One of the main objectives of computational chemistry studies is the interpretation of chemical mechanisms whose data were obtained from quantum mechanical software packages. In these mechanisms, starting from the reactant, the reactant and the product states are connected through intermediates and transition states, in an alternating order. Generally, the reactivity of a given pathway is determined by the overall barrier height. Sometimes, a comparison becomes necessary for a given step with another possible step that can be realized within the same mechanism, and in this case as well the step with the lowest-lying transition state is preferred. However, there are some exceptions in the order of these states. There are states known as pre-reaction complexes that reside between a reactant, or an intermediate, and a transition state. Excluding some first principle quantum dynamics studies, the effect of a pre-reaction complex is generally not discussed in most of the computational chemistry studies, and the overall barrier heights become the main considerations, as usual. In this work, a mathematical model that allows obtaining the rate constant of a pathway without a pre-reaction complex, and that of a pathway with a pre-reaction complex was described. The model was built using time-dependent quantum perturbation theory and quantum time-correlation functions. This work can improve our understanding of the nature of chemical reactions that include pre-reaction complexes by enabling us to differentiate the seemingly identical reaction pathways.