magnetic circular dichroism spectroscopy -...
TRANSCRIPT
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Magnetic Circular Dichroism Spectroscopy
Frank Neese
Max Planck Institute for Chemical Energy Conversion Stiftstr.34-36
Mülheim an der Ruhr
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The Faraday Effect
f : Rotation angle of plane polarized light
V : Verdet Constant
B : Magnetic Field
d : Length of Light Path
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 effect 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)
Michael Faraday 1791-1867
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The Faraday Effect
Faradays actual horseshoe magnet (1845)
(Faraday Museum, London)
Molecular property (wavelength dependent)
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Circular Dichroism vs Optical Rotary Dispersion
ORD : optical rotation of plane polarized light as f(l) (dispersive)
CD : Differential absorption of right and left circularly polarized light as f(l) (absorptive)
Kramers-Kronig Transform
ABSCD
ORD
l
q
e De
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Photons, Electrons, States, Spectra & all that
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Anatomy of a Light Wave
★ Wavelength: λ ★ Frequency: ω=2πc/λ ★ Electric Field: E ★ Magnetic Field: B ★ Propagation Direction: e ★ Wave vector k (|k|= 2π/λ) ★ Momentum: p=h/2πk ★ Angular Momentum:±h/2π
E
B
λ
★ Linear Polarization
1
2k + + k−( )
★ Circular Polarization (RCP, LCP) k + or k−
k
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Energy Scale of Optical Spectroscopy
4 - 1eV 8000 2000 0.1-0.01 10-4 -10-5 10-6 -10-7
X-Ray UV/vis Infrared Microwave RadiowaveGamma
EPR ENDOR
NMR
IR
Raman
ABS
MCD
CD
XAS EXAFS
Möss- bauer
14000
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STATES of a SystemO
rbita
l ene
rgy
ONE-ELECTRONIC-STATE of a molecule:
Configuration:Distribution of electrons among orbitals (singly- and doubly occupied orbitals) nI
|nISMG> ≡ ΨISM ;Γ
„wavefunction“ for this STATEa−3 B
1g≡ Ψ
0
11;B1g
Total spin:Coupling of unpaired electrons to a given total spin S and spin-projection M
Symmetry:Direct product of symmetries of singly occupied molecular orbitals G
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Excited States in Transition Metal ComplexesO
rbita
l Ene
rgy
} } } }
Ligand1
Ligand2
Metal d-shell
Ligand1
d-d Excitation
LMCT Excitation
MLCT Excitation
Intra Ligand
Excitation
Ligand-to Ligand (LLCT)
Excitation
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d-d Excited States of Transition Metals: LFT!
dxy dxz dyz
dx2-y2 dz2
dxy dxz dyz
dx2-y2 dz2hν
[V(H2O)6]3+
dxy dxz dyz
dx2-y2 dz2
3T1,2 3A23T1
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Electronic Difference Densities
d-d Transition
Red = Electron Gain Yellow= Electron Loss
LMCT Transition MLCT Transition π→π* Transition
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Spectroscopy and States
0SMΓ
I ′S ′M ′Γ
J ′′S ′′M ′′Γ
K ′′′S ′′′M ′′′Γ
Ener
gy
Apply some kind of oscillating perturbing field with Hamiltonian H1(ω) in order to induce transitions between different states of the system
Intensity
Transition Probability („Fermi‘s Golden Rule“)
I ∝ Ψ
initial| H
1| Ψ
final
2
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Light Matter Interaction
H1= Z
A
!RA,a
A∑ −
!ri,a
i∑
H1= (
!ri,a
!ri,b− 13ri2δab)
i∑
H1= 12(!li+ 2!si)a
i∑
Electric Dipole
Magnetic Dipole
Electric Quadrupole
In atomic units for a randomly oriented sample
fED
=23(E
f−E
i) Ψ
i|!µ
ED,a| Ψ
f
2
a=x ,y,z∑
fMD
=23α2(E
f−E
i) Ψ
i|!µ
MD,a| Ψ
f
2
a=x ,y,z∑
fEQ
=120α2(E
f−E
i)3 Ψ
i|!µ
EQ,ab| Ψ
f
2
ab=x ,y,z∑
ABS, MCD
XAS
CD, EPR
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Spectroscopic Selection Rules
Ψinitial| H
1|Ψ
final
2
★ The information about the allowedness of a transition is contained in:
★ Spin-Selection rule: ➡ The initial and final states must have the same total spin ➡ This is a strong selection rule up to the end of the first transition row. Beyond
this, strong spin-orbit coupling leads to deviations
★ Spatial-Selection rule: ➡ The direct product of Ψi, Ψf, and μ must contain the totally
symmetric irreducible representation ➡ This is a weak selection rule:something breaks the symmetry all the
time (environment, vibronic coupling, spin-orbit coupling, etc.)
