Barrier Widths, Barrier Heights, and the Origins of Anomalous Kinetic H/D Isotope Effects

Saul Wolfe, Chan Kyung Kim, Shmaryahu Hoz, Kiyull Yang

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Abstract

Proton transfer between MeO- and HOMe has been studied using ab initio molecular orbital theory. At the highest level employed (mP2/6-31+G(d)//6-31G(d) + ZPE),-ΔH298 and-ΔG298 for the formation of the ion-molecule complex MeO-…HOMe from the separated reactants are 26.3 and 15.2 kcal/mol, respectively. At the 6-31G(d)//6-31G(d) level of theory, the (MeO-H-OMe)- transition structure is 2.19 kcal/mol higher in energy than the ion-molecule complex (ΔE = 2.19), but this barrier disappears when zero-point energies are taken into account. The performance of AMI on this system is quantitatively different (-Δ298 = 13.3;-ΔG298 = 6.9; ΔE = 4.91; kH/kD = 5.13, increasing to 5.79 when quantum mechanical tunneling is invoked) but appears to be acceptable for the research envisaged in the title. The effect of an enforced separation of the heavy atoms upon proton transfer barriers and isotope effects (which simulates “steric effects”) has been studied briefly at the 6-31G(d) level and in some detail using AMI. As predicted by a simplified two-parabola model of the barrier, ΔE increases linearly as the square of the heavy atom distance, and such plots extrapolate to the heavy atom distances of the fully optimized transition structures. The increase in the barriers is accompanied by a small increase in the semiclassical kinetic isotope effect, as expected from KIE theory, and a much larger increase in the tunneling correction, using Bell's treatment, in which the correction factor QH/QD depends upon the height of the barrier. Because of the relationship between barrier heights and widths, this correction becomes substantial when “steric hindrance” exists. Thus, in proton transfer between pyrrole anions and pyrroles, the KIE including the tunneling correction increases progressively from 6.6 to 9.0 to 15.6 as methyl groups are attached to the 2,5-positions and coplanarity of the two rings is enforced; for proton transfer between pyridinium cations and pyridines, the KIE's including the tunneling correction change from 5.2 to 4.6 to 5285(!) as methyl groups are attached to the 2,6-positions and coplanarity of the two rings is enforced. The energetics of proton transfer between pyridines conform to the Marcus equation, but the isotope effect and tunneling correction are smaller in the exoergic direction. The implications of the present findings for effects of pressure upon proton tunneling and tunneling effects in enzymatic hydrogen-transfer reactions are noted.

Original languageEnglish
Pages (from-to)4186-4191
Number of pages6
JournalJournal of the American Chemical Society
Volume112
Issue number11
DOIs
StatePublished - Jan 1990

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