The reaction path is an important concept of theoretical chemistry. We use a projection operator for the following of the Newton trajectory (NT) along the reaction valley of the potential energy surface. We describe the numerical scheme for the string method, adapting the proposal of a growing string (GS) by [Peters et al.,J. Chem. Phys. 120, 7877 (2004)]. The combination of the Newton projector and the growing string idea is an improvement of both methods, and a great saving of the number of iterations needed to find the pathway over the saddle point. This combination GS-NT is at the best of our knowledge new. We employ two different corrector methods: first, the use of projected gradient steps, and second a conjugated gradient method, the CG+ method of Liu, Nocedal, and Waltz, generalized by projectors. The executed examples are Lennard-Jones clusters, LJ7 and LJ22, and an N-methyl-alanyl-acetamide (alanine dipeptide) rearrangement between the minima C7ax and C5. For the latter, the growing stŕing calculation is interfaced with the GASSIAN03 quantum chemical software package.

The reaction path is a central subject in theoretical chemistry. It is a pathway imagined on the potential energy surface (PES). It provides a one-dimensional description of a chemical reaction in an N-dimensional configuration space. Additionally, one can apply mechanical stress in a defined direction to the molecule and generate an effective PES. Changes for minima and saddle points by the stress are described by Newton trajectories on the original PES. The barrier of a reaction fully breaks down for the maximal value of the norm of the gradient of the PES along a pulling Newton trajectory. This point is named barrier breakdown point. We discuss topologically different, two-dimensional examples for this model to understand and classify the mechanochemistry of molecules.