Electric Dipole: Transforms as x,y,z If there is a center of inversion only g→u or u→g transitions are allowed, e.g. d-d transitions are said to be „Laporte forbidden“
Magnetic Dipole: Transforms as Rx,Ry, RzIf there is a center of inversion only g→g or u→u transitions are allowedElectric Quadrupole: Transforms as x2,y2,z2, xy,xz,yz
}
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MCD Spectroscopy - How and Why?
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LCPRCPLight SourceDetector
z
x
y
x
y
B-Field
The Magnetic Circular Dichroism Experiment
Monochromator Modulator
Sample
Liq. He Cryostat
Magnet
MCD = ALCP
B,T( )−ARCP
B,T( )− ALCP−A
RCP⎡⎣⎢
⎤⎦⎥B=0
Natural CD! "####### $#######
∝ cd Ef−E
i( ) Nj(B,T)
initialstates
∑ Ψj|%µ
ED,LCP| Ψ
f
2
− Ψj|%µ
ED,RCP| Ψ
f
2⎧⎨⎪⎪⎩⎪⎪
⎫⎬⎪⎪⎭⎪⎪final
states
∑
Does NOT Require a chiral substance!
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Shielded Detector
Focussing Lens
Magneto Cryostat
B,T-Control
CD SpectrometerSample Cell
The MCD Instrument @ MPI/Mülheim
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Why MCD Spectroscopy ?
‣ Sensitive Technique (esp. near-IR)‣ High Resolution (Signs)‣ Site Selective (Multiple Metal Sites)‣ Multidimensional (B,T,λ)‣ Does not require Isotopic Enrichment and is
not restricted to certain elements
‣ Has no Problems with Integer Spin ‣ Is not restricted to Para-
magnetic Species‣ Studies the Ground and
Excited States at the same
time‣ Puts Severe Constraints on
Possible Assignments
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Dimensions of a MCD Experiment
λfix, Variable B,T
= Lineshape function
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
ΔεE
= γβB −A1
∂f E( )∂E
+ B0
+C
0
kT
⎛
⎝
⎜⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟⎟f E( )
⎧⎨⎪⎪⎪
⎩⎪⎪⎪
⎫⎬⎪⎪⎪
⎭⎪⎪⎪
Linear Limit:
Spectral Dimension Magnetic Dimension („VTVH MCD“)
General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847
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MCD: Multidimensional Nature
[Fe(EDTA)(O2)]3-
Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829
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MCD: Resolution
Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122, 11703-11724
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MCD: Site Selectivity
CuAHa
Ha3-CuB
e-
O2
H2O
Cytochrome c Oxidase
Thomson, A.J. (1997) In: Andrews, D.L. (Ed.) Perspectives in Modern Chemical Spectroscopy, Springer, Berlin, p. 243
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MCD Fingerprinting: Heme-Cofactors
Marker Bands NIR-LS Fe(III)
CT-Spectra Axial LigandsCheesman, M. R.; Greenwood, C.; Thomson, A. J. Adv. Inorg. Chem. (1991), 36, 201
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MCD: Integer Spin Systems
0+/-1
B-Field
hν (EPR)S=1 Ground State
S=1 Exc. State
0+/-1
hν (MCD)
Dgs
Des
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Solvent Spectra
Thomson, A.J.; Cheesman, M.R.; George, S.K. (1993) Meth. Enzymol., 226, 199
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MCD Spectroscopy of 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-1
5,000 10,000 15,000Wavenumber (cm-1)
eg
t2g
a1
e
e
a1e
b1
b2
t2
e
Solomon et al. (1995) Coord. Chem. Rev., 144, 369
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Studying Enzyme Mechanisms
O2, 2e-, 2H+
Rieske-Dioxygenases
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Active Site Geometry from d-d Spectra
Holoenzyme
Rieske only
Difference
-Substrate +Substrate
6000 8000 10000 12000 14000 14000Energy (cm-1)
6000 8000 10000 12000 14000 14000Energy (cm-1)
Δε (M
-1 c
m-1
T-1
)
Δε (M
-1 c
m-1
T-1
)
Solomon et al., (2000) Chem. Rev., 100, 235-349
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Mechanistic Ideas from Ligand Field Studies
Solomon et al., (2000) Chem. Rev., 100, 235-349
Fe2+ Fe2+ Fe2+
Fe4+ Fe3+Fe4+Fe4+
COO--OOCCOO--OOC COO--OOC
OO
COO--OOC
(O O)2-
COO--OOC
-O O (H+)
COO--OOC
H H-O O-
2H+COO--OOC
H H
HO OH
2e- from reductase
products
or
+O2
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MCD Intensities
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Some General Trends
✓ MCD spectra that show about equal amount of positive and negative intensity are typically dominated by SOC between excited states
✓ MCD spectra that predominantly show one sign are typically dominated by SOC between the G.S. and the excited states (e.g. orbitally nearly degenerate systems)
