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We have measured the merged-beams rate coefficient for the titular isotope exchange reactions as a function of the relative collision energy in the range of ∼3 meV–10 eV. The results appear to scale with the number of available sites for deuteration. We have performed extensive theoretical calculations to characterize the zero-point energy corrected reaction path. Vibrationally adiabatic minimum energy paths were obtained using a combination of unrestricted quadratic configuration interaction of single and double excitations and internally contracted multireference configuration interaction calculations. The resulting barrier height, ranging from 68 meV to 89 meV, together with the various asymptotes that may be reached in the collision, was used in a classical over-the-barrier model. All competing endoergic reaction channels were taken into account using a flux reduction factor. This model reproduces all three experimental sets quite satisfactorily. In order to generate thermal rate coefficients down to 10 K, the internal excitation energy distribution of each H3+ isotopologue is evaluated level by level using available line lists and accurate spectroscopic parameters. Tunneling is accounted for by a direct inclusion of the exact quantum tunneling probability in the evaluation of the cross section. We derive a thermal rate coefficient of <1×10−12 cm3 s−1 for temperatures below 44 K, 86 K, and 139 K for the reaction of D with H3+, H2D+, and D2H+, respectively, with tunneling effects included. The derived thermal rate coefficients exceed the ring polymer molecular dynamics prediction of Bulut et al. [J. Phys. Chem. A 123, 8766 (2019)] at all temperatures.
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ℏ2 expansion of the transmission probability through a barrier
Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.
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- Award ID(s):
- 1800301
- PAR ID:
- 10593500
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 157
- Issue:
- 7
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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