Magnetic Circular Dichroism Spectroscopy - uni …obelix.physik.uni-bielefeld.de/~schnack/molmag/material/Muehlheim... · Magnetic Circular Dichroism Spectroscopy. Frank Neese. Max

Magnetic Circular Magnetic Circular

Dichroism SpectroscopyDichroism Spectroscopy

Frank NeeseMax Planck Insitut für Bioanorganische Chemie

Mülheim an der Ruhr

Max Planck Institute for Bioinorganic Chemistry, Mülheim an der Ruhr

OutlineOutline

1. Introductiona) General Features of MCDb) Experimental Aspects

2. Theory of MCD Spectroscopya) A-, B- and C-termsb) MCD Signsc) Variable Temperature, Variable Field MCD

3. Applications of MCDa) Geometric Structure (Hemes, HS-Fe(II))b) Electronic Structure (CuA)c) VTVH MCD of Dimersd) MCD of Molecular Magnets

I.I. IntroductionIntroduction


MCD MCD Versus GroundVersus Ground State State MethodsMethods

ElectronicallyExcited State

Multiplet

ElectronicGround State

Multiplet

Total Spin S

2S+1 ComponentsMS=S,S-1,...,-S

Total Spin S‘

2S‘+1 ComponentsM‘S=S‘,S‘-1,...,-S‘

∆E~5,000-45000 cm-1

∆E~0-10 cm-1

∆E~0-10 cm-1

∝ Ground StateSH: ggs,Dgs,Jgs,...

EPRTransition

21−

21+

Bg gsβ

∝ Excited StateSH: ges,Des,Jes,...

21−

21+

Bg esβ

ElectronicTransitions

Probed with MCD

Magnetic Field


The The MCD ExperimentMCD Experiment

Sample

z

x

y

x

y

B-Field

liq. HeKryostat

Monochromator

Modulator

DetectorLight SourceRCP LCP

Magnet

( ) ( ) ( )[ ]4444 34444 21

CDNatural

BRCPALCPARCPALCPAMCD 0)( =−−−≡

( ) ( ) ( ) ( ) ( ) ( )∑ ∑ ΨΨ−ΨΨ∝

statesinitial

j

statesfinal

k

AbsorptionPhotonRCPforyProbabilit

kRCPj

AbsorptionPhotonLCPfortyProbablili

kLCPjj BmBBmBTBNcdE444 3444 21444 3444 21

22,


The The MCD Instrument in MülheimMCD Instrument in Mülheim

Sample Cell

FocussingLens

MagnetoCryostat

B,T-Control

CD Spectrometer

ShieldedDetector


The The Faraday Faraday EffectEffect

Today worked with lines of magnetic force, passing them across different bodies (transparent in different directions) and at the same time passing a polarised ray of light through them.,,,A piece of heavy glass which was 2 inches by 1.8 inches, and an inch thick, being a silico borate of lead, and polished on the two shortest edges was experimented with. It gave no effects when the same magnetic poles or the contrary poles were on opposite sides (as respect the course of the polarised ray) – nor when the same poles were on the same side, either with the constant or intermitting current – BUT when the contrary magnetic poles were on the same side, there was an effectt produced on the polarised ray, and thus magnetic force and light were proved to have relation to each other. This fact will most likely prove exceeding fertile and of great value in the investigations of both conditions of natural force(Faraday‘s diary – 13th September 1845. Vol. IV, G. Bell and Sons Ltd., London 1933)

VBd=φ: Rotation angle of plane polarized light

V : Verdet Constant

B : Magnetic Field

d : Length of Light Path


Why Why MCD MCD Spectroscopy Spectroscopy ??

