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<div class="moz-cite-prefix">Dear Dmitry,<br>
the total force che be calcualted from the unperturbed wfcs
due to Hellmann-Feynman theorem that relies on the fact that total
energy satisfy a variational principle.<br>
no variational principle is defined for a component of the
energy (Hubbard, Hartree , XC, Kinetic ...) therefore you can't
calculate their derivatives from the unperturbed wfcs only.<br>
<br>
stefano<br>
<br>
On 10/23/2014 10:24 AM, Dmitry Novoselov wrote:<br>
</div>
<blockquote
cite="mid:CAAruPGXdAw42COvgwW=Fw3+vYonHUxxkq5VmGWN__geEGG2vJw@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>Dear all,<br>
<br>
</div>
I have performed the set of <span class="" id=":20p.1"
tabindex="-1" style="">LSDA</span>+U calculations to determine
the Hubbard forces acting on Ni atom in a <span lang="en"><span>well-known
<span class="" id=":20p.2" tabindex="-1" style="">NiO</span>.<br>
</span></span>
<div>
<div>For this purpose I was displacing one Ni atom in the
x-direction up to 0.1 angstroms with 0.025 angstroms step.</div>
<div><br>
</div>
<div>How we know a force may be evaluate like:<br>
<div style="margin-left:40px">$F_{\alpha i} =
-\frac{\partial E}{\partial \tau_{\alpha i}}$.<br>
</div>
</div>
<div>That allows us to calculate a force by <span lang="en"><span>taking</span>
a<span> numerical derivative of the energy </span></span><span
lang="en">with respect to the displacement $</span><span
lang="en">\tau_{\alpha i}$ by least square approximation
for example.</span></div>
<div><span lang="en"><br>
</span></div>
<div><span lang="en">If I make it for the total energy (see
total_energy.<span class="" id=":20p.3" tabindex="-1"
style="">eps</span>) I get a good agreement between
analytical </span>(x-component for the displaced Ni atom)
and numerical value of the total force (see total_force.<span
class="" id=":20p.4" tabindex="-1" style="">eps</span>).</div>
<div><span lang="en">But if I repeat it for the Hubbard energy
(see <span class="" id=":20p.5" tabindex="-1" style="">hubbard</span>_energy.<span
class="" id=":20p.6" tabindex="-1" style="">eps</span>)
I get some discrepancy expressed in the mismatch between
analytical (x-component for the displaced Ni atom) and
numerical value of the Hubbard force (</span>see <span
class="" id=":20p.7" tabindex="-1" style="">hubbard</span>_force.<span
class="" id=":20p.8" tabindex="-1" style="">eps</span>)
with -0.5 factor (see expected_<span class="" id=":20p.9"
tabindex="-1" style="">hubbard</span>_force.<span class=""
id=":20p.10" tabindex="-1" style="">eps</span>).</div>
<div><br>
</div>
<div>What can be the reason for this discrepancy?<br>
</div>
<div><br>
</div>
<div>Thank you!</div>
<div><br>
</div>
<div>P.S.</div>
<div>The values of the energy and forces (x-component for the
displaced Ni atom) obtained during the <span class=""
id=":20p.11" tabindex="-1" style="">LSDA</span>+U
calculation respect to the displacement of one Ni atom in
the x-direction are contained in the attached file result.<span
class="" id=":20p.12" tabindex="-1" style="">dat</span>. <br>
</div>
<div><br>
</div>
<div>-- <br>
<div dir="ltr">
<p><b><i><span
style="border-collapse:collapse;color:rgb(51,51,51);font-family:arial,sans-serif;font-size:13px;font-style:normal;font-weight:normal"></span></i></b></p>
<div><i><span
style="border-collapse:collapse;color:rgb(51,51,51);font-family:arial,sans-serif;font-size:13px"><i>Best
regards,</i></span></i><br>
</div>
<div><i><span style="border-collapse:collapse"><i
style="color:rgb(51,51,51);font-family:arial,sans-serif;font-size:13px">Dr.
<span class="" id=":20p.13" tabindex="-1" style="">Dmitry</span>
<span class="" id=":20p.14" tabindex="-1" style="">Novoselov</span></i><br>
<br>
<font color="#333333" face="arial, sans-serif">Institute
for Metal Physics,</font></span></i></div>
<div><i><span style="border-collapse:collapse"><font
color="#333333" face="arial, sans-serif">Yekaterinburg,
Russia</font></span></i></div>
</div>
</div>
</div>
</div>
<br>
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<br>
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