Tsuji Yuta, Yoshizawa Kazunari
Institute for Materials Chemistry and Engineering and IRCCS, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan.
ACS Omega. 2021 Jan 7;6(2):1339-1351. doi: 10.1021/acsomega.0c04913. eCollection 2021 Jan 19.
In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Hückel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.
本文详细阐述了最低能量电子的性质。此类电子所占据的轨道可称为最低占据分子轨道（LOMO）。化学中的休克尔方法与数学中的图论之间存在良好的对应关系；化学家视为具有特定能量的电子分布的分子轨道，对数学家而言是一个代数实体，即一个特征向量。LOMO在数学上的对应物被称为特征向量中心性，这是一种表征网络中节点的中心性度量。它可能有助于解决化学中的一些问题，并且对当今人类面临的挑战也有启示。本文首先展示了传染病在社交网络中的传播情况，尽管这在化学论文中并不常见，但可能是理解中心性（LOMO）究竟是什么的一个合适例子。网络上感染患者的收敛分布与具有相同网络结构或拓扑的分子的LOMO分布相吻合。这是因为图论和量子力学背后的数学结构是相同的。此外，LOMO系数可被视为原子集合中原子中心性的一种体现，表明哪个原子在集合中起最重要的作用，或者哪个原子对这些原子的网络影响最大。因此，有人提出可以根据其LOMO系数预测金属原子与其簇的结合能。还讨论了使用更复杂的中心性度量对描述符进行可能改进的问题。
