Paths of chemical reactions and their networks: from geometry optimization to automated search and systematic analysis

Reaction paths obtained through quantum chemical calculations have helped to understand reactivity and selectivity of many chemical reactions. Therefore, techniques for obtaining reaction paths have been one of the indispensable tools in modern computational chemistry. There have been considerable efforts in developing such computational techniques as introduced in this chapter. Moreover, there are methods that can find many paths automatically and generate a so-called reaction path network. Such automated reaction path search methods are also described in this chapter. Resultant reaction path networks may consist of hundreds or more of reaction paths, and it becomes hard to see the whole picture of such a complex network by human eyes. Hence, some kinetic theories are also presented as tools to analyse such a complex reaction path network. In the latter half of this chapter, actual reaction path networks are explained. At first, the size of the reaction path network depending on the number of atoms and elements included is discussed. Then, reaction path networks constructed by a specific reaction path search method are showcased. Simple systems are chosen as illustrative examples, and their reaction path networks are analysed systematically using a kinetic theory. Ways to study paths of nonadiabatic transitions are also discussed briefly. Finally, the chapter is summarized, and future perspectives are discussed. We hope that this chapter will help readers grasping the current state-of-the-art methodologies concerning paths of chemical reactions and their networks.