Toward Prediction of Nonradiative Decay Pathways in Organic Compounds I: The Case of Naphthalene Quantum Yields

Many emerging technologies depend on our ability to control and manipulate the excited-state properties of molecular systems. These technologies include fluorescent labeling in biomedical imaging, light harvesting in photovoltaics, and electroluminescence in light-emitting devices. All of these systems suffer from nonradiative loss pathways that dissipate electronic energy as heat, which causes the overall system efficiency to be directly linked to the quantum yield (Phi) of the molecular excited state. Unfortunately, Phi is very difficult to predict from the first principles because the description of a slow nonradiative decay mechanism requires an accurate Reaction Coordinate description of long-timescale excited-state quantum dynamics. In the present study, we introduce an efficient semi-empirical method of calculating the fluorescence quantum yield (Phi(fl)) for molecular chromophores, which converts simple electronic energies computed using time-dependent density functional theory into an estimate of Phi(fl). As with all machine learning strategies, the algorithm needs to be trained on fluorescent dyes for which Phi(fl)'s are known, so as to provide a black-box method which can later predict Phi'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-n or T-n) 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 and a distorted local minimum near an S-1/S-0 conical intersection (which governs IC) and the magnitude of the spin-orbit coupling (which governs ISC). The resulting Phi(fl)'s are predicted with reasonable accuracy (+/- 0.22), making our approach a promising ingredient for high-throughput screening and rational design of the molecular excited states with desired Phi's. We thus conclude that our model, while semi-empirical in nature, does in fact extract sound physical insight into the challenge of describing nonradiative relaxations.