Modified vibrational perturbation theory as applied to the collinear H + H2 and D + H2 reactions

A multidimensional version of the modification to vibrational perturbation theory is developed in this article. The modifications to the action are of two types: one is by shifting the energy scale with the VPT2 zero point energy E0 (mVPT2) and the other is by shifting the action by a constant VPT2-based action ΔS and is denoted mYF. These modifications give a continuous "modified" action over the whole energy range. The multidimensional versions of the mVPT2 and mYF theories have been applied to the collinear H + H2 and D + H2 reactions to calculate thermal reaction rates. The results show that the rates computed using the mVPT2 theory are marginally better than those computed by the mYF theory. The corresponding kinetic isotopic effects have also been computed. Both the theories account for the correct ℏ2 limit at high temperature and not the parabolic barrier limit as in various other theories. The mVPT2 and mYF theories also improve upon the thermal rates in the low temperature limit due to the shifting of the action by the zero point energy shift E0. The resulting theory is more accurate than the ring polymer molecular dynamics based approximation over the whole temperature range probed. The results presented here indicate that the multidimensional version of the modified VPT2 theory may be the recommended method for computing thermal tunneling rates in multidimensional systems.