In the quantum chemical approach, chemical reaction mechanisms are investigated based on a potential energy surface (PES). Automated reaction path search methods enable us to construct a global reaction route map containing multiple reaction paths corresponding to a series of elementary reaction processes. The on-the-fly molecular dynamics (MD) method provides a classical trajectory exploring the full-dimensional PES based on electronic structure calculations. We have developed two reaction analysis methods, the on-the-fly trajectory mapping method and the reaction space projector (ReSPer) method, by introducing a structural similarity to a pair of geometric structures and revealed dynamic aspects affecting chemical reaction mechanisms. In this review, we will present the details of these analysis methods and discuss the dynamics effects of reaction path curvature and reaction path bifurcation with applications to the CH3OH + OH- collision reaction and the Au5 cluster branching and isomerization reactions.