<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV><BR class="khtml-block-placeholder"></DIV>Dear Cyrille<DIV><BR class="khtml-block-placeholder"></DIV><DIV>let me add last comments too and ask few questions.<BR> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "></SPAN><DIV><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><BR class="Apple-interchange-newline"></SPAN> </DIV><BR><DIV><DIV>On Nov 22, 2007, at 7:30 AM, Cyrille Barreteau wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">A final comment concerning this tricky problem.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I think I got the reason of my troubles.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I have two scf solutions:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">1) one that (almost) satisfies the symmetry of the real dimer</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and for which xy and x^2-y^2 eigenfunctions are degenerate.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">However this solution has the bad idea of having an unfilled homo</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">state.</DIV></BLOCKQUOTE><DIV><BR class="khtml-block-placeholder"></DIV><DIV>I think this is the same bad idea of e.g. transition metal oxides that turn out to be metals (instead of insulators) in DFT.</DIV><DIV>The difference is that in your case you don't have a particular reason to suppose that the electron should instead</DIV><DIV>be localized on one of the degenerate states, while in a crystal you may appeal to crystal field, symmetry etc.</DIV><DIV>Are the degenerate xy and x^2-y^2 orbitals part of the unfilled homo? if so, do you get one of them above the "Fermi energy" and one below</DIV><DIV>when you get the other, lower energy solution? If this is true I think that you would obtain the same energy with the two states</DIV><DIV>inverted (the one that was above ef goes below and vice versa). Can you check this?</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>I agree with Stefano in general and prefer the broken symmetry solution. I think this gives you the "right" (of course in a DFT sense) energy.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>However I don't feel completely confident about the fact that you can obtain it just with nosym = true and placing the molecule in a generic </DIV><DIV>orientation w r t the cell. Your ground will still have the symmetry of the fake crystal that you construct (even f you don't impose it) </DIV><DIV>unless a broken symmetry solution exists.</DIV><DIV>I guess my question is: is the numerical noise produced in the diagonalization (and of course not washed out by the imposing of the symmetry) </DIV><DIV>always enough for the code to recognize a broken symmetry solution and to choose it? I'm not sure.</DIV><DIV>In your case I would feel more confident simulating a "supercell" with few molecules randomly oriented wrt each other. This would be</DIV><DIV>a more faithful simulation of the gas phase you are probably thinking of than the fake crystal you are using. Of course this will be more expensive though...</DIV><DIV>Maybe the answer to this doubt of mine is trivial. Does anybody have more clear ideas than mine on how to avoid symmetry?</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Regards,</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Matteo</DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">2) an other that do not satisfy the symmetry of the real dimer</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(but of course satisfy the symmetry of the crystal) since a</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">rather large spitting of xy and x^2-y^2 is observed.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The second solution is the most stable for reasons related</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">to the so called Jahn-Teller effect. There is no true Jahn</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Teller distorsion but the dissymetrization of xy and x^2-y^2</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">leads to a splitting of levels that decreases energy....</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">bad luck!</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I guess this problem will disappear if I add spin-orbit coupling</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">since it will induce splittings and the (bad) chance to have</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">an unfilled homo state is smaller.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">that's all folks.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-converted-space"> </SPAN>cyrille</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">==================================================================</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Cyrille Barreteau<SPAN class="Apple-converted-space"> </SPAN>| phone : +33 (0)1 69 08 29 51</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">CEA Saclay <SPAN class="Apple-converted-space"> </SPAN>| fax <SPAN class="Apple-converted-space"> </SPAN>: +33 (0)1 69 08 84 46</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">DSM/DRECAM/SPCSI <SPAN class="Apple-converted-space"> </SPAN>| email <A href="mailto:cyrille.barreteau@cea.fr">cyrille.barreteau@cea.fr</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Batiment 462 <SPAN class="Apple-converted-space"> </SPAN>|</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">91191 Gif sur Yvette Cedex<SPAN class="Apple-converted-space"> </SPAN>FRANCE</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-converted-space"> </SPAN>~~~~~~~~~~~~~~~~~~~~~~~~</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://www-drecam.cea.fr/Images/Pisp/cbarreteau/cbarreteau_fr.html">http://www-drecam.cea.fr/Images/Pisp/cbarreteau/cbarreteau_fr.html</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">==================================================================<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Matteo Cococcioni</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Department of Chemical Engineering and Materials Science</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">University of Minnesota</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">151 Amundson Hall</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">421 Washington Av. SE</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Minneapolis, MN 55455</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Tel. +1 612 624 9056 Fax +1 612 626 7246</DIV></BLOCKQUOTE><BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</DIV></BLOCKQUOTE></DIV><BR></DIV></BODY></HTML>