Magnetic Circular Dichroism Spectroscopy

Transcription

1 Magnetic Circular Dichroism Spectroscopy Frank Neese Max Planck Institute for Chemical Energy Conversion Stiftstr Mülheim an der Ruhr

2 The Faraday Effect 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 13 th September Vol. IV, G. Bell and Sons Ltd., London 1933) f : Rotation angle of plane polarized light V : Verdet Constant B : Magnetic Field d : Length of Light Path Michael Faraday

3 The Faraday Effect Faradays actual horseshoe magnet (1845) (Faraday Museum, London) Molecular property (wavelength dependent)

4 Circular Dichroism vs Optical Rotary Dispersion ORD CD e De : optical rotation of plane polarized light as f(l) (dispersive) : Differential absorption of right and left circularly polarized light as f(l) (absorptive) ABS CD Kramers-Kronig Transform q ORD l

5 Photons, Electrons, States, Spectra & all that

6 Anatomy of a Light Wave B E λ k 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 Linear Polarization 1 2 ( k + + k ) Circular Polarization (RCP, LCP) k + or k

7 Energy Scale of Optical Spectroscopy Gamma X-Ray UV/vis Infrared Microwave Radiowave ev IR ABS EPR ENDOR Möss- XAS bauer EXAFS MCD Raman CD NMR

8 STATES of a System ONE-ELECTRONIC-STATE of a molecule: Orbital energy Configuration: Distribution of electrons among orbitals (singly- and doubly occupied orbitals) ni 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 a 3 B 1g Ψ 0 11;B 1g nismg> Ψ I SM ;Γ wavefunction for this STATE

9 Excited States in Transition Metal Complexes Orbital Energy } } } } Ligand1 Metal d-shell Ligand2 Ligand1 d-d Excitation LMCT Excitation MLCT Excitation Intra Ligand Excitation Ligand-to Ligand (LLCT) Excitation

10 d-d Excited States of Transition Metals: LFT! d x2-y2 d z2 hν d x2-y2 d z2 d x2-y2 d z2 d xy d xz d yz 3 T1 d xy d xz d yz 3 T1,2 d xy d xz d yz 3 A2 [V(H 2 O) 6 ] 3+

11 Electronic Difference Densities d-d Transition LMCT Transition MLCT Transition π π * Transition Red = Electron Gain Yellow= Electron Loss

12 Spectroscopy and States Apply some kind of oscillating perturbing field with Hamiltonian H1(ω) in order to induce transitions between different states of the system K S M Γ Energy J S M Γ I S M Γ Transition Probability ( Fermi s Golden Rule ) I Ψ initial H 1 Ψ final 2 0SMΓ Intensity

13 Light Matter Interaction Electric Dipole A Ĥ 1 = Z A! RA,a i! r i,a ABS, MCD a=x,y,z f ED = 2 3 (E f E i ) Ψ i! µ ED,a Ψ f 2 Electric Quadrupole i Ĥ 1 = (! r i,a! ri,b 1 3 r i2 δ ab ) XAS ab=x,y,z f EQ = 1 20 α2 (E f E i ) 3 Ψ i! µ EQ,ab Ψ f 2 Magnetic Dipole Ĥ 1 = 1 ( l! 2 i + 2 s! i ) a i CD, EPR a=x,y,z f MD = 2 3 α2 (E f E i ) Ψ i! µ MD,a Ψ f 2 In atomic units for a randomly oriented sample

14 Spectroscopic Selection Rules The information about the allowedness of a transition is contained in: Spin-Selection rule: Ψ initial Ĥ1 Ψ final 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, Rz } If there is a center of inversion only g g or u u Electric Quadrupole: Transforms as x 2,y 2,z 2 transitions are allowed, xy,xz,yz 2

15 MCD Spectroscopy - How and Why?

16 The Magnetic Circular Dichroism Experiment Sample Monochromator Modulator x x B-Field Light Source y RCP y LCP z Detector Does NOT Require a chiral substance! Magnet Liq. He Cryostat MCD = A LCP cd E f ( B,T ) A ( RCP B,T ) A LCP A!###### "####### RCP B=0 $ ( ) N j (B,T) E i initial states Natural CD Ψ j µ % 2 ED,LCP Ψ f Ψ j µ % 2 ED,RCP Ψ f final states

