On the calculation of the electric polarizability for the itinerant oscillator model

Author： Corcoran P.M. Coffey W.T. Evans M.W.

ISSN： 1362-3028

Source： Molecular Physics, Vol.61, Iss.1, 1987-05, pp. : 1-14

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Abstract

Estimation of the complex polarizability of the itinerant oscillator (I.O.) model of polar fluids has hitherto been based on a truncation of the series expansion of the double transcendental function describing the decay of the dipole moment. The essence of this method is to expand the decay function as a series of single transcendental functions. The resulting series is then Fourier transformed term-by-term by means of the usual response theory formula. The series is generally truncated after the first two terms so as to yield simple analytic formulae analogous to the Rocard equation. Corcoran has developed a numerical algorithm using Fast Fourier Transform techniques which allows the complex polarizability to be calculated to a high degree of precision from the decay function without recourse to any series expansion. The numerical method shows that the analytic approximations to the polarizability which have hitherto been used are quite accurate. Furthermore, if friction does not act on the inner dipole (the form of the model which has hitherto been almost exclusively used to represent spectra), it is found that the moment of inertia of the outer cage should be less than that of the inner dipole in order to achieve a good fit with the experimental data. This conclusion is inconsistent with the physical concept of the I.O., namely a dipole surrounded by a cage of neighbours, and has led to much criticism of the model. On the other hand, when friction acts on the inner dipole and is approximately the same (per unit inertia) as that acting on the outer cage, the model can produce physically realistic spectra for acceptable parameter values. This suggests that the two-friction form of the model should always be used for comparison with experimental spectra.