  Among all the freezing transitions, that of water into ice is probably the
most relevant to biology, physics, geology or atmospheric science. In this work
we investigate homogeneous ice nucleation by means of computer simulations. We
evaluate the size of the critical cluster and the nucleation rate for
temperatures ranging between 15K and 35K below melting. We use the TIP4P/2005
and the TIP4P/Ice water models. Both give similar results when compared at the
same temperature difference with the model's melting temperature. The size of
the critical cluster varies from $\sim$8000 molecules (radius$ = 4$nm) at 15K
below melting to $\sim$600 molecules (radius$ = 1.7$nm) at 35K below melting.
We use Classical Nucleation Theory (CNT) to estimate the ice-water interfacial
free energy and the nucleation free energy barrier. We obtain an interfacial
free energy of 29(3)mN/m from an extrapolation of our results to the melting
temperature. This value is in good agreement both with experimental
measurements and with previous estimates from computer simulations of
TIP4P-like models. Moreover, we obtain estimates of the nucleation rate from
simulations of the critical cluster at the barrier top. The values we get for
both models agree within statistical error with experimental measurements. At
temperatures higher than 20K below melting we get nucleation rates slower than
the appearance of a critical cluster in all the water of the hydrosphere in the
age of the universe. Therefore, our simulations predict that water freezing
above this temperature must necessarily be heterogeneous.
