Basic concepts of Mößbauer spectroscopy (Mossbauer)

Basic concepts of Mößbauer spectroscopy (Mossbauer) 1961 Nobel price in Physics..for his researches concerning the resonance absorption of γ-radiation and his discovery in this connection of the effect which bears his name. http://nobelprize.org/nobel_prizes/physics/laureates/1961/mossbauer-bio.html

Mößbauer Spectroscopy Nuclear-Spectroscopy possible via hyperfine interactions between nucleus and electronic shell (Zeeman interaction) selected metals like 57 Fe, 61 Ni, 67 Zn, 99 Ru, 119 Sn, 181 Ta, 197 Au, various W and Os, Ir, Pt and Hg-isotopes, and some radioactive isotopes (e.g. 129 I)

E R Ev 2 2 R p 2 n 2 M Mößbauer Effect 1 Mössbauer effect (nuclear resonance absorption) In order to observe the Mössbauer effect 3 prerequisites are required: 1. Solid state in order to obtain nuclear resonant absorption 2. A radioactive source of γ-radiation delivering photons of the energy of the nuclear transition ground state excited state 3. The source energy must be tuned

E R Ev 2 2 R p 2 n 2 M 1. Solid state

Mößbauer Effect 4 Recoil no resonance absorption! Resonance absorption! Recoil-free emission of γ-radiation is only possible in a solid Qualitatively, The Mössbauer effect can be explained by a simple consideration: The recoil energy of a single nucleus is taken up by the whole lattice and the formula of the recoil energy (equation 4) does not contain the mass of the nucleus anymore. Instead, the mass is the mass of the lattice which is much larger leading to a negligible recoil energy, thus eventually enabling resonance absorption E Moss R 2M E 2 0 2 latticec 0

E R Ev 2 2 R p 2 n 2 M Mössbauer effect Mößbauer Effect 2 (nuclear resonance absorption) Gonser, topics in applied physics 5, Mössbauer spectroscopy,1975, p.4

E R Ev 2 2 R p 2 n 2 M Mößbauer Effect 2 2. Source of Gamma-Radiation

-energy source for 57 Fe Mößbauer spectroscopy Mößbauer Effect 5 57 Co-decay scheme energy spectrum of 57 Co(PHA), Ge(Li) detector Solid state matrices: -Pd, f 293K = 0.66 -Rh, f 293K = 0.78 Half life: 271.8 d K capture 57 Co I>=-7/2 57 Fe, I e2 >=-11/2 137 kev, t ½ = 9x10-9 s I e =-3/2 I g =-1/2 transition: - at 14.4 kev -internal conversion α= 8.21 -Life time t ½ : 97.810-9 s -Natural line width 2Γ= 0.194 mms -1 Solid state matrices: -Pd, f 293K = 0.66 -Rh, f 293K = 0.78

E R Ev 2 2 R p 2 n 2 M Mößbauer Effect 8 3. Energy-Tuning of the Mössbauer Source

E R Ev 2 2 R p 2 n 2 M Mössbauer effect Mößbauer Effect 8 (nuclear resonance absorption)

Mößbauer Effect 9 Resonant absorption (sample) Electrostatic energy shift due to s-electrons (isomer shift) Bbb Resonant emission(source) how can we meet resonance conditions?

Mößbauer Effect 10 magnetic field modulation in EPR Frequency modulation in NMR Wavelength modulation in IR, UV, Vis How is a precise modulation achieved with γ-rays?

Christian Doppler 1842 Mößbauer Effect 11 Observer Source λν=c Appplies for: λ O =λ S v/ν S sound waves, photons (light, γ-radiation etc.)

