We present a new systematic set of algorithms for interpolated variational transition-state theory by mapping (IVTST-M). In this method, which is designed to allow efficient direct dynamics calculations, rate constants for chemical reactions are evaluated by variational transition-state theory with multidimensional tunneling approximations based on reaction-path data. The data (energies, energy gradients, and Hessians) are computed at a small number of points along a reaction path and fitted to splines under tension as functions of a mapped independent variable that is a nonlinear function of the reaction coordinate. The theory is illustrated and tested by several examples, and standard choices are employed for all parameters and functional forms to provide a realistic test of how the method might perform when applied as an automatic scheme without fine-tuning each reaction. For eight test cases, we obtain reasonable accuracy (as compared to calculations with the same potential surface with the reaction path followed as far as necessary for convergence) with Hessians at only six nonstationary points.

We report calculations of the reaction rates of O( 3 P) + CH 4 f OH + CH 3 and O( 3 P) + CD 4 f OD + CD 3 over the temperature range 300-2500 K. The calculations are based on variational transition state theory in curvilinear coordinates with transmission coefficients calculated by the microcanonical optimized multidimensional tunneling approximation. A dual-level algorithm is used for the dynamical calculations. The higher level is UMP2/cc-pVTZ, and two lower levels are employed: PM3-SRP and an analytical potential energy surface. Using the canonical unified statistical model with microcanonical optimized multidimensional tunneling contributions, we obtain good agreement with experimental rate constants.

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