Benzo[α]pyrene is one of the polycyclic aromatic hydrocarbon compounds present in the atmosphere, produced through the incomplete combustion of fossil fuels, and is a known carcinogen. This study investigates the potential deactivation of benzo[α]pyrene through a reaction with C₂₀ fullerene using quantum computational methods. For this purpose, the thermodynamic and kinetic parameters of the [4+2] reaction between benzo[α]pyrene and fullerene were calculated. The results showed that this reaction is thermodynamically favorable with negative enthalpy and free energy. Kinetically, it occurs with a rate constant of 9.24 ×10⁻⁵ s⁻¹ at a temperature of 25^oC. Using Fukui functions, the active sites of benzo[α]pyrene for the reaction were identified. The effective orbital for the FERMO reaction of this molecule was also determined. This orbital is located at an energy level of -0.2564 a.u., where the contributions from the active site atoms (atoms 1 and 4) are maximized and can interact with the LUMO orbital of fullerene. The results from the General Electron Density Transfer (GEDT) calculations indicated that in this reaction, an electron is transferred from benzo[α]pyrene to fullerene, and the reaction exhibits some polar character. Finally, the calculations of reaction synchrony showed a low degree of synchrony, indicating that the progress of forming two bonds between fullerene and benzo[α]pyrene in the transition state is not identical.