  Over the last number of years several simulation methods have been introduced
to study rare events such as nucleation. In this paper we examine the crystal
nucleation rate of hard spheres using three such numerical techniques:
molecular dynamics, forward flux sampling and a Bennett-Chandler type theory
where the nucleation barrier is determined using umbrella sampling simulations.
The resulting nucleation rates are compared with the experimental rates of
Harland and Van Megen [J. L. Harland and W. van Megen, Phys. Rev. E 55, 3054
(1997)], Sinn et al. [C. Sinn et al., Prog. Colloid Polym. Sci. 118, 266
(2001)] and Schatzel and Ackerson [K. Schatzel and B.J. Ackerson, Phys. Rev. E,
48, 3766 (1993)] and the predicted rates for monodisperse and 5% polydisperse
hard spheres of Auer and Frenkel [S. Auer and D. Frenkel, Nature 409, 1020
(2001)]. When the rates are examined in long-time diffusion units, we find
agreement between all the theoretically predicted nucleation rates, however,
the experimental results display a markedly different behaviour for low
supersaturation. Additionally, we examined the pre-critical nuclei arising in
the molecular dynamics, forward flux sampling, and umbrella sampling
simulations. The structure of the nuclei appear independent of the simulation
method, and in all cases, the nuclei contain on average significantly more
face-centered-cubic ordered particles than hexagonal-close-packed ordered
particles.