Sensitive Technique (esp. near-IR)High Resolution (Signs)Site Selectivity (Multiple Metal Sites)Multidimensional (B,T,λ)Does not require Isotopic Enrichment and is not restricted to certain elements

Has no Problems withInteger SpinIs not restricted to Para-magnetic SpeciesStudies the Ground andExcited States at the sametimeSolution or Solid SamplesPuts Severe Constraints onPossible Assignments


Solvent Solvent SpectraSpectra

Thomson, A.J.; Cheesman, M.R.; George, S.K. (1993) Meth. Enzymol., 226, 199


MCD: ResolutionMCD: Resolution

30000 25000 20000 15000

0

100

200

300

400

Wavenumber (cm-1

)

MCD-20

-10

0

10

20 CD0

2

4

ABS

Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122, 11703-11724


MCD: Site MCD: Site SelectivitySelectivity

30000 25000 20000 15000 10000 5000

-3

-2

-1

0

1

2

Wavenumber (cm-1)

∆ε

(mM

-1

cm-1

T-1)

0

20

40

60

80

100

MCD

ABS

ε (

mM

-1 c

m-1)

0.0 0.5 1.0 1.5

CuAHa

Ha3-CuB

O2

H2O

Thomson, A.J. (1997) In: Andrews, D.L. (Ed.) Perspectives in Modern Chemical Spectroscopy, Springer, Berlin, p. 243

Cytochrome c Oxidase

e-


MCD: Multidimensional NatureMCD: Multidimensional Nature

25000 20000 15000 1000030000

25K15K

5K

10K

5K

3K

1.5K

25K15K

10K

5K

MC

D in

tens

ity (a

.u.)

Wavenumber (cm-1)

31,055 cm-1

band 618,350 cm-1

band 322,470 cm-1

band 4

MC

D in

tens

ity (a

.u.)

βB/2kT = 0..1.6

[Fe(EDTA)(O2)]3-[Fe(EDTA)(O2)]3-

Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829


MCD: Integer Spin SystemsMCD: Integer Spin Systems

0+/-1

S=1 Ground State

B-Field

hν (EPR)

S=1 Exc. State

0+/-1

Des

hν (MCD)

Dgs

II. II. Theory Theory of MCDof MCD


MCD: Traditional MCD: Traditional TheoryTheory

( ) ( )

++−=

∆ EfkTCB

EEfAB

E0

01 ∂∂γβε

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,40,0

0,2

0,4

0,6

0,8

1,0

βB/2kT

MC

D S

igna

l (a.

u.)

=

kTBgAMCD

2tanhsatlim

β

30000 25000 20000 15000 10000

-400

-200

0

200

400

Wellenzahl (cm-1)

∆ε (

M-1 c

m-1 T

-1)

λfix, Variable B,T

S=1/2 system

( )Ef = Lineshape function

Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197


Angular MomentumAngular Momentum

Photons:Photons: ElectronsElectrons::

Energy: Energy:λ/hcE = λ/hcE =

Momentum:kp π2/h= kp π2/h=Momentum:λπ /2=k

π2/21 h± spinAngular Momentum: Angular Momentum:π2/h±

π2/nh± orbit

• The Total Angular Momentum (Electrons and Photons) is Conserved• A Linearly Polarized Light Beam Contains Photons in a SuperpositionState

• A Circularly Polarized Light Beam Contains Photons in a PureAngular Momentum State

)(2 2/1 −++− kk

−+ kk or

Cohen-Tanudji, C. et al. (1977) Quantum Mechanics, John-Wiley & Sons

Craig, DP; Thrunamachandran, T (1984) Molecular Quantum Electrondynamics, Dover Publications


MCD MCD AA--Terms: A Terms: A 11S S 11P P TransitionTransition

1S0

m+1

[ ]

−×

+−+=

+−

∑2

1

2

1

11

λαλα

ααλλαλ

JmAJmA

ASgLAJSgLJd

A ZeZZeZA

24000 22000 20000 18000 16000

Wavenumber (cm-1)

Abs

orpt

ion

lcp rcp

24000 22000 20000 18000 16000

Wavenumber (cm-1)

