The cross sections and thermal rate coefficients for various rotational excitations in the collision of molecules as reported by us in Ref. 1 are inaccurate due to an error of the program code used. A phase factor was missing in the grid-to-basis transformation matrix of the extended Legendre discrete variable representation.2 However, this error is irrelevant if there is no azimuthal -dependence of the potential, which means that older results obtained with the same program code (e.g., the calculation from Ref. 2) are not affected. Furthermore, the error in question only appears when negative values of the angular momentum projections are dominant; therefore the ortho-para scattering calculations of Panda et al.,3 which were also obtained with our program code, are only very lightly affected by this problem. (In the ortho-para case, the initial wave functions for nonzero were mostly set up with positive . Due to symmetry these results can then be directly mirrored into the results for and ).
This error affects our results for all rotational transitions in question and for all the potential energy surfaces considered. Therefore, our data in Figs. 3, 4, 5, 7, and 9 of the original work are incorrect. After fixing the program error, we find that for all considered potential energy surfaces, our corrected cross sections lie consistently higher than our previously reported values. For the transitions and , the low energy region is unaffected, while the high energy region sees an increase by up to ≈20%. For the other transitions, the low energy region is strongly affected, wherein the cross sections are increased by a factor of 1.5–3.0; this increase falls off toward higher energies.
When comparing our corrected results to previous and recent theoretical data, we can now see a much clearer picture. For the full-dimensional results obtained with the Boothroyd-Martin-Keogh-Peterson (BMKP) surface, we can now also compare with recent results of Quéméner and Balakrishnan4 obtained with a new time-independent quantum scattering code. Our corrected results turn out to be in excellent agreement with this new data. Lin and Guo5 performed full-dimensional calculations using the coupled-states approximation (CSA), leading to considerable lower cross sections. Our comparison CSA calculations are in excellent agreement with their results, except for the high energy range.
For the reduced-dimensional results [rigid rotor (RR) approximation], we compare with previous theoretical data of Sultanov and Guster6 and of Lee et al.7,8 For both RR surfaces in question (the Diep–Johnson surface and the RR version of BMKP, ), we now find that our corrected cross sections agree very well with those of Lee et al., while we see slight to considerable deviations from the results of Sultanov and Guster.
For the thermal rate coefficients, we found that the results for the transitions and are virtually not affected by the correction, while the rates see a ≈50%–100% increase, independent of the considered PES.
Figures showing our corrected results (along with the above mentioned comparison data) as well as an extended discussion can be found in the supplementary material published online.9