30.9 to -36.5 ppm. The trends in MCS values are similar to the variations in the bond length alternations, Delta r: Thus, the qualitative relationships between geometric and magnetic criteria of aromaticity found earlier for the smaller clusters extends to the larger closo-borane dianions, BnHn2- (n = 13-17).
