1. APPLICATIONS OF
ESR
TO
METAL COMPLEXES
V.SANTHANAM
DEPARTMENT OF CHEMISTRY
SCSVMV

2. METAL COMPLEXES – A SURVEY
 Metal complexes are important- Diverse biological
roles
 Griffiths and Owen proved the M-L covalency by
taking complexes (NH4)2[IrCl6] and Na2[IrCl6]
 The hyperfine splitting by Chloride ligands showed
the covalent nature of M-L bond

3.  Proved the back donation (pi-bonding) concept
 With the ESR data they were able to calculate ξ,ζ
and λ of metal ions and the extent of delocalization
 In metal complexes the above said parameters
were having lower values than the free metal ions.

4. THINGS TO BE CONSIDERED
 Nature of the metal
 Number of ligands
 Geometry
 No of d electrons
 Ground term of the ion

5.  Electronic degeneracy
 Inherent magnetic field
 Nature of sample
 Energy gap between g.s and e.s
 Experimental temperature

6. NATURE OF THE METAL ION
 Since d metal ions have 5 d orbitals situations are
complicated
 But the spectra are informative
 In 4d and 5d series L-S / j-j coupling is strong
making the ESR hard to interpret

7.  Crystal field is not affecting the 4f and 5f e- so the
ESR spectra of lanthanides and actinides are
quite simple.
 If ion contains more than one unpaired e- ZFS may
be operative

8. GEOMETRY OF THE COMPLEX
 Ligands and their arrangement –CFS
 CFS in turn affect the electronic levels hence the
ESR transitions
 The relative magnitude of CFS and L-S coupling is
giving three situations.

9.  If the complex ion is having cubic symmetry
(octahedral or cubic) – g is isotropic
 Complexes with at least one axis of symmetry
show two g values
 Ions with no symmetry element will show three
values for g.

10. SYSTEM WITH AN AXIS OF SYMMETRY NO SYMMETRY

11.  Symmetry of the complex ion- important – why?
 ESR is recorded in frozen solutions
 Spins are locked
 Lack of symmetry influences the applied field
considerably.

12.  Spin Hamiltonian of an unpaired e- if it is present in a
cubic field is
H = g β | Hx.Sx + Hy.Sy + Hz.Sz|
 If the system lacks a spherical symmetry and possess at
least one axis ( Distorted Oh,SP or symmetric tops) then
H = β |gxx Hx.Sx +gyy Hy.Sy + gzz Hz.Sz|
 Usually symmetry axis coincides with the Z axis and H is
applied along Z axis then
gxx = gyy = gL ; gzz = g||

13.  If crystal axis is not coinciding with Z axis
 The sample is rotated about three mutually
perpendicular axis and g is measured.
 g is got by one of the following relations
for rotation about
X axis - g2 = gyy2Cos2θ + 2gyz2 Cos2θ Sin2θ +gzz2 Sin2θ
Y axis - g2 = gzz2Cos2θ + 2gzx2 Cos2θ Sin2θ +gxx2 Sin2θ
Z axis - g2 = gyy2Cos2θ + 2gxy2 Cos2θ Sin2θ +gyy2 Sin2θ

14. NUMBER OF d ELECTRONS
 Magnetically active nucleus cause hyperfine
splitting.
 If more than one unpaired e- present in the ion,
more no of transitions possible leads to fine
structure in ESR spectrum.
 Here we have to consider two things
Zero field splitting – due to dipolar interaction
Kramer’s degeneracy

15. ZERO FIELD SPLITTING
 Considering a system
with two unpaired e-s
 Three combinations
S = +1
possible
 In absence of external
∆E2
field all three states are
S=0
having equal energy
∆E1  With external field three
S = -1 levels are no longer
with same energy.
 Two transitions
H≠0 possible; both with
ZFS = 0 same energy

16.  SPLITTING OF ELECTRONIC LEVELS EVEN IN
ABSENCE OF EXTERNAL MAGNETIC FIELD IS
CALLED ZERO FIELD SPLITTING (ZFS)
 The splitting may be assisted by distortion and L-S
coupling also.