Doppler modulation of a Mössbauer source Eγ= (1+v/c)E 0 source v/c 5x10-4 [ev] Mößbauer Effect 12 Electrostatic shift (isomer shift): 5.10-4 ev(iron) In case of 57 Fe, v is in the order of [mms -1 ]

Mößbauer Effect 13 In order to obtain resonant absorption in Mössbauer spectroscopy, an energy modulation is required. This is achieved by Doppler modulation of a Mössbauer source. The energy of a resonance transition is described, therefore, by a velocity. The source is commonly moved in constant acceleration in order to cover a broad velocity range. Other sources: synchotron radiation

Most Mössbauer investigations are performed with 57 Fe Natural ambundance of 57 Fe: 2.2% of iron content.in biological samples enrichment with 57 Fe is required. Source of resonant radiation: 57 Co Novel radiation sources at synchotron sites (eg ESRF, DESY: Mößbauer spectroscopy in the time domain). Advantage: All states of iron can be observed in the sample. In biological samples, all 57 Fe binding biomolecules within the detectable concentration range of Mößbauer spectroscopy are detectable. In situ analysis of cells or cell compartments is possible. Disadvantage: The lower limit per species in a sample in case of 6-line transitions is 1mM 57 Fe, for a quadrupole doublet 350µM Sample must be in the solid state ( frozen solutions or cells, powders, foils) Sample volume of frozen cells is typically 0.5-1ml The method is expensive Mößbauer Effect 14

Electronic spins of Fe

57 Fe-Mößbauer Spectroscopy Chemical Informations on: Spin- and oxidation state (δ, ΔE Q ) Type of ligand (O,N,S) coordination number and geometry of bonding dynamics cooperative phenomena phase transitions in solids

57 Fe-Mößbauer Spectroscopy Biological Informations on: Iron transport processes In vivo redox processes Iron regulation Iron storage Dynamics of iron metabolism In situ analysis of enzyme systems

Typical iron proteins which have been analyzed by Mössbauer spectroscopy Cytochromes Hemoglobin Myoglobin Iron sulfur proteins oxygen bound dimeric iron centers transferrin Ferritins siderophores Mößbauer Effect 13

Cells, tissues and cell compartments that have been analyzed by Mössbauer spectroscopy Magnetosomes Bacteria Fungi Neuronal cancer cell lines Liver tissue Brain tissue Blood Spleen Heart tissue Plant leaves Algae Mößbauer Effect 14

Mößbauer Effect 15 TheMössbauerparameters 1. Isomer shift δ [mm.s -1 ] 2. Quadrupole splitting ΔEQ[mm.s -1 ] 3. Magnetic splitting B hf [T] or [kg] In addition: crystal field parameters D, E, coupling constant J

1. Isomer shift (δ) in mm/s Isomer shift 1

Isomer shift 1 Isomer shift (δ) Due to the Heisenberg uncertainty principle there is a small probability for the presence of s-electrons at the site of the nucleus. This small charge density leads to electric monopole interaction E(0)(Coulomb interaction) between nuclear charge and and electronic charge at the nuclear site altering the nuclear energy levels The electric monopole interaction is proportional to the s-electron density at the nucleus, ψ(0) 2, and is given by the following expression: E = 2/3π Ze 2 ψ(0) 2. <r 2 > δe (9) whith Ze= nuclear charge and <r 2 >=mean-square nuclear radius.

The ratio (δr/r) is known for most Mössbauer nuclides. In a Mössbauer experiment (δr/r) remains constant electron density of source and absorber will differ. If a standard source is employed ψ(0) S 2 is constant yielding δ = const (δ R/R) [ ψ(0) A 2 -C]

Isomer shift 2 Isomer shift Resonance absorption (isomer shift), observed by Doppler modulation Lorentzian line shape

Isomer shift 3 Fe FeII.tpa(NCS) 2 (tpa=tris(2-pyridylmethyl)amine) As an example a single line spectrum of FeII.tpa(NCS) 2 is shown. The isomer shift is 0.47 mm s 1 referenced against the isomer shift of metallic iron at 300 K (Trautwein and Winkler 1999). S=0

III.1. Meaning of δ[mm. s -1 ] in case of 57 Fe ψ 4s 2 δ ψ 3d,f 2 ψ valence tot 2 screening ψ 4s 2 δ Isomer shift 4 No 4s: ψ 3d 2 ψ 3s 2 (exchange interaction,core polarization) δ For example: Fe 2+ has a electron configuration of of (3d) 6 and Fe 3+ of (3d) 5. The ferrous ions have less 3s-electron density at the nucleus due to the greater screening of the d-electrons yielding a positive isomer shift greater in ferrous iron than in ferric.

