Towards High-Quality Black-Box Chemical Reaction Rates with System-Specific Potential Energy Surfaces

Steffen, Julien ORCID

The calculation of highly-accurate reaction rate constants (k(T)) is one of the central topics in theoretical chemical kinetics. Two approaches for doing this are dominant in literature: application of heuristic corrections of the transition state theory (TST) and wave packet propagation with the aim to represent exact quantum mechanical dynamics. While the first approach is easy to handle but suffers from intrinsic approximations and limited accuracy, the second approach enables convergence towards the exact result, but at the expense of a complex handling and massive costs. This limits its application to a small circle of highly-specialized theoreticians. A new method that might be able to bridge the gap between easy application and convergence towards the exact result is the ring polymer molecular dynamics (RPMD) method. It is based on the isomorphism between quantum statistical mechanics and classical statistical mechanics of a fictitious ring polymer. With this, configurational state sums and free energy surfaces can be obtained from probabilistic samplings of the system's accessible phase space with classical MD of ring polymers. Based on these free energy surfaces reaction rate constants can be obtained that converge towards the results of wave packet propagations, if the size of the ring polymer is adequate. In order to conduct RPMD calculations, a sufficiently accurate representation of the thermally accessible potential energy surface (PES) of the system on which the ring polymers are propagated is needed. In principle, this surface could be represented by ad hoc calculations of energies and gradients based on quantum chemical methods like density functional theory (DFT) or second order Moller-Plesset perturbation theory (MP2). However, since many millions of single gradient calculations are needed to converge a free energy surface and the associated k(T) value, this approach is impractical. Instead, analytical representations of PESs that are fitted to DFT or MP2 results are commonly used. The parametrization of these representations is quite demanding, though, thus being a task for experts. The present thesis deals with new methods for the automated parametrization of analytical PES representations of reactive systems and the successive k(T) calculations based on RPMD. These representations are built on a combination of the quantum mechanical derived force field (QMDFF) method by \Grimme and the empirical valence bond method (EVB) by Warshel, being plugged together recently by Hartke and Grimme (EVB-QMDFF). In line with this thesis a crucial improvement of this combination of methods was done, complementing it with newly developed EVB concepts. For practical usage a new program package was developed, which enables the automated generation of an EVB-QMDFF-PES representation and calculations of RPMD-free-energy surfaces, recrossing corrections as well as k(T) values and Arrhenius parameters for comparison with experimental data, based on the preoptimized reaction path of an arbitrary thermal ground state system. The abilities of the new methods and the associated implementation were thoroughly benchmarked in different kinds of applications. These are calculations of k(T) values and Arrhenius parameters of arbitrary systems from a reaction data base and their comparison to literature values, theoretical molecular force experiments with quantitative investigations of force-dependent reactivities for different systems, a thorough study of urethane synthesis being part of our cooperation with Covestro AG and finally a combination of calculated rate constants of several elementary reactions for describing the dynamics of larger systems based on the kinetic Monte Carlo (KMC) method.

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Steffen, Julien: Towards High-Quality Black-Box Chemical Reaction Rates with System-Specific Potential Energy Surfaces. 2020.

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