Oscillations in the electronic entropy with SIGMA

[Neutrino]

I'm trying to optimize the best smear and K-point to study Zr metal. For that purpose, I displaced one atom in the unit cell by 10% of Zr-Zr distance and I'm studying the convergence of energy and forces as a function of K-point and SIGMA. I'm using Methfessel-Paxton 2nd order . The problem is that I noticed that the electronic entropy oscillates as a function of SIGMA between positive values (fine) and negative values (unphysical). This trend persists even if you I increase the K-POINT density or increase the order of smearing (ISMEAR > 0). For example at 24x24x16 k-points and with ISMEAR=2 I get something like:

SIGMA=0.00 entropy T*S EENTRO = 0.00000000
SIGMA=0.04 entropy T*S EENTRO = -0.00008793
SIGMA=0.08 entropy T*S EENTRO = -0.00002490
SIGMA=0.12 entropy T*S EENTRO = 0.00067747
SIGMA=0.16 entropy T*S EENTRO = 0.00097835
SIGMA=0.20 entropy T*S EENTRO = 0.00095312
SIGMA=0.24 entropy T*S EENTRO = 0.00130208

As one can see in all cases |TS_elec| per atom is less than 1 meV (the cell has 2 atoms) but the annoying thing is the negative values. Can one tolerate and trust results based on these negative entropies? Is there a way to resolve this issue?

For reference, this is the typical INCAR I use:
Zr metal
ISTART=0 ; ICHARG = 2
ISMEAR = 2 ; SIGMA = 0.20
ENCUT= 500
IBRION=-1 ; NSW=1 ;ISIF=2
EDIFF = 1E-04
LWAVE = .FALSE.
PREC=Accurate
LCHARG=.FALSE.


Thank you for help!

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