Abs

orpt

ion

lcp-rcp sum

1S

1P 1P0

1P1

1P-1

rcp lcpm-1



MCD MCD CC--Terms: A Terms: A 11P P 11S S TransitionTransition

1S

1P1P-1

m-1

24000 22000 20000 18000 16000

Wavenumber (cm-1)

Abs

orpt

ion

rcp lcp

1S0

lcp rcp

−×

+−=

+−

∑2

1

2

1

01

λαλα

αααλ

JmAJmA

ASgLAd

C ZeZA

1P0

1P1

m+1

16000 18000 20000 22000 24000

Wavenumber (cm-1)

Abs

orpt

ion

-rcp lcp sum



MCD MCD BB--Terms:Terms:

From Perturbation Theory:

[ ]

[ ]κλλακλλα

ακ

ακλαακλα

κλ

αλ κ

αλ κ

KmJJmAKmJJmA

EEASgLK

d

AmKJmAAmKJmA

EEKSgLJ

dB

AK AK

zez

A

JK JK

zez

A

1111

1111

0

2

2

−++−

≠

−++−

≠

−×

−

++

−×

−

+=

∑ ∑

∑ ∑

Mixing of the excited state or the ground State to potentially all other states via

the Zeeman interaction

Inversely proportional to ∆E

Absorption Shaped and Temperature Independent

Physically Intuitive Picture ?

Dominates MCD of Organic Molecules with Nondegerate Singlet Ground States



Relative Relative MagnitudeMagnitude of of AA-- BB-- and and CC--TermsTerms

For the Model 1P to 1S Transition2

0 32 gmC −=2

1 32 gmA −=Insert:

( )( )

2

2

1 σ

πσ

EE

eEf−

−= ( )σ2ln2FWHM=Assume:

( ) ( )EfEgmEEfA

−=− 2

21

232

σ∂∂A-term:

( ) ( )EfkT

gmEfkTC

−=

132 20

kTE1:1:1

∆σ

C-term:

Ratio A:B:C ≈

A:B:C ≈ 1 : 0.1 : 51200000,101000 −==∆= cmkTEσ



VVariableariable TTemperatureemperature VVariableariable HH--FieldField MCDMCD

Bg esβ

lcp rcp

( )( ) ( )kTBgkTBg

kTBgN/exp/exp

/exp2

12

1

21

βββ

−+±

=m

=

+

−=∆

kTBg

kTBg

kTBgN

2tanh

...241

21 3

β

ββ

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,40,0

0,2

0,4

0,6

0,8

1,0

βB/2kT

Frac

tiona

l Pop

ulat

ion

Diff

eren

cePopulation Difference

=

kTBgAMCD

2tanhsatlim

β

Bg gsβ


Boltzmann Population


VTVH MCD VTVH MCD for for S>1/2 SystemsS>1/2 Systems

0 .0 0 .6 1 .2β B /2 k T

Norm

aliz

ed M

CD

Inte

nsi

ty

T

Observations:• The MCD Signal Varies Nonlinearly with B and T• The Curves Recorded at Different Temperaturesdo not Overlay (=Nesting)

• The Signal may Pass Through a Maximum and then Decrease Again or may even Change Sign

Behavior was not Understood

A New Theory was Needed


General General Theory for Nonlinear Theory for Nonlinear MCDMCDNeese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

0 0

sin4

eff eff effi x yz y xz z xy

iN l M l M l M d d

E S

π πε γ θ θ φπ

2∆ = + + ∑∫ ∫ x y zi iiS S S

( ) ( )2 2

,a j

a j

K N N f EEε∆ = − − ∑ LCP RCPa m j a m j

Assumptions + Perturbation Theory (Hso, Hze)

|AS,-S> |AS,-S+1> |AS,-S+2> …

|JS,-S> |JS,-S+1> |JS,-S+2> …

Electric Dipole Operator

Spin-Orbit Coupling Operator

General Ansatz:

