An experimental realization of our spin-1/2 particle version of the Einstein-Podolsky-Rosen (EPR) experiment will be briefly reviewed. In the proposed experiment, two 199Hg atoms in the ground 1S0 electronic state, each with nuclear spin I=1/2, are generated in an entangled state with total nuclear spin zero. Such a state can be obtained by dissociation of a 199Hg2 molecule (dimer) using a spectroscopically selective stimulated Raman process. From symmetry considerations, the nuclear spin singlet state is guaranteed if the initial 199Hg2 molecule is in a rotational state with an even quantum number. Consequently, a thorough investigation and analysis of the rotational structure of the 199Hg2 molecule is required; results of this analysis will be presented.