Concerted proton-electron transfer reactions in the Marcus inverted region

Abstract

Electron transfer reactions slow down when they become very thermodynamically favorable, a counterintuitive interplay of kinetics and thermodynamics termed the inverted region in Marcus theory. Here we report inverted region behavior for proton-coupled electron transfer (PCET). Photochemical studies of anthracene-phenol-pyridine triads give rate constants for PCET charge recombination that are slower for the more thermodynamically favorable reactions. Photoexcitation forms an anthracene excited state that undergoes PCET to create a charge-separated state. The rate constants for return charge recombination show an inverted dependence on the driving force upon changing pyridine substituents and the solvent. Calculations using vibronically nonadiabatic PCET theory yield rate constants for simultaneous tunneling of the electron and proton that account for the results.

Fig. 1. Schematic of photochemical e^–/H⁺ charge separation (CS) and charge recombination (CR) in anthracene-phenol-pyridine triads 1 to 8.

Photoexcitation of the ground state (GS) populates the local excited state (LES), which converts to the e^–/H⁺ charge-separated state (CSS) and then back to the GS. Within the chemical structures of the LES and CSS, arrows indicate the direction of electron and proton transfers in LES→CSS (CS) and CSS→GS (CR) reactions. Circled diagrams show schematic proton potentials and lowest proton vibrational wave functions for O–H (blue) and N–H (red) bonds.

Fig. 2. TA and characterization of e^–/H⁺ CSSs.

For 1 in CH₂Cl₂, global fitting of the time evolution of the visible (A) and mid-IR (C) TA spectra give the evolution-associated visible spectra (B) and mid-IR spectra (D) of the LES and CSS. In CH₂Cl₂ (but not in other solvents), there is a small contribution of a longer-lived transient. Arrows in (A) to (D) indicate spectral changes between the LES and CSS. In (E to H), time traces (circles) and fits from global analysis (lines) show the KIE for CS and CR of 1 in CH₂Cl₂ (E), the solvent polarity effect on CR time constants for 1 (F), and the relative CR time constants for 1 to 3 in CH₂Cl₂ (G) and DMF (H). For (F) to (H), the time traces are at wavelengths for isosbestic points for the LES and CSS spectra, so the traces only show the CSS→GS (CR) reaction in CH₂Cl₂ (at 533 nm) and n-BuCN and DMF (at 550 nm).

Fig. 3. The free energy dependence of CPET rate constants showing the normal and inverted regions.

Plot of ln(k_CPET) from TA versus computed ∆G° (17). Rising blue parabola: k_CS (charge separation) in 1 to 8 versus ∆G°_CS; falling red parabola: k_CR (charge recombination) in 1 to 3 versus ∆G°_CR. The uncertainties in k_CPET are smaller than the data points. The uncertainties in ∆G° are estimated to be ±0.05 eV; the relative uncertainties for CPET-CR in 1 to 3 in the inverted region are smaller, as these differences arise solely from changes in the pyridine substituents.

Fig. 4. Illustration of the lowest CSS (blue) and multiple product GS (red) vibronic state free energy curves for the CPET-CR reaction.

Nonadiabatic transitions can occur at the intersection points between the reactant (μ) and product (ν) parabolas (black dots). Circled diagrams show proton potential energy curves for the reactant (blue) and product (red) and the corresponding proton vibrational wave functions for a state pair with significant overlap integral (S₀₃) and a state pair with near-zero overlap integral (S₀₇) at the dominant proton donor-acceptor distance for 1.