✓ d-d excited states SOC effectively with each other and hence show relatively strong MCD. LMCT/MLCT states SOC more weakly and hence show weak MCD. ➡ The ratio of Absorption to MCD intensity
(=C/D ratio) is an effective means to determine the nature of the transition as d-d or CT
Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122, 11703-11724
Low-Spin Fe3+
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MCD C/D Ratios and d-d vs CT Assignments ★ MCD intensity is associated with Spin-Orbit Coupling (SOC) ★ MCD (C-term) intensities are larger for d-d than for LMCT/MLCT transitions. ★ LMCT/MLCT transitions are usually much more intense in absorption. ➡ The ratio of Absorption to MCD intensity is a diagnostic of a d-d vs CT transition:
CD
=kTβB
ΔεMCD
(ν)
νdν∫
εABS
(ν)
νdν∫
Area under MCD band
Area under Absorption band
εABS > 5000-10000 AND C/D<0.01 → CT transition
εABS < 5000-10000 AND C/D>0.01 → d-d transition
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MCD Example: CuCl42-
LMCT d-d
C/D~0.02
C/D~0.002
dz2→dx2-y2 dxz,yz→dx2-y2
dxy→dx2-y2
Established signs for CuII-MCD: dxz,yz→dx2-y2 : (+,-) ,pseudo-A‘ dxy→dx2-y2 : (-) dz2→dx2-y2 : (+)
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Theory of MCD Spectroscopy
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MCD Versus Ground State Methods
Electronic Ground State
Multiplet
Electronically Excited State
Multiplet
Total Spin S
2S+1 ComponentsMS=S,S-1,...,-S
Total Spin S‘
2S‘+1 ComponentsM‘S=S‘,S‘-1,...,-S‘
ΔE~5,000-45000 cm-1
ΔE~0-10 cm-1
ΔE~0-10 cm-1
∝ Ground State SH: ggs,Dgs,Jgs,...
∝ Excited State SH: ges,Des,Jes,...
Electronic Transitions
Probed with MCD
EPR Transition
21−
21−
21+
21+
Magnetic Field
Bg gsβ
Bgesβ
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Dimensions of a MCD Experiment
λfix, Variable B,T
= Lineshape function
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
ΔεE
= γβB −A1
∂f E( )∂E
+ B0
+C
0
kT
⎛
⎝
⎜⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟⎟f E( )
⎧⎨⎪⎪⎪
⎩⎪⎪⎪
⎫⎬⎪⎪⎪
⎭⎪⎪⎪
Linear Limit:
Spectral Dimension Magnetic Dimension („VTVH MCD“)
General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847
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Angular Momentum
Photons:
Cohen-Tanudji, C. et al. (1977) Quantum Mechanics, John-Wiley & Sons
Energy:
Momentum:
Angular Momentum:
• The Total Angular Momentum (Electrons and Photons) is Conserved• A Linearly Polarized Light Beam Contains Photons in a Superposition State• A Circularly Polarized Light Beam Contains Photons in a Pure Angular Momentum State
Craig, DP; Thrunamachandran, T (1984) Molecular Quantum Electrondynamics, Dover Publications
Electrons:Energy:
Momentum:
Angular Momentum: spin
orbit
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MCD A-Terms: A 1S 1P Transition
1S
1P
1S0
1P0
1P-1
1P1
rcp lcpm+1 m-1
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
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MCD C-Terms: A 1P 1S Transition1S
1P
1S0
1P0
1P-1
1P1
rcplcpm+1m-1
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
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MCD B-Terms:From Perturbation Theory:
Ø Mixing of the excited state or the ground State to potentially all other states via
the Zeeman interactionØ Inversely proportional to ΔE
Ø Absorption Shaped and Temperature IndependentØ Physically Intuitive Picture ?Ø Dominates MCD of Organic Molecules with Nondegerate Singlet Ground States
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
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For the Model 1P to 1S Transition
Insert:
Assume: FWHM=
A-term:
C-term:
Ratio A:B:C
Relative Magnitude of A- B- and C-Terms
A:B:C ≈ 1 : 0.1 : 5
Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197
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rcplcp
Boltzmann Population
Population Difference
Variable Temperature Variable H-Field MCDStephens, P.J. (1976) Adv. Chem. Phys., 35, 197
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Magnetization Curves of S=1/2 Systems
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VTVH MCD for S>1/2 Systems
T
Observations: • The MCD Signal Varies Nonlinearly with B and T • The Curves Recorded at Different Temperatures do 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
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Assumptions + Perturbation Theory (Hso, Hze)
Spin Hamiltonian!!FN; Solomon, E.I. (1999) Inorg. Chem., 38, 1847
General Ansatz:
(Lengthy Derivation)
Summary: A general theory of MCD
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General Theory for Nonlinear MCD
Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847
Direction Cosines (Orientation of B in the Molecular Frame)
Expectation Value of Sx,y,z for the SH Eigenstate i
Boltzmann Population of SH Eigenstate i
Orthogonal Effective Product of Transition Dipole Moments
Collection of ConstantsExperiment
Spin-Hamiltonian
(ALL B,T dependence)
Nature of Ground and
Excited States
Parameterization in terms of Spin-Hamiltonian and State Specific Polarization Parameters Achieved for the First Time
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Experimental Test: Fe(TPP)Cl (S=5/2)
Experimental Data: Browett, WR; Fucaloro, AF; Morgan, TV; Stephens, PJ J. Am. Chem. Soc., 105
Theoretical Prediction: 4D
2D
6S
S=5/2
Sum
Exp.
Theo.
Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847
Check the theory
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The effective g-value perpendicular to the plane of polarization
determines the amount of nesting
4D
2D
6S
(The Effective g-values are read from the rhombogram)
Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847
MCD and ZFS: Weak field case
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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!
Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847
MCD and ZFS: Strong field case
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Intermediate Field Case
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Transition Polarizations
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Electronic Transitions have a Direction
xy
z
E-Vector Orientation
x
yz
[Cu1.5...Cu1.5(SCys)2(NHis)4]+
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The MCD Equations knows something about it!
ΔεE=γ4πS
NilxMyzeff S
x i+ l
yMxzeff S
y i+ l
zMxyeff S
z i
⎡
⎣⎢⎢
⎤
⎦⎥⎥i
∑ sin θdθdφ∫∫
effective transition dipole productMxyeff (one direction is intrinsically allowed and an
orthogonal direction has to come from spin-orbit coupling with an orthogonally polarized excited
state)
If you have fitted the three products for a given band, you can figure out the linear polarization:
%mx= 100x
(MxyeffM
xzeff )2
(MxyMxz)2 + (M
xyMyz)2 + (M
xzMyz)2
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Transition Polarizations from Randomly Oriented Samples
Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829
z-pola rized
yz-pola rized
xz-pola rized
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Transition Assignments from MCD
Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829
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Insights into Metal-Ligand Bonding
Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829
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✓ MCD measures the differential absorption of left- and right circularly polarized light as a function of:
- Wavelength
- Magnetic Field
- Temperature
‣ MCD exists in all matter, does not require isotopes, paramagnetism, half-integer spin … ‣ MCD can be applied over the whole spectral range (200-2000 nm) ‣ MCD provides powerful fingerprints (even if you understand nothing what it means!) ‣ MCD can be site selective in systems with multiple sites ‣ MCD - unlike SQUID - is NOT a bulk measurement and hence impurity insensitive ‣ MCD as a function of B,T can be viewed as an optical measurement of magnetism
‣ MCD as a function of B,T and l provides transition polarization information in solution
‣ MCD to ABS ratios provide information about d-d vs charge transfer transitions ‣ MCD signs are powerful probes of the nature of electronic transitions ➡ MCD is an extremely powerful link between electronic ground state (EPR) and excited
states (ABS) methods
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Summary and Conclusions
★ MCD is a powerful and versatile spectroscopic technique for investigating open shell species.
★ It roughly contains the information of (polarized) absorption spectroscopy and magnetic susceptibility in a site selective fashion.
★ The theory of the nonlinear MCD behavior is now understood and widely used.
★ The quantum chemical calculation of MCD spectra of larger molecules very challenging as multireference, dynamic correlation, spin dependent relativistic effects and magnetic field perturbations must be considered simultaneously.
★ A particularly challenging case is met for magnetically interacting transition metal ions for which MCD golds great promise.
Have fun with .... ORCA
http://www.thch.uni-bonn.de/tc/orca