17.  When there is a strong dipolar interaction the +1 level
is raised in energy –Dipolar shift (D)
 This dipolar shift reduces the gap between S = -1 and
S = 0 state
 Now the two transitions do not have same energy
 Results in two lines

18. EFFECT OF DIPOLAR SHIFT
Ms = +1 D
Ms = ±1
∆E1 = ∆E2
Ms = ±1,0
Ms = 0 Ms = 0
D
Ms = -1
ZFS = 0

19. KRAMER’S THEOREM
 Systems with even no. of unpaired e-s will contain
a state with S = 0
 But in the case of odd e- s no state with S = 0
since Ms = ½
 In such cases even after ZFS the spin states with
opposite Ms values remain degenerate which is
called Kramer’s degeneracy

20.  The levels are called Kramer’s doublets
 “ IN ANY SYSTEM WITH ODD NUMBER OF
UNPAIRED e-s THE ZFS LEAVES THE GROUND
STATE AT LEAST TWO FOLD DEGENERATE ”

21. EFFECT OF ZFS ON Mn(II)
+5/2
±5/2 +3/2
6
S +1/2
±3/2
±1/2 - 1/2
FREE ZFS AND RESULTING - 3/2
ION KRAMER’S DOUBLETS
- 5/2

22. CONSEQUENCES OF ZFS
 Insome cases ZFS magnitude is very high
than the splitting by external field.
 Then transitions require very high energy
 Some times only one or no transitions occur.
 Examples V3+ and Co2+

23. EFFECTIVE SPIN STATE - Co(II)
 Co(II) in cubic field has a ground term of 4F.Since it is a
d8 system it have ±3/2 and ±1/2 levels.
 ZFS splits the levels by 200 cm-1
 Since the energy gap is higher only the transition -1/2
to + 1/2 is seen.
 So it appears as if Co(II) has only one unpaired e-
(Effective spin S’ = ½)

24. +3/2
±3/2
- 3/2
±3/2,
±1/2 ≈ 200 cm-1
+1/2
±1/2 ONLY
OBS.TRANSITION
-1/2

25. BREAK DOWN OF
SELECTION RULE
 In some cases like V(III) the magnitude of ZFS very
high.
 It exceeds the normal energy range of ESR transitions
 Normal transitions occur with ∆Ms = ±1 . But its energy
exceeds the microwave region
 Then the transition from -1 to +1 levels with ∆Ms = ±2
occurs ,which is a forbidden one

26. +1
FORBIDDEN
Ms= ±1
TRANSITION
-1
Ms = 0, ±1
NOT OCURRING
Ms =0
0

27. MIXING OF STATES
 The magnitude of ZFS can be taken as originating
from CFS.
 But orbitally singlet state 6S is not split by the
crystal field even then Mn(II) shows a small
amount of ZFS.
 This is attributed to the mixing of g.s and e.s
because of L-S coupling

28.  The spin – spin interaction is negligible.
 But for triplet states spin – spin terms are
important and they are solely responsible for ZFS
 Naphthalene trapped in durene in diluted state
shows two lines as if it has ZFS.
 Since there is no crystal field or L-S coupling this
is attributed to spin – spin interaction of the πe- s
in the excited triplet state

29. ESR AND JAHN-TELLER DISTORTION
 Jahn – Teller theorem :
Any non-linear electronically
degenerate system is unstable, hence it will
undergo distortion to reduce the symmetry,
remove the degeneracy and hence increase its
stability.
 But this theorem does not predict the type of
distortion
 Because of J-T distortion the electronic levels are
split and hence the number of ESR lines may
increase or decrease.

30. FACTORS AFFECTING
THE g-VALUES
 Operating frequency of the instrument
 Concentration of unpaired e-
 Ground term of the metal ion present
 Direction and temperature of measurement
 Lack of symmetry
 Inherent magnetic field in the crystals
 Jahn – Teller distortion
 ZFS

31. SUSTAINING EFFECT
 The g value for a gaseous atom or ion for which L-S
coupling is applicable is given by
g = 1 +[J(J+1) + S(S +1) – L(L+1)] / 2J(J+1)
 For halogen atoms the g values calculated and
experimental are equal.
 But for metal ions it varies from 0.2 -8

32.  The reason is the orbital motion of the e- are
strongly perturbed by the crystal field.
 Hence the L value is partially or completely
quenched
 In addition to this ZFS and J-T distortion may also
remove the degeneracy

33.  The spin angular momentum S of e- tries
to couple with the L
 This partially retains the orbital
degeneracy
 The crystal field tries to quench the L
value and S tries to restore it
 This phenomenon is called sustaining
effect

