When considering the effect of magnetic field into the terms resulted from LS (orbital spin) coupling each term splits into 2J'+1 and the separation between two levels = gJmBB0 (gJ is is Lande' Splitting Constant, mB= Bohr Magenaton and B0 is the magnetic field. This is significant in ESR experiment is it can show hyperfine splitting in ESR signal.

e.g.

3F2   splits into 5 levels 2J'+1 = 5 ; and the separation between each is as given above.

If the separation between J levels is large then:

meff = gJ√J(J+1)

Where gJ = 1 + {[S(S+1)–L(L+1)+J(J+1)]/2J(J+1)}

Eq. 20.20

gj is Landé Splitting Factor

Strictly this applies to free-ion energy levels and gives good meff values for lanthanoid ions with l ≈1000 cm-1).

I hope this will help. Check Inorganic Chem Housecroft.

Dear Shivaji,

Further to Mohammed's point. In EPR spectroscopy

g= 2 [1 - alpha.k.lambda/DeltaE]

lambda is the spin orbit coupling constant. It scales as Z^4 so is small for light atom structures and increases for TM and is large for lanthanides.

Notably lambda is negative for more than half filled shells so g > ge. Conversely lambda is positive for less than half filled shells so lambda < 2.

alpha depends on the electronic configuration and DeltaE reflects the energy gap to higher lying d(or f) orbitals which contribute to orbital angular momentum.

On descending a group of TM lambda increases and the crystal field splitting Delta(oct) increases but lamda increases faster as it scales as Z^4.