Electron Transfer Assisted by Vibronic Coupling from Multiple Modes

Understanding the effect of vibronic coupling on electron transfer (ET) rates is a challenge common to a wide range of applications, from electrochemical synthesis and catalysis to biochemical reactions and solar energy conversion. The Marcus-Jortner-Levich (MJL) theory offers a model of ET rates based on a simple analytic expression with a few adjustable parameters. However, the MJL equation in conjunction with density functional theory (DFT) has yet to be established as a predictive first-principles methodology. A framework is presented for calculating transfer rates modulated by molecular vibrations, that circumvents the steep computational cost which has previously necessitated approximations such as condensing the vibrational manifold into a single empirical frequency. Our DFT-MJL approach provides robust and accurate predictions of ET rates spanning over 4 orders of magnitude in the 10⁶-10¹⁰ s^-1 range. We evaluate the full MJL equation with a Monte Carlo sampling of the entire active space of thermally accessible vibrational modes, while using no empirical parameters. The contribution to the rate of individual modes is illustrated, providing insight into the interplay between vibrational degrees of freedom and changes in electronic state. The reported findings are valuable for understanding ET rates modulated by multiple vibrational modes, relevant to a broad range of systems within the chemical sciences.