Nonlinear dimensionality reduction for nonadiabatic dynamics: The influence of conical intersection topography on population transfer rates

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Conical intersections play a critical role in the nonadiabatic relaxation of excited electronic states. However, there are an infinite number of these intersections and it is difficult to predict which are actually relevant. Furthermore, traditional descriptors such as intrinsic reaction coordinates and steepest descent paths often fail to adequately characterize excited state reactions due to their highly nonequilibrium nature. To address these deficiencies in the characterization of excited state mechanisms, we apply a nonlinear dimensionality reduction scheme (diffusion mapping) to generate reaction coordinates directly from ab initio multiple spawning dynamics calculations. As illustrated with various examples of photoisomerization dynamics, excited state reaction pathways can be derived directly from simulation data without any a priori specification of relevant coordinates. Furthermore, diffusion maps also reveal the influence of intersection topography on the efficiency of electronic population transfer, providing further evidence that peaked intersections promote nonadiabatic transitions more effectively than sloped intersections. Our results demonstrate the usefulness of nonlinear dimensionality reduction techniques as powerful tools for elucidating reaction mechanisms beyond the statistical description of processes on ground state potential energy surfaces.