Applied Physical Inorganic · PDF file•One of the least sensitive spectroscopic methods...

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Applied Physical Inorganic Chemistry:

Spectroscopy from a Chemist’s Point of View

Inorganic & General Chemistry Summer 2006

Karsten Meyer

04/25/06

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The Organic Chemist’s Toolbox

N

NN

NHH

H H

• Nuclear Magnetic Resonance Spectroscopy, e.g. 1H, 13C, 14N

• Vibrational Spectroscopy (Infrared & Raman)

• Mass Spectroscopy (GC-MS)

• Electronic Absorption Spectroscopy (UV/Vis/NIR)

The Bioinorganic’s Chemist Toolbox

N

NN

NHH

H H

Fe

NMR (especially paramagnetic NMR techniques!), IR, Raman, UV/Vis

…but way more info, e.g.:

Electronic & Molecular Structure

Electron Paramagnetic Resonance (EPR) Spectroscopy

combine with NMR: ENDOR: Electron Nuclear Double Resonance (Sensitivity of EPR, Positive Linewidth Characteristics of NMR)

Magnetization Measurements (SQUID, Faraday, Gouy, Evans)

Mößbauer Spectroscopy, Magnetic Circular Dichroism (MCD)

EXAFS, Resonance Raman (UV/Vis & Raman), and many more…

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• Paramagnetic NMR - the general idea.

• In Detail: The Glorious Three: EPR, SQUID, Mössbauer

Electronic & Structural Information:

• Number of unpaired electrons,

• Electron configuration: low-spin vs. high-spin

• Nuclearity (mononuclear, di-, or polynuclear species

• Ligand Environment, Symmetry, Structure

same as ENDOR but for smaller ALiiElectron Spin Echo

Envelope Modulation

see aboveidentification of ligand electric field gradient at ligand nuclei

ALii

nuclear Zeeman effect (gNβNH),ligand quadrupole coupling P

Electron Nuclear Double Resonance (ENDOR)

see abovecovalency of M-Li bond

gi, AMi, D, E,

ligand super-hyperfine coupling (ALii)

Electron Paramagnetic Resonance (EPR)

oxidation state and spin stateorbital angular momentum and metal covalency of ground state

isomer shift (δ), metal quadrupole splitting (∆EQ), metal hyperfine (AM), electron Zeeman effect (gi, i =x,y,z), zero-field splitting

Moessbauer

ground state spin

low symmetry splitting of d-orbitals and their relative covalency

molar susceptibility (χM), effective magnetic moment µ= 2.828(χMT)-1/2, axial (D) and rhombic (E) zero-field splitting, exchange coupling constants

Magnetism

Ground State Methods

Information ContentParametersMethod


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probes ground state parametersvariable temperature variable field

see aboveprobes nature of excited state

energies, bandshapesintensities (A, B, C – Term)

Magnetic Circular Dichroism

see above + character of transitionresolution of bands, magnetic dipole

energies/bandshapesintensities (R = rotational strength)

Circular Dichroism

selection rules for transition allows assignments,

parallel (π), perpendicular (σ) and axial (α) polarized spectra

Polarized Single Crystal Absorption

LF splitting of d-orbitals = geometrydistortion of site from centrosymmetric excited state distortions—probes change in bonding on excitation

energies, intensities (f = oscillator strength), bandshapes

Electronic Absorption

Ligand-Field Excited State Methods



effective charge on ligand and metalcovalency of M-Li bond

energyintensity

Ligand K-edge XAS

multiplet splitting gives oxidation and spin statecovalency of metal ion

energy dependence of intensity

intensity

L-edge XAS

effective nuclear charge on metal ionquadrupole and 4p mixing due to distortion of site from centrosymmetric

energyintensity

Metal K-edge X-ray Absorption Spectroscopy (XAS)

Core-Excited State Methods

assign vibrationsas with bandshapes gives excited state distortion

depolarization ratio (ρ)enhancement profiles

Resonance Raman

sensitive probe M-Li bond—quantitative ligand donor interaction

see aboveAbsorption/CD/MCD

Charge-Transfer Excited State Methods



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Basic Principles of NMR in diamagnetic species can be applied:

, = µN B0 = gNβNB0Iz = -(h/2π)γNB0Iz

γN: nuclear gyromagnetic momentgN: nuclear g factorβN: nuclear magnetonI : nuclear spin quantum number

Transition between the two energy levels I±1/2 of the 1H nucleusrequires an electromagnetic wave in the radio frequency range

Include shielding and deshielding:H = µN B0 (1-σ)

Paramagnetic NMR

deshielding effect:down-field shift, higher frequencies

3 3 9 3 3 3 3 9 9Integration:

[(TIMENXyl)FeCl]Cl

[(TIMENMes)FeCl]Cl

80 60 40 20 0 -20ppm

3 3 9 3 6 9 912Integration:

**+

Paramagnetic 1H NMR

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Paramagnetic NMR

Equations used for the description of NMR transitions are very similar to those for Electron Paramagnetic Resonance (EPR) transitions, but ∆E is very different!

