Comprehensive ab initio calculations RMP2(fc)/6-31G on the closo-monocarbaboranes, CB(n)()(-)(1)H(n)()(-) (n = 5-12), and the closo-dicarboranes, C(2)B(n)()(-)(2)H(n)() (n = 5-12), show that the relative energies of all the positional isomers agree with the qualitative connectivity considerations of Williams and with the topological charge stabilization rule of Gimarc. The reaction energies (DeltaH) of the most stable positional isomers, 1-CB(4)H(5)(-), CB(5)H(6)(-), 2-CB(6)H(7)(-), 1-CB(7)H(8)(-), 5-CB(8)H(9)(-), 1-CB(9)H(10)(-), 2-CB(10)H(11)(-), CB(11)H(12)(-), as well as 1,5-C(2)B(3)H(5), 1,6-C(2)B(4)H(6), 2,4-C(2)B(5)H(7), 1,7-C(2)B(6)H(8), 4,5-C(2)B(7)H(9), 1,10-C(2)B(8)H(10), 2,3-C(2)B(9)H(11), and 1,12-C(2)B(10)H(12) (computed using the equations, CBH(2)(-) + (n - 1)BH(increment) --> CB(n)()H(n)()(+1)(-) (n = 4-11) and C(2)H(2) + nBH(increment) --> C(2)B(n)()H(n)()(+2) (n = 3-10)), show that the stabilities of closo-CB(n)()(-)(1)H(n)()(-) and of closo-C(2)B(n)()(-)(2)H(n)() generally increase with increasing cluster size from 5 to 12 vertexes. This is a characteristic of three-dimensional aromaticity. There are variations in stabilities of individual closo-CB(n)()(-)(1)H(n)()(-) and closo-C(2)B(n)()(-)(2)H(n)() species, but these show quite similar trends. Moreover, there is rough additivity for each carbon replacement. The rather large nucleus independent chemical shifts (NICS) and the magnetic susceptibilities (chi), which correspond well with one another, also show all closo-CB(n)()(-)(1)H(n)()(-) and closo-C(2)B(n)()(-)(2)H(n)() species to exhibit "three-dimensional aromaticity". However, the aromaticity ordering based on these magnetic properties does not always agree with the relative stabilities of positional isomers of the same cluster, when other effects such as connectivity and charge considerations are important.

The relative stabilities of the unknown larger closo-borane dianions B(n)()H(n)()(2)(-) (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: B(n)()(-)(1)H(n)()(-)(1)(2)(-) + B(6)H(10) --> B(n)()H(n)()(2)(-) + B(5)H(9) (n = 6-17). Starting with the small closo-borane, B(5)H(5)(2)(-), the sequential addition of BH groups is represented by formal transfer from B(6)H(10) to build up larger and larger clusters. Most of the energies for these sequential steps are exothermic, but not for the B(12)H(12)(2)(-) to B(13)H(13)(2)(-) and the B(14)H(14)(2)(-) to B(15)H(15)(2)(-) stages. The cumulative total energies (DeltaH(add)) of these BH group additions, based on B(5)H(5)(2)(-) as the reference zero, tend to increase with increasing cluster size. DeltaH(add) indicates that the larger unknown closo-boranes B(13)H(13)(2)(-) to B(17)H(17)(2)(-) are more stable than B(9)H(9)(2)(-), B(10)H(10)(2)(-), and B(11)H(11)(2)(-); this agrees with E/n and with Lipscomb's earlier conclusion based on the PRDDO average energies. B(13)H(13)(2)(-), B(14)H(14)(2)(-), and B(15)H(15)(2)(-) are less stable than B(12)H(12)(2)(-), which has the lowest average energy on a per vertex basis among the closo-borane dianions. However, the total DeltaH(add) treatment indicates the larger B(16)H(16)(2)(-) and B(17)H(17)(2)(-) to be favorable relative to B(12)H(12)(2)(-), because of the larger number of vertexes. The formation of B(13)H(13)(2)(-) from B(12)H(12)(2)(-) is especially unfavorable. The further formation of B(14)H(14)(2)(-) and B(15)H(15)(2)(-) via BH transfer also is endothermic. These are not the only thermodynamic difficulties in building up large closo-borane dianions beyond B(12)H(12)(2)(-). The highly exothermic disproportionation of larger and smaller closo-borane dianions, e.g., B(12+)(n)()H(12+)(n)()(2)(-) + B(12)(-)(n)()H(12)(-)(n)()(2)(-) --> 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-B(n)()H(n)()(2)(-) (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 NICS values are similar to the variations in the bond length alternations, Deltar. Thus, the qualitative relationships between geometric and magnetic criteria of aromaticity found earlier for the smaller clusters extends to the larger closo-borane dianions, B(n)()H(n)()(2)(-) (n = 13-17).

reaction mechanism ͉ DNA ͉ RNA ͉ density functional theory ͉ gas phase model

Assessment of the cyclic electron delocalization of the oxocarbon dianions, C(n)()O(n)()(2)(-) and their neutral counterparts C(n)()O(n)() (n = 3-6), by means of structural, energetic, and magnetic criteria, shows that C(3)O(3)(2)(-) is doubly aromatic (both sigma and pi cyclic electron delocalization), C(4)O(4)(2)(-) is moderately aromatic, but C(5)O(5)(2)(-), as well as C(6)O(6)(2)(-), are less so. Localized orbital contributions, computed by the individual gauge for localized orbitals method (IGLO), to the nucleus-independent chemical shifts (NICS) allow pi effects to be disected from the sigma single bonds and other influences. The C-C(pi) contribution to (NICS(0,pi) (i.e., at the center of the ring) in oxocarbon dianions decreases with ring size but shows little ring size effect at points 1.0 A above the ring. On the basis of the same criteria, C(4)O(4) exhibits cyclic electron delocalization due to partial occupancy of the sigma CC bonds. However, the dissociation energies of all the neutral oxocarbons, C(n)()O(n)(), are highly exothermic.