APPLICATIONS OF APPLICATIONS OF ESR ESR TO TO

METAL COMPLEXESMETAL COMPLEXESV.SANTHANAM

DEPARTMENT OF CHEMISTRYSCSVMV

METAL COMPLEXES – A SURVEYMETAL COMPLEXES – A SURVEY

Metal complexes are important- Diverse biological Metal complexes are important- Diverse biological rolesroles

Griffiths and Owen proved the M-L covalency by Griffiths and Owen proved the M-L covalency by taking complexes (NHtaking complexes (NH44))22[IrCl[IrCl66] and Na] and Na22[IrCl[IrCl66]]

The hyperfine splitting by Chloride ligands showed The hyperfine splitting by Chloride ligands showed the covalent nature of M-L bondthe covalent nature of M-L bond

Proved the back donation (pi-bonding) conceptProved the back donation (pi-bonding) concept

With the ESR data they were able to calculate With the ESR data they were able to calculate ξξ,,ζζ and and λλ of metal ions and the extent of delocalization of metal ions and the extent of delocalization

In metal complexes the above said parameters In metal complexes the above said parameters were having lower values than the free metal ions.were having lower values than the free metal ions.

THINGS TO BE CONSIDEREDTHINGS TO BE CONSIDERED

Nature of the metalNature of the metal

Number of ligandsNumber of ligands

GeometryGeometry

No of d electronsNo of d electrons

Ground term of the ionGround term of the ion

Electronic degeneracyElectronic degeneracy

Inherent magnetic fieldInherent magnetic field

Nature of sampleNature of sample

Energy gap between g.s and e.sEnergy gap between g.s and e.s

Experimental temperatureExperimental temperature

NATURE OF THE METAL IONNATURE OF THE METAL ION

Since d metal ions have 5 d orbitals situations are Since d metal ions have 5 d orbitals situations are complicatedcomplicated

But the spectra are informativeBut the spectra are informative

In 4d and 5d series In 4d and 5d series L-S / j-jL-S / j-j coupling is strong coupling is strong making the ESR hard to interpretmaking the ESR hard to interpret

Crystal field is not affecting the 4f and 5f e- so the Crystal field is not affecting the 4f and 5f e- so the ESR spectra of lanthanides and actinides are ESR spectra of lanthanides and actinides are quite simple.quite simple.

If ion contains more than one unpaired e- ZFS may If ion contains more than one unpaired e- ZFS may be operativebe operative

GEOMETRY OF THE COMPLEXGEOMETRY OF THE COMPLEX

Ligands and their arrangement –CFSLigands and their arrangement –CFS

CFS in turn affect the electronic levels hence the CFS in turn affect the electronic levels hence the ESR transitionsESR transitions

The relative magnitude of CFS and L-S coupling is The relative magnitude of CFS and L-S coupling is giving three situations.giving three situations.

If the complex ion is having cubic symmetry If the complex ion is having cubic symmetry (octahedral or cubic) – g is isotropic(octahedral or cubic) – g is isotropic

Complexes with at least one axis of symmetry Complexes with at least one axis of symmetry show two g valuesshow two g values

Ions with no symmetry element will show three Ions with no symmetry element will show three values for gvalues for g..

SYSTEM WITH AN AXIS OF SYMMETRY NO SYMMETRYSYSTEM WITH AN AXIS OF SYMMETRY NO SYMMETRY

Symmetry of the complex ion- important – why?Symmetry of the complex ion- important – why?

ESR is recorded in frozen solutionsESR is recorded in frozen solutions

Spins are lockedSpins are locked

Lack of symmetry influences the applied field Lack of symmetry influences the applied field considerablyconsiderably..

