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*
expected_hubbard_force.eps
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hubbard_energy.eps
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hubbard_force.eps
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result.dat
Description: Binary data
total_energy.eps
Description: PostScript document
total_force.eps
Description: PostScript document
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