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).