Parameter dependent rates in transition state theory for periodically driven systems

Abstract

It is known from simple middle school chemistry that reactants react into products during a chemical reaction. Such a transition is only possible, when the energy of the reactant configuration exceeds a certain threshold, which, in chemistry, is known as the activation energy. Fig. 1.1 illustrates a simplified chemical reaction in which a ball, as a simple example for a reactant, has to overcome a barrier of a certain height in order to reach the other side of this barrier and become a product. As soon as the reactant’s total energy exceeds the barrier’s energy, it is able to transition into a product. In this simple one-dimensional example the maximum of the barrier, i.e. the saddle, clearly separates reactants from products, meaning if the ball passes the maximum of the barrier, it will fall down to the product side. When the separation of reactants and products is known, it is possible to propagate reactants along the reaction coordinate and estimate the flux of reactants transitioning into products. The calculation of reaction rates and reaction pathways is the central topic of the Transition State Theory (TST) [1-18]. A real chemical reaction usually holds many degrees of freedom. Therefore it is a great challenge in TST to accurately describe a higher-dimensional system with one direction "over the saddle" (the reaction coordinate) and many other degrees of freedom (the bath coordinates). When a chemical reaction is pertubated, i.e. driven by a time-dependent external force, the potential energy surface of the system will become time-dependent itself. In reality, such an external force could be the result of a time-dependent electric field, for example. The separation of reactant and product configurations, which enables the calculation of reaction rates, is much more complex when the system is highdimensional and time-dependent. Previous research of the ITP1 in this field [19-21] has led to the separation of phase space of periodically driven systems through a timedependent hypersurface, the Dividing Surface (DS) [19, 20]. This research has recently laid the foundation for the computation of reaction rates which are determined by the flux of reactants through this dividing surface. Building on the previous research of the ITP1, this work deals with the task of calculating rate constants for a numerical simulation of reactants crossing the DS in a two-dimensional time-dependent system. These rate constants depend on multiple aspects of the system such as the concrete properties of the external driving as well as the composition of the propagated ensemble of reactants. The central task of this work is to determine in what manner the rate constant depends on the specific structure and movement of the potential energy surface. For this purpose, the work aims at the development of an ensemble that leads to a rate constant that is a reflection of the system’s dynamics, as well as the development of a uniform procedure that can be used to estimate these rate constants.