Temperature and loading rate dependent rupture forces from universal paths in mechanochemistry

Mechanical breaking of covalent bonds is induced by thermal fluctuations which leads to temperature and loading rate dependent rupture forces. These forces are much smaller than the maximum slope of the bond potential at practically accessible loading rates. Calculation of force-dependent activation energies obtained with a one-dimensional constrained geometry method is shown to work for isolated weak bonds or very simple molecules only. The situation is analyzed in a two-dimensional picture taking the broken bond explicitly into account. A single force-independent universal path appears that contains full information about the force dependence of the minima and transition states. The activation energies obtained from this path are of similar accuracy as those from force-dependent nudged elastic band calculations. Strong variations of rupture forces with loading rate and temperature are found for mechanochromophores, where the rupture force is more than one order of magnitude smaller than the maximum slope in agreement with experiment.