Chemical reaction surface vibrational frequencies evaluated in curvilinear internal coordinates: Application to H+CH4⇄H2+CH3

We consider the general problem of vibrational analysis at nonglobally optimized points on a reduced dimensional reaction surface. We discuss the importance of the use of curvilinear internal coordinates to describe molecular motion and derive a curvilinear projection operator to remove the contribution of nonzero gradients from the Hessian matrix. Our projection scheme is tested in the context of a two-dimensional quantum scattering calculation for the reaction H+CH4 -> H-2+CH3 and its reverse H-2+CH3 -> H+CH4. Using zero-point energies calculated via rectilinear and curvilinear projections we construct two two-dimensional, adiabatically corrected, ab initio reaction surfaces for this system. It is shown that the use of curvilinear coordinates removes unphysical imaginary frequencies observed with rectilinear projection and leads to significantly improved thermal rate constants for both the forward and reverse reactions.