Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces

TL;DR

This paper introduces a simplified stochastic method using moment equations for simulating complex surface reaction networks, especially effective when reactant numbers are small and fluctuations are significant.

Contribution

The authors develop a moment equation-based stochastic simulation approach that reduces computational complexity for complex surface reaction networks.

Findings

Method accurately models reactions on microscopic dust grains.

Significantly reduces the number of equations needed for simulations.

Applicable to various fields like catalysis, aerosol chemistry, and cellular networks.

Abstract

Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds and genetic networks in cells.