Method

  The calculations were performed using a variety of clusters. The structural and vibrational data presented here comes from large 150 atom clusters, $\rm Si_{79}H_{68}O_2$, the same size as used to study the STDs and TDs. The diffusion data was obtained from 113-115 atom clusters, $\rm Si_{57}H_{56}O_n, n=1,2$, similar to those used to explore the structure and vibrational modes of O_i, VO, VO_2i and VO_3i defects [99].

In order to investigate diffusion barriers and determine the saddle point configuration of O_i and O_2i it is necessary to introduce constraints on the positions of atoms during the relaxation. Unless this is done, the cluster would relax away from the saddle point to the nearest stable configuration.

There are two methods that we have used to constrain the system, one based on an orthogonality constraint and the other on constraining certain bond lengths within the system. The first is a method common amongst the literature but has a tendency to overconstrain the system.