  We perform direct large molecular dynamics simulations of homogeneous SPC/E
water nucleation, using up to $\sim 4\cdot 10^6$ molecules. Our large system
sizes allow us to measure extremely low and accurate nucleation rates, down to
$\sim 10^{19}\,\textrm{cm}^{-3}\textrm{s}^{-1}$, helping close the gap between
experimentally measured rates $\sim 10^{17}\,\textrm{cm}^{-3}\textrm{s}^{-1}$.
We are also able to precisely measure size distributions, sticking
efficiencies, cluster temperatures, and cluster internal densities. We
introduce a new functional form to implement the Yasuoka-Matsumoto nucleation
rate measurement technique (threshold method). Comparison to nucleation models
shows that classical nucleation theory over-estimates nucleation rates by a few
orders of magnitude. The semi-phenomenological nucleation model does better,
under-predicting rates by at worst, a factor of 24. Unlike what has been
observed in Lennard-Jones simulations, post-critical clusters have temperatures
consistent with the run average temperature. Also, we observe that
post-critical clusters have densities very slightly higher, $\sim 5\%$, than
bulk liquid. We re-calibrate a Hale-type $J$ vs. $S$ scaling relation using
both experimental and simulation data, finding remarkable consistency in over
$30$ orders of magnitude in the nucleation rate range, and $180\,$K in the
temperature range.
