Two Examples of Deterministic versus Stochastic Modeling of Chemical Reactions

Abstract

The numerical simulation of chemical reactions can be carried out using deterministic or stochastic models. The deterministic simulation gives the average behavior of the system, which is a suitable representation of the reaction when the number of molecules involved is large. The stochastic simulation requires stronger mathematical foundations, mainly from probability theory but allows prediction of the so-called stochastic effects, which are relevant when the number of molecules is small. A more accurate representation of processes dependent on the behavior of a small number of molecules is of increasing importance in current chemistry and can be achieved through stochastic modeling. From an educational point of view, the simultaneous use of stochastic and deterministic models in the simulation of chemical reactions results in a better understanding of the chemical dynamics. The two approaches are reviewed in this paper by using two selected examples of chemical reactions and four MATLAB programs, which implement both the deterministic and stochastic modeling of the examples.