  We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density $\rho=4.38$~g/cm$^3$, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate $\Delta G(n)$, the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of $\Delta
G(n)$ fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that $n^*$, the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, $n^*$ decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of $\Delta G(n)$ when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of $\Delta G(n)$ at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.
