This thesis proposes useful tools, on-the-fly trajectory mapping method and Reaction Space Projector (ReSPer), to analyze chemical reaction mechanisms by combining the reaction route map and the ab initio molecular dynamics. The key concept for the proposed tools is the Cartesian distance between pairwise molecular structures, and a practical procedure to get the optimal distance is introduced. The on-the-fly trajectory mapping method tracks the distance function between reference structures and molecular structures along the trajectory. Although this method provides fruitful insight into...