Spatial decomposition is conducted for the electrical conductivity. The contribution per ion pair at a certain distance is identified in terms of a two-body velocity time correlation function and is integrated over the whole distance of the ion pair to provide the cross-correlation term of the conductivity. The spatial-decomposition formula is an exact expression at any concentrations of ions and incorporates physically appealing pictures in the space domain into the theory of time correlation functions. Illustrative analyses are presented for 1m NaCl aqueous solution and the [C4 mim][NTf2 ] ionic liquid. The contrast between the two systems is discussed for the time and spatial ranges of correlations, and it is shown that the ion-pair contribution to the conductivity for the [C4 mim][NTf2 ] system is not localized and extends beyond the first coordination shell of the cation-anion pair.
Keywords: Green-Kubo formula; electrical conductivity; molecular dynamics simulation; spatial decomposition; time correlation function.
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