[Pw_forum] Hubbard force discrepancies

[stefano de gironcoli]

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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