We use ab initio simulations based on density functional theory to calculate the electrical and thermal conductivities of electrons in partially ionized water plasmas at densities above 0.1 g/cm3. The resulting conductivity data are then fitted to analytic expressions for convenient application. For low densities, we develop a simple and fully analytic model for electronic transport in low-density plasmas in the chemical picture using the relaxation-time approximation. In doing so, we derive a useful analytic expression for electronic transport cross sections with neutral particles, based on a model potential. In the regime of thermal ionization, electrical conductivities from the analytic model agree with the ab initio data within a factor of 2. Larger deviations are observed for the thermal conductivity, and their origin is discussed. Our results are relevant for modeling the interior and evolution of water-rich planets as well as for technical plasma applications.
Note that this procedure is only applicable to the off-diagonal matrix elements. It does not yield the correct diagonal matrix elements (electron velocities). However, those do not contribute in Eq. (1).
We include helium here because it has an electronic structure (two occupied 1s orbitals) for which the ansatz for the model potential, Eq. (24), is most reasonable. Otherwise, helium does not appear in the calculations made for water.