Fundamentals and Applications of Electron …sites.psu.edu/bioinorganic/wp-content/uploads/sites/29389/2015/08/...Fundamentals and Applications of Electron Paramagnetic Resonance

K. V. Lakshmi

Department of Chemistry and Chemical Biology

Rensselaer Polytechnic Institute

Troy, NY 12180

Fundamentals and Applications of Electron

Paramagnetic Resonance Spectroscopy

Second Penn State Bioinorganic Chemistry Workshop

May 31-June 9, 2012

• Magnetic moments of nuclei No mixing of nuclear wave functions Very weak interactions Very small magnetic moments • Consequences: All nuclei of a particular type resonate at

about the same frequency • Nuclear wave functions do not overlap

• All nuclear wave functions can be treated equivalently

NMR Spectroscopy

• Magnetic moments of unpaired electrons • Unpaired electrons are usually the valence electrons • Greatly affected by bonding

• Electronic wave functions do overlap

• Treat different cases separately

EPR Spectroscopy

Outline

• Single unpaired electron (the Zeeman interaction)

• Single electron spin plus nuclear spins (hyperfine interactions)

• Two or more electron spins (spin-spin interactions)

• Single electron spin with spin orbit coupling • Half-integer high spin systems

• Applications

References:

Carrington and McLachlan (1967) “Introduction to Magnetic Resonance” Abragam and Bleaney (1970) “Electron Paramagnetic Resonance of Transition Ions” Pilbrow (1990) “Transition Ion Electron Paramagnetic Resonance” Poole (1983) “Electron Spin Resonance: A Comprehensive Treatise on Experimental Techniques”

The Zeeman Interaction

EPR Line Shapes

g

• Detection is limited by noise components • Phase-sensitive amplitude detection • Small amplitude sinusoidal field is modulated during a scan • Detects signals that change amplitude as the field changes • Allows for amplification using AC techniques • Results in derivative line shapes • Enhanced sensitivity, improved signal-to-noise level and resolution

• It is an inherent property of an unpaired spin

• Similar to the chemical shift in NMR

• Measures how far the magnetic environment of the spin differs from a free gas-phase electron

• The g value for a single unpaired electron is: ge = 2.002

• The g value for an S = 1/2 system is usually near ge (with exceptions)

What is g?!

Sensitivity

• EPR detects net absorption • Absorption is proportional to the number of spins in the lower

energy level • Emission is proportional to the number of spins in the upper

energy level • Net Absorption depends on N– and N+

• Ratio of populations at equilibrium is given by the Boltzmann distribution

• EPR sensitivity increases with decreasing temperature and increasing magnetic field strength

N-/N+ = e geb

eH/kT

Saturation

• AT RT, the energy levels are nearly equally populated • Intense radiation will tend to equalize the population of spins • Leads to a decrease in net absorption • Effect is called "saturation” • Spin system returns to thermal equilibrium via energy transfer

to surroundings • Known as spin-lattice relaxation with time constant, T1 • Spins with a long T1 are easily saturated • Spins with shorter T1 are more difficult to saturate • Spin-orbit coupling provides an important energy transfer

mechanism

mS=1/2

mS=-1/2

I=1/2 S=1/2 B

Electron

Nucleus

Hyperfine Interaction Between an Electron and Nucleus

Hyperfine Interaction Between an Electron and Nucleus

• Isotropic component provides information on chemical bonding

• Dipolar component provides information about location of the

nucleus

Electron

Nucleus r

Y(r)

Aiso ~ [Y(r)]2

Electron

Nucleus

r

Q

T~ (1-3cos2q)/r3

Through-space dipolar interaction

B

Isotropic contact interaction

Spin-spin Interactions

• Isotropic exchange interaction requires overlap of the electron wave

functions. J is very small for inter-spin distances > ~ 1 nm

• Dipolar interaction depends on inter-spin distance and angle of the inter-

spin vector with external magnetic field

S1

Y1(r)

Hex ~ JS1S2

r

Q

D ~ (1-3cos2q)/r3

Through-space dipolar interaction

B

Exchange interaction

Y2(r)

