The definition of reaction coordinates for reaction-path dynamics

We present equations for generalized-normal-mode vibrational frequencies in reaction-path calculations based on various sets of coordinates for describing the internal motions of the system in the vicinity of a reaction path. We consider two special cases in detail as examples, in particular three-dimensional atom-diatom collisions with collinear steepest descent paths and reactions of the form CX₃ + YZ→CX₃Y+Z with reaction paths having C_3v symmetry. We then present numerical comparisons of the differences in harmonic reaction-path frequencies for various coordinate choices for three such systems, namely, H + H₂ → H₂ + H, O + H₂ → OH + H, and CH₃ + H ₂ → CH₄ + H. We test the importance of the differences in the harmonic frequencies for dynamics calculations by using them to compute thermal rate constants using variational transition state theory with semiclassical ground-state tunneling corrections. We present a new coordinate system for the reaction CH₃ + H₂ that should allow for more accurate calculations than the Cartesian system used for previous reaction-path calculations on this and other polyatomic systems.