Using Hessian Updating To Increase the Efficiency of a Hessian Based Predictor-Corrector Reaction Path Following Method.

The reaction path is a key concept in the theoretical description of a chemical reaction. The intrinsic reaction coordinate is defined as the steepest descent path in mass-weighted Cartesian coordinates that connects the transition state to reactants and products on the potential energy surface. Recently, a new Hessian based predictor-corrector reaction path following algorithm was presented that is comparable to a fourth-order algorithm developed earlier. Although the method is very accurate, it is costly because second derivatives of the energy are required at each step. In this work, the efficiency of the method is greatly enhanced by employing Hessian updating. Three different updating schemes have been tested:  Murtagh and Sargent, Powell-symmetric Broyden, and Bofill. Bofill's update performs the best and yields excellent speed-up.