Identification of Important Normal Modes in Nonadiabatic Dynamics Simulations by Coherence, Correlation, and Frequency Analyses

Nonadiabatic dynamics simulations of molecular systems with a large number of nuclear degrees of freedom become increasingly feasible, but there is still a need to extract from such simulations a small number of most important modes of nuclear motion, for example to obtain general insight or to construct low-dimensional model potentials for further simulations. Standard techniques for this dimensionality reduction employ statistical methods that identify the modes that account for the largest variance in nuclear positions. However, large-amplitude motion is not necessarily a good proxy for the influence of a mode on the excited-state wave function evolution. Hence, here we report a number of analysis techniques aimed at extracting from nonadiabatic dynamics simulations the vibrational modes that are most strongly affected by the electronic excitation process and that most significantly affect the interaction of the electronic states. The first technique identifies coherent nuclear motion after excitation from the ratio between total variance and variance of the average trajectory. The second strategy employs linear regression to find normal modes that have a statistically significant effect on excitation energies, energy gaps, or wave function overlaps. The third approach uses time-frequency analysis to find normal modes where the vibrational frequencies change in the course of the dynamics simulation. All three techniques are applied to the case of surface hopping trajectories of [Re(CO)₃(Im)(Phen)]⁺ (Im=imidazole; Phen=1,10-phenanthroline), showing that in this transition metal complex the nonadiabatic dynamics is dominated by a small number of carbonyl and phenanthroline in-plane stretch modes.