Wave function for ionized iron?

[Joqe]

Hi.
Suppose that you want to fint the wave function for ionized iron which have the electron configuration 1s2 2s2 2p6 3s2 3p6 3d6

And suppose that the LS-coupling scheme gives accuret enouhgt description och the energy levels.

Paulis exclusion principle and Hunds rule gives then that the lowest term is 5D (notation of LS-coupling).

Then we know then that S=2, how do we construct the total wave function?

What do we know about the wave function for the spin, I mean tripplet, dubblet, singlet, symmetric or anti-symmetric?

With regards
/Joqe

 

[NateD]

The total wave function is constructed by multiplying the spatial wave function (which describes the motion of the electrons in space) with the spin wave function (which describes the spin of the electrons). The spin wave function depends on the configuration of the electrons. In the case of the 5D configuration, there are two electrons in the same orbital. According to the Pauli Exclusion Principle and Hund's Rule, these two electrons must have opposite spins (i.e. a spin singlet). Therefore, the spin wave function for this configuration is a symmetric combination of the two spin states: |Ψspin> = 1/√2(|↓↑> + |↑↓>) where |↓↑> and |↑↓> denote the spin states of the two electrons.