  This paper provides new insights concerning the simulation of plasmon driven
chemical reactions using real-time TDDFT based on the tight-binding electronic
structure code DFTB+, with applications to the dissociation of H$_2$ on
octahedral silver and gold nanoparticles with 19-489 atoms. A new component of
these calculations involves sampling a 300 K canonical ensemble to determine
the distribution of possible outcomes of the calculations, and with this
approach we are able to determine the threshold for dissociation as a function
of laser intensity, wavelength, and nanocluster size. We show that the
threshold intensity varies as an inverse power of nanocluster size, which makes
it possible to extrapolate the results to sizes that are more typical of
experimental studies. The intensities obtained from this extrapolation are
around a factor of 100 above powers used in the pulsed experiments. This is a
closer comparison of theory and experiment than has been obtained in previous
real-time simulations, and the remaining discrepancy can be understood in terms
of electromagnetic hot spots that are associated with cluster formation. We
also compare the influence of plasmon excitation versus inter-band excitation
on reaction thresholds, revealing that for silver clusters plasmon excitation
leads to lower thresholds, but for gold clusters, inter-band excitation is more
effective. Our study also includes an analysis of charge transfer to and from
the H$_2$ molecule, and a determination of orbital populations during and after
the pulse, showing the correlation between metal excitations and the location
of the antibonding level of H$_2$.