(Lengthy Derivation)

Spin Hamiltonian!!izyx NS ,,, ...ˆˆˆˆ ++= SSSH BgD β


General General Theory for Nonlinear Theory for Nonlinear MCDMCD

0 0

sin4

eff eff effi x yz y xz z xy

iN l M l M l M d d

E S

π πε γ θ θ φπ

2∆ = + + ∑∫ ∫ x y zi iiS S S

Neese, F.; Solomon, E.I. (1999)Inorg. Chem., 38, 1847

izyxS ,,

effxyM

zyxl ,, Direction Cosines (Orientation of B in the Molecular Frame)

Collection of ConstantsExperimentγ

Expectation Value of Sx,y,z for the SH Eigenstate i Spin-Hamiltonian

(ALL B,T dependence)iN Boltzmann Population of SH Eigenstate i

Nature of Ground and

Excited StatesOrthogonal Effective Product of Transition Dipole Moments

Parameterization in terms of Spin-Hamiltonian and State Specific Polarization Parameters Achieved for the First Time


Mechanisms for Mechanisms for MCD MCD IntensityIntensity

( ) ( )JJAA

m

AJm

mJA

AJMM

DDMS

mMS

Y

DMJSmASM

rr

rr

−

′

−∆+

=′

∑ −−

′

111

δ

( )∑ ∑≠

−−

′

−∆−JAK m

AKKJm

mKJ D

MS

mMS

Y,

1 11

r

A

( )∑ ∑≠

−−

′

−∆−JAK m

KJAKm

mKA D

MS

mMS

Y,

1 11

r

|J >

|A >

|K >r

D A J

rD A K

L K J

A

B

C

|A>

|J>

rD AJ LAJ

instrinsic

|J>

|K>

|A>

rD AJ

rDKJ

LAK

B

C

Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847


MCD and ZeroMCD and Zero--Field Field Splitting: Splitting: Weak Field CaseWeak Field Case

0.0 0.5 1.0 1.5

xz-polarizedxy-polarized

0.5 1.0 1.5

1.5K

25K 1.5K25K 1.5K

MC

D-in

tens

ity

βB/2kT

yz-polarized

0.5 1.0 1.5

The Effective g-ValuePerpendicular to thePlane of Polarization

Determines the Amountof Nesting

4D

2D2

1±=SM

23±=SM

25±=SM

6S

2/1~g

2/3~g

2/5~g

(The Effective g-values are read from the rhombogram)



Test of Test of the Theorythe Theory

Theoretical Prediction:

0.00 0.05 0.10 0.15 0.200.0

0.1

0.2

0.3

0.4

0.5

1/T (K-1

)

+/- 5/2

+/- 3/2

+/- 1/2total MCD

Present Theory

Browett et al.

Sum

Exp.

Theo.