S1

S2

S2

Spin Orbit Couplings

• The coupling between the electron spin and the orbital

angular momentum • In the reference frame of the electron, the nucleus is moving

charge that generates a magnetic field • The magnetic field interacts with the spin magnetic moment • These are relativistic effects • Effects are small for organic radicals • The heavier atoms (e.g. transition metals) have spin orbit

couplings much larger than the Zeeman interaction • This leads to significant g anisotropy • Spin-orbit coupling provides an important energy transfer

mechanism

Half-integer High Spin Systems • Non-degenerate energy levels even at zero field • Known as zero-field splittings • Involves spin orbit coupling combined with deviations from

regular symmetry

2 2 2 21( ) ( )

3z x yg H S D S S E S Sb

Zeeman

Interaction Zero-Field Splitting Interaction

• Axial zfs parameter, D, removes the microstate degeneracy and produces Kramer’s doublets

• Rhombic zfs parameter, E, further splits the Kramers’ doublets • Ion is axially symmetric if E = 0

S = 3/2

0 2D

Zero Field

Splitting Interaction Zeeman Interaction

3

2

3

2

1

2

1

2

Magnetic Field

1

2

3

2

S = 5/2

0 4D

Zero Field

Splitting Interaction Zeeman Interaction

5

2

1

2

5

2

5

2

1

2

1

2

Magnetic Field

3

2

3

2

3

2

2D

Rhombograms

• Assume weak field limit (zero-field energies >> Zeeman

energy) • The S = n/2 high-spin multiplet forms (n+1)/2 Kramers’

doublets • Kramers’ doublets are separated by significantly large energies • Each doublet can yield a spectrum which is an effective S = ½

transition with three effective g values • g effective values no longer depend on D and E but only on the

E/D ratio • Thus, any high-spin half integer spin system has an EPR

spectrum that is a function of a single parameter, E/D

Reading of Rhombograms

• All possible g values for a subspectrum from a Kramers’

doublet are represented by three curves • Spectral analysis means moving horizontally and matching the

g effective values • A given rhombicity should reproduce the experimentally

observed g values • The g effective values can then be reproduced by numerical

simulations • Note that not all transitions are observed in the experimental

system

3305 3306 3307 3308 3309

Magnetic field (Gauss)

High-Frequency EPR Spectroscopy

12460 12480 12500


46360 46400 46440


X-band

9.28 GHz

Q-band

35.5 GHz

D-band

130 GHz

• Enhanced resolution

• Increased sensitivity

• Smaller spin concentrations

Simulated semiquinone EPR signals

gX

gY

gZ

gX

gY

gZ

Bruker 95 GHz 3T Spectrometer

g value and anisotropy reports: structure and local environment oxidation states ligand symmetry hydrogen bonding

Advantages: high specificity, rich spectral content and enhanced sensitivity

Splittings and relaxation report: on neighboring spins e.g. how many unpaired electrons, nuclei, distances, orientation?

A structural picture of the active site develops

Chemical Insights from EPR Spectroscopy

Spectrometer Arrangement

I. Microwave System 1. Source 2. Components to direct microwaves to and from the

resonant cavity 3. Resonant cavity 4. Detector 5. Amplifier 6. Computer

II. Field Modulation System III. Magnet System: Electromagnet to provide a stable, linearly variable, homogeneous magnetic field

Schematic of an EPR Spectrometer

Source Circulator Detector

electromagnet Modulation coils Resonator (cavity)

http://www.acert.cornell.edu

X-Band 9 GHz EPR Spectrometer

Applications of EPR Spectroscopy

• Interstitial hydrogen atoms in metal oxides • Tyrosyl radicals in photosystem II and RNR • Manganese monomers, dimers and tetramers • Interaction spectra of photosystem II • Heme centers in cytochromes • Iron sulfur centers in photosystem I • Interaction spectra of photosystem I • High-spin iron centers in transferrins • Copper (II) centers • Progressive power saturation

Interstitial Hydrogen Atoms in Metal Oxides: Indium Oxide Nanotubes

Kumar, Chatterjee, Milikisiyants, Lakshmi, Mehta, Singh and Singh (2009) Appl. Phys. Lett., 95, 13102.

~ 45 G ~ 45 G

Tyrosyl Radicals of Photosystem II (PSII)

Stromal Surface

Lumenal Surface

O2 + 4H++ 4e- 2H2O

Q

QH2

Ferreira, Iverson, Maghlaoui, Barber and Iwata (2004) Science, 303, 1831. Umena, Kawakami, Shen and Kamiya (2011) Nature, 473, 55.

