Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn, Bonn, Germany.
Acc Chem Res. 2013 Apr 16;46(4):916-26. doi: 10.1021/ar3000844. Epub 2012 Jun 15.
Aromatic interactions play a key role in many chemical and biological systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with standard wave function theory (WFT). Although density functional theory (DFT) can easily treat systems of more than 200 atoms, standard semilocal (hybrid) density functional approximations fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramolecular noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the investigation and analysis of a wide range of complex aromatic systems. In this Account, we start with an analysis of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The minima for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of saturated and aromatic model complexes, we show that increased dispersion coefficients for sp(2)-hybridized carbon atoms play a major role in aromatic stacking. Modern dispersion-corrected DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate reference data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, density-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramolecular interactions that arise in the molecular crystals of aromatic molecules. In studies of hexahelicene, dispersion-corrected DFT yields "the right answer for the right reason". By comparison, standard DFT calculations reproduce intramolecular distances quite accurately in single-molecule calculations while inter- and intramolecular distances become too large when dispersion-uncorrected solid-state calculations are carried out. Dispersion-corrected DFT can fix this problem, and these results are in excellent agreement with experimental structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calculations for the formation of a cationic, quadruply charged dimer of a porphyrin derivative, a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-corrected DFT with an adequate continuum solvation model can accurately reproduce experimental free association enthalpies in solution. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qualitatively or quantitatively correct picture of the interactions of this complex.
芳香相互作用在许多化学和生物系统中起着关键作用。然而，即使选择了非常简单的模型，感兴趣的系统通常也太大，无法用标准的波函数理论（WFT）来处理。尽管密度泛函理论（DFT）可以轻松处理超过 200 个原子的系统，但标准的半局部（混合）密度泛函近似无法描述伦敦色散能，而这对于准确预测分子间和分子内非共价相互作用至关重要。因此，色散校正的 DFT 为广泛的复杂芳香系统的研究和分析提供了独特的工具。在本报告中，我们首先分析了六氟苯（HFB）和苯的简单模型二聚体中的非共价相互作用，重点是静电相互作用和色散相互作用。只有考虑到相互作用能的所有贡献，而不仅仅是静电相互作用，才能解释 HFB/HFB 和 HFB/苯的平行位移二聚体的最小值。通过比较饱和和芳香模型配合物，我们表明，增加 sp(2)杂化碳原子的色散系数在芳香堆积中起着重要作用。对于相对较大的卟啉和冠烯二聚体，现代色散校正的 DFT 可以产生准确的结果（二聚化能的误差约为 5-10%），而 WFT 只有在巨大的计算工作量下才能提供准确的参考数据。在这个例子中，还证明了新的非局部、密度依赖的色散校正和原子对方案彼此一致。色散能对于芳香分子的分子晶体中出现的复杂的分子间和分子内相互作用也很重要。在对六螺旋烯的研究中，色散校正的 DFT 给出了“正确的答案，出于正确的原因”。相比之下，在单分子计算中，标准 DFT 计算可以相当准确地再现分子内距离，而在未校正的固态计算中，分子间和分子内距离变得过大。色散校正的 DFT 可以解决这个问题，并且这些结果与实验结构和能量（升华）数据非常吻合。未经校正的处理甚至不能产生绑定的晶体状态。最后，我们提出了对卟啉衍生物的阳离子、四重电荷二聚体形成的计算，这种情况下需要色散来克服强烈的静电排斥。将色散校正的 DFT 与适当的连续体溶剂化模型相结合，可以准确地再现实验溶液中的自由缔合焓。与前面的例子一样，仅考虑静电相互作用不能定性或定量地描述这种复杂相互作用的情况。
