In the specific case of the O2 molecule, in a molecular orbital picture O2 has two degenerate pi-star HOMO orbitals that need to be filled with 2 electrons. The ground state is a triplet S=1 (up,up), (up,down)+(down,up),(down,down), the next state is a singlet (up,down)-(down,up). A good representation of the triplet should be given by the ground state of a spin-polarized calculation. The ground state should have nup-ndown=2, and the two unpaired electrons fill the two pi-star orbitals (with the same spin). I believe you don't need to impose any symmetry to find this ground state. If you force the system to have total spin=0 (in a spin-polarized calculation), you should obtain the state (up,down) (or its degenerate counterpart (down,up)). This state does not satisfy the correct symmetry of the 2-electron wfc, so in principle does not correspond to any of the correct many-electron states above. However this spurious state can be expressed as a linear combination (sum or difference) of one of the triplet states ((up,down)+(down,up)) and the singlet state ((up,down)-(down,up)). Perhaps its energy corresponds to the average energy of the triplet and the singlet??!?
Best regards Sandro On 06/12/2010 09:45, Stefano de Gironcoli wrote: > Nicola Marzari wrote: >> I've never managed to get from anyone, including some of the luminaries >> in the fundamentals of DFT, a clear answer to which solution is the >> "correct" one. Note that even with nosym=.true. you ahve the option >> of having occupation 2.0 on 2 of the p orbitals, or occupation >> 1.3333333 on oeach of the 3 p orbitals - the latter solution >> would probably be similar to the symmetrized solution (but shouldn't >> be identical). >> > I think there's no general consensus whether it's "more correct" to have > the lowest possible energy giving up the known symmetry of the true GS > or to constraint the system to the expected symmetry accepting a > slightly higher energy... Of course the "true" xc functional would not > put you in this dilemma, but while awaiting for it, I think the > important thing is to be aware of the two alternatives and clearly state > which one one chooses to conpare with. > > stefano > > > >> nicola >> >> >> >> On 12/3/10 5:27 PM, elbuesta at icqmail.com wrote: >> >>> Dear all, >>> >>> I recently evaluated with PW the binding energy of a O2 molecule using >>> the regular ultra-soft PP from the webpage. I noticed that the energy >>> obtained could be 5.7eV or 6.7eV depending if the flag "nosym=.true." is >>> used or not in the energy evaluation of the isolated oxygen atom. I >>> would like to know if anyone could help me understand why such a large >>> difference is obtained for this system, since for many other systems >>> (such as metals) the inclusion of "nosym=.true." for the isolated atom >>> do not affect so much (or not at all) the value of the binding/cohesive >>> energy. >>> >>> >>> Thanks very much for your time, and all best for all! >>> >>> Fabio Negreiros >>> IPCF - CNR, Pisa - Italia >>> >> >> > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum > -- Sandro Scandolo -- http:/www.ictp.it/~scandolo
