Table 2.
T (K) | Solution parametersa | Computational datab | Expt.c | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
ε | pKW | pOH | gd | ge | ΔGd | ΔGe | kd (s−1) | ke (s−1) | ve/vd | kexp | |
298 | 78.5 | 14.0 | 7.00 | 1.05 | 1.03 | 38.7 | 31.7 | 2.2×10−16 | 3.0×10−11 | 1.4×1012 | 4.0×10−12 |
402 | 47.8 | 11.9 | 5.95 | 1.03 | 1.02 | 43.2 | 36.7 | 2.3×10−11 | 8.0×10−8 | 3.1×109 | 8.4×10−8 |
408 | 46.7 | 11.8 | 5.90 | 1.03 | 1.02 | 43.4 | 36.8 | 4.0×10−11 | 1.4×10−7 | 2.8×109 | 1.2×10−7 |
425 | 42.7 | 11.6 | 5.80 | 1.02 | 1.02 | 44.2 | 37.2 | 1.4×10−10 | 5.6×10−7 | 2.6×109 | 4.3×10−7 |
433 | 41.6 | 11.6 | 5.80 | 1.02 | 1.02 | 44.6 | 37.4 | 2.3×10−10 | 1.0×10−6 | 2.8×109 | 1.0×10−6 |
437 | 40.7 | 11.5 | 5.75 | 1.02 | 1.02 | 44.7 | 37.5 | 3.4×10−10 | 1.4×10−6 | 2.3×109 | 1.3×10−6 |
456 | 37.2 | 11.4 | 5.70 | 1.02 | 1.01 | 45.6 | 37.8 | 1.1×10−9 | 6.3×10−6 | 2.8×109 | 2.4×10−6 |
467 | 35.5 | 11.3 | 5.65 | 1.02 | 1.01 | 46.1 | 38.1 | 2.2×10−9 | 1.2×10−5 | 2.6×109 | 4.3×10−6 |
473 | 34.7 | 11.2 | 5.60 | 1.02 | 1.01 | 46.3 | 38.2 | 3.4×10−9 | 1.9×10−5 | 2.3×109 | 7.1×10−6 |
482 | 33.1 | 11.2 | 5.60 | 1.02 | 1.01 | 47.2 | 38.4 | 3.4×10−9 | 3.4×10−5 | 4.0×109 | 1.1×10−5 |
493 | 30.9 | 11.1 | 5.55 | 1.02 | 1.01 | 47.5 | 38.6 | 7.6×10−9 | 6.9×10−5 | 3.2×109 | 1.7×10−5 |
503 | 29.5 | 11.1 | 5.55 | 1.02 | 1.01 | 47.7 | 38.8 | 1.7×10−8 | 1.3×10−4 | 2.7×109 | 2.9×10−5 |
512 | 28.2 | 11.1 | 5.55 | 1.02 | 1.01 | 47.8 | 39.0 | 3.6×10−8 | 2.1×10−4 | 2.1×109 | 4.1×10−5 |
523 | 26.9 | 11.0 | 5.50 | 1.02 | 1.01 | 48.5 | 39.3 | 5.1×10−8 | 3.6×10−4 | 2.3×109 | 6.1×10−5 |
The experimental dielectric constant (ε) and pKW values of water at various temperatures came from ref.44 and ref.57, respectively. The pOH (=−log[OH−]) values were determined from the corresponding pKW values.
The subscripts d and e refer to the alkaline and two-water APNE pathways of Me4U hydrolysis, respectively. ΔGx (x = d or e) represents the calculated Gibbs free energy barrier in aqueous solution. The obtained free energy barriers were based on the best-estimate single-point energy (MP2/CBS), plus the zero-point vibration and thermal corrections calculated at the B3LYP/6-31+G* level and the solvent shifts calculated at the HF/6-31+G* level (using the default 0.001 a.u. contour). gx (x = d or e) is the calculated transmission coefficient (tunneling factor), and kx (x = d or e) is the rate constant calculated accounting for the tunneling factor. The ratio of the neutral hydrolysis rate to the alkaline hydrolysis rate was defined as ve/vd = ke[Me4U][H2O]/kd[Me4U][HO−] in which [H2O] = 55.6 M.
The experimental rate constant (kexp) values at 402–523 K were based on the Figure 1 reported in ref.19. The figure in ref.19 was digitized to obtain the values of 1000/T (which gives T in K) and logkexp (which gives kexp in s−1) at all of the available data points. When one temperature was associated with two different logkexp values in the figure, the average of the two logkexp values was taken. The kinetic data from the digitized figure show an empirical equation: . This empirical equation was used for extrapolation to 298.15 K, giving kexp(298.15K) = 4.0×10−12 s−1. The extrapolated kexp(298.15K) value of 4.0×10−12 s−1 is close to the kexp(298.15K) value of 4.2×10−12 s−1 extrapolated by the original authors of ref.19, suggesting that the digitization of the figure was reasonable and the possible errors of the digitization may be close to ~5%.