Typical isomer shifts of iron in different oxidation states Isomer shift 5 In contrast to EPR spectroscopy, all spin states of iron can be observed in a Mössbauer experiment. If various oxidation states of iron are present in a sample they can be discriminated qualitatively and quantitavily.

Informations obtained from isomer shifts oxidation state symmetry and spin(together with ΔE Q ) (best is a spin Hamiltonian analysis) ligand type (0, N, S) Isomer shift 6 Strong electrostatic field of a ligand interacting with a nucleus compared to more covalent (weak) interaction: No 4s: ψ 3d 2 ψ 3s 2 (exchange interaction,core polarization) δ Example [Fe 2+ O 6 ]: δ 1.1-1.35 Example [Fe 2+ S 4 ]: δ 0.65-0.75 Iron II high spin Example [Fe 2+ N 4,N,O]: δ 0.85-1.1

η V xx V V zz yy Quadrupole splitting 1 2. Quadrupole Interaction (E2), Splitting ΔE Q

η V xx V V zz yy Quadrupole splitting 1 IV. Quadrupole Interaction (E2), Splitting ΔE Q

η V xx V yy zz IV. Quadrupole Interaction (E2), Splitting ΔE Q V Quadrupole splitting 1 Requirements for an electric quadrupole interaction between the electronic shell and the nucleus are: a) an electric field gradient (EFG) caused by an asymmetric charge distribution of the electronic shell. b) a non-spherical charge distribution Q at the nucleus, described by an nuclear quadrupole tensor eq A nucleus with a spin I 1 always exhibits a non-spherical charge distribution. For nuclei with halfinteger spin I quadrupole interaction leads to I=+1/2 states. In case of an integer spin I, I+1 states are observed. In the nuclear excited state of 57 Fe, I e = 3/2 we obtain a non-spherical charge distribution of the nucleus. The interaction with an EFG will partially lift the degeneracy: I e3/2 m Ie =±1/2 and m Ie =±3/2 ΔE Q is a measure of the deviation from octahedral, tetrahedral or axial symmetries

Quadrupole splitting 2 We yield: a ground state Ig=1/2 with m Ig =±1/2 an excited state I e =3/2 m Ie =±1/2 and I e =3/2, m Ie =±3/2 The energy difference beween the two states is given by the quadrupole splitting ΔE Q

Quadrupole splitting 2

Based on an appropriate Hamiltonian the energy eigenvalues for I=3/2 have exact solutions. Quadrupole splitting 2 ΔE Q 1 2 eqv zz 1 η 3 2 The largest component of the EFG-tensor, V zz and the asymmetry parameter η can only be determined separately when an magnetic interaction is present in addition. Complete analysis in an applied field is possible only employing the Hamiltonian formalism

example myoglobin deoxy myoglobin, PDB: 1A6N b-type heme (1 axial histidine), 16.7kDa MM, oxygen binding in muscle. Function not completely clear. Fe 2+ high spin,

