Group Conductivity and Nonadiabatic Born Effective Charges of Disordered Metals, Warm Dense Matter, and Hot Dense Plasma

The average ionization state is a critical parameter in plasma models for charged particle transport, equations of state, and optical response. The dynamical or nonadiabatic Born effective charge (NBEC), calculated via first principles time-dependent density-functional theory, provides exact ionic partitioning of bulk electron response for both metallic and insulating materials. The NBEC can be transformed into a ``group conductivity,'' i.e., the electron conductivity ascribed to a subset of ions. We show that for disordered metallic systems, such as warm dense matter (WDM) and hot dense plasma, the static limit of the NBEC is different from the average ionization states, but that the ionization state can be extracted from the group conductivity even in mixed systems. We demonstrate this approach using a set of archetypical examples, including cold and warm aluminium, low- and high-density WDM carbon, and a WDM carbon-beryllium-hydrogen mixture.