( ) ( ) ( )( )∑ ++=∆

ddsatlim

~~~ effxy

dz

effxz

dy

effyz

dx MgMgMg

kTBA

Eβαε 4D

Experimenteller Test: Fe(TPP)Cl (S=5/2)

Experimental Data: Browett, WR; Fucaloro, AF; Morgan, TV; Stephens, PJ J. Am. Chem.

Soc., 105 (1983), 1868

2D2

3±=SM

25±=SM

6S

21±=SM

S=5/2



MCD and ZeroMCD and Zero--Field Field Splitting: Splitting: Strong Field CaseStrong Field Case

0.0 0.5 1.0 1.5

MCD for S=5/2 D=-10 cm-1 E/D=0 Mxy polarization

S=1/2 ... S=9/2Brillouin curves

MC

D-in

tens

ity

βB/2kT

The MCD Magnetization

for Vanishing ZFS behaves

Exactly like a Brillouin

Function for spin S

Attention: May be Difficult

to Distinguish from Case

with large ZFS and Easy

Axis Polarization

Uncritically Assumed in

(too) Many Studies!



MCD and ZeroMCD and Zero--Field Field Splitting: Splitting: Intermediate Field StrengthIntermediate Field Strength

Complicated Patterns Observed

0 5 10 15 20

D= 0 cm-1

= Brillouin curve for S=5/2

D=-1 cm-1

βB/2kT

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-2-1012

MC

D in

tens

ity

βB/2kT=1.56

θ (rad)

N1<

S z>1

MC

D-in

tens

ity βB/2kT=0.25


0,0 0,5 1,0 1,5βB/2kT

D =-1 cm-1

E/D= 0xy-polarized

25K

1.5K

Competing Zeeman and ZFs


VTVHVTVH--MCD: Fitting SoftwareMCD: Fitting Software

VTVH

Simulated Magnetization

CurvesMCD=f(βB/2kT)

ExperimentalMagnetization

CurvesMCD=f(βB/2kT)

SimulationLeast Square

Fit

Experience:• Should Fit Multiwavelength Data

Simultaneously with One Set ofSH Parameters

• Requires Careful BaselineSubtraction Procedures

• Often Constrain Mxz=Myz=M⊥

Since E/D is often PoorlyDetermined.

Spin-Hamiltonian ParametersEffective Transition Polarizations

III. III. ApplicationsApplications


MCDMCD SpectroscopySpectroscopy of HS Fe(II) Systemsof HS Fe(II) Systems

5C

5C

4C

6C10,000 cm-1

10,000 cm-15,000 cm-1

7,000 cm-1<5,000 cm-1

5,000 cm-1t2

e

a1

e

e

a1

e

b1

b2

eg

t2g

5,000 10,000 15,000 Solomon et al. (1995) Coord. Chem. Rev., 144, 369

Wavenumber (cm-1)


MCD MCD Spectroscopy Spectroscopy of LS Fe(III) of LS Fe(III) HemesHemes

Marker BandsMarker Bands NIR-LS Fe(III)NIR-LS Fe(III)

CT-Spectra Axial LigandsCheesman, M. R.; Greenwood, C.; Thomson, A. J. Adv. Inorg. Chem. (1991), 36, 201


MCD MCD CC--Term Term SignsSigns: [Fe(CN): [Fe(CN)66]]33--

eg

t2g

t1u

t2u

LMCT 1

LMCT 2

LMCT 3t1u

Piepho, S.B.; Schatz, P.N. (1983) Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism, John Wiley & sons, New York


Disgression: The Wigner-Eckart Theorem for Point Groups

( ) Γ′Γ

′

Γ′Σ−Γ

−=′Γ′Γ Σ+ΓΣ bOaVbOaγσγ

γγ γσ 1

Griffith, J.S. (1962) The Irreducible Tensor Method for Molecular Symmetry Groups, Prentice-Hall Inc., Englewood Cliffs

• A Single Matrix Element must be calculated to determine the ReducedMatrix Element from Inversion of the Equation.

