Hot carriers generated by plasmonic damping have been suggested to promote photocatalysis, yet it remains unclear how the nonthermalized hot carriers dynamically activate and promote the energy transfer processes. Here, we present an Anderson-Newns model to describe the vibrational excitation and bond dissociation induced by plasmonic hot carriers. The nonthermal distribution of the hot carriers generated by plasmon damping is accounted for on equal footing with thermal carriers at a given temperature in the electron-molecule scattering. We found that the nonthermal electrons in the high energy region can, albeit in much smaller populations, provide an efficient and dominant channel for photodissociation especially in the low-temperature and quantum plasmon regime. Our model captures the wavelength dependence and reproduces the enhancement factors observed by experiments for oxygen dissociation on silver nanoparticles. It also paves a way to harvesting nonthermal plasmonic energy for photocatalysis in the quantum regime.