A one-dimensional stack of polarizable charge distributions ( here). Within the extreme Clausius–Mossotti model, the distributions are assumed as pointlike.
Log-log plot of the difference of and the local polarizabilities per site for a stack of Clausius–Mossotti sites. , whereas the asymptotic value . Solid circles correspond to the actual CM values. The solid line represents the fit according to Eq. (9) while the dashed line is only one quadratic term from this fitting expression. The inset contains semilog plot of the CM values and the fit.
One-dimensional Clausius–Mossotti-type model: asymptotic convergence of the linear polarizability per site as a function of . We have used and ; only a sparse set of values of is shown for the sake of clarity. ; ; . The slope of the straight lines in the logarithmic plot is for , and for the other cases with the shift in the lines caused by a factor-of-four difference in prefactors.
First-principle longitudinal polarizabilities of chains of molecules, within HF and DFT, for two different intermolecular separations. ; ; . The slope of the straight solid lines in the logarithmic plots is for and for . In the former case an expansion to the next leading term beyond the first is used for the actual fit (dashed lines).
First-principle longitudinal polarizabilities of transpolyacetylene chains within HF and DFT. ; ; . The slope of the straight solid lines in the logarithmic plots is for and for . In the former case the expansion to the next leading term beyond the first is used for the actual fit (dashed lines).
Local polarizabilities per site , for a stack of sites at bohrs separation. Crosses: values obtained from the Maestro–Moccia (Ref. 25) decomposition in the HF case. Circles: values obtained for the classical system, where we have used . By construction, the classical and the quantum system share the same asymptotic value .
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