• All Other Matrix Element follow from the V-coefficients that are Tabulatedfor a Variety of Point Groups.

• Most Powerful for Highly Symmetric (i.e. Cubic and Higher) Groups.

• BEWARE: Different Phase Choices Exist and Confusion May Arise.

( )

∑

∑

−

−

−−

−=

−−= +−

M

xugxugz

xug

Mxugxugzxu

TTV

TTVMg

TmT

MTmMTMTmMTMgTC

;;

22

22

2

2

;;

2212

222

1222

0

11

11

6

61

λα

λα

λαλα

λαλα



MCD CMCD C--Term Term SignsSigns: [Fe(CN): [Fe(CN)66]]33-- ((ctdctd))2T1u

2T2u+1 Since There are

Two 2T1u terms And One 2T2u Term

I expect Two PositiveAnd One Negative

Band in MCD

0Excited State

2T1u or 2T2u-1

lcpm-1

lcpm-1

rcpm+1

rcpm+1

Matches Observation+1

0 Gives ConfidenceIn AssignmentGround state

2T2g-1

NEGATIVEC-TERM

POSITIVEC-TERM



Graphical Method for Sign PredictionGraphical Method for Sign PredictionS-

Cu1.5

S-Cu1.5

R

R

LL

Acceptor MO Ψo(b3u symmetry)

Transition Density

Donor MO Ψi(ag symmetry)

Intermediate MO Ψj(b1g symmetry)

Transition Dipole Moment

Spin-OrbitRotation

Donor MO Ψi(ag symmetry)

Intermediate MO Ψj(b1g symmetry)

Counter clockwise rotation of orbitals constitutingΨj around z gives negative overlap with Ψi

ResultingCoordinateSystem

x

yz

mxmy

Lz

E

mx my

CuA Chromophorex

y

LCP absorption positve MCD Neese,F.; Solomon, E.I. Figure 11

A

B

C

D

F

If you know the MOs involved in a given Electronic Transition you can Use a Simple Graphical Method to Reasonably Predict the MCD C-Term Sign. (Details in Inorg. Chem. (1999) 38, 1847)


The The Electronic Electronic Structure Structure of of CuCuAA

A=120 MHz

g=2.180

exp

sim

Met

HisHis

Asp Cys

Cys

Dimer; S=1/2“Mixed-valence”

[Cu(1.5)...Cu(1.5)]

Cyt.c

O2 + 4H+ 2H2O

e-

Cytochrom c Oxidase EPR Spectra Conclusions

X-Ray Structure

Iwata, S.; Ostermeier, C.; Ludwig, B.; Michel, H. (1995) Nature, 376, 660Neese, F.; Zumft, W.G.; Antholine, W.E.; Kroneck, P.M.H. (1996) J. Am. Chem. Soc., 118, 8692


Quantum Quantum Chemical Calculation Chemical Calculation of MCDof MCD

0

1

2

3

4

theo.theo.

exp.

MCDABS

exp.

8

7

6

54

3

287

65

42 -1

0

1

∆ε

(mM

-1 c

m-1 T

-1)

ε (m

M-1 c

m-1)

25 20 15 100

1

2

3

2a2g

3a1g

2b1g

1b3g

1b2g

1b1g1ag

2a2g

Wellenzahl (1000 cm-1)

3

25 20 15 10

-0.2

0.0

0.2

3ag2b1g

1b3g

1b2g

1b1g

1ag

2a2g

CuA

Farrar, J.; Neese, F.; Lappalainen, P.; Zumft, W.G.; Kroneck, P.M.H.; Thomson, A.J. J. Am. Chem. Soc. (1996), 118, 11501


Electronic Electronic Structure Structure & & Function Function of of CuCuAA

♦ ‘‘Suspicious’Suspicious’ Axial Axial LigandsLigands⇒⇒ Finetuning Finetuning of Eof E00

’’

⇒⇒ ‘‘EntaticEntatic State’State’⇒⇒ RegulationRegulation

♦ Coordination NumberCoordination Number 33--44⇒⇒ Coordinatively UnsaturatedCoordinatively Unsaturated⇒⇒ CuCu--Cu BindungCu Bindung CompensatesCompensates

