Nonadiabatic rare events from transition-path sampling of MASH trajectories

Abstract

Rare nonadiabatic reactions are a key component of many important molecular processes but are challenging to capture with direct dynamical simulations. In this paper, we combine our recently developed mapping approach to surface hopping (MASH) with transition-path sampling to create a framework to efficiently simulate these rare events. This is possible because MASH trajectories are Markovian, time-reversible and obey Liouville's theorem. The combined approach generates nonadiabatic reactive pathways without biasing the underlying dynamics. The resulting ensemble allows for a detailed analysis of reaction mechanisms and the unraveling of statistical and dynamical properties, including rate constants. We apply the method to study a spin-boson model in thermal equilibrium over a wide range of diabatic coupling strengths. Our results demonstrate how this approach provides a practical and systematic tool for investigating rare nonadiabatic processes, potentially beyond the reach of brute-force simulations.

Figures (7)

• Figure 1: Diabatic (dashed lines) and adiabatic (solid colored lines) potentials of the spin--boson model with $\beta\Delta=1$. The adiabatic energy gap (avoided crossing) at the transition state $R=0$ is $2\Delta$.
• Figure 2: An example of the unweighted probability distributions for the 9 overlapping regions, $\lambda$, for the spin--boson model with $\beta\Delta=1$, obtained with the procedure outlined in Sec. \ref{['SEC:rate_const']}.
• Figure 3: The graph of (connected) probability distribution averaged over six separate experiments where we first performed MASH-TPS calculations for the 9 overlapping regions (as the example shown in Fig. \ref{['FIG:SB_disconnected_Ctprime']}) and then reconstructed with the WHAM, as outlined in Sec. \ref{['SEC:rate_const']}. The colors correspond to different values of $\Delta$. The shaded area around each distribution represents a $2\sigma$ error estimate after the averaging. As indicated in the figure, the value of $C(T')$ is obtained by numerically integrating the mean distributions in the product state.
• Figure 4: The reaction rate constant of spin--boson models with varying diabatic couplings, calculated through brute-force (blue triangles) and MASH-TPS (red circles) experiments. The error bars show $2\sigma$ confidence interval of the MASH-TPS rates, whereas the direct MASH simulations are fully converged. Both sets of experiments have quantitatively good overall agreement. The values for Classical BO, Marcus theory and HEOM (taken from Ref. MASHrates) are included for comparison.
• Figure 5: The distribution of accepted shooting moves in the transition-path ensemble of spin--boson models with a range of diabatic couplings.