NMR:Radio frequency:300 – 900 MHz

EPR:Microwave frequency:1 GHz: L-band3 GHz: S-Band9 GHz: X-Band34 GHz: Q-Band94 GHz: W-Band

• Very small energy gap between the two nuclear levels

• Small difference in spin population (Boltzman distribution)

• One of the least sensitive spectroscopic methods

Remember:The electron magnetic moment is 658 times larger than that of the proton!

The Chemical Shift δ

• Provides valuable info about the local environment of a nucleus.• Reflects subtle changes of the paired electron cloud on the nucleus due to perturbations by nearby atoms and electrons!• Electron spin density on the resonating nuclei controls δ• Large magnetic moment of the unpaired electron dramatically alters δ

Paramagnetic NMR

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Paramagnetic NMR

The Origin of the Paramagnetic Shift δ

1. Fermi Contact Interaction:Unpaired spin interacts with the nuclei via delocalizationonto the nuclei via chemical s and p orbitals.For example, high-spin Fe(III) and Fe(II) complexes usually show large down-field shifts (σ-delocalization). In contrast, low-spin Fe(III) porphyrins display smaller shifts (pyrrole H is usually upfield shifted) π-delocalization. Remember: Fe(II) l.s. is diamagnetic!

2. Dipolar Interaction:Through space coupling between the magnetic momentsof the nucleus and the unpaired electron

1. Fermi Contact Interaction:

Unpaired spin interacts with the nuclei via delocalization onto the nuclei through σ and π bonds.

Paramagnetic NMR

, = geβeB0S − gNβNB0I + Ac S I

electronic nuclear Zeeman term

Fermi contact term

Ac: Hyperfine couplingconstant is independentof the orientation of themolecule with respect tomagnetic field

∆B −∆v −g β S(S+1) AcB0 v 3hγNkT

• Isotropic shift• Fermi contact shift = f(1/T)• Pos. Ac gives rise to

downfield shifted signals

Contact shift term:

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Fermi Contact Shift in paramagnetic molecules is caused by the unpaired electron density at the nucleus

Electron density at the nucleus results from a) direct delocalization and b) spin polarization

X = N, O, S

Paramagnetic NMR

Paramagnetic NMRFermi contact shift: through-bond interaction

a) Direct delocalization

b) Spin polarization

N

Fe

α

β

γ

N

Fe

α

β

γ

S o

m

p

Pathways can be distinguished by different shift pattern

Can be corroboratedby CH3 substitution

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2. Dipolar Interactionalternatively: through-space interaction

Paramagnetic NMR

Most clearly demonstrated by lanthanide complexes.

f-orbitals in La are shielded and generally donot participate in direct covalent bonding withLigand orbitals -> no mechanism for Fermi shift.

• Ligand binding is the same for different La

• Shift directly reflects magnetic properties of La

• Opposite shifts for different La is due to the opposite sign of magnetic susceptibility tensor

Application: Lanthanide ions as NMR shift probes of sites further away from metal ion

Paramagnetic NMR

Concluding remarks:

The NMR linewidth depends on nuclear relaxation mechanisms

Electronic relaxation time τe

slow relaxation -> broad lines10-8 – 10-11s: relaxation agents

h.s. Mn2+, h.s. Fe3+, Cu2+, Gd3+

fast relaxation -> sharp lines10-11 – 10-13: shift agents

h.s. Fe2+, Cu2+, Ni2+

low-spin FeIII hemes, Dy3+, Yb3+

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Electron Paramagnetic Resonance

EPR is the oldest magnetic resonance techniques (1944)

EPR measures the absorption of electromagnetic radiation by a paramagnetic system placed in a static magnetic field:

constant frequency ∆E = hν, varying magnetic field µBgB; “g” is wanted

(remember: NMR varying frequency, constant field!)