Mn4Ca oxo

TyrZ

PheoA PheoB

QA QB

TyrD P680

Fe(II) QH2

Ferreira, Iverson, Maghlaoui, Barber and Iwata (2004) Science, 303, 1831. Umena, Kawakami, Shen and Kamiya (2011) Nature, 473, 55.

3400 3440 3480

Magnetic Field (G)

EPR Spectrum of Tyrosine D

Hoganson and Babcock (1992) Biochemistry, 31, 11874.

Tyrosyl Radicals of Ribonucleotide Reductase (RNR)

Norlund and Eklund (1994) J. Mol. Biol., 232, 123.

Tyrosyl Radicals of Ribonucleotide Reductase (RNR)

Trp-48

Gln-43

Tyr-122

Asp-84 Glu-204

Glu-238

His-241

Asp-237

His-118 Ser-114

Fe1 Fe2

Norlund and Eklund (1994) J. Mol. Biol., 232, 123.

Tyrosyl Radicals of Ribonucleotide Reductase

3300 3350 3400 3450

Magnetic Field (G) Courtesy Prof. Carsten Krebs

Bender et al. (1989) J. Am. Chem. Soc., 111, 8076.

• Tyrosyl line shapes are very sensitive to the relative orientation of the b-methylene protons

pZ

High-frequency D-band (130 GHz) EPR Spectroscopy of Tyrosyl Radicals

46300 46350 46400 46450

Field (Gauss)

125 G

30 G

gx

gz

gy

YD• at X-band (9 GHz)

YD• at D-band (130 GHz)

Manganese Monomers: Hexa-aquo Manganese Ions

How many peaks in the EPR spectrum?!

[Mn (H2O)6]2+

Electron spin: S = 5/2 Nuclear spin: I = 5/2

EPR Spectrum of Hexa-aquo Manganese Ions

Manganese Dimers: Dimanganese ‘di-m’ Oxo Complexes

[H2O(terpy)MnIII(m-O)2MnIV(terpy)OH2](NO3)3 [(bpy)2MnIII(m-O)2MnIV(bpy)2](NO3)3

Cooper and Calvin (1977) J. Am. Chem. Soc., 99, 6623. Limburg, Vrettos, Liable-Sands, Rheingold, Crabtree and Brudvig (1999) Science, 283, 1524.

Manganese Dimers: EPR Spectra of Dimanganese ‘di-m’ Oxo Complexes

3000 3500 4000

Magnetic Field (G)

[(bpy)2MnIII(m-O)2MnIV(bpy)2](NO3)3

[H2O(terpy)MnIII(m-O)2MnIV(terpy)OH2](NO3)3

Chatterjee, Milikisiyants & Lakshmi (2012) Phys. Chem. Chem. Phys., In Press.

S-state cycle

S0 S1

S3

S2 S4

O2

2H2O

H+

2H+

H+

e-

e- e-

e-

hν

hν hν

hν

The Oxygen-Evolving Complex of Photosystem II

Umena, Kawakami, Shen and Kamiya (2011) Nature, 473, 55.

Kok, Forbush and McGloin (1970) Photochem. Photobiol., 11, 457.

Manganese Tetramers: The S2 State of Photosystem II

hnhnhnhnS4S3S2S1S0

2H2OO2 + 4H+

Dark State

Dark spectrum of PSII

Light spectrum of PSII

Light - dark difference spectrum

Why so many lines?!

S2 state of PS II S = 1/2

PS II: [Mn4]

S = ½ I = 5/2 * 4

2500 3000 3500 4000

Field (Gauss)

Experimental

Simulated - 4 eq 55 Mn

Simulated - (3+1) eq 55 Mn

Lakshmi, Eaton, Eaton, Frank & Brudvig (1998) J. Phys. Chem. B, 102, 8327.

2500 3000 3500 4000

Field (Gauss)

Experimental

Simulated - 4 eq 55 Mn

Simulated - (3+1) eq 55 Mn


S2YZ• State of the Oxygen-evolving Complex of

Photosystem II

Trapping the S2YZ• State of Photosystem II

Boussac et al. (1990) Nature, 347, 303; MacLachlan & Nugent (1993) Biochemistry, 32, 9772.

