  Recent molecular dynamics (MD) simulations of liquid silica, using the
``BKS'' model [Van Beest, Kramer and van Santen, Phys. Rev. Lett. {\bf 64},
1955 (1990)], have demonstrated that the liquid undergoes a dynamical crossover
from super-Arrhenius, or ``fragile'' behavior, to Arrhenius, or ``strong''
behavior, as temperature $T$ is decreased. From extensive MD simulations, we
show that this fragile-to-strong crossover (FSC) can be connected to changes in
the properties of the potential energy landscape, or surface (PES), of the
liquid. To achieve this, we use thermodynamic integration to evaluate the
absolute free energy of the liquid over a wide range of density and $T$. We use
this free energy data, along with the concept of ``inherent structures'' of the
PES, to evaluate the absolute configurational entropy $S_c$ of the liquid. We
find that the temperature dependence of the diffusion coefficient and of $S_c$
are consistent with the prediction of Adam and Gibbs, including in the region
where we observe the FSC to occur. We find that the FSC is related to a change
in the properties of the PES explored by the liquid, specifically an inflection
in the $T$ dependence of the average inherent structure energy. In addition, we
find that the high $T$ behavior of $S_c$ suggests that the liquid entropy might
approach zero at finite $T$, behavior associated with the so-called Kauzmann
paradox. However, we find that the change in the PES that underlies the FSC is
associated with a change in the $T$ dependence of $S_c$ that elucidates how the
Kauzmann paradox is avoided in this system. Finally, we also explore the
relation of the observed PES changes to the recently discussed possibility that
BKS silica exhibits a liquid-liquid phase transition, a behavior that has been
proposed to underlie the observed polyamorphism of amorphous solid silica.
