Cha Minjeong, Ma Jessica, Kim Ji-Young, Emre Emine Sumeyra Turali, Kotov Nicholas A
Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, USA.
Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan, USA.
Chirality. 2024 Jun;36(6):e23678. doi: 10.1002/chir.23678.
Chirality is an essential geometric property unifying small molecules, biological macromolecules, inorganic nanomaterials, biological microparticles, and many other chemical structures. Numerous chirality measures have attempted to quantify this geometric property of mirror asymmetry and to correlate these measures with physical and chemical properties. However, their utility has been widely limited because these correlations have been largely notional. Furthermore, chirality measures also require prohibitively demanding computations, especially for chiral structures comprised of thousands of atoms. Acknowledging the fundamental problems with quantification of mirror asymmetry, including the ambiguity of sign-variable pseudoscalar chirality measures, we revisit this subject because of the significance of quantifying chirality for quantitative biomimetics and describing the chirality of nanoscale materials that display chirality continuum and scale-dependent mirror asymmetry. We apply the concept of torsion within the framework of differential geometry to the graph theoretical representation of chiral molecules and nanostructures to address some of the fundamental problems and practical limitations of other chirality measures. Chiral gold clusters and other chiral structures are used as models to elaborate a graph-theoretical chirality (GTC) measure, demonstrating its applicability to chiral materials with different degrees of chirality at different scales. For specific cases, we show that GTC provides an adequate description of both the sign and magnitude of mirror asymmetry. The direct correlations with macroscopic properties, such as chiroptical spectra, are enhanced by using the hybrid chirality measures combining parameters from discrete mathematics and physics. Taking molecular helices as an example, we established a direct relation between GTC and optical activity, indicating that this chirality measure can be applied to chiral metamaterials and complex chiral constructs.
手性是一种基本的几何特性，它统一了小分子、生物大分子、无机纳米材料、生物微粒以及许多其他化学结构。众多手性度量方法试图量化这种镜像不对称的几何特性，并将这些度量与物理和化学性质相关联。然而，它们的实用性受到广泛限制，因为这些相关性在很大程度上只是概念性的。此外，手性度量还需要极其苛刻的计算，特别是对于由数千个原子组成的手性结构。认识到镜像不对称量化存在的基本问题，包括符号可变的赝标量手性度量的模糊性，由于量化手性对于定量仿生学以及描述显示手性连续体和尺度依赖性镜像不对称的纳米级材料的手性具有重要意义，我们重新审视了这个主题。我们将微分几何框架内的挠率概念应用于手性分子和纳米结构的图论表示，以解决其他手性度量的一些基本问题和实际局限性。手性金簇和其他手性结构被用作模型来阐述一种图论手性（GTC）度量，证明其适用于不同尺度下具有不同手性程度的手性材料。对于特定情况，我们表明GTC对手性不对称的符号和大小都提供了充分的描述。通过使用结合离散数学和物理学参数的混合手性度量，与宏观性质（如手性光谱）的直接相关性得到了增强。以分子螺旋为例，我们建立了GTC与光学活性之间的直接关系，表明这种手性度量可应用于手性超材料和复杂的手性结构。
