Zero field splitting
- 1. ZERO-FIELD SPLITTING & KRAMER’S DEGENERACY Compiled by: Yaseen Aziz Roll number: 23609 M.Sc. Chemistry Semester 3rd
- 2. 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.
- 3. CAUSES & MECHANISM : 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 coupling iii. 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.
- 4. 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:
- 5. Odd number Kramer’s degeneracy Magnetic Applies and field if only each level Spi n 1 electron is must remain doubly degener acy present degenerate Even number can be Crystal Crystal field field if more removes the r emoved by spin than 1 unpaired degeneracy completely electron is i.e. non- present degenerate
- 6. 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 transitions are 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 is observed. This system has even number of unpaired electrons. Hence, Kramer’s degeneracy is not operative. That is, each level will not be doubly degenerate.
- 7. 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.
- 8. 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 ion ground state is S6. The zero – field splitting produces three doubly degenerate spin states, namely, mS=+5/2,+3/2,+½ (Kramer ’s degeneracy).
- 9. 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.
- 10. THANK YOU