Functions of several variables, such as the electron density and the nuclear Born–Oppenheimer potential, may be analysed very effectively using orthogonal trajectories. In particular the behaviour of these trajectories at critical points of the functions is investigated in detail. The use of orthogonal trajectories in the virial partitioning of Bader and in the definition of reaction coordinates is extended. A chemical interpretation of the critical points is suggested. The relevance of catastrophe theory is illustrated.