wrong Spin multiplicity result

[min_gao]

Hi, my question is why a system with odd number of electron can give a singlet state?
Is there a way to solve this incorrect result?

I did both tests for two system with odd number of electrons Co atom and Co complex.
・VASP gave a correct result for Co atom with mag= 3.00, while gave an unreasonable result for Co complex with mag= 0.00
・It is surprisingly that Nupdown = 0, 2, 4 (which is definitely unreasonable for odd number of electrons ) works for both of these two system
・Someone mentioned that is due to size of PAW sphere, especially in a delocalized system. Does anyone can give more detailed information
One set for INCAR, OUTCAR and OSZICAR is attached.

Thank you in Advance,
Min

[fabien_tran1]

Hi,

A few things:

-When an atom is not isolated but surrounded by other atoms it may acquire or loose electrons depending on the type of the surrounding atoms.

-In the case of a finite system like an atom or molecule, it is indeed not possible to obtain a singlet state if the number of electrons is odd. However, in the case of a periodic system the number of electrons is infinite such that "odd" and "even" have no meaning.

-Still, it may be that the magnetic state that is obtained by DFT is not the correct one. DFT is an approximate method and the used exchange-correlation functional may not be the most appropriate one for the system under consideration.

[min_gao]

Dear fabien_tran1,

Thank you for you reply.
I can understand the situation that you mentioned.

I would like to change my question to the following
"why Nupdown = 0, 2, 4 works for an isolated system/atom (non-periodic system) with an odd number of electrons?"

[fabien_tran1]

Hi,

What do you mean with "Nupdown"? Is Nupdown = Nup - Ndown?

[min_gao]

yes, Nupdown is an option in INCAR.
Nupdown = number of spin-up electron minus spin-down electrons
Nupdown = 0 means singlet, 2 is triplet
As my system have odd number of electrons, it means Nupdown should be 1, 3, 5 ....
while vasp can give a result with Nupdown = 0, which is an unreasonable result....

[fabien_tran1]

Ok, I see. I did not know this tag NUPDOWN that fixes Nup-Ndown if specified. Indeed, for an isolated Co atom NUPDOWN=0, 2 or 4 may look strange, but this is technically still possible since the orbitals are allowed to be partially occupied (the occupations are given towards the end of OUTCAR, search for "k-point"). If the calculation is done without fixing NUPDOWN, then the spin moment for an isolated Co atom comes naturally (with PBE) as 3.

Besides, doing a calculation with a fixed spin moment NUPDOWN is quite unusual, I would say.