This thesis is based on theoretical studies of molecular collisions occurring at relatively low to intermediate collision energies. The collisions are called dissociative recombination (DR) and mutual neutralization (MN). In a molecular quantum mechanical picture, both reactions involve many highly excited molecular electronic states that are interacting by non-adiabatic couplings with each other. The molecular complexes involved in the collisions are relatively (diatomic or triatomic systems) composed of relative light atoms. This allows for accurate quantum chemistry calculations and a quantum mechanical description of the nuclear motions. The reactions studied here are the MN reaction in collisions of H⁺+ H^-, Li⁺+ F^-, and He⁺+ H^- and the DR reaction of H₂O⁺. Rotational couplings are investigated in the study of MN reaction for  He⁺+ H . For some reactions, the electronic resonant states have to be considered. These are not bound states, but are states interacting with the ionization continuum. Electronic structure calculations are combined with electron scattering calculations to accurately compute potential energy curves for the resonant states involved in the DR of H₂O⁺ and the MN of  He⁺+ H. From these calculations, the autoionization widths of the resonant states are also obtained. Once the potential energy curves are computed for the systems, the nuclear dynamics are studied either semi-classically, using the Landau-Zener method or quantum mechanically, employing the time-independent and time-dependant Schrödinger equations. Reaction cross section and final states distribution are computed for all the reactions, showing significantly large cross section at low to intermediate collision energies. For the MN processes, studied here, not only total cross sections are calculated but differential cross sections as well. Where possible, comparisons with previous experimental and theoretical results are performed