Calculating rate constants with updated Hessians using variational transition state theory with multidimensional tunneling

Variational transition state theory with multidimensional tunneling (VTST/MT) has been used for calculating the rate constants of reactions. The updated Hessians have been used to reduce the computational costs for both geometry optimization and trajectory following procedures. In this paper, updated Hessians are used to reduce the computational costs while calculating the rate constants applying VTST/MT. Although we found that directly applying the updated Hessians will not generate good vibrational frequencies along the minimum energy path (MEP), however, we can either re-compute the full Hessian matrices at fixed intervals or calculate the Block Hessians, which is constructed by numerical one-side difference for the Hessian elements in the "critical" region and Bofill updating scheme for the rest of the Hessian elements. Due to the numerical instability of the Bofill update method near the saddle point region, we have suggested a simple strategy in which we follow the MEP until certain percentage of the classical barrier height from the barrier top with full Hessians computed and then performing rate constant calculation with the extended MEP using Block Hessians. This strategy results a mean unsigned percentage deviation (MUPD) around 10% with full Hessians computed till the point with 80% classical barrier height for four studied reactions. This proposed strategy is attractive not only it can be implemented as an automatic procedure but also speeds up the VTST/MT calculation via embarrassingly parallelization to a personal computer cluster.