[Pw_forum] Gibbs Free energy

Uri Argaman argamanu at post.bgu.ac.il
Sat Apr 5 16:48:35 CEST 2014

Dear Pratik,

Within the QHA you must do calculations in constant volume. Therefore, it
is straightforward to calculate the Helmholtz free energy.  To calculate
the Gibbs free energy you must know the pressure. To calculate the pressure
you must calculate several volumes. You can calculate the Helmholtz free
energy at several volumes in some temperature and use the fact that the
pressure is minus the partial derivative of the Helmholtz free energy with
respect to the volume (to do so, you can fit the Helmholtz free energy to
some analytical function, e.g. parabola of Birch-Murnaghan equation of

In addition, I want to mention a few things:

1.    Recently, a bug in the QHA has been corrected in several structures.
It is corrected in the SVN version.

2.    In this approach, you must work with hydrostatic pressure. To do so,
you need to do relaxation.

3.    The pressure you see in the SCF output file is the pressure at zero
Kelvin without phonon zero point energy contribution. It is not the
pressure at non zero temperatures.

4.    There is also a thermal electronic contribution to both Helmholtz
free energy and Gibbs free energy. In most cases, it is very small relative
to the phonon contribution, but you cannot know for sure until you
calculate it. To calculate it, you need to calculate the electron DOS with

I hope I helped.

Uri Argaman

Ben-Gurion University

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