Chemical reaction paths and calculus of variations

The reaction path is an important concept of theoretical chemistry. We analyze different forms of reaction pathways in the light of the abstract theory of calculus of variations such as steepest descent from saddle point, the intrinsic reaction coordinate (IRC), Newton trajectory, variationally optimized reaction paths and others. The paper is both a mathematical review and a pointer to future research. Besides the theoretical definitions, we shortly discuss hints at the numerical effect of the definitions.