Spin Hamiltonian of an unpaired e- if it is present in a Spin Hamiltonian of an unpaired e- if it is present in a cubic field iscubic field is

H = g H = g ββ | H | Hxx.S.Sxx + H + Hyy.S.Syy + H + Hzz.S.Szz||

If the system lacks a spherical symmetry and possess at If the system lacks a spherical symmetry and possess at least one axis ( Distorted Oh,SP or symmetric tops) thenleast one axis ( Distorted Oh,SP or symmetric tops) then

H = H = ββ |g |gxxxx H Hxx.S.Sxx +g +gyyyy H Hyy.S.Syy + g + gzzzz H Hzz.S.Szz||

Usually symmetry axis coincides with the Z axis and H is Usually symmetry axis coincides with the Z axis and H is applied along Z axis thenapplied along Z axis then

ggxx xx = g= gyyyy = g = gLL ; g ; gzzzz = g = g||||

If crystal axis is not coinciding with Z axisIf crystal axis is not coinciding with Z axis The sample is rotated about three mutually The sample is rotated about three mutually

perpendicular axis and g is measured.perpendicular axis and g is measured. g is got by one of the following relationsg is got by one of the following relations

for rotation aboutfor rotation about X axis - g2 = gyy

2Cos2θ + 2gyz2 Cos2θ Sin2θ +gzz

2 Sin2θ Y axis - g2 = gzz

2Cos2θ + 2gzx2 Cos2θ Sin2θ +gxx

2 Sin2θ Z axis - g2 = gyy

2Cos2θ + 2gxy2 Cos2θ Sin2θ +gyy

2 Sin2θ

NUMBER OF d ELECTRONSNUMBER OF d ELECTRONS

Magnetically active nucleus cause hyperfine Magnetically active nucleus cause hyperfine splitting.splitting.

If more than one unpaired e- present in the ion, If more than one unpaired e- present in the ion, more no of transitions possible leads to fine more no of transitions possible leads to fine structure in ESR spectrum.structure in ESR spectrum.

Here we have to consider two things Here we have to consider two things

Zero field splitting – due to dipolar Zero field splitting – due to dipolar interaction interaction

Kramer’s degeneracyKramer’s degeneracy

ZERO FIELD SPLITTINGZERO FIELD SPLITTING Considering a system Considering a system

with two unpaired e-swith two unpaired e-s Three combinations Three combinations

possible possible In absence of external In absence of external

field all three states are field all three states are having equal energyhaving equal energy

With external field three With external field three levels are no longer levels are no longer with same energy.with same energy.

Two transitions Two transitions possible; both with possible; both with same energy same energy

∆E2

∆E1

S = +1

S = 0

S = -1

H ≠ 0ZFS = 0

SPLITTING OF ELECTRONIC LEVELS EVEN IN SPLITTING OF ELECTRONIC LEVELS EVEN IN ABSENCE OF EXTERNAL MAGNETIC FIELD IS ABSENCE OF EXTERNAL MAGNETIC FIELD IS CALLED ZERO FIELD SPLITTING (ZFS)CALLED ZERO FIELD SPLITTING (ZFS)

The splitting may be assisted by distortion and L-S The splitting may be assisted by distortion and L-S coupling also.coupling also.

When there is a strong dipolar interaction the +1 level When there is a strong dipolar interaction the +1 level is raised in energy –Dipolar shift (D)is raised in energy –Dipolar shift (D)

This dipolar shift reduces the gap between S = -1 and This dipolar shift reduces the gap between S = -1 and S = 0 stateS = 0 state

Now the two transitions do not have same energyNow the two transitions do not have same energy

Results in two linesResults in two lines

EFFECT OF DIPOLAR SHIFTEFFECT OF DIPOLAR SHIFT

Ms = ±1,0

Ms = ±1

Ms = 0

Ms = -1

Ms = 0

Ms = +1

∆E1 = ∆E2

ZFS = 0

D

D

KRAMER’S THEOREMKRAMER’S THEOREM

Systems with even no. of unpaired e-s will contain Systems with even no. of unpaired e-s will contain a state with S = 0a state with S = 0

But in the case of odd e- s no state with S = 0 But in the case of odd e- s no state with S = 0 since Ms = ½since Ms = ½

In such cases even after ZFS the spin states with In such cases even after ZFS the spin states with opposite Ms values remain degenerate which is opposite Ms values remain degenerate which is called Kramer’s degeneracycalled Kramer’s degeneracy

The levels are called Kramer’s doubletsThe levels are called Kramer’s doublets

“ “ IN ANY SYSTEM WITH ODD NUMBER OF IN ANY SYSTEM WITH ODD NUMBER OF UNPAIRED eUNPAIRED e-s-s THE ZFS LEAVES THE GROUND THE ZFS LEAVES THE GROUND STATE AT LEAST TWO FOLD DEGENERATE STATE AT LEAST TWO FOLD DEGENERATE ””

EFFECT OF ZFS ON Mn(II)EFFECT OF ZFS ON Mn(II)

+5/2

+3/2

+1/2

- 1/2

- 3/2

- 5/2

±5/2

±3/2

±1/2

6S

FREE ION

ZFS AND RESULTING KRAMER’S DOUBLETS

CONSEQUENCES OF ZFSCONSEQUENCES OF ZFS

In some cases ZFS magnitude is very high In some cases ZFS magnitude is very high than the splitting by external field.than the splitting by external field.

