Wide ranging equation of state with Tartarus: A hybrid Green’s function/orbital based average atom code

Abstract Average atom models are widely used to make equation of state tables and for calculating other properties of materials over a wide range of conditions, from zero temperature isolated atom to fully ionized free electron gases. The numerical challenge of making these density functional theory based models work for any temperature, density or nuclear species is formidable. Here we present in detail a hybrid Green’s function/orbital based approach that has proved to be stable and accurate for wide ranging conditions. Algorithmic strategies are discussed. In particular the decomposition of the electron density into numerically advantageous parts is presented and a robust and rapid self consistent field method based on a quasi-Newton algorithm is given. Example application to the equation of state of lutetium (Z  =  71) is explored in detail, including the effect of relativity, finite temperature exchange and correlation, and a comparison to a less approximate method. The hybrid scheme is found to be numerically stable and accurate for lutetium over at least 6 orders of magnitude in density and 5 orders of magnitude in temperature.