EPR is an extremely powerful tool and very versatile

Samples can be recorded in frozen & liquid solutions,in single crystals, in matrices, in gases and in vivo.

inorganic & organic radicals (1A/3B carbene & nitrene, NOx, O2)

paramagnetic transition metal complexes


< 3001.95 – 2.0Xanthine oxidase1/24d1Mo(V)< 3002 – 2.4Plastocyanin1/23d9Cu(II)< 502 – 2.2Hydrogenase1/23d7Ni(III)< 1202.0 – 2.3Cobalamin(B12)1/23d7Co(II)< 5016Methane monooxygenase2-23d6 - 3d6Fe(II) Fe(II)< 501.7 – 2.1Bacterial ferredoxin1/23d5 – (3d6)3Fe(III) 3 Fe(II)< 502 – 2.2HiPIP1/2(3d5)3 - 3d63 Fe(III) Fe(II)< 502 – 2.1Aconitase1/2(3d5)33 Fe(III)< 501.25 – 2.1Spinach ferredoxin1/23d5 - 3d6Fe(III) – Fe(II)< 10010 – 0.25Lipoxygenase5/23d5Fe(III) non- ~< 1008 – 1.8Cytochrome P4505/23d5Fe(III) heme< 1003.8 – 0.25Cytochrome c1/23d5Fe(III) heme< 3002 – 6 Concanavalin5/23d5Mn(II)

~ 2 (Oh)Vanadyl-substituted1/23d1V(IV)

Temp.g-valuesExampleSpin State

Electr. Config.Metal Ion

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Basic equations:

µe = ge β • S

E = -µe • B

E = hν

µe: magnetic moment of the electronge: electron g-value, g factor, electron splitting factorβ: Bohr magneton: e/ 2m x h/2π

S: total Spin (a vector, or more precisely, an operator)

classical quantum mechanicalparticle circulating in a Bohr orbit

The quantum mechanical equivalent:

, = ge β S • B => E = geβmS B with ms = ± 1/2

see appendix: The Discovery of the Electron Spin (1925)


For BL= 3300 G, magn. field corresp. to g = 2 in X-band EPR (~ 9 GHz):∆E = 0.87 cal/mol

ZeemanEffect

0.1% net excess of spins in themore stable spin-down state!

Resonance Requirement:

hν = ∆E = g βB0 = g βBR with

EPR Selection Rule: ∆ms = ± 1(magnetic dipole transition)

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The principal componentsof a CW-EPR spectrometer

low frequency – bulky cavities, high frequency – small cavitiesvery high frequency – no cavities!


The Ferrari of spectrometers: Bruker’s ElexSys E500Dept. of Chemistry, Urey Hall 2nd floor

high-power, ultra-low noise Gunn source, Signal master locking detector, super high Q cavity ER4122SHQ, Temp. as low as 1.7K!

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Electron Paramagnetic Resonancea few practical tips:


The g-factor is a tensor, in general anisotropic, and deviates from 2.0023

in liquid solution in frozen solution, single crystals, proteins

square planar Cu2+ trig. bipyram. Cu2+

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Electron Paramagnetic ResonanceThe origin of the g-factor’s anisotropy:

Anisotropy in g arises from coupling of the spin angular momentum with the orbital angular momentum

, = ge β S • B − gNβNB • I + A I • S

β[Sx Sy Sz]gxx gxx gxxgyx gyy gyzgzx gzy gzz

BxByBz

Matrix is diagonal when the crystal axes are coincident with the molecular coordinate system that diagonalizes g

Both, the orbital and spin angular momenta contribute to the magnetic moment of an atomic electron:Orbital: µL = -- e/2m LSpin: µs = -- g e/2m S

Where g is the spin g-factor and has a value of about 2, implying that the spin angular momentum is twice as effective in producing a magnetic moment.


The origin of the g-factor’s anisotropy (and deviation from ge = 2.0023!):

, = – µz Bz

H atom in the gas phase posses a nonzero magnetic moment µ interacts with a static external magnetic field B via a direct coupling term of the classical form: – µ BZeeman Interaction:

The atomic magnetic moment is related to the total spin, S, and orbital, L, angular momenta.

The proportionality constantbetween µ and S is known as the free electron g value, ge = 2.002319304386(20).