♦ ThiolateThiolate--Bridges/Bridges/Covalent Covalent BondingBonding⇒⇒ VeryVery StrongStrong DimerDimer--InteractionInteraction⇒⇒ DelocalizationDelocalization⇒⇒ LowLow Reorganisation Reorganisation EnergyEnergy⇒⇒ Effektive eEffektive e----TransferTransfer⇒⇒ ee----Transfer Transfer PathwaysPathways

16-20% S

16-20% S

15-20% Cu

3-5% N3-5% N

First MetalFirst Metal--Metal Bond in Metal Bond in BiologyBiology


MCD of MCD of DimersDimers: : Older WorkOlder Work

M. Johnson et al./Ni-DimerM. Johnson et al./Ni-Dimer

( ) ( ) ...1100 ++∝ SNaSNaMCD

( ) ( )( )∑ −

−=

SkTSE

kTSESN/)(exp

/)(exp

[ ])1()1()1()( +−+−+−= BBAA SSSSSSJSE

• Reasonable Model but Never Cleanly Derived

• Works Only in the Region were theResponse with respect to Field is Linear

• Reasonable Model but Never Cleanly Derived

• Works Only in the Region were theResponse with respect to Field is Linear

Unproven Assumption:

Boltzmann-Population:

Spin-State Energy:


MCD of MCD of DimersDimers: A Model : A Model StudyStudy

Ni(C lO 4)2 .nH2O +

NNOH

C r

N

N

N

X

X

X

+A gC lO 4

- A gX

C H3OH

C H3OH+ N(C 2H5)3

C r

N

N

N

O

O

O

N

N

N

Ni

Np y

Np y

Np y

OHNNp y

2+

MIII MII

Ross, S.; Weyhermüller, T.; Bill, E.; Wieghardt, K.; Chaudhuri, P.(2001) Inorg. Chem., 40, 6656-6665

3 Systems: (1) MIII= CrIII MII=ZnII : Paramagnetic CrIII (d3;S=3/2)

(2) MIII= GaIII MII=NiII : Paramagnetic NiII (d8;S=1)

(3) MIII= CrIII MII=NiII : Antiferromagnetic Coupling

1-3 are strictly isostructural with a trigonal distortion (|| M-M axis)


MCD of MCD of DimersDimers: Experimental : Experimental StudyStudy

28 26 24 22 20 18 16

0

10

ν/ 103cm-1

∆ ε,

M-1cm

-1 0

200

400

600

ε, M

-1cm

-1

2A4E 4E2E4A 4A 2A,2E 2EC3

MCD(3T, 5K)

?

[CrZn]800 300

14

O 4T12T2

4T22T1

2E

MCD(3T, 5K)

[GaNi100

200

ε , M

-1cm

-1

0

-10

0

10

∆ ε ,

M-1

cm-1

12 10ν /103cm-1

3A3A3E20

3A

3T1

26 24 22 18 16 1428C3 3E3E

O 3T23T1

Oh

2Eg

2T1g

4T2g

4A2g

2T2g

C3 Obs INDO/S-CI

4A

4A4E2A2E

18466 1822719503 1901520700 1993321159 20796

D(CFT)=0.07 cm-1

D(LFT)=0.08 cm-1

D(INDO/S+CI)=0.12 cm-1

Oh C3 Obs INDO/S-CI3T1g

3A2g

3T2g

3A

3A 11900

3E 12900 13109

12235

D(CFT)= 2.9 cm-1

D(LFT)= 2.6 cm-1

D(INDO/S+CI)=2.9 cm-1

( ) ( ) ( ) ( )

−−

−≈

EEAEEEAED yxzyxz

2,

24,

4

2

34

3κκκκζ

( ) ( )

−≈

EEAED yxz

4,

42 κκζ(along C3) (along C3)


The The „Monomers“ VTVH„Monomers“ VTVH--MCDMCD

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8-100

-50

0

50

100

150

200

250

300

5 4 1 n m

575 nm

473 nm

512 nm

430 nm

5.0 K 3.0 K 2.1 K

MC

D /

mde

g

βB/2kT0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

-250

-200

-150

-100

-50

0

780 nm

830 nm

880 nm

5.0 K2.8 K

2.0 K

MC

D /

mde

gβB/2kT

Consistent with EPR, SQUID and LFT

Consistent with EPR, SQUID and LFT

[CrZn][CrZn] [GaNi[GaNi

D(Fit) ≤ 0.6 cm-1 D(Fit)=3.5 ± 0.5 cm-1


