# Re: [SIESTA-L] Total energy

```Thank you very much for the reference!

I'll use E=1/2(Etot +FreeEng) for my E-V equation of state fit.```
```
I noticed that for semiconductors, Etot = FreeEng; it is in metallic
systems that I see differences between Etot and FreeEng (with FreeEng being
lower). In this regard, using the average of the two energies for T=0 makes
sense.

Thanks again!

On Wed, Jun 22, 2022 at 3:01 PM RCP <pasia...@cnea.gov.ar> wrote:

> Hello,
> May I contribute my 0.01 ?. According to Eq.(21) in,
>
>    Kresse & Furthmüller, Comp. Mat. Sci. 6 (1996) 15-50
>
> a good estimate for the (T=0K) DFT energy is 1/2(Etot +FreeEng), and
> this is the recipe I've always used.
>
> Regards,
> Roberto
>
> On 22/06/2022 13:11, Francisco Garcia wrote:
> > ThanksÂ  for your response Prof. Artacho!
> >
> > So if I have a situation like below for a large metallic system in which
> FreeEng
> > is lower than Etot, should I use Etot? Specifically, if I want to plot
> the E-V
> > curve from single point runs to obtain the equation of state I should
> use Etot
> > instead of FreeEng? Or if I want to compute the cohesive energy, Etot
> should be
> > used instead of FreeEng?
> >
> > siesta: Program's energy decomposition (eV):
> > siesta: Ebs Â  Â  = Â  Â  Â -859.157108
> > siesta: Eions Â  = Â  Â  Â 9568.777238
> > siesta: Ena Â  Â  = Â  Â  Â  277.651800
> > siesta: Ekin Â  Â = Â  Â  Â 4247.415878
> > siesta: Enl Â  Â  = Â  Â  -1698.956164
> > siesta: Eso Â  Â  = Â  Â  Â  Â  0.000000
> > siesta: Edftu Â  = Â  Â  Â  Â  0.000000
> > siesta: DEna Â  Â = Â  Â  Â  162.636813
> > siesta: DUscf Â  = Â  Â  Â  Â 26.981770
> > siesta: DUext Â  = Â  Â  Â  Â  0.000000
> > siesta: Exc Â  Â  = Â  Â  -6715.533109
> > siesta: eta*DQ Â = Â  Â  Â  Â  0.000000
> > siesta: Emadel Â = Â  Â  Â  Â  0.000000
> > siesta: Emeta Â  = Â  Â  Â  Â  0.000000
> > siesta: Emolmec = Â  Â  Â  Â  0.000000
> > siesta: Ekinion = Â  Â  Â  Â  0.000000
> > siesta: Eharris = Â  Â Â  -13268.580292
> > siesta: Etot Â  Â = Â  Â  Â Â  -13268.580250
> > siesta: FreeEng = Â  Â -13269.911499
> >
> > On Tue, Jun 21, 2022 at 2:07 PM Emilio Artacho <e.arta...@nanogune.eu
> > <mailto:e.arta...@nanogune.eu>> wrote:
> >
> >
> >>     On 20 Jun 2022, at 17:16, Francisco Garcia <garcia.ff....@gmail.com
> >>     <mailto:garcia.ff....@gmail.com>> wrote:
> >>
> >>     Dear users,
> >>
> >>     In metallic systems with a fairly sizable electronic smearing
> temperature
> >>     T, is it accurate to claim that
> >>
> >>     (i) in a single point calculation, the free energy is the
> representative
> >>     energy of the system (due to the addition of -TS to the total
> energy U)
> >
> >     No, the -TS term for the phononic entropy is missing.Â
> >
> >     It is the free energy defining the finite temperature equilibrium
> for the
> >     purely electronic
> >     problem for fixed external potential (fixed nuclei), as in
> Merminâ€™s finite
> >     -T DFT.
> >
> >
> >>     (ii) in a variable cell optimization, the enthalpy is the
> representative
> >>     energy of the system (due to the addition of the PV term to the
> energy).
> >
> >     Yes, it is the free energy of the system (minimum defines
> equilibrium) for T=0.
> >
> >     Emilio
> >
> >>
> >>     Thanks!
> >>     Â
> >>
> >>     --
> >>     SIESTA is supported by the Spanish Research Agency (AEI) and by the
> >>     European H2020 MaX Centre of Excellence (http://www.max-centre.eu/)
> >
> >     --
> >     Emilio Artacho
> >
> >     Theory Group, Nanogune, 20018 SanÂ Sebastian, Spain, and
> >     Theory of Condensed Matter,Â Department of Physics,
> >     Cavendish Laboratory, University ofÂ Cambridge, Cambridge CB3 0HE, UK
> >
> >
> >
> >
> >
> >     --
> >     SIESTA is supported by the Spanish Research Agency (AEI) and by the
> European
> >     H2020 MaX Centre of Excellence (http://www.max-centre.eu/)
> >
> >
> >
>
> --
> Dr. Roberto C. Pasianot         Phone: 54 11 4839 6709
> Gcia. Materiales, CAC-CNEA      FAX  : 54 11 6772 7362
> Avda. Gral. Paz 1499            pasia...@cnea.gov.ar
> 1650 San Martin, Buenos Aires
> ARGENTINA
>
```
```--
SIESTA is supported by the Spanish Research Agency (AEI) and by the European
H2020 MaX Centre of Excellence (http://www.max-centre.eu/)
```