  In high temperature density functional theory simulations (from tens of eV to
keV) the total number of Kohn-Sham orbitals is a critical quantity to get
accurate results. To establish the relationship between the number of orbitals
and the level of occupation of the highest orbital, we derived a model based on
the electron gas properties at finite temperature. This model predicts the
total number of orbitals required to reach a given level of occupation and thus
a stipulated precision. Levels of occupation as low as 10-4, and below, must be
considered to get converged results better than 1%, making high temperature
simulations very time consuming beyond a few tens of eV. After assessing the
predictions of the model against previous results and ABINIT minimizations, we
show how the extended FPMD method of Zhang et al. [PoP 23 042707, 2016] allows
to bypass these strong constraints on the number of orbitals at high
temperature.
