[Pw_forum] Hubbard force discrepancies

[Matteo Cococcioni]

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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