Gradient extremal bifurcation and turning points: An application to the H2CO potential energy surface

Gradient extremals are curves on potential energy surfaces connecting points where the derivative of the gradient norm, subject to the constraint that the energy is constant, is zero. The bifurcation of such curves is analyzed, and exemplified by tracing out some of the gradient extremals on the HF/STO-3G surface for H2CO. It is shown that gradient extremal following provides a semisystematic way of locating stationary points.