34.  Depending upon which effect dominate the L value
deviates from the original value
 So L and hence J is not a good quantum number
to denote the energy of e- hence the g value also

35. COMBINED EFFECT OF CFS AND L-S COUPLING
 Three cases arise depending upon the relative
magnitudes of strength of crystal field and L-S
coupling
L-S coupling >>CFS
CFS > L-S coupling
CFS >> L-S coupling

36. L-S COUPLING >>CFS
 When L is not affected much by CFS, then J is
useful in determining the g value
 Example rare earth ions
 4f e- buried inside so not affected, g falls in
expected region
 All 4f and 5f give agreeing results other than
Sm(III) and Eu(III)

37. CFS > >L-S COUPLING
 IfCFS is large enough to break L-S
coupling then J is not useful in determining
g.
 Now the transitions are explained by the
selection rule and not by g value
 The magnetic moment is given by
μs = [n(n+2)] 1/2

38.  All 3d ions fall in this category.
 Systems with ground terms not affected by CFS ie
L=0 are not affected and the g value is close to
2.0036
 There may be small deviations because of L-S
coupling, spin – spin interaction and gs and es
mixing

39. CFS >> L-S COUPLING
 In strong fields L-S coupling is completely broken and
L= 0 which means there is covalent bonding.
 Applicable to 3d strong field , 4d and 5d series.
 In many cases MOT gives fair details than CFT.

40. Example1: Ni (II) in an Oh field
 For Ni(II) g calculation includes mixing of 3A2g(g.s)
and 3T2g(e.s)
g = 2 – [8λ/10Dq]
 For Ni (II) the g value is 2.25 hence 8λ/10 Dq must
be - 0.25
 From the electronic spectrum 10Dq for Ni(II) in an
Oh field is known to be 8500 cm-1,λ is -270 cm-1

41.  For free Ni(II) ion the λ is about -324 cm-1 the
decrease is attributed to the e.s ,g.s mixing
 This example shows how λ and 10Dq can affect
the g value

42. Example2: Cu (II) in
a tetragonal field
 Cu (II) a d9 system. Ground term 2D
 2
D Eg + 2T2g ( CFS)
2
 Since Cu (II) is a d9 system it must undergo J-T
distortion.
 So the Oh field becomes tetragonal.

43.  T2g
2
Eg + 2B2g (J-T distortion)
2
 Eg
2
B1g + 2A1g
2
 The unpaired e- is present in 2A1g
 on applying the magnetic field the spin levels are
split and we get an ESR line.

44. Cu (II) in various fields
(E3)
2
Eg
2
T2g
2
B2g
(E2)
2
D
(E1) 2
B1g
2
Eg
+ 1/2
(E0)
2
A1g ESR
- 1/2
Free ion Oh field Tetragonal field H

45.  The g value is given by
g|| = 2 – 8 λ / (E2 – E0)
g┴ = 2 – 2 λ / (E3 – E0)
 From electronic spectrum (E2 – E0) and (E3 – E0)
can be calculated.
 From the above values λ can be calculated.

46.  It is seen that when splitting by distortion is high g
value approaches 2
 If the distortion splitting is lower then resulting
levels may mix with each other to give deviated g
values.

47. d1 system ( Ti3+, VO2+)
The energy gap is very less. The 2B2g may be further
vibrations mix these levels so T1 lowered by L-S coupling
is very low-leading to broad lines which is not shown.
2
Eg
2
D
2
Eg
2
T2g
∆E + 1/2
B2g
2
ESR
- 1/2
Free ion Oh field Tetragonal field H

48. d2 systems ( V3+ ,Cr4+)
3
A2g
3
A2g
3
F
3
Eg
+1
3
T1g ±1
3
A2g
0
0
-1
Free ion Oh field J-T Distortion ZFS H

49. d3 systems ( Cr3+)
4
T1
4
T1 +3/2
± 3/2
4
F
+1/2
4
A2 4
B2
± 1/2
- 1/2
+ 3/2
Free ion Oh field J-T Distortion ZFS H

50. d4- system (weak field)
5
Eg
(10)
T2g
5
5
B2g +2
(15)
(5) 5
A2g +1
D
5
(5)
(25)
5
Eg ± 2 (2)
± 1 (2)
(10) 5
B1g
0 (1)
(5) 0
-1
-2