Transition state determination by the X-method

A simple direct procedure to locate saddle points (transition states) on energy surfaces is described. The advantage of the method is that it may utilize effective unconstrained optimization techniques while convergence may occur only to saddle points and not to minima. Thus no further tests are needed to decide the nature of the critical point located. Both the simplex and conjugate gradients optimization techniques were applied within the framework of the proposed method (the X-method) and numerical tests were carried out on both 'mathematical' and 'chemical' model surfaces.