Then transitions require very high energyThen transitions require very high energy

Some times only one or no transitions occur.Some times only one or no transitions occur.

Examples VExamples V3+3+ and Co and Co2+2+

EFFECTIVE SPIN STATE - Co(II)EFFECTIVE SPIN STATE - Co(II)

Co(II) in cubic field has a ground term of Co(II) in cubic field has a ground term of 44F.F.Since it is Since it is a da d88 system it have system it have ±3/2 and ±1/2 levels.±3/2 and ±1/2 levels.

ZFS splits the levels by 200 cmZFS splits the levels by 200 cm-1-1

Since the energy gap is higher only the transition -1/2 Since the energy gap is higher only the transition -1/2 to + 1/2 is seen.to + 1/2 is seen.

So it appears as if Co(II) has only one unpaired e- So it appears as if Co(II) has only one unpaired e- (Effective spin S’ = ½)(Effective spin S’ = ½)

±3/2,±1/2

±3/2

±1/2

+3/2

- 3/2

+1/2

-1/2

ONLY OBS.TRANSITION

≈ 200 cm-1

BREAK DOWN OF BREAK DOWN OF SELECTION RULESELECTION RULE

In some cases like V(III) the magnitude of ZFS very In some cases like V(III) the magnitude of ZFS very high.high.

It exceeds the normal energy range of ESR transitionsIt exceeds the normal energy range of ESR transitions

Normal transitions occur with Normal transitions occur with ∆Ms = ±1 . But its energy ∆Ms = ±1 . But its energy exceeds the microwave regionexceeds the microwave region

Then the transition from -1 to +1 levels with Then the transition from -1 to +1 levels with ∆Ms = ±2 ∆Ms = ±2 occurs ,which is a forbidden oneoccurs ,which is a forbidden one

Ms = 0, ±1

Ms= ±1

Ms =0

+1

-1

0

FORBIDDEN TRANSITION

NOT OCURRING

MIXING OF STATESMIXING OF STATES

The magnitude of ZFS can be taken as originating The magnitude of ZFS can be taken as originating from CFS.from CFS.

But orbitally singlet state But orbitally singlet state 66S is not split by the S is not split by the crystal field even then Mn(II) shows a small crystal field even then Mn(II) shows a small amount of ZFS.amount of ZFS.

This is attributed to the mixing of g.s and e.s This is attributed to the mixing of g.s and e.s because of L-S couplingbecause of L-S coupling

The spin – spin interaction is negligible.The spin – spin interaction is negligible.

But for triplet states spin – spin terms are But for triplet states spin – spin terms are important and they are solely responsible for ZFSimportant and they are solely responsible for ZFS

Naphthalene trapped in durene in diluted state Naphthalene trapped in durene in diluted state shows two lines as if it has ZFS.shows two lines as if it has ZFS.

Since there is no crystal field or L-S coupling this Since there is no crystal field or L-S coupling this is attributed to spin – spin interaction of the is attributed to spin – spin interaction of the ππee- - s s in the excited triplet statein the excited triplet state

ESR AND JAHN-TELLER DISTORTIONESR AND JAHN-TELLER DISTORTION

Jahn – Teller theorem :Jahn – Teller theorem :Any non-linear Any non-linear

electronically degenerate system is unstable, electronically degenerate system is unstable, hence it will undergo distortion to reduce the hence it will undergo distortion to reduce the symmetry, remove the degeneracy and hence symmetry, remove the degeneracy and hence increase its stability.increase its stability.

But this theorem does not predict the type of But this theorem does not predict the type of distortiondistortion

Because of J-T distortion the electronic levels are Because of J-T distortion the electronic levels are split and hence the number of ESR lines may split and hence the number of ESR lines may increase or decrease.increase or decrease.