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The origin of the g-factor’s anisotropy (and deviation from ge = 2.0023!):

, = – µz Bz

Energy eigenvalues can be found in the Russel-Saunders coupling scheme by using the z-component of J = L + S to label the states as:

EmJ = gJ µB mJ B (…recognize it? with ms = ½ : E"½ = "½ g µB B;and ∆E = g µB B)

Landé splitting factor gJ

The simplest EPR experiment can be performed on a free electron, or on a 2S1/2 atom in the gas phase (see atomic spectra) two Zeeman levels with mJ = ms = " ½, with magnetic field B:

hν0 = geµB B0 for any other species gexp = geB0/Br


The origin of the g-factor’s deviation from ge = 2.0023:

Key-word: Spin-orbit coupling: λ L • S with λ = ± ζ/2S

• The spin-orbit coupling constant, ζ, has the dimension of energy (cm-1).• Value depends on Z, the atomic number of the nucleus.• ζ(Ti3+) = 150 cm-1, ζ(Cu2+) = 830 cm-1, ζ(U5+) = 2180 cm-1

+ d1 – d4

− d6 – d9

U(V) f1

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λ L • S with λ = ± ζ/2S

• ∆i from UV/vis spectra• ζ is often reduced (covalency)

Electron Paramagnetic ResonanceEPR g-factors from single-crystallineCytochrome C Oxidase with the magnetic field aligned to each of the principal axes

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The origin of the g-factor’s deviation from ge = 2.0023:

• Mononuclear transition metal complexes with S = ½• Spin coupled di- or polynuclear complexes with Stot = ½

Fe O Fe

d5, S=5/2 O2-

dxy dxypx

π-exchange

σ-exchange

d5, S=5/2

dz2 pz dz2

For details on spin-exchange see:Goodenough & Kanamori rules

• Transition metal complexes with half-spin systems S > ½

• Molecules and cluster with integer-spin systems S = 1, 2, 3…carbene, nitrene, mono-, di-, and polynuclear complexes and cluster


=> a) Zero-field splitting D, b) (Super-) Hyperfine coupling A

d1, S = ½d2, S = 1

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In molecules with more than one unpaired electron a new phenomenon has a great impact on the EPR spectrum,

namely axial zero-field-splitting (zfs) parameter D

Energy separation of mS states in theabsence of an applied magnetic field:

,zfs= D[Sz2 – 1/3 S2

+ E/D(Sx2 – Sy

2)]

Electron Paramagnetic ResonanceNO zfs, D = 0 small zfs, 0 ≤ D ≤ hν

Energy(ms) =D {ms

2 − 1/3[S(S + 1)]}

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Electron Paramagnetic ResonanceBest-case scenario: Spectrum of a single crystal of Mn2+ doped into MgV2O6

showing the five allowed transition each split by the Mn nucleus (I =5/2, 100% - hyperfine structure)


,zfs= D[Sz2 – 1/3 S2+ E/D(Sx

2 – Sy2)]

D >> hν

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D >> hν, E/D = 1/3

Splitting of the three Kramer’s dublets arising from an S = 5/2 spin state by the effect of zero field splitting and the magnetic field

Electron Paramagnetic ResonanceIn practice: Spectrum of high-spin Fe3+ containing biological systems D = 1 – 10 cm-1:

⎮5/2 ⟩⎮3/2 ⟩⎮1/2 ⟩

uppermiddlelower

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Effective g-values for the three Kramers doublets of an S=5/2 spin multiplettvs. the rhombicity parameter E/D (g0 = 2)…same thing, different view

Electron Paramagnetic ResonanceS= 3/2 Spectra: Spin-Spin coupled complexes and cluster,

intermediate-spin Fe3+

a) Isopenicillin N synthase, E/D = 0.015b) Fe-Mo cluster of Nitrogenase E/D = 0.03c) FeIIIFeII(bpmp)(OPr)2, E/D = 0.32

T = 3K, T = 44K (low lying exc. state S=5/2)

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Electron Paramagnetic ResonanceHyperfine Interaction:

A(MHz) = µB/(hg A(G))= 1.39962 g A(G)

A(cm-1) = A(MHz)/c= 4.66863 10-4 g A(mT)

Ahfs is commonly reported in units of G (function of the g-value)

(2I n + 1) hf-linesequally spaced,equally intense

A⊥ is not resolved


25 (comb)5/295,97Mo7.51/277Se13/261Ni

100 (comb)3/263,65Cu1007/259Co2½57Fe

1005/255Mnca. 1007/250V

100½31P0.73/233S100½19F0.045/217O0.4½15N

ca. 100114N1½13C

0.0112Dca. 100½1H

% natural AbundanceSpinNucleus

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50, 52, 54Cr: I = 0, 90.5%53Cr: I = 3/2, 9.5% (n = 1)

14N, I = 1, 99.45% (n = 5(6))1H, I = 1/2, I = 99.985% (n = 4)

problem: too many interactions - solution: add D2O

“100%” 2H, I = 1, but γN(2H) = 1/7 γN(1H)

keep in mind:(2I n + 1) hf-lines

last but not least: hyperfine coupling in anisotropic spectra

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d1, S = ½

Mo(IV), d2, S = 1

Mo(norbornyl)4 Schrock et al.Mo(V), d1, S = 1/2

µB = 1.73 B.M. µB = 2.83 B.M.

