Towards Prediction of Non-Radiative Decay Pathways in Organic Compounds I: The Case of Naphthalene Quantum Yields

<div>Many emerging technologies depend on human’s ability to control and manipulate the excited-state properties of molecular systems. These technologies include fluorescent</div><div>labeling in biomedical imaging, light harvesting in photovoltaics, and electroluminescence in light-emitting devices. All of these systems suffer from non-radiative loss pathways that dissipate electronic energy as heat, which causes the overall system efficiency to be directly linked to quantum yield (Φ) of the molecular excited state. Unfortunately, Φ is very difficult to predict from first principles because the description of a slow non-radiative decay mechanism requires an accurate description of long-timescale excited-state quantum dynamics. In the present study, we introduce an efficient semiempirical method of calculating the fluorescence quantum yield (Φ<sub>fl</sub>) for molecular chromophores, which, based on machine learning, converts simple electronic energies computed using time-dependent density functional theory (TDDFT) into an estimate of Φ<sub>fl</sub>. As with all machine learning strategies, the algorithm needs to be trained on fluorescent dyes for which Φ<sub>fl</sub>’s are known, so as to provide a black-box method which can later predict Φ<sub>fl</sub>’s for chemically similar chromophores that have not been studied experimentally. As a first illustration of how our proposed algorithm can be trained, we examine a family of 25 naphthalene derivatives. The simplest application of the energy gap law is found to be inadequate to explain the rates of internal conversion (IC) or intersystem crossing (ISC) – the electronic properties of at least one higher-lying electronic state (S<i><sub>n</sub></i> or T<i><sub>n</sub></i>) or one far-from-equilibrium geometry are typically needed to obtain accurate results. Indeed, the key descriptors turn out to be the transition state between the Franck–Condon minimum a distorted local minimum near an S<sub>0</sub>/S<sub>1</sub> conical intersection (which governs IC) and the magnitude of the spin–orbit coupling (which governs ISC). The resulting Φ<sub>fl</sub>’s are predicted with reasonable accuracy (±22%), making our approach a promising ingredient for high-throughput screening and rational design of the molecular excited states with desired Φ’s. We thus conclude that our model, while semi-empirical in nature, does in fact extract sound physical insight into the challenge of describing non-radiative relaxations.</div>