[Pw_forum] Hubbard force discrepancies

[Dmitry Novoselov]

Dear all,

I have performed the set of LSDA+U calculations to determine the Hubbard
forces acting on Ni atom in a well-known NiO.
For this purpose I was displacing one Ni atom in the x-direction up to 0.1
angstroms with 0.025 angstroms step.

How we know a force may be evaluate like:
$F_{\alpha i} = -\frac{\partial E}{\partial \tau_{\alpha i}}$.
That allows us to calculate a force by taking a numerical derivative of the
energy with respect to the displacement $\tau_{\alpha i}$ by least square
approximation for example.

If I make it for the total energy (see total_energy.eps) I get a good
agreement between analytical (x-component for the displaced Ni atom) and
numerical value of the total force (see total_force.eps).
But if I repeat it for the Hubbard energy (see hubbard_energy.eps) I get
some discrepancy expressed in the mismatch between analytical (x-component
for the displaced Ni atom) and numerical value of the Hubbard force (see
hubbard_force.eps) with -0.5 factor (see expected_hubbard_force.eps).

What can be the reason for this discrepancy?

Thank you!

P.S.
The values of the energy and forces (x-component for the displaced Ni atom)
obtained during the LSDA+U calculation respect to the displacement of one
Ni atom in the x-direction are contained in the attached file result.dat.

-- 

*Best regards,*


*Dr. Dmitry NovoselovInstitute for Metal Physics,*
*Yekaterinburg, Russia*
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