Magnetization Measurements

Magnetization MeasurementsConsider N molecules with S = ½,

in the presence of a magnetic induction B, each molecule has one of the two following energies: ½ g β B or −½ g β B (see EPR)

Each molecule projects a magnetic field on B equal to ½ g β and −½ g β

The distribution of N molecules into the two states obeys Boltzmann’s law:

g = Landé factor, β = 9.2740154 x 10-24 J T-1, NA = Avogadro’s number, µ0 = 4π x 10-7 A-1mTk = Boltzmann’s constant

The Magnetization M is obtained by summing the magnetic moments:

since N1 > N2, M is positive & parallel to magnetic induction: PARAMAGNETIC

if gβB/kT << 1:

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What do we learn from this equation? M % B and M % T-1

… but how do we get from here to:

1.731/2d1

7.947/2f7

6.933f6

5/2, 3/2, or 1/2d5

4.902 or 1d4

3.873/2 or 1/2d3

2.831 or 0d2

µeff (spin-only) @ RTSelectron configuration


χ = µ0M/B, χ is the magnetic susceptibility, and – at this point – dimensionless

take M (from SQUID @ 1T) and divide by mass of sample used (10-30 mg)

² χg multiply with molecular weight: χM

Important: χM has a diamagnetic contribution, which is opposite in sign!

χM = χM, exp. = χM, para + χM, dia => χM, para = χM, exp − χM, dia

Remember: χM, dia < 0

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Correction for χM, dia is especially important in bio-molecules


Fe(III)Fe(II)- 49.0Pyridine- 13.0H2O- 23.0Se- 26.3P- 15.0S- 1.7O (carbonyl)- 44.6I- 4.6O (ether or R-OH)- 30.6Br- 5.6N (open chain)- 20.1Cl- 6.0C- 6.3F- 2.9H

DiamagneticSusceptibility10-6 cm3mol-1

Atom or Molecule

DiamagneticSusceptibility10-6 cm3mol-1

Atom or Molecule


Measurements:

A) Measurement of Susceptibility by Faraday’s MethodB) Measurement of Magnetization with a SQUID Magnetometer

Principle: In an inhomogeneous field a paramagnetic sampleis attracted into the zone with the largest field; a diamagneticsample is repulsed.

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Measurements:

A) Measurement of Susceptibility by Faraday’s Method

dF = ½ µ0(χ – χmed)grad(H2)dv

Fz = µ0(χ – χmed)vH dH/dzin vacuum or helium:

Fz = µ0χg m H(dH/dz) + F’

standard with known χg* and m*

χM = χg* [m* / (Fz* - F’)][Fz – F’)/m] M0

B) Measurement of Magnetization with a SQUID Magnetometer


Sensitivity: magnetic flux produced by a typical sample in a SQUID is 1/1000 of a flux-quantum; magnetic flux through 1 cm2

in the earth’s magnetic field corresponds to 2 million 2.07 x 10-7 Gcm2 flux quanta!

… it’s all about sensitivity!

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Magnetization MeasurementsScheme for a SQUID Magnetometer

SQUID involves a lot of hi-tech,…but in practice: no magic involved, sample weight is approx. 10 mg,

sample holder is a medicinal gel capsule and a soda straw!

Magnetization MeasurementsMpara = f(T, B) = χpara = f(T)

reasonable approximation for mono-nuclear first-row transition metal complexes

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Magnetization MeasurementsModel fails to describe low-temperature behavior of spin system > ½: Zero-field splitting (D), spin-orbit coupling


Polynuclear Complexes of First-Row Transition Metal Complexes

Interaction (usually) mediated by bridging atoms (or short M−M distances)Spin-spin interaction creates new energy levels that are thermally accessible

non-Curie behavior

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Magnetization MeasurementsHeisenberg-Dirac-van Vleck (HDVV) Hamiltonian describes the effect of electronic spin coupling between two ions in a bridged complex: , = -2J SA • SB

with J = exchange-coupling parameter (cm-1)Case I:SA = SBStot = 0Stot = 2Si

Spin-spin interaction in dinuclear and polynuclear TM complexes:

a) Ferromagnetic (FM) spin-spin interaction: at temperatures lower than TC (Curie-Temp.) the spin on each metal ion orientates parallel to each other to yield a maximum spin Stot = |SA + SB|; χ follows the Curie-Weiss law at T > TC.

b) Antiferromagnetic (AFM) spin-spin interaction: The spin on each metal ion pairs to yield a minimum spin at low temperatures Stot = |SA – SB|. At temperatures above TN (Neel-Temp.) χ follows Curie-Weiss law.

