58 | December 2021 www.facs.website molecules can be assembled on a computer as if building up Lego brocks. Moreover, it is possible to efficiently calculate and automatically search for the actual reaction path based on the path followed by the system in the process of minimizing FAFIR. The AFIR method has made it possible to automatically search for stable structures that the system can adapt in its chemical composition, isomerization paths among them, and their decomposition and formation paths, by starting from a set of input molecules. The connections between stable structures via reaction paths can be visualized as a reaction path network, where each node in the reaction path network represents a stable structure, and the edges between them represent the connections between stable structures. In the reaction path network, an enormous number of paths exist between the node of the reactant and that of the product, so are energy profiles. Among them, the path that gives the most favorable energy profile is the one for the actual chemical reaction. The reaction path network obtained by the AFIR method often contains over 1000 stable structures. Kinetic analysis is necessary to identify the product among those structures, considering the experimental conditions. To easily analyze a huge reaction path network, the RCMC method was devised. The RCMC method, which is a kinetic analysis method, forms superstates by clustering stable structures that the system moves back and forth within below or equal to a time constant tMAX given by a user. Each superstate is represented as a linear combination of stable structures as if each stable structure was distributed into multiple superstates. While the stable structure is distributed into superstates, by distributing the initial population given to a specific stable structure in the same way, one can simulate how the population propagates during the thermal equilibration process for tMAX seconds. Thus, one can obtain the population after thermal equilibration for tMAX seconds. The magnitude of the population of each stable structure is comparable to the reaction yield of the stable structure; therefore, one can identify the stable structures corresponding to the major and minor products. From the propagation of the initial population, one can also identify the path that contributes the most to the reaction. Most importantly, the RCMC method can be used as kinetic navigation for automated reaction path search. Starting from a single stable structure, the AFIR method searches and obtains another stable structure. The AFIR method, then, is applied to the obtained stable structures successively to construct a reaction path network. However, applying the AFIR method to all the obtained stable structures is extravagant. Kinetic navigation solves this problem by applying the RCMC method periodically to the reaction path network during the search, where stable structures that cannot be accessed kinetically from the input structure are excluded from the search target. This process reduces the number of stable structures to which the AFIR method is applied, and hence dramatically cuts down the cost. This can be referred to as on-thefly kinetic simulation, which performs kinetic simulation without any prior information. In the backward search from a product to various reactant candidates, the kinetic navigation for backward search is also available, where the search target is narrowed down based on the yield of products from each reactant candidate.20 Strecker Synthesis First, we discuss the application to the Strecker synthesis, which is one of the classical organic reactions and is still used in the chemical synthesis of α-amino acids. The typical Strecker synthesis employs a carbonyl compound, ammonium chloride, and cyanide to yield aminonitrile. In this calculation, acetone as a carbonyl compound, ammonium chloride, and sodium cyanide were mixed in water at three different reaction temperatures, 250 K, 300 K, and 350 K, and reacted for one day. The initial structure of the search was generated by the random arrangement of acetone, ammonium cation, cyanoanion, sodium cation, and chloroanion. The initial search was performed by DFT calculations using the ωB97X-D functional, where SV basis functions were used for H, C, N, and O atoms, and Def2-SVP basis functions for Na and Cl atoms. Subsequently, single-point calculations at the ωB97X-D/Def2-SVP level were performed for all discrete points on all paths obtained in the search, where the solvent effect of water was considered by the SMD method. Fig. 2(a) shows the obtained reaction path network. The above procedure yielded 8042 stable structures and 19543 reaction paths Figure 1 (a) AFIR function applying an artificial force between fragments A and B, (b) reactions induced by the artificial force between different fragment pairs.
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