Entanglement Effect and Angular Momentum Conservation in a Nonseparable Tunneling Treatment

Abstract

The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for nonseparable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor−harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for nonseparable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and Eresolved rate constants over broad ranges of temperatures and energies.

A Machine Learning Approach for Rate Constants. III. Application to the Cl(2P) + CH4 → CH3 + HCl Reaction

“…The Gaussian Process regression method for machine learning of thermal rate constants developed previously 47,48 important at temperatures below about 250 K and that recrossing is important at temperatures above about 500 K. The results are in fairly good agreement with RPMD calculations by Liu and Li, 42 but neither method is as accurate in predicting the experimental results as the predictions of the method used by Georgievskii and Klippenstein 45 or, especially, the quantum calculations of Hoppe and Manthe, 46 in the deep tunneling regime. However, the present ML and RMPD results are closer to experiment at higher temperatures, where recrossing becomes significant.…”

“…The agreement between the two is good, but neither agrees perfectly with the experimental results, a sampling of which is shown along with the green line fit to all the experimental data. The results from the method of Georgievskii and Klippenstein are shown in the dotted red line. Hoppe and Manthe used the LL PES to perform quantum calculations of the rate constant as a function of temperature, and their results are shown in the dashed red line extending from 1000/ T = 1.85–6.67.…”

“…Top: Comparison of results for the Cl + CH 4 reaction showing a sampling of experimental results and the fit to all the experimental data (solid green), the quantum results from ref (dashed red), the results from ref (dotted red), our GP results using the original training set (solid black), the RPMD results of ref (solid red), and the TST results (solid blue). Bottom: Expansion of the High- T region.…”

“…40 High-level, CCSD(T)-based potential energy surfaces for this reaction have been reported by Czakóand Bowman (CB) 41 and, quite recently, by Li and Liu (LL), 42 and substantial theoretical investigations have also been reported. 43 Barker, Nguyen, and Stanton 44 have reported kinetic isotope effects in the reaction using ab initio semiclassical transition state theory, while Georgievskii and Klippenstein (GK) 45 have recently studied how tunneling is affected by the nonseparability of the reaction coordinate from other modes. The approach of the latter report provides a method that substantially improves on the one-dimensional estimation of tunneling; the comparison with experiment in that paper was limited to temperatures below 300 K, where agreement is very good.…”

“…This reaction is a challenge for our ML approach both because its parameters are at the edge of those of the training set and it brings up possible issues, such as spin−orbit coupling and van der Waals wells in both the entrance and exit channels. Detailed comparisons are made with the GP results of this work and the results from GK 45 as well as with the QM results from HM 46 and the RPMD results from LL. 42 We then incorporate "learning" this reaction into the correction data sets and verify that when used with ML we do get good agreement with the experiment, as expected.…”