The detailed descriptions of the expressions for 𝜀 𝐷𝐷 (𝜔), 𝜀 𝐽𝐽 (𝜔) and 𝜀 𝐷𝐽 (𝜔) are provided in the Appendix A2 (supplementary material). We next present in Fig. the simulated dipole moment-current cross correlation functions for ions in these three DESs. These correlation functions are fitted numerically and the fit parameters are shown in Table (supplementary material). This cross term is important because it embodies 'translation-rotation coupling' and contributes to both the frequency dependent permittivity and the conductivity. Note the nonmonotonic behaviour of this crosscorrelation function with a peak at ~100 fs. This behaviour can be understood as follows.