Quadrupole splitting 2 As an example the Mössbauer spectrum of deoxy-myglobin at 4.2 K is shown. It is influenced by combined electric monopole and quadrupole interaction. The centre of the doublet yields an isomer shift of 0.98 mm s 1 referenced against metallic iron at 300 K. The splitting is the quadrupole splitting ΔE Q = -2.22 mm s 1 (taken from Ober et al 1997). The minor component represents Mb which is ligated to CO. A very small third doublet indicates the presence of another impurity Fe 2+ high-spin

example myoglobin purplish brownish Cherry-red red

example myoglobin oxy myoglobin, PDB: 1A6M δ=0.29 mm.s -1 ; ΔE Q =1.71 mm.s -1, S=0

example myoglobin met myoglobin, : δ= 0.42 mm.s -1 ; ΔE Q = 1.24mm.s -1 Fe 3+, high spin; distal: histidin, H 2 O or OH-

example: Blocking of O 2 storage in the muscle protein myoglobin by CO Quadrupole splitting 3 δ=0.29mms -1, ΔE Q =0.39mms -1 Fe 2+, low spin; S=0 PDB: 3E50; PNAS v106, p.2612-2616

myoglobin Carboxy-Mb (MbCO) (0.4% CO sealed) Deoxy-Mb (vacuum sealed) Not allowed in the EU

Myoglobin, Mössbauer summary Compound Iron, coordination Spin δ [mm.s -1 ] ΔE Q [mm.s -1 ] Deoxy-Mb Fe 2+ ; 5 2 0.98-2.22 Oxy-Mb Fe 2+ ; 6 0 0.29 1.71 Met-Mb Fe 3+, 6 5/2 0.42 1.24 CO-Mb Fe 2+, 6 0 0.29 0.39

Quadrupole splitting 3 example: rubredoxin [FeS 4 ] Small protein, 7kDa size functions not clear yet. Oxidative stress response? coordination of iron by 4 sulfur chelating groups

Quadrupole splitting 3 example: rubredoxin Mössbauer parameter: [Fe 2+ S 4 ]:δ 0.7 mms -1,ΔE Q 3.1 mms -1 [Fe 3+ S 4 ]:δ 0.32 mms -1 ΔE Q -0.5 mms -1 Fe 2+ high spin, S=2 Fe 3+ high spin, S=5/2

For comparison Quadrupole splitting 3 [Fe 2+ O 6 ], S=2: δ 1.1-1.3 mms -1 ΔE Q 2.4-3.3 mms -1 [Fe 3+ O 6 ], S=5/2: δ 0.48-0.75 mms -1 ΔE Q 0.55-0.8 mms -1 E. coli cells, grown with Fe(citrate) 2 measured at 4.3 K [Fe 2+ O 6 ], S=2: δ=1.31 mms -1 ; ΔE Q =3.08 mms -1 ferrochelatin [Fe3+O 6 ], S=5/2: δ=0.52 mms -1 ; ΔE Q = 0.58 mms -1 Ftn

[2Fe-2S] cluster Inorganic sulfur bridges Fe {[(Fe 2 S 2 )] 3+ S 4 } 5-, {[(Fe 2 S 2 )] 2+ S 4 } 6- Rieske protein Spin coupling: a) Fe3+/Fe2+ S=5/2 + 2 = ½ b) Fe3+/Fe3+ S=5/2 + 5/2 = 0 {[(Fe 2 S 2 )] 3+ N 2 S 2 } 5-, {[(Fe 2 S 2 )] 3+ N 2 S 2 } 6- Negative charge: delocalization MO calculations

FhuF- Protein of E.coli : Cells were grown in 57 Ferich medium and the protein was isolated by chromatography. The Mössbauer spectra (Fig.1) display features of an -cys 2 [2Fe-2S]cys 2 - motif (S=1/2-system, parameters see table 1). δ mms -1 ΔE Q mms -1 % Γ mm s -1 Partially reduced FhuF(190K, H ext = 200 G perp.) 0,584(4) 3,030(133) 37,82 0,400(1) 0,298(5) 0,978(13) 37,82 0,480(1) 0,222(8) 0,458(46) 24,36 0,288(1) Oxidized FhuF,as isolated(4.2k, H ext =200 G perp.) 0,287(6) 0,474(11) 100 0,31(1) SOD Oxidized FhuF,as isolated(190k,h ext = 200 G perp.) 0,222(2) 0,458(3) 100 0,286(1)

