<div dir="ltr"><p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span style="font-size:12pt;font-family:Arial,sans-serif">Dear </span><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Pratik,</span><span style="font-size:12pt;font-family:'Times New Roman',serif"></span></p>


<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Within the QHA you must do calculations in
constant volume. Therefore, it is straightforward to calculate the Helmholtz
free energy.  </span><span style="font-size:12pt;font-family:Arial,sans-serif">To calculate the Gibbs
free energy you must know the pressure. To calculate the pressure you must
calculate several volumes. You can calculate the </span><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Helmholtz free energy</span><span style="font-size:12pt;font-family:Arial,sans-serif"> at several volumes in some temperature and use the fact that
the pressure is minus the partial derivative of the </span><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Helmholtz free energy</span><span style="font-size:12pt;font-family:Arial,sans-serif"> with respect to the volume (to do so, you can
fit the </span><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Helmholtz free energy</span><span style="font-size:12pt;font-family:Arial,sans-serif"> to some analytical function, e.g. parabola of
Birch–Murnaghan equation of state). </span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif"></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">In addition, I want to
mention a few things:</span></p>

<p class="" style="margin:0cm 0cm 0.0001pt 36pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">1.<span style="font-size:7pt;font-family:'Times New Roman'">    </span></span><span dir="LTR"></span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">Recently,
a bug in the QHA has been corrected in several structures. It is corrected in
the SVN version. </span></p>

<p class="" style="margin:0cm 0cm 0.0001pt 36pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">2.<span style="font-size:7pt;font-family:'Times New Roman'">    </span></span><span dir="LTR"></span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">In
this approach, you must work with hydrostatic pressure. To do so, you need to
do relaxation.</span></p>

<p class="" style="margin:0cm 0cm 0.0001pt 36pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">3.<span style="font-size:7pt;font-family:'Times New Roman'">    </span></span><span dir="LTR"></span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">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. </span></p>

<p class="" style="margin:0cm 0cm 0.0001pt 36pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">4.<span style="font-size:7pt;font-family:'Times New Roman'">    </span></span><span dir="LTR"></span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">There
is also a thermal electronic contribution to both </span><span style="font-size:12pt;font-family:Arial,sans-serif;color:black">Helmholtz free energy</span><span style="font-size:12pt;font-family:Arial,sans-serif"> and Gibbs free energy. In most cases, it is
very small relative to the </span><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">phonon contribution, but you cannot know
for sure until you calculate it. To calculate it, you need to calculate the
electron DOS with dos.x. </span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">I hope I helped.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">Uri Argaman</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">Ben-Gurion University</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;direction:ltr"><span lang="EN" style="font-size:12pt;font-family:Arial,sans-serif">Israel </span></p></div>