  The dynamics of (few) electrons dissolved in an ionic fluid--as when a small
amount of metal is added to a solution while upholding its electronic
insulation--manifests interesting properties that can be ascribed to nontrivial
topological features of particle transport (e.g., Thouless' pumps). In the
adiabatic regime, the charge distribution and the dynamics of these dissolved
electrons are uniquely determined by the nuclear configuration. Yet, their
localization into effective potential wells and their diffusivity are dictated
by how the self-interaction is modeled. In this article, we investigate the
role of self-interaction in the description of localization and transport
properties of dissolved electrons in non-stoichiometric molten salts. Although
the account for the exact (Fock) exchange strongly localizes the dissolved
electrons, decreasing their tunneling probability and diffusivity, we show that
the dynamics of the ions and of the dissolved electrons are largely
uncorrelated, irrespective of the degree to which the electron self-interaction
is treated, and in accordance with topological arguments.
