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

Abstract

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 + CH(4) --> H(2) + CH(3) and its reverse H(2) + CH(3) --> H + CH(4). 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.

Reduced dimensionality spin-orbit dynamics of CH3 + HCl $\rightleftharpoons$⇌ CH4 + Cl on ab initio surfaces

“…Previous studies have shown that the curvilinear projection method 50,51 is an improvement upon the rectilinear scheme;…”

“…49 Internal degrees of freedom (DOF) are divided into two active modes explicitly treated in the quantum scattering, and 3N −8 spectator modes, which are approximately treated via inclusion of curvilinear-projected zero-point energies (ZPE) in the PES. 50,51 Variants of this approach have been successfully applied to a number of ground state reactions, 49,[52][53][54][55][56] including Cl + CH 4 − → HCl + CH 3 . 11 In this paper, the method is extended to include multisurface characterization of nonadiabatic transitions.…”

Quantum scattering study of the abstraction reaction of H atoms from tetramethylsilane

“…As pointed out in [45,46,21,23], this method may lead to unphysical imaginary frequencies which could be removed by the use of curvilinear internal coordinates. The curvilinear projection scheme derived by Banks and Clary [26] to remove the contribution of nonzero gradients from the Hessian matrix leads to a significant improvement of thermal rate constants for various systems [22]. Improvement of our results should be obtained by using the above approach, this is planned in a future work.…”

“…However, it can be seen that the experimental results are close to the (CVT/SCT) results and lower than the present ones, which exhibit a relatively pronounced curvature. Such behavior, also found for other systems [24], could be due to the application of the rectilinear coordinate projection method used for removing the contribution of the two active modes from the Hessian [26]. As pointed out in [45,46,21,23], this method may lead to unphysical imaginary frequencies which could be removed by the use of curvilinear internal coordinates.…”

“…Quantum tunneling is found to be important and the calculated thermal rates agree well with the experiments. Various improvements of the method were proposed recently to reduce the computational effort and improve the accuracy of the results [23,24,26, and references therein].…”