Department of Chemistry, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan.
Molecules. 2023 Jun 2;28(11):4509. doi: 10.3390/molecules28114509.
Since chemistry, materials science, and crystallography deal with three-dimensional structures, they use mathematics such as geometry and symmetry. In recent years, the application of topology and mathematics to material design has yielded remarkable results. It can also be seen that differential geometry has been applied to various fields of chemistry for a relatively long time. There is also the possibility of using new mathematics, such as the crystal structure database, which represents big data, for computational chemistry (Hirshfeld surface analysis). On the other hand, group theory (space group and point group) is useful for crystal structures, including determining their electronic properties and the symmetries of molecules with relatively high symmetry. However, these strengths are not exhibited in the low-symmetry molecules that are actually handled. A new use of mathematics for chemical research is required that is suitable for the age when computational chemistry and artificial intelligence can be used.
由于化学、材料科学和结晶学都涉及三维结构，因此它们使用几何和对称等数学方法。近年来，拓扑学和数学在材料设计中的应用取得了显著的成果。也可以看出，微分几何在很长一段时间内已经应用于化学的各个领域。还有可能将新的数学方法（如代表大数据的晶体结构数据库）应用于计算化学（Hirshfeld 表面分析）。另一方面，群论（空间群和点群）对于晶体结构很有用，包括确定其电子性质和具有较高对称性的分子的对称性。然而，这些优势在实际处理的低对称性分子中并没有体现出来。需要为化学研究找到一种新的数学应用方法，这种方法适合于计算化学和人工智能可以使用的时代。
