Calculations of the effect of tunneling on the Swain-Schaad exponents (SSEs) for the 1,5-hydrogen shift in 5-methyl-1,3-cyclopentadiene. Can SSEs be used to diagnose the occurrence of tunneling?

MPW1K density functional calculations, carried out with the 6-31+G(d,p) basis set, have been combined with canonical variational transition state theory (CVT) and small-curvature tunneling (SCT) corrections in order to compute the primary kinetic isotope effects for rearrangement of 5-methyl-1,3-cyclopentadiene (1) to 1-methyl-1,3-cyclopentadiene (2). The Swain-Schaad exponents, SSE = ln(kH/kT)/ln(kD/kT), for this reaction have been computed over the temperature range 100-600 K. Tunneling results in both large positive and large negative deviations from the value of SSE = 3.26, expected from consideration of only the effect of the isotopic mass on passage over the reaction barrier. In the rearrangement of 1 to 2, SSE approximately 3.26, not only at temperatures >400 K, where tunneling is relatively unimportant, but also around 170 K, where tunneling by both H and D is the dominant mode of reaction. Thus, from an experimental finding that SSE approximately 3.26 at a single temperature, it cannot be rigorously concluded that tunneling is unimportant. Measurement of SSEs over a broad temperature range is advisable; but measurement of the temperature dependence of just kH/kD can be used to establish more unequivocally whether tunneling is important, without the necessity of measuring kT.