Empirical rules formed by Goodenough & Kanamori state i) if the orbitals containing the unpaired electrons (magnetic orbitals) have net-overlap the interaction is AFM; ii) if the orbitals are orthogonal to each other (net-overlap is zero) the interaction is FM in nature. (The interaction is also ferromagnetic, if iii) the magnetic orbital overlaps with an empty or fully occupied orbital)


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Magnetization MeasurementsAFM, SA = SB = 5/2


Dinuclear µ-oxo and bis-µ(S2-) bridged iron complexes aretypically very strongly J = -100 – -300 cm-1 antiferromagnetically coupled.

J depends on nature of bridging ligand (and M-M distance).

Magnetism provides “fingerprint” forthe synthesis of model complexes.

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Wieghardt et al.[{(tacn)FeIII}2(µ-O)(µ-O2CCH3)2]2+ [{(tacn)FeII}2(µ-OH)(µ-O2CCH3)2]+J = -236 cm-1 J = -26 cm-1

d(Fe…Fe) = 3.06 D d(Fe…Fe) = 3.32 D

Magnetization MeasurementsMixed-Valence Complexes (class II and III):Dinuclear iron complexes and polynuclear iron-sulfur cluster

Exp.:• identical Fe ions• intense absorption band

in at 13,000 cm-1 (NIR)• µB at 300K = 9.95 B.M.

2+

Exception to the rule!

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Double-Exchange in Class III Mixed-Valence Complexes:

β from optical spectroscopy:band at 13,000 cm-1

β = 6,500 cm-1

Recoilless Nuclear (γ-Ray) Absorption Spectroscopy

1949: Study of Physics @ Technical University Munich, BS 1952, MS 19551955: Doctoral Thesis @ TU Munic & Max-Planck-Institute for Medical Research in Heidelberg, 1958: Observation and Experimental Proof for “Recoilless Nuclear Resonance Absorption”1958: PhD Degree under Prof. Maier-Leibnitz, First Report: Zeitschrift fuer Physik 1958, 151, 1241959: Assistant at the TU Munich1960: Acceptance of an “Invitation” to CALTech1961: Nobel-Prize in Physics, Professor of Physics at the California Institute of Technology.

Rudolf Ludwig Mössbauer,born January 31, 1929.

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Interview with Professor Rudolf Mössbauer by Professor Anders Bárány at the meeting of Nobel Prize Winners in Lindau, 2000. The interview is divided into three parts.

Early education, advantages of receiving the Nobel Prize at a young age (4,30 min.)

Creative environments (5 min.)

Recoilless Nuclear (γ-Ray) Absorption

The "Mössbauer effect" (7,30 min.)

Recoilless Nuclear (γ-Ray) Absorption Spectroscopy

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“From a strange effect to Mössbauer Spectroscopy”Topics in Applied Physics, Vol.5 “Mössbauer Spectroscopy”

Ed. by U. Gonser, Springer Verlag 1975

Increased probability of recoilless transition in solids.Note: not 100% - Excitation of lattice vibrational modes

In practice, spectra are recorded at low temperature.

The Recoil-Energy ER:

“From a strange effect to Mössbauer Spectroscopy”

The Doppler-Energy ED:

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Mössbauer Spectroscopy

Experimental Setup (Scheme):


Experimental Setup:

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Mössbauer SpectroscopyThe Line-Widths Γ :

By going from gaseous to solid-state samples/sources reduces the widthsof the line by a few orders of magnitude.Doppler broadening is negligible, ER ~ 10-4 eV, for Eγ = 100 keV, m = 100

The full width at half height ΓFWHH of a resonance line is given by theHeisenberg-Uncertainty-Principle:

(∆E) C (∆t) $ h/2π ∆E = Γ = h/2π C τ-1/2The excited state has a mean lifetime τ, or half-lifetime t½ = τln2; the ground state is stable(or has a long lifetime).

Γ = natural line width

Γ = 0.693 (h/2π) C t½-1

Γ is an important criteria for which elements MB spectroscopy is available.