17 The MCD MPI/Mülheim Sample Cell CD Spectrometer Shielded Detector B,T-Control Magneto Cryostat Focussing Lens

18 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

19 Dimensions of a MCD Experiment Linear Limit: Δε E = γβb A 1 f ( E) = Lineshape function E + B + C 0 0 kt ( ) f E Spectral Dimension Magnetic Dimension ( VTVH MCD ) λ fix, Variable B,T Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197 General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847

20 MCD: Multidimensional Nature [Fe(EDTA)(O 2 )] 3- Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829

21 MCD: Resolution Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122,

22 MCD: Site Selectivity Cytochrome c Oxidase e - Cu A H a H 2 O H a3 -Cu B O 2 Thomson, A.J. (1997) In: Andrews, D.L. (Ed.) Perspectives in Modern Chemical Spectroscopy, Springer, Berlin, p. 243

23 MCD Fingerprinting: Heme-Cofactors Marker Bands NIR-LS Fe(III) CT-Spectra Axial Ligands Cheesman, M. R.; Greenwood, C.; Thomson, A. J. Adv. Inorg. Chem. (1991), 36, 201

24 B-Field MCD: Integer Spin Systems +/-1 0 S=1 Exc. State D es hν (MCD) +/-1 0 S=1 Ground State D gs hν (EPR)

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

26 MCD Spectroscopy of HS Fe(II) Systems 10,000 cm -1 6C e g t 2g 5,000 cm -1 10,000 cm -1 5C b 2 e a 1 b 1 <5,000 cm -1 7,000 cm -1 5C a 1 e e 5,000 cm -1 4C t 2 e 5,000 10,000 15,000 Solomon et al. (1995) Coord. Chem. Rev., 144, 369 Wavenumber (cm -1 )

27 Studying Enzyme Mechanisms Rieske-Dioxygenases O 2, 2e -, 2H +

28 Active Site Geometry from d-d Spectra -Substrate +Substrate Holoenzyme Rieske only Difference Δε (M -1 cm -1 T -1 ) Δε (M -1 cm -1 T -1 ) Solomon et al., (2000) Chem. Rev., 100, Energy (cm -1 ) Energy (cm -1 )

29 Mechanistic Ideas from Ligand Field Studies - OOC COO - - OOC COO - - OOC COO - O O +O2 Fe 2+ Fe 2+ Fe 2+ 2e - from reductase Fe 4+ - OOC COO - H H - O O - Fe 4+ - OOC COO - - OOC (O O) 2- Fe 4+ or Fe 3+ COO - - O O (H+ ) - OOC COO - H H HO OH products 2H + Solomon et al., (2000) Chem. Rev., 100,

30 MCD Intensities

31 Some General Trends MCD spectra that show about equal amount of positive and negative intensity are typically dominated by SOC between excited states Low-Spin Fe 3+ 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,

32 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: C D = kt βb Δε MCD (ν) dν ν ε ABS (ν) dν ν Area under MCD band Area under Absorption band εabs > AND C/D<0.01 CT transition εabs < AND C/D>0.01 d-d transition

33 MCD Example: CuCl4 2- LMCT d-d Established signs for Cu II -MCD: dxz,yz dx2-y2 : (+,-),pseudo-a dxy dx2-y2 : (-) dz2 dx2-y2 : (+) C/D~0.02 dz2 dx2-y2 dxz,yz dx2-y2 C/D~0.002 dxy dx2-y2

34 Theory of MCD Spectroscopy

35 MCD Versus Ground State Methods Electronically Excited State Multiplet Total Spin S 2S +1 Components M S =S,S -1,...,-S ΔE~5, cm -1 g es βb ΔE~0-10 cm -1 Excited State SH: g es,d es,j es,... Total Spin S Electronic Ground State Multiplet 2S+1 Components M S =S,S-1,...,-S EPR Transition g gs βb Electronic Transitions Probed with MCD 1 2 ΔE~0-10 cm -1 Ground State SH: g gs,d gs,j gs,... Magnetic Field

