Intermolecular hydrogen tunneling in solids. Comparison between diabatic and adiabatic rate expressions

Abstract

. Can. J. Chem. 66, 875 (1988). Rate expressions are derived for hydrogen transfer between two molecules in a solid, typical examples being hydrogen abstraction by methyl radicals in solid methane and in glassy methanol. These expressions are based on two-dimensional potential-energy surfaces describing the motion of the hydrogen atom along with that of the atoms between which it is transferred. A diabatic rate expression, based on the Golden Rule, is compared with an adiabatic rate expression, based on transition-state theory with a tunneling correction. In both cases, the two degrees of freedom must be treated quantum-mechanically rather than classically. For the adiabatic case, this leads to a new expression in which the barrier permeability is averaged over the wavefunction of the slow motion. ' The result differs from the Golden-Rule expression but yields similar rate constants. Numerical estimates are presented to illustrate the temperature and isotope dependence of these rate constants. The concept of a tunneling path is shown to break down at low temperature, so that the conventional one-dimensional tunneling approach becomes invalid. PHILIP D. PACEY et WILLEM SIEBRAND. Can. J. Chem. 66, 875 (1988). On a dCrivC des Cquations representant la vitesse du transfert d'hydrogtne entre deux moltcules dans un solide; I'enlkvement d'hydrogkne par des radicaux mtthyles dans du methane solide et dans du mtthanol vitreux en sont des exemples typiques. Ces Cquations sont bastes sur des surfaces d'tnergie potentielle en deux dimensions qui dtcrivent le mouvement de l'atome d'hydrogkne ainsi que ceux des atomes entre lesquels le transfert se produit. On compare une tquation de vitesse diabatique qui est basCe sur la ccrkgle d'orn avec une tquation de vitesse adiabatique qui est basCe sur la thtorie des ttats de transition avec une correction pour l'effet tunnel. Dans les deux cas, on doit faire appel i la mtcanique quantique plut6t qu'i la mtcanique classique pour traiter des deux degrks de liberte. Dans le cas adiabatique, ceci conduit h une nouvelle expression dans laquelle on fait une moyenne de la barrikre i la permCabilit6 sur toute la fonction d'onde du mouvement lent. Le rtsultat est difftrent de celui obtenu i l'aide de l'expression dCrivCe de la ccrtgle d'orn; toutefois, on obtient des constantes de vitesse qui sont semblables. On prksente des Cvaluations numCriques pour illustrer l'influence de la temptrature et des isotopes sur ces constantes de vitesse. On montre que le concept de trajet de tunnel ne tient pas i basse temperature; il en rtsulte que l'approche conventionnelle par effet tunnel i une dimension devient invalide.[Traduit par la revue]

Quantum chemical calculation of the barrier for tunneling of hydrogen in hydrogen abstraction from methane by methyl

“…Nevertheless, from the present analysis, it is possible to conclude that at very low temperatures in an isolated system tunneling of hydrogen is not too slow to be observable. At this point, we like to mention that an explicit two-dimensional approach of tunneling by Pacey and Siebrand [17] leads to an extremely low value of rate constant (K = s-I) at low temperature. They conclude that hydrogen exchange between methyl and methane in solid methane via tunneling is too slow to be observable.…”

“…We wish to emphasize that the reaction coordinate "X" in Figures 2(b) and 4 for tunneling involves implicitly two degrees of freedom: one describing the motion of hydrogen relative to methyl radical and the other describing the motion of two methyl groups between which hydrogen is transferred. In a recent paper [17] dealing with tunneling in the hydrogen-transfer reaction, the authors employed the adiabatic barriers for various C -C separations, obtained by Wildman [24].…”

“…Typically, one adopts a convenient analytical form for the barrier shapes and adjusts its height and width until they yield an acceptable reproduction of data. Recently, Pacey and Siebrand [17] emphasized that, at least, two degrees of freedom should be involved in any intermolecular hydrogen-transfer process, via tunneling.…”

Kinetic Analyses Combining Quantum Chemical and Quantum Statistical Methods: Some Case Studies

“…Since both reactions under investigation involve the transfer of hydrogen, it is essential to include a tunneling correction for the rate constants. The symmetric Eckart potential is often used to include the contribution of hydrogen tunneling to the rate constant. The symmetric Eckart potential is given by 34 where x is the reaction coordinate, V * is the activation barrier, and F * is the curvature at the potential energy maximum.…”

Role of tunneling of hydrogen in photoenolization of a ketone

“…To calculate the tunneling probability of hydrogen, usually an Eckart potential is used to describe the shape of the tunnel barrier [5][6][7]131. Figure 1 shows that an Eckart function fits very poorly with the theoretically calculated potential energy curve for the enolization process.…”