Molecular dynamics calculation of the dielectric constant

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Abstract
Molecular dynamics (MD) simulations of an isolated dipolar system (made of Stockmayer molecules) has been performed. A two dimensional system has been adopted, using a ‘2-D electrostatics’ dipolar interaction. The isolated system was a disc in vacuo. The autocorrelation function (ACF) of the moment of the disc was extracted from our runs, together with the ACF of the moment of a small inner disc (‘microscopic’ or ‘multimolecular’ ACF). Comparison of these two ACF has allowed us to compute the response function of the annulus between the two discs. The behaviour of the latter was that predicted by the theory of Fatuzzo and Mason. It is thus shown, for the first time, that one can obtain, by numerical simulation of a few hundred molecules, reliable values of the complex permittivity of highly polar fluids, despite the long range character of the dipolar interaction. Its behaviour is surprisingly realistic when compared with that of real 3-D polar liquids. Monomolecular ACF have also been extracted from the MD runs. They recall that of the Itinerant Oscillator model, the long time behaviour of t)> being diffusive, but shorter-lived than that of the multimolecular ACF. Compared to the free rotation, the monomolecular orientational correlation time dt (u(0). u(t)> cannot be explained quantitatively using the theory of dielectric friction derived from the Onsager reaction field. Finally a comparison between this monomolecular correlation time and the multimolecular one is made: Models linking the ratio of these two times to the Kirkwood g K factor are examined.