The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface

We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden-Fletcher-Goldfarg-Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton-Raphson method. Some examples are presented and analyzed.