  We investigate the kinetics and the free energy landscape of the
crystallization of hard spheres from a supersaturated metastable liquid though
direct simulations and forward flux sampling. In this first paper, we describe
and test two different ways to reconstruct the free energy barriers from the
sampled steady state probability distribution of cluster sizes without sampling
the equilibrium distribution. The first method is based on mean first passage
times, the second on splitting probabilities. We verify both methods for a
single particle moving in a double-well potential. For the nucleation of hard
spheres, these methods allow to probe a wide range of supersaturations, and to
reconstruct the kinetics and the free energy landscape from the same
simulation. Results are consistent with the scaling predicted by classical
nucleation theory although a quantitative fit requires a rather large,
effective interfacial tension.
