Dear Prof. Baroni, Thank you so much. It clarified a lot.
Yours, Mohaddeseh On Tue, Aug 2, 2011 at 10:20 PM, Stefano Baroni <baroni at sissa.it> wrote: > > On Aug 2, 2011, at 8:18 AM, mohaddeseh abbasnejad wrote: > > Dear Prof. Baroni > > Thanks again > >> Dear Prof. Baroni >> >> Thanks for your reply. >> I wonder shouldn't the plot show the same frequency for a range of >> displacements? >> >> >> what range? why should it? >> >> > -- Because if we are in the neighberhood of a minimum "where a quadratic > could be fitted", any displacement in that range should result the same > frequency. By displacement, I mean the same pattern but different in > amplitude. > > > who said this? around a minimum, the only thing you can say is that the > Taylor expansion of the energy in powers of the atomic displacements lacks > any linear terms. In general, it has both quadratic terms (which are the one > you are interested in), as well as higher order terms ... No reason why the > Taylor expansion should be *exactly* quadratic (which is what would give > rise to a "same frequency"). Note however, that it is your definition of > frequency that is probably flawed. I suspect that you define the frequency > as the ratio between the energy variation and the square of the > displacement, which obviously depends on the magnitude of the displacement, > if the energy variation is not exactly quadratic. The correct definition, > instead, is the *limit* of that ration when the displacement goes to zero. > That limit is obviously well defined, independently of the magnitude of any > particular distortion that you may consider. > > > >> And the same freq. for the range to be the harmonic frequency? or the >> zero displacement limit, is the harmonic frequency? >> >> >> yes, by definition >> > > See the above discussion > > >> And when I test the displacements with the same amplitude, but different >> in sign (regarding the inward and outward atomic movements in the basis) I >> do not get the same results. >> >> >> why should you? >> >> Shouldn't the plot have symmetry vs. the vertical axis? >> >> >> why? >> > > -- Consider for example a linear chain of atoms, with 2 atoms per basis. > The optical mode is the result of the outward movement of the atoms (The one > in +a/2 moves towards +x and the one in -a/2 moves towards -x). I expect > that if I displace the atoms in an inward movement with the same amplitude > as the outward, I should see the same frequency (The one in +a/2 moves > towards -x and the one in -a/2 moves towards +x) because the 2 patterns > present the same mode, right? That is what I've done in the case of Diamond. > Is my expectation wrong? > > > Yes. If the Taylor expansion of the energy difference vs displacement has > cubic terms (as it usually has, but in very special cases dictated by > symmetry), there is no reason why the energy difference should be even with > respect to energy displacement. Actually, it usually isn't ... > > Hope this clarifies a bit the situation ... > > Take care > SB > > --- > Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste > http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / > stefanobaroni (skype) > > La morale est une logique de l'action comme la logique est une morale de la > pens?e - Jean Piaget > > Please, if possible, don't send me MS Word or PowerPoint attachments > Why? See: http://www.gnu.org/philosophy/no-word-attachments.html > > > > > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum > > -- --------------------------------------------------------- Mohaddeseh Abbasnejad, Room No. 323, Department of Physics, University of Tehran, North Karegar Ave., Tehran, P.O. Box: 14395-547- IRAN Tel. No.: +98 21 6111 8634 & Fax No.: +98 21 8800 4781 Cellphone: +98 917 731 7514 E-Mail: m.abbasnejad at gmail.com Website: http://physics.ut.ac.ir --------------------------------------------------------- -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110803/9523c4fc/attachment-0001.htm
