Gimarc Benjamin M., Zhao Ming
Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208.
Inorg Chem. 1996 Feb 14;35(4):825-834. doi: 10.1021/ic9506668.
We have recently developed a 3-dimensional Hückel method for cluster compounds. The method uses a set of approximations for Coulomb, resonance, and overlap integrals very similar to those employed in the familiar 2-dimensional Hückel theory for the pi electrons of planar conjugated hydrocarbons. The method can be adapted to heteroatomic clusters by introducing heteroatomic Coulomb integrals, alpha(Y) = alpha(X) + hbeta, whereh is a parameter for heteroatom Y. In this paper, we use the 3-dimensional Hückel method to study the properties of the closo-carboranes, C(2)B(n)()(-)(2)H(n)(). We calibrate the method by choosing a value of the heteroatomic parameter h that distinguishes positional isomers by energy and gives them relative energies in rough agreement with those established by observation and ab initio calculations. We obtain modest improvement in matching ab initio relative energies of isomers by means of a three-parameter, first-order perturbation treatment. We use the calibrated method to evaluate various mechanisms proposed for the isomerizations of C(2)B(4)H(6), C(2)B(5)H(7), and C(2)B(6)H(8), all of which have been observed to undergo intramolecular isomerizations. Rearrangements of C(2)B(6)H(8) have been satisfactorily explained by a single-DSD (diamond-square-diamond) process. Those for C(2)B(5)H(7) require at least two DSD processes, concerted, consecutive, or overlapping. Several different mechanisms have been proposed for the rearrangement of C(2)B(4)H(6). In evaluating intermediate and transition state structures, the 3-dimensional Hückel method gives higher energies to those structures with a larger number of nontriangular faces, a plausible conclusion except that occasionally it is wrong. In comparison with ab initio results, the 3-dimensional Hückel method fails to give low energies for classical structures.
我们最近为簇合物开发了一种三维休克尔方法。该方法对库仑积分、共振积分和重叠积分采用了一组近似，这与用于平面共轭烃π电子的常见二维休克尔理论中所采用的近似非常相似。通过引入杂原子库仑积分α(Y)=α(X)+hβ，其中h是杂原子Y的参数，该方法可适用于含杂原子的簇合物。在本文中，我们使用三维休克尔方法研究闭式碳硼烷C₂Bₙ⁻₂Hₙ的性质。我们通过选择杂原子参数h的值来校准该方法，该值能按能量区分位置异构体，并给出它们的相对能量，与通过观察和从头算计算确定的相对能量大致相符。通过三参数一阶微扰处理，我们在匹配异构体的从头算相对能量方面取得了一定的改进。我们使用校准后的方法评估为C₂B₄H₆、C₂B₅H₇和C₂B₆H₈的异构化提出的各种机制，所有这些化合物都已观察到会发生分子内异构化。C₂B₆H₈的重排已通过单一的DSD（菱形-方形-菱形）过程得到了令人满意的解释。C₂B₅H₇的重排至少需要两个DSD过程，协同、连续或重叠。对于C₂B₄H₆的重排提出了几种不同的机制。在评估中间体和过渡态结构时，三维休克尔方法对具有较多非三角形面的结构给出了更高的能量，这是一个合理的结论，只是偶尔会出错。与从头算结果相比，三维休克尔方法未能为经典结构给出低能量。
