Efficient stochastic simulations of complex reaction networks on surfaces

Area of Science:

• Chemical Kinetics
• Astrophysical Chemistry
• Computational Chemistry

Background:

• Surface reactions are typically modeled using rate equations based on mean-field approximations for large systems.
• Microscopic domains, like interstellar dust grains, exhibit significant stochastic fluctuations where rate equations fail.
• Complex reaction networks pose computational challenges for traditional stochastic methods like the master equation.

Purpose of the Study:

• To develop a computationally feasible stochastic method for simulating surface reactions in systems with small, fluctuating reactant populations.
• To address the limitations of rate equations and master equations in complex reaction networks occurring in microscopic domains.
• To provide a new simulation tool applicable to diverse fields including astrochemistry, nanoscience, and cellular biology.

Main Methods:

• Introduction of a novel stochastic method based on moment equations.
• Reduction of the number of equations to one per species and one per reaction.
• Utilization of a diagrammatic approach for constructing the moment equations.

Main Results:

• The moment equation method dramatically reduces the number of equations compared to the master equation.
• The method is demonstrated for astrophysically relevant reaction networks of increasing complexity.
• The approach offers a significant computational advantage for simulating stochastic surface reactions.

Conclusions:

• The moment equation method provides an efficient and feasible approach for simulating surface reactions in systems with small, fluctuating reactant numbers.
• This method overcomes the limitations of traditional rate equations and master equations for complex reaction networks.
• The technique is broadly applicable to various scientific domains involving surface catalysis and complex chemical processes.