Dear Dmitry,
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.
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.
stefano
On 10/23/2014 10:24 AM, Dmitry Novoselov wrote:
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 anumerical 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 Novoselov/
Institute for Metal Physics,/
/Yekaterinburg, Russia/
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