Hello Until the smearing is not fully negligible (so that you still have appreciable fractional occupations) also E=F-(-TS)=(E-TS)-(-TS) (that is the difference between the two quantities directly provided by the code) will be a function of the spreading paramater. On the other hand, if you get the energy with a small enough smearing, a good estimate for the energy without smearing is given by the equation
[F(T)+E(T)]/2=E(0)+O(T^n), with n>2, which you can find in O. Grotheer and M. Fa?hnle, PRB (1998), 58, 13459. Best, Agostino Migliore CMM, Chemistry Department, UPenn Philadelphia, PA
