Thermal rates for driven isomerization reactions

Abstract

Chemical reactions happen all the time. The car that slowly rusts, the hemoglobin constantly binding oxygen in the lung and transporting it through our bodies, and the photosynthesis. In industry, reactions are used to create materials for our daily life. They create metals for cars, create textiles for different equipment and closing, and the silicon dioxide by oxidation for microchips. Simulations are used, as for example in the oxidation of silicon, to optimize the reactions or to make predictions. The optimization of reactions, e.g. via driving them by external fields or changing the pressure, saves costs for the industry and energy, which is important with regard to the climate change. One successful method for computing reaction rates is the mean first-passage time (MFPT) method. It is able to predict reaction rates of both non-driven and driven chemical reactions and is also successful in the fields of neuron dynamics, dynamics of a spin system, electrostatics, and stochastic systems. The reaction rate is the decrease of reactant concentration per unit time at the reactant side because the reactants react to the product at the product side. The reactants do not react instantly to the product, because both sides are separated by an energy barrier. The energy, which the reactant needs to overcome that barrier and react to the product side, is called the activation energy. This energy could be provided due to thermal energy. The first-passage time is the time at which the reactive particle overcomes the barrier for the first time. For the first time, because the particle could also react back to the reactant side again after some time. The MFPT is the average of first-passage times of many particles. With the inverse of the MFPT the reaction rate can be calculated. In the limit of a harmonic energy barrier, the MFPT rate has been seen to be precisely equal to the transition state (TS) rate, and both are equal to the correct Kramers rate. The transition state theory (TST), on which the TS rate is based, describes the transition between the reactant and the product with its intermediate state, the TS also called activated complex. This intermediate state in a one-dimensional system is located at the maximum of the energy barrier, which is called the saddle point. The theory presents a further development of Arrhenius' law, which describes only an empirical observation and makes no statement about the intermediate state of a reaction. Intentionally the TST deals with chemical reactions, but it finds its application in various fields such as Bose-Einstein condensates, astronomy, atomic and solid state physics, and cluster formation. With TST it is possible to study trajectories in multidimensional systems, which are unstably bound to the saddle region, perform movements orthogonally to the reaction direction, and never fall off the saddle to one or the other side. In calculating their instability on the saddle via decay rates, the saddle, which is the bottleneck of a reaction, can be further studied. The decay rate has no preferred direction in contrast to the reaction rates. The behavior of such trajectories and their decay rates were recently studied for a thermal model system and the non-thermal LiCN isomerization. The LiCN isomerization is studied several times in the field of TST and other fields. So far, reaction rates of LiCN isomerization could only be determined for high temperatures without external driving. Furthermore, thermal decay rates were only studied in a model system, missing the link to a real reaction. In this thesis the MFPT rates and the thermal decay rates are calculated for both the non-driven and the driven LiCN system. Therefore, the goal of this thesis is to study the thermal decay rates in a real reaction using the LiCN isomerization and to use the MFPT rates to study the behavior of the reaction rates for different temperatures, frictions, and external influences. Furthermore, the calculation of both the MFPT and the decay rates offers the opportunity to take a next step in comparing the reaction rates and the decay rates in this work.