<br>Dear Prof. Baroni,<br><br>Thank you so much.<br>It clarified a lot.<br><br>Yours,<br>Mohaddeseh<br><br><div class="gmail_quote">On Tue, Aug 2, 2011 at 10:20 PM, Stefano Baroni <span dir="ltr"><<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="word-wrap:break-word"><br><div><div class="im"><div>On Aug 2, 2011, at 8:18 AM, mohaddeseh abbasnejad wrote:</div>
<br><blockquote type="cite">Dear Prof. Baroni<br> <br>Thanks again<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word">
<div><div>
<blockquote type="cite"><div>Dear Prof. Baroni</div>
<div> </div>
<div>Thanks for your reply.</div>
<div>I wonder shouldn't the plot show the same frequency for a range of displacements?<span dir="ltr"> </span></div></blockquote><div><br></div></div>what range? why should it?</div><div><div><br></div></div>
</div></blockquote><div><br style="background-color:rgb(255, 255, 255)"><font style="background-color:rgb(255, 255, 255)">-- 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.</font><br></div></div></blockquote><div><br></div></div>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.</div>
<div><div class="im"><br><blockquote type="cite"><div class="gmail_quote"><div> </div><blockquote class="gmail_quote" style="margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204, 204, 204);padding-left:1ex">
<div style="word-wrap:break-word">
<div><div><blockquote type="cite"><div><span dir="ltr">And the same freq. for the range to be the harmonic frequency? or the zero displacement limit, is the harmonic frequency?</span><br></div></blockquote><div>
<br></div></div>yes, by definition</div></div></blockquote></div></blockquote><div><br></div></div>See the above discussion</div><div><div class="im"><br><blockquote type="cite"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204, 204, 204);padding-left:1ex">
<div style="word-wrap:break-word"><div><div><br><blockquote type="cite"><div>
</div>
<div>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. </div></blockquote><div><br></div></div>why should you?</div><div><div><br><blockquote type="cite"><div>Shouldn't the plot have
symmetry vs. the vertical axis?</div></blockquote><div><br></div></div>why?</div></div></blockquote><div><br><font style="background-color:rgb(255, 255, 255)">-- 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?</font><br style="background-color:rgb(255, 255, 255)"></div></div></blockquote><div><br></div></div>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 ...</div>
<div><br></div><div>Hope this clarifies a bit the situation ...</div><div><br></div><div>Take care</div><div>SB</div><div class="im"><br><div>
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<font size="3"><span style="font-size:12px">Stefano Baroni - SISSA</span></font><font size="3"><span style="font-size:12px"> </span></font><font size="3"><span style="font-size:12px">&</span></font><font size="3"><span style="font-size:12px"> </span></font><font size="3"><span style="font-size:12px">DEMOCRITOS National Simulation Center - Trieste</span></font></div>
<div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font-size:14px"><font size="3"><span style="font-size:12px"><a href="http://stefano.baroni.me/" target="_blank">http://stefano.baroni.me</a> <a href="tel:%5B%2B39%5D%20040%203787%20406" value="+390403787406" target="_blank">[+39] 040 3787 406</a> (tel) -528 (fax) / stefanobaroni (skype)</span></font></div>
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<span style="font-size:14px"><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><font size="3"><span style="font-size:12px">La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget</span></font></div>
<div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><font size="3"><span style="font-size:12px"><br></span></font></div></span></div><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font-size:14px">
<font size="3"><span style="font-size:12px">Please, if possible, don't</span></font><font size="3"><span style="font-size:12px"> </span></font><font size="3"><span style="font-size:12px">send me MS Word or PowerPoint attachments</span></font></div>
<div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font-size:14px"><font size="3"><span style="font-size:12px">Why? See:</span></font><font size="3"><span style="font-size:12px"> </span></font><font color="#0023E9" size="3"><span style="font-size:12px"><a href="http://www.gnu.org/philosophy/no-word-attachments.html" target="_blank">http://www.gnu.org/philosophy/no-word-attachments.html</a></span></font></div>
</div><div><font color="#0023E9" size="3"><br></font></div></span><br>
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<br></blockquote></div><br><br clear="all"><br>-- <br>---------------------------------------------------------<br><br>Mohaddeseh Abbasnejad, <br>Room No. 323, Department of Physics, <br>University of Tehran, North Karegar Ave.,<br>
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