Fragmentation of free liquids in Inertial Confinement Fusion reactors could determine the upper bound on reactor pulse rate because increased surface area will enhance the cooling and condensation of coolant ablated by the fusion x rays. Relaxation from the suddenly (neutron) heated state will move a liquid into the negative pressure region under the liquid-vapor P-V dome. The resulting expansion in a diverging geometry will hydrodynamically force the liquid to fragment, with vapor then forming from the new surfaces to fill the cavities. An energy minimization model is used to determine the fragment size that produces the least amount of non-fragment-center-of-mass energy; i.e., the sum of the surface and dilational kinetic energies. This model predicts fragmentation dependence on original system size and amount of isochoric heating as well as liquid density, Grüneisen parameter, surface tension, and sound speed. A two dimensional molecular dynamics code was developed to test the model at a microscopic scale for the Lennard-Jones fluid with its two adjustable constants chosen to represent lithium. The numerical experiments produced reasonable agreement with the model. Considerable fragmentation is predicted in the high energy density HYLIFE reactor, with minimum fragmentation in other (low energy density) reactors.