Requirements for very high temperature Kohn-Sham density functional simulations and how to bypass them.

In density functional high temperature simulations (from tens of eV to keV) the total number of Kohn-Sham orbitals is a critical quantity to get sound results. The occupation of the highest orbital in energy is here derived from the properties of the homogeneous electron gas, which gives a prescription on the total number of orbitals to reach a given level of occupation. Very low levels of occupation (10-5 to 10-6) must be considered to get convergence with Kohn-Sham orbitals, making high temperature simulations unreachable beyond a few tens of eV. After testing these predictions against ABINIT oftware package results, we test the implementation of the Extended method of Zhang et al. [PoP 23 042707, 2016] in the ABINIT package to adress very high temperatures by bypassing these strong orbital constraint.