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 <[email protected]>: > > 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 <[email protected]> > 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* >> >> >> _______________________________________________ >> Pw_forum mailing list >> [email protected] >> http://pwscf.org/mailman/listinfo/pw_forum >> > > > _______________________________________________ > Pw_forum mailing list > [email protected] > http://pwscf.org/mailman/listinfo/pw_forum > -- *Best regards,* *Dr. Dmitry NovoselovInstitute for Metal Physics,* *Yekaterinburg, Russia*
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