Remember: 1mm/s = hν(1mm/s)/c = 14.4 keV/3x10-11 = 4.8 x 10-8 eV

Common Isotopes for Mössbauer Spectroscopy (in theory!):Mössbauer Spectroscopy

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4.5510.2490.9170224544.91599.27238U242PuO2

1.9570.194256.61/23/297.8114.4132.1957Fe/59Co

39.990.80272.123/25/25.0667.401.2561Ni175.40.2304.3001/25/28.7136.462.1957Fe

ER

10-3 eV2Γmm/s

σ0

10-20cm2I grIexc

t½ns

Eγ

keVau%

Isotope/source

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Common Isotopes for Mössbauer Spectroscopy (in practice!):

+1.8613.8573/21/21.9077.35100197mPt (18h)197Au

+0.5953.0583/21/26.3073.0362.7193mOs n(30h)193Ir

+0.14914.285/23/220.589.3612.7299Rh (16d)99Ru

-2.50021.375/27/21.9057.6100127mTe (105d)127I

121mSb (77y)

119mSn (240d)

57Co (270d)

Source (t½)

-0.194256.61/23/297.8114.412.1957Fe

-2.10419.705/27/23.5037.1557.25121Sb

+0.646140.31/23/217.7523.878.58119Sn

sign ofδR/R

2Γmm/s

σ0

10-20cm2I grIexc

t½ns

Eγ

keVa%

Isotope



Hyperfine Interactions and Mössbauer Parameters:

, = ,(e0) + ,(m1) + ,(e2) • • • •

,(e0) Coulomb Interaction between the electrons and the nuclear site.without altering their degeneracye0 affects the position of the resonance line on the energy scale– giving rise to the so-called isomer shift δ.

,(m1) Coupling between the nuclear magnetic dipole momentand an effective magnetic field at the nucleus.m1 interactions split the nuclear levels into sub-levels,without shifting the center of gravity of the multiplet. – giving rise to the so called quadrupole splitting ∆EQ

,(e2) Electric quadrupole/ magnetic hyperfine interaction(will only be sketched in spring 2002)

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• Magnetic properties (e.g. ferro-, antiferro-, para-, diamagnetism, abs. value and direction of local magnetic fields)

Magnetic Splitting ∆EM

Magnetic dipole interaction between magnetic dipole moment of the nucleus and magnetic field at the nucleus

• Molecular symmetry• Oxidation states• Spin state• Bonding properties

Quadrupole Splitting ∆EQ

Electric quadrupole interaction between electric quadrupole moment of the nucleus and electric field gradient at the nuclear site

• Oxidation state (nominal valence) of the Mössbauer atom.• Bonding properties in coordination compounds (covalency); Delocalization of d-electrons due to back-bonding, shielding of s-electrons by p- and d-electrons.• Electronegativity of ligands

Isomer Shift δ

Electric monopole interaction between nucleus and electrons at the nuclear site

InformationMössbauer ParameterType of Interaction


Electric Monopole Interaction; Isomer Shift δ:

The origin of the isomer shift, δ, arises from the fact that an atomic nucleus occupies a finite volume, and s-electrons have the ability of penetrating the nucleus.

δ is a measure of the s-electron density at the nucleus, Ψ(0), and therefore, a direct measure of the metal centers’oxidation state, spin-state, coordination environment.

Ψ(0) can be altered via s - (de-)population of a valence shell, (de-) shielding effects, de- and increasing the electron density with p- or d-character.

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sign ofδR/R

2Γmm/s

σ0

10-20cm2

I grIexct ½

nsEγ

keVa%

Source (t ½ ) Isotope

+ (pos)0.14914.285/23/220.589.3612.7299Rh (16d)99Ru- (neg.)0.194256.61/23/297.8114.412.1957Co (270d)57Fe

When δR/R is negative, a positive isomer shift implies a decrease of the electron density at the nucleus.…or in other words: the higher the oxidation state, the smaller the isomer shift.

For δR/R positive, a positive isomer shift indicates an increase in the electron density at the nucleus.

Mössbauer SpectroscopyElectric Quadrupole Interaction; Quadrupole Splitting ∆EQ:

Assumption for isomer shift (monopole interaction): Uniform and spherically symmetrical charge distribution.Only for nuclei with spin I = 0, ½

Any nuclear state with I > ½ has a non-zero quadrupole moment Q and can interact with an inhomogeneous electric field described by the electric field gradient (EFG)

,(e2) = Q • LE

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EFG is a second-rank tensor. The “principal axes of the EFG tensor”can be defined, so that the off-diagonal elements vanish and thediagonal elements can be ordered as: |Vzz| $ |Vxx| $ |Vyy|.

