Effects of external electric fields on double proton transfer kinetics in the formic acid dimer

Abstract

Molecules can be exposed to strong local electric fields of the order of 10⁸–10¹⁰ V m⁻¹ in the biological milieu. The effects of such fields on the rate constant (k) of a model reaction, the double-proton transfer reaction in the formic acid dimer (FAD), are investigated. The barrier heights and shapes are calculated in the absence and presence of several static homogenous external fields ranging from 5.14 × 10⁸ to 5.14 × 10⁹ V m⁻¹ using density functional theory (DFT/B3LYP) and second order Møller–Plesset perturbation theory (MP2) in conjunction with the 6-311++G(d,p) Pople basis set. Conventional transition state theory (CTST) followed by Wigner tunneling correction is then applied to estimate the rate constants at 25 °C. It is found that electric fields parallel to the long axis of the dimer (the line joining the two carbon atoms) lower the uncorrected barrier height, and hence increase the raw k. These fields also flatten the potential energy surface near the transition state region and, hence, decrease the multiplicative tunneling correction factor. The net result of these two opposing effects is that fields increase k(corrected) by a factor of ca. 3–4 (DFT–MP2, respectively) compared to the field-free k. Field strengths of ∼3 × 10⁹ V m⁻¹ are found to be sufficient to double the tunneling-corrected double proton transfer rate constant at 25 °C. Field strengths of similar orders of magnitudes are encountered in the scanning tunneling microscope (STM), in the microenvironment of a DNA base-pair, in an enzyme active site, and in intense laser radiation fields. It is shown that the net (tunneling corrected) effect of the field on k can be closely fitted to an exponential relationship of the form k = aexp(bE), where a and b are constants and E the electric field strength.