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Hi VASP community,

I would like to clarify the meaning of entropy-related energy values in VASP output:

In my calculation, I get:

werner@x13dai-t:~/Desktop/std_vasp_slurm/b1/fe/cd/b1fecd84-2a91-41fa-b7e0-f63215ca6329_1$ ug -B2 22428357 OUTCAR | tail -3
  free  energy   TOTEN  =       -24.22450672 eV

  energy  without entropy=      -24.22361411  energy(sigma->0) =      -24.22428357
  
werner@x13dai-t:~/Desktop/std_vasp_slurm/b1/fe/cd/b1fecd84-2a91-41fa-b7e0-f63215ca6329_1$ ug EENTRO | tail -1
OUTCAR:  entropy T*S    EENTRO =        -0.00089262

From the relationship: TOTEN = Energy without entropy + (entropy T*S EENTRO), I can verify: -24.22361411 + (-0.00089262) ≈ -24.22450673 eV

My question is: Why is "entropy T*S EENTRO" a negative value?

Since:
- Temperature T is always positive
- Entropy S is always positive (as it measures disorder)
- Therefore T×S should be positive

However, VASP outputs a negative value. Is this because:
1. VASP actually outputs "-T×S" (the contribution to free energy) rather than "T×S" itself?
2. Or is there something about how VASP calculates electronic entropy that I'm missing?

For now, I'm planning to use the "Energy without entropy" value as U(V) in QHA (Quasi-Harmonic Approximation) calculations, so I need to understand the correct relationship between these energy terms.

Thank you for any clarification!

Regards,
Zhao

Dear hszhao,

Yes you are correct in the line entropy TS EENTRO VASP writes the negative entropy. In this way the TOTEN can be obtained as a sum over the energy table in the OUTCAR file. Example:

   alpha Z        PSCENC =      1363.31358291
   Ewald energy   TEWEN  =    247838.17329901
   -Hartree energ DENC   =   -282067.70155624
   -exchange      EXHF   =         0.00000000
   -V(xc)+E(xc)   XCENC  =      1348.61735250
   PAW double counting   =     29410.74263967   -28786.08102701
   entropy T*S    EENTRO =        -0.01527901
   eigenvalues    EBANDS =      1076.85460609
   atomic energy  EATOM  =     34751.67368736
   Solvation  Ediel_sol  =         0.00000000
   ext. energy  EPLUGINS =         0.00000000
   ---------------------------------------------------
free energy    TOTEN  =      4935.57730528 eV

energy without entropy =     4935.59258429  energy(sigma->0) =     4935.58494478

And TOTEN can be obtained by 1363.31358291+247838.17329901-282067.70155624+0.00000000+1348.61735250+29410.74263967-28786.08102701-0.01527901+1076.85460609+34751.67368736+0.00000000+0.00000000.
So to have negative entropy is just a convention in VASP to make the table in the OUTCAR file a little easier to use.

All the best Jonathan

Dear Jonathan,

Thank you for your reply. You confirmed that "entropy T*S EENTRO" in VASP output is indeed the negative entropy, mainly as a convention to allow the energy table in the OUTCAR file to sum directly to TOTEN. I understand this point.

However, I would like to further clarify two aspects:

1. This negative entropy has essentially lost its physical meaning, correct? It's merely a convention adopted by VASP internally to satisfy the energy representation convention.

2. More importantly, this entropy is introduced due to the SIGMA parameter setting, which primarily aims to accelerate the convergence of electronic structure calculations - essentially a numerical technique. Therefore, the so-called "entropy" introduced this way is actually an artificial quantity without real physical significance.

Based on this understanding, for subsequent physical property calculations (such as QHA), I should use energy(sigma->0) as the only reliable physical quantity, rather than TOTEN or Energy without entropy, correct?

Thank you for your further explanation!

See below for the related discussions:

https://www.vasp.at/forum/viewtopic.php?t=20192
https://www.vasp.at/forum/viewtopic.php?t=18970
https://ww.vasp.at/forum/viewtopic.php?t=1333
https://wwww.vasp.at/forum/viewtopic.php?t=8658

Best regards,
Zhao