Exact quantum dynamics calculations are performed for the bound rovibrational states of the neon tetramer (Ne4) in its ground electronic state, using pair-wise Lennard-Jones potentials and the ScalIT suite of parallel codes. The vibrational states separate into a low-lying group mostly localized to a single potential well and a higher-energy delocalized group lying above the isomerization threshold - with such a structure serving as a testament to the "intermediate" quantum nature of the Ne4 system. To accurately and efficiently represent both groups of states, the phase-space optimized discrete variable representation (PSO-DVR) approach was used, as implemented in the ScalIT code. The resultant 1D PSO effective potentials also shed significant light on the quantum dynamics of the system. All vibrational states were computed well up into the isomerization band and labeled up to the classical isomerization threshold - defined as the addition of the classical energy of a single bond, ϵ = 24.7 cm-1, to the quantum ground state energy. Rovibrational energy levels for all total angular momentum values in the range J = 1-5 were also computed, treating all Coriolis coupling exactly.