An improved treatment of spectator mode vibrations in reduced dimensional quantum dynamics: Application to the hydrogen abstraction reactions μ+CH4, H+CH4, D+CH4, and CH3+CH4

A method for projecting chemical reaction surface coordinates from a Hessian in curvilinear internal coordinates has recently been developed. Here we introduce a modification to this approach which allows for analytical evaluation of the necessary coordinate derivatives, thus reducing the number of ab initio calculations required. We apply this method to the determination of spectator mode frequencies and zero-point energies for the series of hydrogen abstraction reactions X+CH4 -> XH+CH3, X=muonium (mu), H, D, CH3. Comparison of these frequencies with those obtained using rectilinear coordinates allows us to examine how the mass of X affects the coordinate sensitivity of the spectator modes. We carry out two-dimensional quantum reactive scattering calculations for these reactions to highlight instances where the choice of coordinates may have a significant impact on the evaluated thermal rate constants.