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Average atom models are widely used to make equation of state tables and forcalculating other properties of materials over a wide range of conditions, fromzero temperature isolated atom to fully ionized free electron gases. Thenumerical challenge of making these density functional theory based models workfor any temperature, density or nuclear species is formidable. Here we presentin detail a hybrid Green's function/orbital based approach that has proved tobe stable and accurate for wide ranging conditions. Algorithmic strategies arediscussed. In particular the decomposition of the electron density intonumerically advantageous parts is presented and a robust and rapid selfconsistent field method based on a quasi-Newton algorithm is given. Exampleapplication to the equation of state of lutetium (Z=71) is explored in detail,including the effect of relativity, finite temperature exchange andcorrelation, and a comparison to a less approximate method. The hybrid schemeis found to be numerically stable and accurate for lutetium over at least 6orders of magnitude in density and 5 orders of magnitude in temperature.

Wide Ranging Equation of State with Tartarus: a Hybrid Green's Function/Orbital based Average Atom Code