A Theory of Ultrafast Charge Transfer Relaxation with Non-Innocent Solvent Molecules

We revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE-HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797-4810, 1994] that has long challenged the applicability of Marcus's theory of electron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TDDFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the solvent relaxation time); for nonpolar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge transfer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born-Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).