FACTORS AFFECTING FACTORS AFFECTING THE g-VALUESTHE g-VALUES

Operating frequency of the instrumentOperating frequency of the instrument Concentration of unpaired e-Concentration of unpaired e- Ground term of the metal ion presentGround term of the metal ion present Direction and temperature of measurementDirection and temperature of measurement Lack of symmetryLack of symmetry Inherent magnetic field in the crystalsInherent magnetic field in the crystals Jahn – Teller distortionJahn – Teller distortion ZFSZFS

SUSTAINING EFFECTSUSTAINING EFFECT The g value for a gaseous atom or ion for which L-S The g value for a gaseous atom or ion for which L-S

coupling is applicable is given bycoupling is applicable is given by

g = 1 +[J(J+1) + S(S +1) – L(L+1)] / 2J(J+1)g = 1 +[J(J+1) + S(S +1) – L(L+1)] / 2J(J+1)

For halogen atoms the g values calculated and For halogen atoms the g values calculated and experimental are equal.experimental are equal.

But for metal ions it varies from 0.2 -8But for metal ions it varies from 0.2 -8

The reason is the orbital motion of the e- are The reason is the orbital motion of the e- are strongly perturbed by the crystal field.strongly perturbed by the crystal field.

Hence the L value is partially or completely Hence the L value is partially or completely quenchedquenched

In addition to this ZFS and J-T distortion may also In addition to this ZFS and J-T distortion may also remove the degeneracyremove the degeneracy

The spin angular momentum The spin angular momentum SS of e- tries of e- tries to couple with theto couple with the L L

This partially retains the orbital This partially retains the orbital degeneracydegeneracy

The crystal field tries to quench the L The crystal field tries to quench the L value and S tries to restore it value and S tries to restore it

This phenomenon is called sustaining This phenomenon is called sustaining effecteffect

Depending upon which effect dominate the L value Depending upon which effect dominate the L value deviates from the original value deviates from the original value

So L and hence J is not a good quantum number So L and hence J is not a good quantum number to denote the energy of e- hence the g value alsoto denote the energy of e- hence the g value also

COMBINED EFFECT OF CFS AND L-S COUPLINGCOMBINED EFFECT OF CFS AND L-S COUPLING

Three cases arise depending upon the relative Three cases arise depending upon the relative magnitudes of strength of crystal field and L-S magnitudes of strength of crystal field and L-S couplingcoupling

L-S coupling >>CFSL-S coupling >>CFS

CFS > L-S couplingCFS > L-S coupling

CFS >> L-S couplingCFS >> L-S coupling

L-S COUPLING >>CFSL-S COUPLING >>CFS

When L is not affected much by CFS, then J is When L is not affected much by CFS, then J is useful in determining the g valueuseful in determining the g value

Example rare earth ionsExample rare earth ions

4f e- buried inside so not affected, g falls in 4f e- buried inside so not affected, g falls in expected regionexpected region

All 4f and 5f give agreeing results other than All 4f and 5f give agreeing results other than Sm(III) and Eu(III)Sm(III) and Eu(III)

CFS > >L-S COUPLINGCFS > >L-S COUPLING

If CFS is large enough to break L-S If CFS is large enough to break L-S coupling then J is not useful in determining coupling then J is not useful in determining g.g.

Now the transitions are explained by the Now the transitions are explained by the selection rule and not by g valueselection rule and not by g value

The magnetic moment is given by The magnetic moment is given by

μμss = [n(n+2)] = [n(n+2)] 1/21/2

All 3d ions fall in this category.All 3d ions fall in this category.

Systems with ground terms not affected by CFS ie Systems with ground terms not affected by CFS ie L=0 are not affected and the g value is close to L=0 are not affected and the g value is close to 2.00362.0036

There may be small deviations because of L-S There may be small deviations because of L-S coupling, spin – spin interaction and gs and es coupling, spin – spin interaction and gs and es mixingmixing

CFS >> L-S COUPLINGCFS >> L-S COUPLING In strong fields L-S coupling is completely broken and In strong fields L-S coupling is completely broken and

L= 0 which means there is covalent bonding.L= 0 which means there is covalent bonding.

