Quantum chemistry is quantum mechanics based on physics. By solving the molecular wave function, the relevant information of molecular structure characteristics is obtained, and the obtained parameters have strict and clear physical significance. In principle, quantum chemistry method can accurately express all the electronic and geometric information of molecules and their interactions, and has unique advantages in dealing with the three-dimensional structure and electronic structure of molecules. Topological chemistry is based on mathematical graph theory, and the basis and essence of graph theory is the problem of path and connection. The introduction of chemistry into graph theory provides a theoretical tool for establishing the mathematical model of molecular structure. The common feature of chemical systems is the existence of "places" and the relationship between these "places". Sites can be atoms, electrons, molecules, molecular fragments, intermediates and so on, and the connections between these sites can represent chemical bonds, reaction steps, van der Waals forces and so on. For simplicity, vertices are used to represent "places" and edges are used to represent connections, so that the chemical system can be transformed into the form of chemical diagrams. The topological index of molecules can be extracted by molecular diagram. Topological chemistry method has the advantages of simple calculation and objective value, and has its unique convenience in the study of quantitative structure, properties and activities of compounds, so it has been paid more and more attention by chemists.
It should be noted that due to the requirements of mathematical theory and the difficulty of calculation technology, the application of quantum chemical parameters is not as extensive as that of traditional molecular structure parameters. Although there is no systematic error in the experimental measurement of quantum chemical parameters, in order to simplify the calculation, multi-step approximation is adopted, which leads to inherent errors, and there are still shortcomings such as long calculation time and excessive dependence on basis sets. In addition, quantum chemical parameters can't explain the volume effects such as the shape, size and branching of molecules, and it is not convenient to calculate the local information of molecules, especially when calculating the macroscopic properties such as boiling point, heat capacity and thermal conductivity. In addition, although the topological index method of topological chemistry is simple and fast to calculate, it is difficult to express the three-dimensional information of molecules, and it is powerless to express the internal information of molecules such as electronic configuration and orbital energy level. Moreover, the physical meaning of the obtained index is not clear, and the model equation is difficult to explain.
In view of the advantages and disadvantages of the above two methods, some researchers tried to combine them and put forward the quantum topological chemistry method. Firstly, the electronic distribution of each atom in the molecule is obtained by quantum chemical calculation, then the atomic charges are substituted into the connection matrix, distance matrix or correlation matrix of the molecular diagram, and then the quantum topological index of organic molecules is obtained by further mathematical processing, which is used for the quantitative structural properties/activity related research of organic compounds. The quantum topological index obtained by this method is indeed more abundant than the molecular structure information expressed by topological index, and it can effectively distinguish the vertex information of molecular diagram, and the quantitative structure performance/activity correlation result is better. However, the application of quantum topological chemistry method must have a deep mathematical and physical foundation, and at the same time it will encounter the same difficulties as quantum chemistry method, which brings inconvenience to the use and is difficult to popularize and apply.
It can not only give full play to the advantages of quantum chemistry and topological chemistry, but also avoid complicated mathematical and physical calculations and extract more effective molecular structure parameters, which will be a very meaningful work. Our research group has made a useful exploration in this respect and put forward a topological quantum chemistry method.