Diffusion and electrical conductivity in water at ultrahigh pressures

We calculate the electrical conductivity of water for ultrahigh pressures up to 80 Mbar and temperatures up to 130 000 K as relevant for planetary physics by using ab initio molecular-dynamics simulations. The electron system is treated within density-functional theory and the electronic conductivity is obtained from an evaluation of the Kubo-Greenwood formula. The ionic conductivity is determined via diffusion coefficients. Our calculations reproduce most of the available experimental conductivity data within the error bars while the conductivity plateau measured by Mitchell and Nellis cannot be reproduced. At high densities a pressure-induced nonmetal-to-metal transition is predicted within the superionic phase. Furthermore, we study the influence of exchange and correlations on the electronic conductivity in more detail by applying a standard generalized gradient approximation and a hybrid functional as well that includes screened Fock exchange. The latter treatment yields a larger band gap and thus more reliable electrical conductivities, especially in the region of the nonmetal-to-metal transition. These results are relevant as input for future interior and dynamo models of giant, water-rich planets.