With respect to the principal axes, the EFG tensor is described bytwo parameters:

Vzz = eq and η = (Vxx – Vyy)/Vzz , 0 # η # 1asymmetry parameter

Two fundamental sources which contribute to the total EFG:

a) ligand contribution: charges on distant atoms or ions (ligands), surrounding the Mössbauer atom in non-cubic symmetry.

b) valence electron contribution: non-cubic electron distribution inpartially filled valence orbitals of the Mössbauer atom.


where mI = I, I-1, ..-I nuclear magnetic spin quantum number

a nuclear state with I > ½ , (2I + 1) fold degenerate, splits into sub-states |I, mI ⟩

Quadrupole Splitting ∆EQ:

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The source:

Co57 is electrochem. depositedon metallic support, diffused intothe metal at high temperature.

• Emission line should be narrow & intense, unsplit & unbroadened.• The recoil-free material should be as high as possible.• Source material should be chemically inert and resistant against autoradiolysis.• Host material should not give rise to interfering X-rays, and Compton scattering.

57Fe-Mössbauer Spectroscopy


Selection Rules forMB-spectroscopy:

∆I = ± 1, ∆mΙ = 0, ± 1

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57Fe-Mössbauer SpectroscopyMagnetic Hyperfine Interaction (not covered in spring 2002):

Remember: 57Fe γ-ray 14.4 keV, typical hyperfine splitting: 3 x 10-7, line width 1.5 x 10-8 eV


0.85—1.00.6—0.71.1—1.30.3—0.45

1.5—3.02.0—3.02.0—3.2< 1.5

hemesFe—SFe—(O,N)hemes

S = 2S = 2S = 2S = 0

Fe(II)

0.35—0.450.20—0.350.40—0.600.30—0.400.15—0.250.10—0.25

0.5—1.5< 1.00.5—1.53.0—3.61.5—2.52.0—3.0

hemesFe—SFe—(O,N)hemeshemesFe—(O,N)

S = 5/2S = 5/2S = 5/2S = 3/2S = 1/2S = 1/2

Fe(III)

0.0—0.10.0—0.1-0.20—0.1

0.5—1.01.0—2.00.5—4.3

Fe—(O,N)hemesFe—(O,N)

S = 2S = 1S = 1

Fe(IV)

δ (mms-1)∆EQ (mms-1)Ligand SetSpin StateOxidation State

Values for ∆EQ and δ for some Compounds of Biological Interest:

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57Fe-Mössbauer SpectroscopyApproximate ranges of isomer shifts in iron compounds:

relative to α−Fe @ 300K

Synthesis, IR, UV/Vis, E-Chem,EPR, SQUID, and 57Fe-Mössbauer Spectroscopy

A Case Study:

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Case Study: The Geometric & Electronic Isomers of Iron Cyclam Complexes

Magnetization Measurements: SQUID Study


Electron Paramagnetic Resonance Spectroscopy

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Zero-Field Mössbauer Spectroscopy

2.39trans-[(cyclam)Fe(N3)2]+2.2380.2885.89cis-[(cyclam)Fe(N3)2]+0.2850.485

µB @ 300KisomerΓmms-1

∆EQ

mms-1

δmms-1


Electrochemistry & Mössbauer Spectroscopy

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Photolysis of trans-[(cyclam)Fe(N3)2]+ in liquid solution at 300K


Photolysis of trans-[(cyclam)Fe(N3)2]+ in frozen solution at 4K

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Photolysis of trans-[(cyclam)Fe(N3)2]+ in frozen solution at 4K


How to prove an iron(V) oxidation state

• All iron centers in complexes listed above have a [(cyclam)Fe(N3)]-fragmentand an t2g

n electron configuration:

• the higher the oxidation state - the higher the s electron density at the Fe-nuclei(the less electrons in the 3d shell - the less deshielded the nuclear charge at the Fe-nuclei)-> the lower the isomer shift (since δ = const. (∆R/R) [|Ψ(0)|A2 - C] and ∆R/R < 0)

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Appendix

Picture taken from: http://www.chem.fsu.edu/editors/ndalal/Giese/seminar/slide1title.htm

S.A. Goudsmit “The Discovery of the Electron Spin”http://www.lorentz.leidenuniv.nl/history/spin/goudsmit.html

R. L. Moessbauer “Resonance Absorption of GammaRadiation”

http://www.nobel.se/physics/laureates/1961/mossbauer-video.html

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