Our recently developed trajectory surface hopping method uses numerical time derivatives of adiabatic potential gradients to estimate the nonadiabatic transition probability and the hopping direction. To demonstrate the practicality of the novel method, we applied it to the intermolecular photodissociation of a carbon dioxide dimer cation (CO2)2+. Our simulations reproduced the measured velocity distribution of CO2+ fragments consisting of two (fast and slow) components and revealed that nonadiabatic transitions occur promptly toward the electronic ground state regardless of the fragment velocity. The structure of (CO2)2+ at optical excitation governs the fate of subsequent nonadiabatic dynamics leading to a fast or slow dissociation. Our method gave similar results to the fewest switches algorithm at lower computational expense. Our fast and robust surface hopping method is promising for the investigation of nonadiabatic dynamics in large and complex systems.