6 DIPPIM 300 601 894 FPMD 10 244 498 787 Exp. 1 2 280 567 858 Exp. 2 3 315 585 915 Exp. 3 4 560 870 TABLE II: Characteristic frequencies of the imaginary part of the dielectric function as obtained from the DIPPIM model, compared to previous FPMD simulations 10,11 and to experi- mental results $^{2–4}$. All the frequencies are given in cm $^{$_{−}$1}$. This potential was used by Micoulaut et al. 7 and they indeed obtained diffusion coefficients which were more than one order of magnitude larger than the values ob- tained by Hawlitzky et al. 12 (who incorrectly explained this discrepancy in terms of lack of equilibration of the simulations, it is obvious here that the real reason was the difference between the two potentials). The so-called rescaled potential was obtained by taking the normal OE potential and rescaling the ionic charges, the van der Waals coefficient and the repulsive parameters in order to get a better agreement with the experimental vibra- tional spectrum for the crystal. To do this the parame- ters which are responsible for the strength of the the O-O and O-Ge short range repulsion were lowered by a factor of approximately 2.5; as a consequence, these ions can diffuse much more easily in a softer environment. the total dielectric function [ n ( ν ) α ( ν ) = 2 πν ℑ ( ϵ ( ν ))], which can be determined following Caillol, Levesque and Weis 27,28 as The infrared spectra of ionic melts with polyvalent cations exhibit discrete bands attributable to the vibra- tional motion of the local coordination complexes around the cations. They originate from the polarization fluc- tuations associated with motion of the ionic charges. The inclusion of polarization effects for the oxide ions in our model may influence the predicted spectrum in two ways $^{26}$. First, the interactions of the oxide ion dipoles may alter the local structure of the network and the strength of the bonds, which may introduce a shift of the vibrational frequencies. Second, the induced dipoles will themselves be responsible for absorption, as they too contribute to the total polarization fluctuations. ∑ i =1 µ $_{i}$( t ). Figure 5 shows the imaginary part of the total di- electric function calculated for simulations carried out with the DIPPIM potential, compared to the one ob- tained from FPMD simulations 10,11 and from several experiments 2,3 (the spectrum proposed by Kamitsos et al. shows the absorption coefficient, here we transformed it into the dielectric function to facilitate comparisons). Three main bands are observed on the spectra, in good agreement with the other studies. The corresponding characteristic peak frequencies for the absorption spec- tra are summarized in table II. The agreement is very satisfactory; the frequencies obtained match very closely to the various experimental results (even though these show a significant scatter), while the FPMD simulation seems to systematically underestimate them. The rela- tive intensities of the bands is also in good agreement with experiment, though the highest frequency band at around 894 cm − 1 is not intense enough in our spectrum. J ( t ) is the charge current J ( t ) = ∑ N i =1 q$_{i}$ v $_{i}$( t ) and M ( t ) is the total system induced dipole moment, M ( t ) = N The importance of polarization effects in determining the relative intensities of the bands can be demonstrated by separating the various contributions to the absorption spectrum. In the case of glassy silica 26 and beryllium fluoride $^{29}$, it was observed that the interference between the induced dipoles and permanent charge contributions to the total polarization, contained in the 〈 M · J 〉$_{ν}$ cross term, is responsible for the changes of the relative intensi- ties. Figure 6 shows the decomposition of the absorption spectrum in the case of glassy GeO$_{2}$. The two main con- tributions are the charge fluctuation and the cross term; both show bands at the same intensities. Note that the The absorption coefficient in the presence of these ex- tra moments is calculated from the imaginary part of FIG. 5: Imaginary part of the dielectric function, calculated for simulations carried out with the DIPPIM potential, com- pared to FPMD simulation 10 and experimental results $^{2,3}$. VI. INFRARED SPECTRUM where ϵ ( ν ) − ϵ$_{∞}$ = β 3 ϵ$_{0}$V ( 〈 M (0) $^{2}$〉 + 2 πıν 〈 M · M 〉$_{ν}$ (9) +2 〈 M · J 〉$_{ν}$ + ı 2 πν 〈 J · J 〉$_{ν}$ ) 〈 J · J 〉$_{ν}$ = ∫ ∞ 0 e 2 $^{πıνt}$〈 J ( t ) · J (0) 〉 d t, (10)