3+ 2+ Model for the spin arrangement in an applied field (a) [Fe 4 S 4 ] 2+ (2Fe 3+ (S=5/2)+2Fe 2+ (S=2) The dashed line indicates electron delocalization:fe 3+ +Fe 2+ 2Fe 2.5+ The total spin is S = 0 for [Fe 4 S 4 ] 2+ and S = ½for [Fe 4 S 4 ] 1+. b) [Fe 4 S 4 ] 1+ (1Fe 3+ (S=5/2)+3Fe 2+ (S=2) The total spin is S = ½for [Fe 4 S 4 ] 1+. [Fe 4 S 4 ] 2+ 2+ 2+ δ= 0.39-0.46 mm.s -1 Δ= 0.85-1.25 mm.s -1

3. Nuclear dipole splitting in 57 Fe (nuclear Zeeman effect)

Magnetic splitting 1 The magnetic field has two contributions, an external field B 0 and an internal hyperfine field B hf. For most cases, the internal field is much higher than the external magnetic fields. For example, metallic iron exhibits a magnetic hyperfine field of -33T at 300K. The magnetic hyperfine field at the nuclear site is B hf = B fc + B so + B dipol + B lattice B fc : Fermi- contact interaction; B so : Spin-orbit interaction ; B dipol : dipole interaction with shell electrons; B lattice : lattice contribution.

Magnetic splitting 1 Magentic Hyperfine Ineraction (M1), Magnetic Hyperfine Splitting ΔE M In a magnetic field (Zeeman interaction), the degeneracy of the nuclear spin states is completely lifted. For 57 Fe, the selection rule ΔI=1, Δm I =0, ±1 gives rise to a six-line pattern. The energy eigenvalue E M of a nuclear spin I in an external/internal magnetic field B 0 is E M = -g N.µ N.B 0 m I with µ N = nuclear Bohr magneton, g N =nuclear g-factor leading to the energy differences between nuclear ground and excited state ΔE M (m e ;m g ) = B 0 (m I,e g N,e µ N m I,g g N,e µ N )

Nuclear dipole splitting in 57 Fe (nuclear Zeeman effect) Magnetic splitting 2 selection rule ΔI=1, Δm I =0, ±1

Combined Magnetic and Quadrupole Interactions Magnetic splitting 3

Conditions for the observation of magnetic splitting Three time scales have to be considered: 1. the lifetime of the Mössbauer event, 2. the Larmor precession time 3. and the relaxation time of electron spins coupling to a nucleus. The lifetime of the Mössbauer event, τ m, which is also the limiting time scale of the measurement technique, is determined by the Heisenberg uncertainty relationship. For 57 Fe this is of the order of 10-7 s. The second time scale to consider is the minimum time required for the nucleus to detect the hyperfine field. This is usually assumed to be equal to the Larmor precession time, τ L, which can be considered as the time taken for a nuclear spin state, I, to split into (2I+1) substates under the influence of a hyperfine field. τ L is proportional to the magnitude of the hyperfine field (and hence related to the nuclear energy levels) with the following relation τ L = 2πh/gµ N B In iron oxides the hyperfine field is 40-50 T giving τ L of the order of 10-8 s. This means that τ m >> τ L and hence the hyperfine fields are detectable by the technique.

Examples compound coordination electron spin rubredoxin [FeS 4 ] 1-5/2 35 Ferricrocin [Fe 3+ (O 3 X 3 ) 3- (OY) 30 ] 0 5/2 56 Ftn (E. coli) FePO 4 5/2 43 ferritin (horse spleen) (FeOOH)8 5/2 50 FeOH 2 PO 4 lepidocrite γ-feooh 5/2 B hf [T] Goethite α-feo(oh) 5/2 50.6 hematite α-fe 2 O 3 5/2 54.2 maghemite γ-fe 2 O 3 5/2 50 Magnetite Fe 3 O 4 2, 9/2 s. A:49.3 s. B:47.1 α-iron α-fe metal 33

Summary