Probability diffusion in non-Markhovian, non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule of C_2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocity V. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V^2(t)V^2(0)>/<V^2(0)V^2(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.