Quantum features of time-dependent molecular interactions are investigated by introducing a time-varying Hamiltonian that involves a generalized non-central potential. According to the Lewis-Riesenfeld theory, quantum states (wave functions) of such dynamical systems are represented in terms of the eigenstates of the invariant operator. Hence, we have derived the eigenstates of the invariant operator of the system using elegant mathematical manipulations known as the unitary transformation method and the Nikiforov-Uvarov method. Based on full wave functions that are evaluated by considering such eigenstates, quantum properties of the system are analyzed. The time behavior of probability densities which are the absolute square of the wave functions are illustrated in detail. This research provides a novel method for investigating quantum characteristics of complicated molecular interactions. The merit of this research compared to conventional ones in this field is that time-varying parameters, necessary for the actual description of intricate atomic and molecular behaviors with high accuracy, are explicitly considered.