Untreated PSII

Ca2+-depleted PSII or Acetate-treated PSII

S2YZ• EPR Spectrum from Acetate-Inhibited Photosystem II

Szalai, Kühne, Lakshmi & Brudvig (1998) Biochemistry, 37, 13594; Tang et al. (1996) J. Am. Chem. Soc., 118, 7638; van Vliet et al. (1994) Biochemistry, 33, 12998.

Experimental and Simulated S2YZ• EPR Spectra


R = 7.7 ± 0.3 Å; J = - 0.028 cm-1


Szalai, Kühne, Lakshmi & Brudvig (1998) Biochemistry, 37, 13594.

Comparison of S2, S2YZ• and S2YZ-NO EPR Spectra

S2

S2YZ•

S2

S2YZ-NO


Temperature Dependence of the S2YZ• EPR Spectra


Temperature Dependence of the S2YZ• EPR Spectra

• Liquids have translational and rotational mobility

• Orientation dependence of electron spin interactions are averaged out!

Orientation Dependence of EPR Spectra in Liquids

Orientation Dependence of EPR Spectra in Solids

• Motion is largely restricted in a solid lattice

• Significant orientation dependence of electron spin interactions!!

90° 0°

H0 r

H0 H0

r r q

w (q)

w (q) ~ 1/2 (3 Cos2 q 1)

Orientation Dependence of Electron-Electron Couplings in Solids

substrate plane

membrane plane

ZsZ1

B0

b

qs

r

Ys

Mylar substrate

PS II membranes

Oriented Photosystem II Membranes

Membrane plane

Substrate plane

Orientation Dependence of the EPR Spectrum of Tyrosine D in Photosystem II

Lakshmi, Eaton, Eaton & Brudvig (1999) Biochemistry, 38, 12758.

Orientation Dependence of the S2YZ• EPR Spectra


Orientation Dependence of S2YZ• EPR Signals


3160

3180

3200

3220

3240

50 100 150 200 250 300

Pea

k i

1 p

osi

tion

(G

au

ss)

Q (degrees)

Simulation Parameters: R = 7.9 ± 0.1 Å, Q = 70°, J = - 0.028 cm-1


Model of the Oxygen-Evolving Complex

Iron(III) Center of Cytochrome C

Iron(III) Center of Cytochrome C

2000 4000 6000 8000

Magnetic Field (G)

gX

gY

gZ

[4Fe4S] Clusters of Photosystem I

A1A A1B

A0A A0B

AB

P700

FX

FA

FB

Jordan et al. (2001) Nature, 411, 909.

AA

EPR Spectra of the [4Fe4S] Clusters of Photosystem I: FA and FB Clusters

Courtesy Prof. John Golbeck Field (G)

Vassiliev, Antonkine and Golbeck (2001) BBA, 1507, 139.

FA

FB

12 Å

The FA and FB Clusters of Photosystem I

Jordan et al. (2001) Nature, 411, 909.

EPR Spectra of the [4Fe4S] Clusters of Photosystem I: Interacting FA and FB Clusters

Courtesy Prof. John Golbeck Field (G)

Vassiliev, Antonkine and Golbeck (2001) BBA, 1507, 139.

EPR spectrum of Copper (II) Sulfate

2500 3000 3500

Magnetic Field (G)

gperp gpara [Cu (H2O)6]2+

Electron spin: S = ½ Nuclear spin: I = 3/2

High Spin Iron(III) Center of Human Serum Transferrin

Sun et al. Acta Crystallogr., Sect.D 1999, 55, 403-407.

High Spin Iron(III) Center of Human Serum Transferrin

1000 2000 3000

Magnetic Field (G)

Progressive Power Saturation: The P700+ Center of

Photosystem I

3400 3420 3440 3460 3480

Magnetic Field (G)

Lakshmi, Jung, Golbeck & Brudvig (1999) Biochemistry, 38, 13210.

P1/2 1/g2 (T1 T2)

• P1/2 is half power at which a spin saturates

• Depends on spin-spin and spin-lattice relaxation • Signal amplitude is related to P1/2

A = K P1/2 (1 + P/P1/2)b/2

log (A/P1/2) = -b/2 log (P1/2 + P) + constant

Galli, C., Innes, J. B., Hirsh, D. J., and Brudvig, G. W. (1996) J. Magn. Reson. B, 110, 284.

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.7

1.4

Sig

na

l

Inte

ns

ity

(a

.u.)

Sqrt Power (mW)

Progressive Power Saturation of P700+

• