Critical points and reaction paths characterization on a potential energy hypersurface

Most of the time, the definitions of minima, saddle points or more generall y order p (p=0,...,n) critical points, do not mention the possibility of ha ving zero Hessian eigenvalues. This feature reflects some flatness of the p otential energy hypersurface in a special eigendirection which is not often taken into account. Thus, the definitions of critical points are revisited in a more general framework within this context. The concepts of bifurcati on points, branching points, and valley ridge inflection points are investi gated. New definitions based on the mathematical formulation of the reactio n path are given and some of their properties are outlined. (C) 2000 Americ an Institute of Physics. [S0021-9606(00)01110-7].