Kinetic isotope effects and tunnelling in the proton-transfer reaction between 4-nitrophenylnitromethane and tetramethylguanidine in various aprotic solvents

Abstract

Rates and equilibirum constants have been determined for the proton-transfer reaction of 4-nitrophenylnitromethane, NO₂C₆H₄CH₂NO₂, and its αα-deuterated analogue NO₂C₆H₄CD₂NO₂, with the strong base tetramethylguanidine [HNC(NMe₂)₂], at temperatures between –60°C and + 65°C in a range of aprotic solvents. Spectrophotometry and the stopped-flow technique were used. The reaction is a simple proton-transfer process leading to an ion-pair. The kinetic isotope effects are correlated with the polarity of the solvents, as measured by the dielectric constant or by the empirical parameter E_T. In the less polar solvents they are exceptionally large. In toluene, for example, at 25°C the rate ratio k^H/k^D= 45 ± 2, the activation energy difference E^D_a–E^H_a= 4.3 ± 0.3 kcal mol^–1(16 kJ mol^–1), and the ratio of the pre-exponential factors log₁₀(A^D/A^H)= 1.5 ± 0.2; and even larger values of log₁₀(A^D/A^H) are found for mesitylene (1.94 ± 0.06) and cyclohexene (2.4 ± 0.2). Positive deviations from linear Arrhenius plots are found for these solvents. Tunnelling is the only interpretation that can account for these results. For the more polar solvents (dielectric constant 7 to 37), the isotope effects are closer to the range predicted by semi-classical theory.

The isotope effects in all solvents have been fitted to Bell's equation for a parabolic barrier, and the barrier dimensions calculated for each solvent, in two ways. (a) It is first assumed that only the proton moves, so that the effective mass m_H= 1 a.m.u.; the best values of the barrier height (E^H) and width at the base (2b) are determined by trial and error. The tunnelling corrections so calculated depend on the solvent polarity; for the less polar solvents they are large, and the values also explain quantitatively the deviations of the Arrhenius plots from linearity. The calculated barrier dimensions are also solvent-dependent; E^H is lower in solvents of higher polarity by a factor of about 2 compared with those of low polarity, and 2b is greater by 0.1–0.2 Å. (b) It is assumed, alternatively, that the effective mass may be increased above 1 by reason of solvent or other motions coupled to that of the proton; the values of E^H derived in (a) are assumed, and the best values of m_H and 2b′ determined by trial and error. The calculated values of 2b′ are then all about equal, those of the less polar solvents being unchanged from (a); the values of m′_H in the less polar solvents are 1.00 a.m.u. as before, but in the more polar solvents they are 1.17–1.27 a.m.u., increasing with polarity.

The suggested interpretation is that the solvent-solute interactions affect the height of the barrier and that motions of solvent molecules are coupled with the motion of the proton in the more polar solvents but not in the less polar ones; reorganization of solvent molecules accompanies the proton-transfer in the more polar solvents, but only electron-polarization in the less polar. Tunnelling has large effects in the less polar solvents, where the proton is the only atom that moves in the rate-determining step, but much smaller effects in the more polar solvents where solvent motion is coupled to that of the proton. Other reactions showing tunnelling effects are considered in the light of this conclusion.