Assessing and rationalizing the performance of Hessian update schemes for reaction path Hamiltonian rate calculations

Abstract

The reaction path Hamiltonian (RPH) can be used to calculate chemical reaction rate constants, going beyond transition-state theory in taking account of recrossing by providing an approximation to the dynamic transmission coefficient. However, the RPH necessitates the calculation of the Hessian matrix at a number of points along the minimum energy path; the associated computational cost stands as a bottleneck in RPH calculations, especially if one is interested in using high-accuracy electronic structure methods. In this work, four different Hessian update schemes (symmetric rank-1, Powell-symmetric Broyden, Bofill, and TS-BFGS updates) are assessed to see whether or not they reliably reproduce calculated transmission coefficients for three different chemical reactions. Based on the reactions investigated, the symmetric rank-1 Hessian update was the least appropriate for RPH construction, giving different transmission coefficients from the standard analytical Hessian approach, as well as inconsistent frequencies and coupling properties. The Bofill scheme, the Powell-symmetric Broyden scheme, and the TS-BFGS scheme were the most reliable Hessian update methods, with transmission coefficients that were in good agreement with those calculated by the standard RPH calculations. The relative accuracy of the different Hessian update schemes is further rationalized by investigating the approximated Coriolis and curvature coupling terms along the reaction-path, providing insight into when these schemes would be expected to work well. Furthermore, the associated computational cost associated with the RPH calculations was substantially reduced by the tested update schemes. Together, these results provide useful rules-of-thumb for using Hessian update schemes in RPH simulations.

Graph-Driven Reaction Discovery: Progress, Challenges, and Future Opportunities

“…Correcting for such effects demands evaluation of α­( T ); this is in itself a computationally expensive exercise, requiring thermal averaging of a number of MD trajectories (typically on an ab initio PES or reactive force-field model) initiated at the TS in order to evaluate the flux-side correlation function. To address this inefficiency, we have recently shown how α­( T ) can be accurately and efficiently approximated using a reaction-path Hamiltonian (RPH) model parametrized using information available from standard NEB optimization of the MEP; importantly, we have also demonstrated that RPH construction can be further accelerated by using a variety of Hessian propagation schemes, thereby avoiding expensive ab initio Hessian calculations for a dense set of intermediate images. , As shown in Figure for the example reaction of molecular hydrogen association at the cobalt center in HCo­(CO) 3 , relatively simple Hessian update schemes combined with MD simulations using the RPH model enable accurate approximation of α­( T ), even for reactions in which recrossing is quite significant. Such methods demonstrate how one can improve on the treatment of TST rate theory in a simple computational scheme; although we note that the challenge of accurately modeling the underlying PES remains.…”

“…(a) MEP for the insertion of molecular hydrogen H 2 at the cobalt center of HCo­(CO) 3 , the active catalytic species in the Heck–Breslow hydroformylation previously studied by ARD simulations. (b) Calculated flux-side correlation functions given by a standard RPH simulation (requiring multiple Hessian matrix evaluations along the MEP) and by our recent work in which Hessian propagation schemes (in this case, Powell–symmetric–Broyden [PSB]) are used to build the RPH …”

“…(b) Calculated flux-side correlation functions given by a standard RPH simulation (requiring multiple Hessian matrix evaluations along the MEP) and by our recent work in which Hessian propagation schemes (in this case, Powell–symmetric–Broyden [PSB]) are used to build the RPH. 135 …”