Zhou Zhiyong, Steigerwald Michael, Hybertsen Mark, Brus Louis, Friesner Richard A
Department of Chemistry, Materials Research Science and Engineering Center, Columbia University, New York, New York 10027, USA.
J Am Chem Soc. 2004 Mar 24;126(11):3597-607. doi: 10.1021/ja039294p.
All-electron static and time-dependent DFT electronic calculations, with complete geometrical optimization, are performed on tubular molecules up to C(210)H(20) that are finite sections of the (5,5) metallic single wall carbon nanotube with hydrogen termination at the open ends. We find pronounced C-C bond reconstruction at the tube ends; this initiates bond alternation that propagates into the tube centers. For the especially low band gap molecules C(120)H(20), C(150)H(20), and C(180)H(20), alternation increases, and a second nearly isoenergic structural isomer of different alternation is found. A small residual C-C bond alternation and band gap may be present in the infinite tube. The van Hove band gap forms quickly with length, while the metallic Fermi point (at the crossing of linear bands) forms very slowly with length. There are no end-localized states at energies near the Fermi energy. The HOMO-LUMO gap and the lowest singlet excited state, whose energies show a periodicity with length as previously calculated, are optically forbidden. However, each molecule shows an intense visible "charge transfer" transition, not present in the infinite tube, whose energy varies smoothly with length; this transition should be an identifying signature for these molecules. The static axial polarizability per unit length increases rapidly with N as the "charge transfer" transition moves into the infrared; this indicates increasing metallic character. However, the ionization potential, electron affinity, chemical hardness, and relative energetic stability all show the length periodicity seen in the HOMO-LUMO gap, in contrast to the optical "charge transfer" transition and the static axial polarizability. These periodicities, due to a one-dimensional quantum size effect as originally modeled by Coulson in 1938, nevertheless cancel in the calculated Fermi energy, which varies smoothly toward a predicted bulk work function near 3.9 eV. A detailed study of C(190)H(20) with up to eight extra electrons or holes shows the total energy is closely fit by a simple classical charging model, as is commonly applied to metallic clusters.
对高达C(210)H(20)的管状分子进行全电子静态和含时密度泛函理论（DFT）电子计算，并进行完全几何优化，这些管状分子是(5,5)金属单壁碳纳米管的有限片段，其开口端有氢终止。我们发现管端存在明显的C-C键重构；这引发了键交替，并传播到管中心。对于带隙特别低的分子C(120)H(20)、C(150)H(20)和C(180)H(20)，键交替增加，并且发现了具有不同交替的第二个近等能结构异构体。在无限长的管中可能存在小的残余C-C键交替和带隙。范霍夫带隙随长度迅速形成，而金属费米点（在线性带的交叉处）随长度形成非常缓慢。在费米能量附近的能量处没有端局域态。如先前计算的那样，最高占据分子轨道（HOMO）-最低未占据分子轨道（LUMO）能隙和最低单重激发态的能量随长度呈周期性变化，它们在光学上是禁阻的。然而，每个分子都显示出强烈的可见光“电荷转移”跃迁，这在无限长的管中不存在，其能量随长度平滑变化；这种跃迁应该是这些分子的一个识别特征。随着“电荷转移”跃迁进入红外区域，单位长度的静态轴向极化率随N迅速增加；这表明金属性增强。然而，电离势、电子亲和能、化学硬度和相对能量稳定性都显示出与HOMO-LUMO能隙中相同的长度周期性，这与光学“电荷转移”跃迁和静态轴向极化率形成对比。这些周期性，由于1938年库尔森最初建模的一维量子尺寸效应，然而在计算的费米能量中相互抵消，费米能量朝着预测的约3.9 eV的体功函数平滑变化。对具有多达八个额外电子或空穴的C(190)H(20)的详细研究表明，总能量可以由一个简单的经典充电模型很好地拟合，该模型通常应用于金属簇。
