Internal conversion (IC) is an electronic relaxation process mediated by molecular vibration without invoking radiation and spin variation, and is the manifestation of interplay between electronic energy relaxation and nuclear motions. The elucidation of IC can thus suggest design principles for a variety of molecular systems and potentially allow us to control their excited state dynamics. In this dissertation, we discuss two distinct approaches to study the process of IC: a golden-rule based rate calculation and a direct dynamics simulation. In the former, we derive a singularity-free golden rule IC rate expression. The calculations of the IC rates of azulene and acenes as well as the recombination rate of the correlated triplet pair state generated by intramolecular singlet fission in a trio of bipentacenes yield near quantitative agreement with experimental rates. By quantifying the contributions of pairs of vibrational modes to the process of recombination, we further identify the key vibrational modes of the bipentacene molecules that drive the recombination. In the dynamics study, we implement a first on-the-fly nonadiabatic simulation with the linearized semiclassical initial value representation (LSC-IVR) method. We compute the population correlation functions of photo-excited ethylene dynamics using three variants of the LSC-IVR which differ in thefunctional form of semiclassical Hamiltonian and the population estimators. By comparing the population dynamics as well as dissociation and isomerization of ethylene to previous experimental and theoretical studies, we show that the LSC-IVR can be a viable, computationally efficient nonadiabatic dynamics method for molecular systems.