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

Abstract

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 onthe-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.

Photoinduced water oxidation in pyrimidine–water clusters: a combined experimental and theoretical study

“…We employed a recently developed Landau-Zener (LZ) surface-hopping algorithm. [44][45][46][47] This algorithm is a computationally efficient and accurate alternative to the widely used fewest-switches surface-hopping (FSSH) method of Tully. 48 In the LZ-based surface-hopping (LZSH) algorithm, the transition probability between electronic states is determined directly from the topography of the adiabatic potentials in energy-crossing regions, avoiding the computation of rapidly varying derivative couplings near avoided crossings and conical intersections (CIs).…”

“…The results of simulations with the LZSH method have been compared with those of simulations with the FSSH method and with the results of exact quantum dynamics calculations in several studies of few-state few-mode model systems. [45][46][47] In the present work, we used an implementation of the LZSH method based on MP2 and ADC (2) energies and gradients computed with the TURBOMOLE program package. 47 Similar ab initio on-thefly LZ-based trajectory SH simulations of the photochemical dynamics of molecular systems were recently performed by Zhu and coworkers 49 and Kono and coworkers 50 .…”

PySurf: A Framework for Database Accelerated Direct Dynamics

“…Pyrazine is a molecule with 24 degrees of freedom and complicated dynamics, which is governed by a conical intersection between the S 1 and S 2 electronic states. A considerable amount of theoretical investigations, ranging from fully quantum dynamics simulations 59 to semiclassical direct dynamics, 54 revealed the S 1 and S 2 vibronic coupling dynamics in pyrazine.…”

“… 22 , 23 Recently, it has been shown that nonadiabatic dynamics simulations with the Landau–Zener algorithm and the FSSH algorithm produce very similar results. 54 The main difference between both approaches is the way how the hopping probability from state i to state j is computed. In Tully’s approach, this is done as a function of the coefficients of the electronic wavefunction and the nonadiabatic coupling vector.…”

“…In Tully’s approach, this is done as a function of the coefficients of the electronic wavefunction and the nonadiabatic coupling vector. 55 The Landau–Zener hopping probability, however, is given purely as a function of the energy gap (Δ V ij = | V i – V j |) between the two states and its second derivative at a certain nuclear position R ( t ), if there is a minimum in the energy difference at time t c ( 54 ) Therefore, nonadiabatic dynamics simulations can be performed using only energies and gradients. This simplicity makes it attractive for excited-state methods, where NACs are not available or too expensive to compute.…”