Path-dependent variational effects and multidimensional tunneling in multi-path variational transition state theory: rate constants calculated for the reactions of HO₂ with tert-butanol by including all 46 paths for abstraction at C and all six paths for abstraction at O

Multi-path variational transition state theory (MP-VTST) provides a conformationally complete framework for calculating gas-phase rate constants. For reactions in which the transition state has distinguishable torsional minima (which include most reactions), there are multiple possible reaction paths. In principle MP-VTST includes the contributions from all the reaction paths, and it should explicitly treat the variational and tunneling effects of each path, but in practice one may need to truncate the number of paths included in MP-VTST calculations in order to achieve a balance between computational cost and accuracy. In this work, we present calculations including all paths for two prototype combustion reactions, namely the two hydrogen abstraction reactions from tert-butanol by HO₂ radical. For both reactions we included all the reaction paths. Since abstraction at C has 46 paths, it provided a good opportunity to carry out a case study in which we investigated the errors introduced by truncating the number of paths. For the reaction studied, we found that the variational and multidimensional tunneling transmission coefficients are very different for different reaction paths, which provides new evidence that MP-VTST is necessary for treating path-dependent variational effects and multidimensional tunneling. We found that tunneling transmission coefficients can be much larger for higher-energy paths than for lower-energy ones. Interestingly, the simple hypothesis that higher barriers are narrower does not explain this finding in the present case; we found instead that the effect is due to higher-energy barriers having the possibility of tunneling at energies farther below the barrier top. We also show that a previously applied criterion for judging convergence with respect to the number of paths may not be reliable at low temperature.