Variational transition-state theory and semiclassical tunnelling calculations with interpolated corrections: A new approach to interfacing electronic structure theory and dynamics for organic reactions

In variational transition-state theory (VTST) and semiclassical tunnelling calculations, especially those with semiempirical potential-energy surfaces, it is sometimes desirable to match the classical energies and vibration frequencies of some points (e.g. the reactant, saddle point, product, van der Waals complex, ion-molecule complex) along the minimum-energy path (MEP) and in the reaction swath with high-level results, as this can improve the accuracy. This can be accomplished by adding a correction function to the calculated energies or frequencies. In this paper, we introduce a three-point or zero-order interpolated correction method which is based on the correction at three points, in particular the saddle point and two stationary points, one on each side of the MEP. We use the corrections at these points to build a correction function for the classical energy and for each vibrational mode frequency along the MEP. The function is calibrated such that the corrected result matches the accurate values at these stationary points. The functional forms to be used depend on the shape of the MEP under consideration and the relative correction values at those points. Similar treatments are applied to the determinant of the moment of inertia tensor along the reaction path and to the potential-energy function in non-adiabatic regions of corner-cutting tunnelling paths. Once parameters in the functional forms are determined, we then use the corrected energy, frequency and moments of inertia information together with other MEP and reaction swath data, as obtained directly from the potential-energy surface, to perform new VTST calculations. Details of the implementation are presented, and applications to reaction rate calculations of the OH + CH₄ → H₂O + CH₃ and CF₃ + CD₃H → CF₃H + CD₃ reactions are included.