[Pw_forum] Oxygen molecule binding energy

[Sandro Scandolo]

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
>>>
>>
>>
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-- 
Sandro Scandolo -- http:/www.ictp.it/~scandolo