The The MCD of MCD of the interacting the interacting systemsystem

28 26 24 22 20 18 16 14 12 10

0

ν/ 103cm-1

∆ ε

, M

-1 c

m -1

0

200

400

600

800

ε, M

-1 c

m -1

3A 3E3E 3A3A3E

4E

3T1

3T13T2

4E 4A 2E 2A 4A

4T12T2

4T2

2A,2E

2T1

2E

2E

0.0 0.5 1.0 1.5 2.0

30 K

20 K

10 K

5 K

3 K 1.6 K

Nor

mal

ized

inte

nsity

βB/2kT

Large NestingSign Changes

Large NestingSign Changes

MCD is Highly Sensitive to the Magnetic Interaction

MCD is Highly Sensitive to the Magnetic InteractionSpectra are to a Good Approximation

the Superposition of the [CrZn and [NiGa] Spectra

Spectra are to a Good Approximation the Superposition of the [CrZn and

[NiGa] Spectra


MCD MCD TheoryTheory: Extension to : Extension to DimersDimers

Following the Previous Approach in [5] a New Master Equation was Derived under the Following Plausible Assumptions:

(1) The Observed Electronic Transition are Strictly Localized on one Site

(2) Excited State Exchange Couplings are small compared to the bandwidth

(3) Multicenter Spin-Orbit Coupling Effects are Small

( )∫ ∫ ∑ ++=∆ π π

φθθπγε

0

2

0,,, sin

4ddMSlMSlMSlN

SE i

effxyizAz

effxziyAy

effyzixAxi

A

Here: = Site spin site ‚A‘, =local transition dipole moment product =local spin expection value for i‘th magnetic eigenstate =its Boltzmann population =direction cosine

AS

iN xlixAS ,

effyzM

iAzyx NS ,,,Calculate From the Dimer Spin-Hamiltonian:

( )BB

AA

BBB

BAA

ABAspin SSBSSSSSSJHrrrrrrrrr

ggDD ++++−= β2ˆ


Application Application of of the the New New TheoryTheory

0.0 0.4 0.8 1.2 1.6

0

50

0.0 0.4 0.8 1.2 1.6

-100

-50

0

0.0 0.4 0.8 1.2 1.6

0

50

100

50 K

20 K

10 K

5 K

2 K

βB / 2kT

βB / 2kT

768 nm514 nm438 nm

MC

D /

mde

g

βB / 2kT

-10 -8 -6 -40

20

40

60

80

100

120

Err

or /

mde

g

J / cm-1

Fit with 3 Parameters (J,M||,M⊥) J= -6.6±~0.5 cm-1

(Fixed Single Ion D and g)

Fit with 3 Parameters (J,M||,M⊥) J= -6.6±~0.5 cm-1

(Fixed Single Ion D and g)

The New Theory Describes the MCD Accurately and Allows Determinantion of

J (and D)

The New Theory Describes the MCD Accurately and Allows Determinantion of

J (and D)


MCD of MCD of Molecular Molecular MagnetsMagnets

1. Collison et al. (2003) J. Am. Chem. Soc., 125, 11682. McInnes et al. (2002) J. Am. Chem. Soc., 124, 92193. Collison et al. (2003) Inorg. Chem., 42, 5293

Contributions of MCD so far:1. Estimate of Single Ion ZFS by using Transition

Energies and Ligand Field Theory2. Independent Measurement of the Total

Cluster D-Value3. Measurement of Hysterisis Curves in Solution4. Detection of Polarization Effects (Magnetic

Readout)

[Mn12O12(OAc)16(H2O)4]

∑−=BA

BAABHDvV SSJH,

ˆˆ2ˆSt=10St=10

Documents

Magnetic Circular Dichroism Spectroscopy - uni …obelix.physik.uni-bielefeld.de/~schnack/molmag/material/Muehlheim... · Magnetic Circular Dichroism Spectroscopy. Frank Neese. Max