Recent work in the aerothermodynamics community has focused on the development of reduced-order non-equilibrium models which avoid the conventional assumptions found in multi-temperature models, and the prohibitive cost of State-to-State (StS) models. This work extends the framework for the construction of reduced order models to study the interaction between two molecules (i.e., the N2(1Σ+ g)-N2(1Σ+ g) system) by coupling the level grouping approach developed by the authors and co-workers with the Quasi-Classical Trajectory (QCT) method for determining group-averaged kinetic parameters (e.g., rate coefficients, energy transfer terms). With this approach two energy level grouping schemes are considered: energy based binning and vibrational specific binning. The two approaches yield very different predictions for the excitation and dissociation processes in an isochoric and isothermal reactor simulation of nitrogen molecules, considering the N2(1Σ+ g)-N2(1Σ+ g) processes. The relaxation process predicted using vibrational binning exhibits a bottleneck caused by the inefficient exchange of vibrational and translational energy for low vibrational states. In contrast, in the energy based binning strategy excitation proceeds through a series of small jumps in energy, akin to the ladder climbing model. This profoundly influences the dynamics of relaxation of the internal state population, and ultimately the macroscopic properties such as internal energy and composition profiles. Moreover, it will be shown that the dissociation process cannot be accurately predicted if quasi-bound states are not considered, as they contribute to over half of the dissociating molecules.