[Pw_forum] Hubbard force discrepancies

[Dmitry Novoselov]

Dear prof. Cococcioni and prof. Gironcoli,

I am deeply grateful for the detailed explanation. Now it's clear for me.

Thank you!

2014-10-23 15:09 GMT+06:00 Matteo Cococcioni <matteo at umn.edu>:

>
> Dear Dmitry,
>
> what you describe is probably true for all the components of the forces,
> not just the Hubbard one. The reason is that the Hellmann-Feynman theorem,
> used to compute the forces printed in the output, only applies to the total
> energy, not to its separate components. In fact, the electronic wave
> functions used in the calculation of the matrix elements are eigenstates of
> the whole Hamiltonian, not of its pieces.
> Of course, the code still compute the forces "piece by piece". So each of
> those term is "wrong" (in the sense it does not equal the derivative of the
> corresponding term of the energy) but when you sum them up together, these
> errors cancel each other and you get the right force.
>
>
> Regards,
>
> Matteo
>
>
>
>
> On Thu, Oct 23, 2014 at 10:24 AM, Dmitry Novoselov <dnovoselov at gmail.com>
> 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 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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>
>
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-- 

*Best regards,*


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