Assessing the performance of trajectory surface hopping methods: Ultrafast internal conversion in pyrazine

Trajectory surface hopping (TSH) methods have been widely used to study photoinduced nonadiabatic processes. In the present study, nonadiabatic dynamics simulations with the widely used Tully's fewest switches surface hopping (FSSH) algorithm and a Landau-Zener-type TSH (LZSH) algorithm have been performed for the internal conversion dynamics of pyrazine. The accuracy of the two TSH algorithms has been critically evaluated by a direct comparison with exact quantum dynamics calculations for a model of pyrazine. The model comprises the three lowest excited electronic states (B _3u (nπ ^∗ ), A _1u (nπ ^∗ ), and B _2u (ππ ^∗ )) and the nine most relevant vibrational degrees of freedom. Considering photoexcitation to the diabatic B _2u (ππ ^∗ ) state, we examined the time-dependent diabatic and adiabatic electronic population dynamics. It is found that the diabatic populations obtained with both TSH methods are in good agreement with the exact quantum results. Fast population oscillations between the B _3u (nπ ^∗ ) and A _1u (nπ ^∗ ) states, which reflect nonadiabatic electronic transitions driven by coherent dynamics in the normal mode Q _8a , are qualitatively reproduced by both TSH methods. In addition to the model study, the TSH methods have been interfaced with the second-order algebraic diagrammatic construction ab initio electronic-structure method to perform full-dimensional on-the-fly nonadiabatic dynamics simulations for pyrazine. It is found that the electronic population dynamics obtained with the LZSH method is in excellent agreement with that obtained by the FSSH method using a local diabatization algorithm. Moreover, the electronic populations of the full-dimensional on-the-fly calculations are in excellent agreement with the populations of the three-state nine-mode model, which confirms that the internal conversion dynamics of pyrazine is accurately represented by this reduced-dimensional model on the time scale under consideration (200 fs). The original FSSH method, in which the electronic wave function is propagated in the adiabatic representation, yields less accurate results. The oscillations in the populations of the diabatic B _3u (nπ ^∗ ) and A _1u (nπ ^∗ ) states driven by the mode Q _8a are also observed in the full-dimensional dynamics simulations.