Zero field splitting

ZERO-FIELD SPLITTING & KRAMER’S DEGENERACY

Compiled by: Yaseen Aziz

Roll number: 23609

M.Sc. Chemistry

Semester 3rd

Zero–field splitting :-

The splitting of spin levels even in the absence of magnetic field is called zero–field splitting.Occurs mainly in in transition metal complexes where there are more than one unpaired electrons.

Removes the degeneracy of transitions and more transitions are observed than expected , in the presence of external magnetic field.Fine structure in ESR spectrum is obtained.

Dipolar interactions among electrons:i. In a d2 system, S=1 both electrons

being parallel. Since each spin produces a small magnetic field in the vicinity of its partner. The dipolar interactions for mS=+1 and mS=-1 or same and mS=0 has different dipolar interaction than +1 or -1 states. Thus -1 and +1 mS states are raised than mS=0 state.

ii. Spin orbit couplingiii. A strong internal electric field

which results in the perturbations to the energy levels of mS=+1 and -1 states but not of mS=0 state.

CAUSES & MECHANISM :

Kramer’s degeneracy /Rule :

Crystal field lifts the spin degeneracy of two or more unpaired electrons in a complex due to electrostatic interactions (ZFS).

When the species contains an odd number of unpaired electrons, the spin degeneracy of every level remains doubly degenerate. This is known as Kramer’s degeneracy.

When the number of  unpaired electrons is even, crystal field may remove the spin degeneracy entirely.

This can be schematically represented as follows:

Spin degeneracy can be removed

byCrystal

field if more than 1

unpaired electron is present

Odd numberKramer’s

degeneracy Applies and each level

must remain doubly

degenerate Even numberCrystal field removes the

spin degeneracy completely

i.e. non-degenerate

Magnetic field if only 1 electron is

present

Some examples :1. In a d2 system with two unpaired electrons, S = +½ + ½ = 1.Therefore, ms= -1, 0, +1. In the absence of zero – field splitting, two transitionsare possible as shown below:

The first transition is ms= 0 to +1 and the second transition is ms= -1 to 0. These transitions have equal energy (i.e. degenerate) and only one signal isobserved. This system has even number of unpaired electrons. Hence, Kramer’s degeneracy is not operative. That is, each level will not be doubly degenerate.

If zero – field splitting is present, it removes the degeneracy in mS as shown below:

zero-field splitting

Subsequent magnetic field splits the levels further as shown below :

Here, two transitions are not degenerate. 2 peaks =>ZFS present, 1 peak =>ZFS absent.

2. In a d5 system like Mn(2+), there is an odd number of unpaired electrons.So, Kramer’s degeneracy is operative here. The term symbol for the free ionground state is S6. The zero – field splitting produces three doubly degenerate spin states, namely, mS=+5/2,+3/2,+½ (Kramer ’s degeneracy).

Consequences of ZFS : Large ZFS => transitions fall out of the microwave

region. e.g. In V(3+)mS= 0 to mS= +1 transition is not observed. However, a weak transition between mS= +1 and mS= -1 has been observed (forbidden). Number of peaks observed in the spectrum is more.

The spectrum becomes much more complex when hyperfine splitting is also incorporated.

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