Correction to “Effects of Roaming Trajectories on the Transition State

Addition/Correction pubs.acs.org/JPCA

Correction to “Effects of Roaming Trajectories on the Transition State Theory Rates of a Reduced-Dimensional Model of Ketene Isomerization” Inga S. Ulusoy, John F. Stanton, and Rigoberto Hernandez* J. Phys. Chem. A 2013, 117 (32), 7553−7560. DOI: 10.1021/jp402322h Wiggins and co-workers1 recently brought to our attention that in our recent paper,2 we retained a typographical error from the original work by Miller and Gezelter3 in the coupling term of the potential. Specifically, a factor of 1/2 is missing in the coupling potential, so that it should read V (qF ,q1) = V1D(qF) + Vcoup(qF ,q1) V1D(qF) = a 2qF 2 + a4qF 4 + a6qF6 + cqF 2 exp−dqF

(1) 2

2 d1qF 4 ⎞ 1 ⎛⎜ ⎟ Vcoup(qF ,q1) = k1⎜q1 + 2 ⎝ k1 ⎟⎠

(2)

Figure 1. Microcanonical reaction rates for different model potentials: (i) 1-dimensional, (ii) 2-dimensional, and (iii) 2-dimensional with coupling, in comparison with experimental rates.4,5

(3)

The parameters used in the potential in our recent work2 quoted those from the earlier publication3 exactly. By omitting the factor of 1/2, we effectively used a different mass for this mode. The correct mass associated with mode q1 (m1) is the hydrogen mass. On the other hand, the effecive mass associated with mode qF is space dependent, which for simplicity we approximate as a constant. In ref 2, we used the mass associated with this mode in the vicinity of ketene. However, as the rate expression is associated with the modes in the barrier region, it is more appropriate to use the mass associated with qF in the flat region of the potential around the oxirene intermediate. Thus, we further correct the choice in ref 2, by improving the accuracy of the constant-mass approximation through the use of the mass associated with the corresponding normal mode of the oxirene intermediate (mF = 5.25564 amu). As the mass associated with the qF motion in the limit of the ketene structure is 55.5% smaller, this does have a small but nonneglible effect. Although a factor of 1/2 in the potential might seem trivial, we have recomputed the rates and the roaming trajectories to confirm that the conclusions of the Article2 remain. In Figure 1, we show the recalculated rates for models (i), (ii), and (iii). This updates Figure 3 in the Article.2 We obtain almost the same TST rates for models (ii) and (iii), where the TST rates for model (iii) are slightly higher. The difference between models (ii) and (iii) increases with increasing energy, which is representative of the fact that the optimal dividing surface for model (iii) is energy-dependentwe use the same dividing surface for all energies in our calculations. The exact classical rates for model (iii), kFlux,iii(E), now exhibit a steplike feature around E = 350 cm−1, which is also present in the experiment. Thus, the agreement between the experimental and computed values appear to have been improved. The roaming trajectories are only slightly affected by the use of the correct masses, as shown in Figure 2. This updates Figure © XXXX American Chemical Society

Figure 2. Trajectories that match the criteria for roaming. Both trajectories do not enter region D of the planar oxirene intermediate.

4 in the Article.2 The potential along q1 is softened modestly, and trajectory 2 moves further out of the oxirene region. The energies of trajectories 1 and 2 are now lower, at E1 = 551 kJ mol−1 (0.21 Eh) and E2 = 1087 kJ mol−1 (0.414 Eh) above the barrier. Nevertheless, the roaming trajectories persist and the qualitative features discussed in the article remain.

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REFERENCES

(1) Collins, P.; Mauguiere, F. A. L.; Ezra, G. S.; Farantos, S. C.; Wiggins, S. Private communication. (2) Ulusoy, I. S.; Stanton, J. F.; Hernandez, R. Effects of roaming trajectories on the transition state theory rates of a reduceddimensional model of ketene isomerization. J. Phys. Chem. A 2013, 117, 7553−7560. (3) Gezelter, J. D.; Miller, W. H. Resonant features in the energy dependence of the rate of ketene isomerization. J. Chem. Phys. 1995, 103, 7868−7876. (4) Lovejoy, E. R.; Kim, S. K.; Alvarez, R. A.; Moore, C. B. Kinetics of intramolecular carbon atom exchange in ketene. J. Chem. Phys. 1991, 95, 4081−4093.

A

dx.doi.org/10.1021/jp408997z | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

Addition/Correction

(5) Lovejoy, E. R.; Moore, C. B. Structures in the energy dependence of the rate constant for ketene isomerization. J. Chem. Phys. 1993, 98, 7846−7854.

B

dx.doi.org/10.1021/jp408997z | J. Phys. Chem. A XXXX, XXX, XXX−XXX