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The Physics of Non–Equilibrium Reliability Phenomena

Chapter F Details of Metadynamics Calculations

In total 30 well–tempered metadynamics (WTMD) simulations have been carried out. The bias factors have been varied between \(\SI {80}{}\) and \(\SI {180}{}\) as well as bias heights ranging from \(\SI {9}{}\) to \(\SI {20}{meV}\). The accessible phase space region was limited during these calculations using a restraining potential which acts on the collective variables, see Fig. F.1 (right panel).


Figure F.1: Left: The accessible spatial region within the simulations is shown as the blue translucent sphere including the direct vicinity of the Si–H bond of interest. A restraining potential has been used to limit the phase space region and prevent the H from potentially moving away. Right: Assessment of the convergence of the simulations. One can see that for \(\SI {1}{ns}\) of simulation time only the region around the equilibrium position has been explored. For longer times a greater phase space region has been sampled, ultimately converging to a MEP at around \(\SI {20}{ns}\). The negligible changes between \(\SI {20}{}\) and \(\SI {25}{ns}\) indicate the convergence of the simulation.

Note that simulations with large bias factors and/or bias heights did not properly converge and have been discarded. Nevertheless, simulations utilizing smaller parameters – bias factors of 80/90 and heights between \(\SI {9}{}-\SI {10}{meV}\) – indeed converged to a rather unique FES, see Sec. 3.2. The final results presented in Sec. 3.2 have been obtained by performing \(\SI {50e6}{}\) time steps with a step size of \(\SI {0.5}{fs}\). In total, \(\SI {1e5}{}\) Gaussian functions have been added to the drive the system, each with a width of \(\SI {0.5}{\angstrom }\) and a height of \(\SI {9}{meV}\). The summed up Gaussian potentials were used to calculate the free energy landscape (FES) and the respective minimum energy path (MEP).

The left panel of Fig. F.1 assesses the convergence of the WTMD run by plotting the evolution of the MEP with simulation time. Clearly visible is the increasing sampling of the spatial regions with time. The reconstructed paths for \(\SI {20}{}\) and \(\SI {25}{ns}\) simulation time are almost identical, thereby indicating the convergence of the simulation.