Analysis of friction kernels for n-butane isomerization in water by the generalized Langevin equation

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Abstract
In this article, the isomerization reaction of n-butane is used to study the dynamic properties of n-butane in aqueous solution. It is assumed that the dihedral angle of n-butane obeys the generalized Langevin equation (GLE), in which an effective potential, a friction damping and a random torque are included. The random torque is calculated using constrained molecular dynamics (MD) simulations and the time-dependent friction kernel is determined by using the fluctuation-dissipation theorem. The results show that for the trans, gauche, and transition states of n-butane, the random torques approximately follow a Gaussian distribution. The friction kernels demonstrate a rapid initial decay and a slow sequential decay, while the half-widths of the Gaussian distributions and the initial values of the friction kernels are somewhat dependent on the conformations. The transmission coefficient for crossing the transition state is also analyzed within the framework of Kramers and Grote–Hynes theories. The result shows that the isomerization of n-butane in water is in the polarization caging regime.