36 Dimensions of a MCD Experiment Linear Limit: Δε E = γβb A 1 f ( E) = Lineshape function E + B + C 0 0 kt ( ) f E Spectral Dimension Magnetic Dimension ( VTVH MCD ) λ fix, Variable B,T Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197 General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847

37 Angular Momentum Photons: Electrons: Energy: Momentum: Angular Momentum: Energy: Momentum: Angular Momentum: spin orbit 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 Cohen-Tanudji, C. et al. (1977) Quantum Mechanics, John-Wiley & Sons Craig, DP; Thrunamachandran, T (1984) Molecular Quantum Electrondynamics, Dover Publications

38 MCD A-Terms: A 1 S 1 P Transition 1 P 1 Stephens, P.J. (1976) Adv. Chem. Phys., 35, P 1 P 0 1 P -1 rcp lcp m +1 m -1 1 S 1 S 0

39 MCD C-Terms: A 1 P 1 S Transition 1 S 1 S 0 Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197 lcp m -1 rcp m +1 1 P 1 1 P 1 P 0 1 P -1

40 MCD B-Terms: From Perturbation Theory: Ø Mixing of the excited state or the ground State to potentially all other states via the Zeeman interaction Ø Inversely proportional to ΔE Ø Absorption Shaped and Temperature Independent Ø Physically Intuitive Picture? Ø Dominates MCD of Organic Molecules with Nondegerate Singlet Ground States Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197

41 Relative Magnitude of A- B- and C-Terms For the Model 1 P to 1 S Transition Insert: Assume: FWHM= A-term: C-term: Ratio A:B:C A:B:C 1 : 0.1 : 5 Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197

42 Variable Temperature Variable H-Field MCD Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197 lcp rcp Boltzmann Population Population Difference

43 Magnetization Curves of S=1/2 Systems

44 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

45 Summary: A general theory of MCD General Ansatz: Assumptions + Perturbation Theory (H so, H ze ) (Lengthy Derivation) Spin Hamiltonian!! FN; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

46 General Theory for Nonlinear MCD Direction Cosines (Orientation of B in the Molecular Frame) Collection of Constants Experiment Expectation Value of S x,y,z for the SH Eigenstate i Boltzmann Population of SH Eigenstate i Orthogonal Effective Product of Transition Dipole Moments 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 Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

47 Check the theory Theoretical Prediction: 4D 6 S 2D Exp. Theo. Experimental Test: Fe(TPP)Cl (S=5/2) Sum S=5/2 Experimental Data: Browett, WR; Fucaloro, AF; Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

48 MCD and ZFS: Weak field case The effective g-value perpendicular to the plane of polarization determines the amount of nesting 6 S 4D 2D (The Effective g-values are read from the rhombogram) Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

49 MCD and ZFS: Strong field case The MCD magnetization for vanishing ZFS behaves exactly like a Brillouin Function for spin S Uncritically Assumed in (too) Many Studies! Attention: May be Difficult to Distinguish from Case with large ZFS and Easy Axis Polarization Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

50 Intermediate Field Case

51 Transition Polarizations

52 Electronic Transitions have a Direction z y x E-Vector Orientation x [Cu Cu 1.5 (SCys)2(NHis)4] + z y

53 The MCD Equations knows something about it! Δε E = γ 4πS i N i l x M yz eff S x i eff +l y M xz S y i eff +l z M xy S z i sin θdθdφ M eff xy effective transition dipole product (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: %m x = 100x (M eff xy M eff xz ) 2 (M xy M xz ) 2 +(M xy M yz ) 2 +(M xz M yz ) 2

54 Transition Polarizations from Randomly Oriented Samples z-pola rized yz-pola rized xz-pola rized Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829

55 Transition Assignments from MCD Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829

56 Insights into Metal-Ligand Bonding Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829

57 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 ( 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

58 Summary and Conclusions MCD is a powerful and versatile spectroscopic technique for investigating open shell species. Have fun with... ORCA 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.