An updated Hessian formula for optimizing transition structures which explicitly contains the potential structure of the desired transition vector

A formula for updating the Hessian matrix during the geometry optimization of first-order saddle points is reported. The updating formula contains explicitly the desired transition vector which, in principle, warrants the correct convergence. The mathematical structure of this formula is close to the Murtagh-Sargent-Powell formula used in the location of transition structures. A sketch of the algorithm and examples are reported.