Schleyer Paul von Ragué, Najafian Katayoun, Mebel Alexander M.
Institut für Organische Chemie der Universität Erlangen-Nürnberg, Henkestrasse 42, D-91504 Erlangen, Germany, and Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10764.
Inorg Chem. 1998 Dec 28;37(26):6765-6772. doi: 10.1021/ic980359c.
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).
通过比较平均能量(E/n)，并使用模型方程：(B(n)^{-1}H(n)^{-1}(2)^- + B_6H_{10} \longrightarrow B(n)H(n)(2)^- + B_5H_9)（(n = 6 - 17)）的能量，在密度泛函理论的B3LYP/6 - 31G水平上评估了未知的较大闭式硼烷二价阴离子(B(n)H(n)(2)^-)（(n = 13 - 17)）的相对稳定性。从较小的闭式硼烷(B_5H_5(2)^-)开始，通过从(B_6H_{10})的形式转移来表示(BH)基团的顺序添加，以构建越来越大的簇。这些顺序步骤中的大多数能量是放热的，但从(B_{12}H_{12}(2)^-)到(B_{13}H_{13}(2)^-)以及从(B_{14}H_{14}(2)^-)到(B_{15}H_{15}(2)^-)阶段不是。基于(B_5H_5(2)^-)作为参考零点，这些(BH)基团添加的累积总能量（(\Delta H_{add})）倾向于随着簇尺寸的增加而增加。(\Delta H_{add})表明，较大的未知闭式硼烷(B_{13}H_{13}(2)^-)到(B_{17}H_{17}(2)^-)比较小的(B_9H_9(2)^-)、(B_{10}H_{10}(2)^-)和(B_{11}H_{11}(2)^-)更稳定；这与(E/n)以及Lipscomb基于PRDDO平均能量的早期结论一致。(B_{13}H_{13}(2)^-)、(B_{14}H_{14}(2)^-)和(B_{15}H_{15}(2)^-)比较小的(B_{12}H_{12}(2)^-)不稳定，(B_{12}H_{12}(2)^-)在闭式硼烷二价阴离子中每个顶点的平均能量最低。然而，总的(\Delta H_{add})处理表明，由于顶点数量较多，较大的(B_{16}H_{16}(2)^-)和(B_{17}H_{17}(2)^-)比较小的(B_{12}H_{12}(2)^-)更有利。从(B_{12}H_{12}(2)^-)形成(B_{13}H_{13}(2)^-)特别不利。通过(BH)转移进一步形成(B_{14}H_{14}(2)^-)和(B_{15}H_{15}(2)^-)也是吸热的。这些并不是构建超过(B_{12}H_{12}(2)^-)的大型闭式硼烷二价阴离子时唯一的热力学困难。较大和较小的闭式硼烷二价阴离子的高度放热歧化反应，例如(B_{12 + n}H_{12 + n}(2)^- + B_{12 - n}H_{12 - n}(2)^- \longrightarrow 2B_{12}H_{12}(2)^-)（(n = 1 - 5)），也表明在存在较小硼烷的条件下制备具有超过12个顶点的较大闭式硼烷时可能存在合成问题。从计算的核独立化学位移（NICS）判断，所有较大的闭式(B(n)H(n)(2)^-)（(n = 13 - 17)）簇都表现出“三维芳香性”，其范围从(-30.9)到(-36.5 ppm)。NICS值的趋势与键长交替变化(\Delta r)相似。因此，早期在较小簇中发现的芳香性几何和磁性标准之间的定性关系扩展到了较大的闭式硼烷二价阴离子(B(n)H(n)(2)^-)（(n = 13 - 17)）。
