The reaction pathway of a potential energy surface as curve with induced tangent

The reaction path is an important concept of theoretical chemistry. We employ the definitions of the Newton trajectory (NT) and of the gradient extremal (GE). An NT follows a curve where the gradient is always a pointer to a fixed direction. A GE is a curve where the gradient of the potential energy surfaces (PES) is eigenvector of the Hessian. Examples are given with the Müller–Brown potential and further model PESs. An induced tangent opens the possibility to follow the curve by a predictor–corrector method. We show that the two kinds of curves can be treated as curves with induced tangent, however, the gradient descent, or intrinsic reaction coordinate not.