[Pw_forum] internal energy

[Stefano Baroni]

On Mar 25, 2010, at 4:16 PM, Jiayu Dai wrote:

> Dear all,
> 
> I found in the previous discussion that the energy in PWscf using Fermi-Dirac smearing is the free energy.

It is *NOT* any free energy of any physical system. It can be interpreted as the free energy of a system of electrons in the field of clamped nuclei, at the *fictitious* temperature corresponding to the smearing you use. The reason why this concept is useful is that the free energy is variational, while the internal energy is not. That's why Hellman-Feynman forces are derivatives of the free energy, but not of the internal energy.

> Is it the total free energy including electrons and ions contribution?

As said, electrons only.

> Furthermore, how to get the internal energy here? The kinetic energy is easy to calculate, but how about the potential energy?

You do not need any internal energy. what you may actually want to estimate is the T->0 extrapolation of both the free and internal energies (which coincide in the T->0 limit). I think that some estimate of this are available in the pw output, but others may know more than me about this.

Stefano B

> 
> Thanks a lot.
> 
> Jiayu
> ----------------
> -------------------------------------------
> Jiayu Dai
> Department of Physics
> National University of Defense Technology, 
> Changsha, 410073, P R China
> -----------------------------------------
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
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