Chapter 8. Semiclassical Multidimensional Tunnelling Calculations

It is now recognized that the calculation of tunnelling probabilities in chemical reactions must include multidimensional effects, in particular, (i) the change in quantized vibrational energies as the system progresses along the reaction coordinate and (ii) corner cutting due to the curvature of the reaction paths in isoinertial coordinates. It is now possible to calculate tunnelling probabilities accurately and efficiently using semiclassical methods that include these effects. This chapter reviews the methods for doing this that have been included in the Polyrate and Pilgrim computer programs, in particular, small-curvature tunnelling, large-curvature tunnelling, optimized multidimensional tunnelling, and least-action tunnelling.