Rotation of the cluster

In a molecular dynamic simulation, conservation of angular momentum is not guaranteed (Allen and Tildesley 1987, page 72), so it is pertinent to consider the rotation of the system as a whole. As the simulation is classical, it is appropriate to compare the rotational kinetic energy with the thermal energy associated with one degree of freedom. The principal moments of inertia (atomic mass units $\mbox{\AA}$²) are approximately (110000, 74000, 130000) for the 160-atom cluster, and (920000, 59000,1100000) for the 552-atom system. Taking 10⁵ as a representative value, and assuming I$\omega^{2}_{}$ = kT we find

$$\omega \sqrt{T}$$ (3)

with $\omega$ in radians per second, T in Kelvin. At 1000 K, then, the rotation period would be approximately 10^{- 10} seconds, which would not be observed in our simulations, which cover total times of the order of one rotation period.