Distance-dependent proton transfer along water wires connecting acid-base pairs

We report time-resolved mid-IR kinetics for the ultrafast acid-base reaction between photoexcited 8-hydroxypyrene-l,3,6-trisulfonic acid trisodium salt (HPTS), and acetate at three concentrations (0.5, 1.0, and 2.0 M) and three temperatures (5, 30, and 65°C) in liquid D₂O. The observed proton-transfer kinetics agree quantitatively, over all times (200 fs - 500 ps), with an extended Smoluchowski model which includes distance-dependent reactivity in the form of a Gaussian rate function, k(r). This distance dependence contrasts with the exponential k(r) that is typically observed for electron-transfer reactions. The width of k(r) is essentially the only parameter varied in fitting the proton-transfer kinetics at each concentration and temperature. We find that k(r) likely represents the rate of concerted (multi)proton hopping across "proton wires" of different length r that connect acid-base pairs in solution. The concerted nature of the proton transfer is supported by the fact that k(r) shows a steeper dependence on r at higher temperatures.