I propose research for an increasingly accurate quantum mechanical computation of small molecular systems including non-adiabatic, relativistic, and radiative effects. The computed rovibronic energy intervals will be directly comparable with high-resolution and precision spectroscopy measurements. The accuracy goal for theory (and experiment) is more than six-orders of magnitude tighter than the usual chemical accuracy defined to be on the order of 1 kcal/mol. The rovibronic eigenstates obtained from effective non-adiabatic, relativistic-radiative Hamiltonians to be developed will provide the most fundamental and most detailed quantum dynamical fingerprint of the molecular system, and as a complete database they are necessary for the simulation of a variety of molecular phenomena including ultrafast laser-molecule interactions.