Applicable to 3d strong field , 4d and 5d series.Applicable to 3d strong field , 4d and 5d series.

In many cases MOT gives fair details than CFTIn many cases MOT gives fair details than CFT..

Example1: Ni (II) in an OExample1: Ni (II) in an Ohh field field

For Ni(II) g calculation includes mixing of For Ni(II) g calculation includes mixing of 33AA2g2g(g.s) (g.s) and and 33TT2g2g(e.s)(e.s)

g = 2 – [8g = 2 – [8λλ/10Dq]/10Dq]

For Ni (II) the g value is 2.25 hence For Ni (II) the g value is 2.25 hence 88λλ/10 Dq must /10 Dq must be - 0.25be - 0.25

From the electronic spectrum 10Dq for Ni(II) in an From the electronic spectrum 10Dq for Ni(II) in an OOhh field is known to be 8500 cm field is known to be 8500 cm-1-1,,λλ is -270 cm is -270 cm-1-1

For free Ni(II) ion the For free Ni(II) ion the λλ is about -324 cm is about -324 cm-1-1 the the decrease is attributed to the e.s ,g.s mixingdecrease is attributed to the e.s ,g.s mixing

This example shows how This example shows how λλ and 10Dq can affect and 10Dq can affect the g valuethe g value

Example2: Example2: Cu (IICu (II) in) in a tetragonal field a tetragonal field

Cu (II) a dCu (II) a d99 system. Ground term system. Ground term 22DD

22D D 22EEg g + + 22TT2g 2g ( CFS) ( CFS)

Since Cu (II) is a dSince Cu (II) is a d99 system it must undergo J-T system it must undergo J-T distortion.distortion.

So the OSo the Ohh field becomes tetragonal. field becomes tetragonal.

22TT2g 2g 22EEgg + + 22BB2g 2g (J-T distortion) (J-T distortion)

22EEgg 22BB1g1g + + 22AA1g1g

The unpaired e- is present in The unpaired e- is present in 22AA1g1g

on applying the magnetic field the spin levels are on applying the magnetic field the spin levels are split and we get an ESR line.split and we get an ESR line.

Cu (II) in various fieldsCu (II) in various fields

2D

2T2g

2Eg

2Eg

2B2g

2B1g

2A1g

+ 1/2

- 1/2

ESR

Free ion Oh field Tetragonal field H

(E3)

(E2)

(E1)

(E0)

The g value is given byThe g value is given by

gg|||| = 2 – 8 = 2 – 8 λλ / (E / (E22 – E – E00))gg┴ ┴ = 2 – 2 = 2 – 2 λλ / (E / (E33 – E – E00))

From electronic spectrum (EFrom electronic spectrum (E22 – E – E00) and (E) and (E33 – E – E00) ) can be calculated. can be calculated.

From the above values From the above values λλ can be calculated. can be calculated.

It is seen that when splitting by distortion is high g It is seen that when splitting by distortion is high g value approaches 2value approaches 2

If the distortion splitting is lower then resulting If the distortion splitting is lower then resulting levels may mix with each other to give deviated g levels may mix with each other to give deviated g valuesvalues..

dd11 system ( Ti system ( Ti3+3+, VO, VO2+2+))

2D

2T2g

2Eg

2B2g

+ 1/2

- 1/2

ESR

Free ion Oh field Tetragonal field H

2Eg

The 2B2g may be further lowered by L-S coupling which is not shown.

The energy gap is very less. vibrations mix these levels so T1 is very low-leading to broad lines

∆E

dd22 systems ( V systems ( V3+3+ ,Cr ,Cr4+4+))

3F

3A2g

3A2g

3T1g

3Eg

3A2g

± 1

00

+ 1

- 1Free ion Oh field J-T Distortion ZFS H

dd33 systems ( Cr systems ( Cr3+3+))

4F

4T14T1

4A2

± 3/2

± 1/2

+3/2

+1/2

- 1/2

+ 3/2

4 B2

Free ion Oh field J-T Distortion ZFS H

dd44- system (weak field)- system (weak field)

5D

(25)

5T2g

(15)

5Eg

(10)

5Eg

(10)

5B2g

(5) 5A2g

(5)

5B1g

(5)

± 2 (2)± 1 (2)

0 (1)

+2

+1

0

-1-2