# [Pw_forum] A little question about total energy

Nicola Marzari marzari at MIT.EDU
Sat May 17 19:25:49 CEST 2003

To add to this - when you have a broadening the PWSCF
total energy is what others call the total free energy F=E-TS.

E.g., if you choose a Fermi-Dirac broadening, the PWSCF
total energy is really the Mermin-Kohn-Sham free energy.

Last, if you are studying isolated atoms, but still use a
broadening, you have an entropy S different from zero if there
are degeneracies giving rise to fractional occupation numbers.
So, you might want to remove the -TS (the correction for metals),
and also make sure your results are converged in the limit of
small T (i.e. small broadening temperatures).

Best,

nicola marzari

Paolo Giannozzi wrote:
> Hi
>
>
>>   In the output of PWSCF, the energy partitions are list
>>following the total energy as I pasted below. I found
>>that the total energy is not equal to the sum of those listed
>>partitions.
>
>
> Total Energy = sum of terms marked with "+" below =
>     one-electron + hartree + xc + ewald + correction for metals
>
> !    total energy              =   -62.07569469 ryd
>      estimated scf accuracy    <     0.00000799 ryd
>
>      band energy sum           =   -14.82580512 ryd
> +    one-electron contribution =   -98.79712762 ryd
> +    hartree contribution      =    51.10053218 ryd
> +    xc contribution           =   -14.02297161 ryd
> +    ewald contribution        =    -0.34484385 ryd
>       scf in/out correction     =     0.02901784 ryd
> +    correction for metals     =    -0.01128379 ryd
>
> The "one-electron contribution" is the kinetic + ionic term:
>   \sum <psi| T + V_ion | psi>
> The "band energy sum" is exactly what it claims to be:
>   \sum epsilon = \sum <psi| T + V_ion + V_scf | psi>
> The "correction for metals" makes forces and energies
> consistent if a broadening scheme is used.
> The "scf in/out correction" is no longer used
> (and no longer useful)
> The "estimated scf accuracy" gives an estimate of the
> error on the energy due to imperfect self-consistency.
>
> Admittedly, it is slightly confusing.
>
> Paolo
>

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