As this set of equations becomes too difficult to solve analytically, the differential rate equations were solved numerically by COPASI. We explored various stoichiometries and equilibrium constants and found that a stoichiometry of 2 with K eq = 12 minimizes the variation in the second rate constant (k 2 ). Whereas the two-step model causes a trend in k 2 that spans more than an order of magnitude, the three-step model reduces the variation to twofold, see Figure . This suggests that the slower precursor decomposition with increasing TOPO concentration is due to an equilibrium that reduces the availability of the auto-catalytic species, such as the formation of a complex with TOPO. Unlike for titania, this auto-catalytic step dominates the overall rate of the reaction.