Electronic Shannon Entropy as an Effective Descriptor of Nonradiative Dynamics in Dense Manifolds of Excited States: Case Study of C₂₀, C₆₀, C₇₀, C₇₆, C₈₄, C₈₆, and C₉₀Fullerenes

In this work, the nonradiative relaxation of excited states in C₂₀, C₆₀, C₇₀, C₇₆, C₈₄, C₈₆, and C₉₀ fullerenes is studied using a nonadiabatic molecular dynamics approach. In qualitative agreement with prior experimental findings, we find that the relaxation rates decrease with an increase in the size of the fullerenes despite the increased densities of excited electronic states and nonadiabatic couplings. We rationalize this trend by coherent population distribution over the dense manifold of electronic excited states facilitated by strong nonadiabatic couplings and small energy gaps between such states. The spreading out of the quantum population over multiple states is quantified by the Shannon entropy, which shows the initial growth consistent with the initial ultrafast coherent transfer. We observe that overall energy relaxation times correlate with the rate of the Shannon entropy decay in the longer time limit. This work suggests the emergence of effective electronic friction in dense manifolds of electronic states as a consequence of the correlation of its enhanced coherent dynamics with the dynamics of electronic Shannon entropy as a practical metric for state diffusion in nonadiabatic dynamics.