Could a fractional spin number be possible

[jianmin]

Dear all and especially Prof. Graeme,

I was trying to calculate the spin charge density of the monomer of a homogeneous catalyst, the ball-and stick structure of which is as in the attachment. The atom in dark yellow and in the center is iron (Fe), linking to two ligands.

After a single-point energy calculation and issuing three commands:
chgsum.pl AECCAR0 AECCAR2
chgsplit.pl CHGCAR
bader CHGCAR_mag -ref CHGCAR_sum
I have got the spin numbers of all atoms of the system.

Oddly, the spin number for Fe atom is calculated to be 3.4991. Does it mean that the Fe atom has 3.5 unpaired electrons? Is it meaningful physically? Or is there anything wrong with my INCAR settings?

[graeme]

That seems ok to me.

[jianmin]

Prof. Graeme, Thanks.

Since it is okay to you, if it was you to report the spin number in a paper, what would you write ? 3.5 ? Isn't a spin number always an integer?

[graeme]

It's true that the total spin will be an integer, but the integrated spin around an atom does not need to be.

This is similar to the charge of an atom. We typically think about formal (integer) charges, but in reality electrons do not completely localize on atoms in the solid state.

[jianmin]

Thanks Prof. Graeme ! Lesson learned.