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Therefore, CASTEP uses the Mermin finite temperature expression for the total energy (Marzari, 1997): E = EKS - TS, where T is the temperature (i.e., smearing width) and S is the Mermin entropy due to the different ways in which the partially filled bands could have been filled.

The CASTEP output is as follows. The line

Final energy, E             =  -861.8315373731     eV

gives the Kohn-Sham energy, EKS, which ignores the entropy. However, it is the total Mermin free energy that is minimized by CASTEP and reported in the SCF cycles in the line

Final free energy (E-TS)    =  -861.8315374521     eV

If you were actually interested in the electronic states at some reasonable nonzero temperature, you would smear the Fermi level with a thermal (i.e., Fermi-Dirac) smearing method and the free energy reported by CASTEP would be the value you require.
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