A direct method of studying reaction rates by equilibrium molecular dynamics: Application to the kinetics of isomerization in liquid n-butane

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Abstract
In this article we describe a straightforward and general method for studying chemical reaction kinetics in equilibrium systems using molecular dynamics computer simulation. We have applied it to the problem of determining the rate constants for the trans–gauche isomerization processes in liquid n‐butane. The method relies upon the fact that if a dynamic equilibrium exists in the system then it must apply to any chosen subset of the system. The power of the method is demonstrated by its high precision and in the discovery that a mechanism for direct gauche to gauche interconversions through the trans well is required to explain the data. The connection between the method applied here and other approaches to the determination of rate constants is discussed. The correlation function for isomerization dynamics is usually formulated as a collective property of the system. Its use leads to poor statistics when applied to simulation data. It is shown that the relaxation functions are equivalent to single particle correlation functions which fully define the isomerization kinetics. An additional observation from our 1.8 ns simulation is that the trans–gauche equilibrium in model liquid n‐butane is shifted by ∼1% to excess gauche in comparison to the ideal gas at the same temperature. This is a smaller solvent effect than has been reported in the past.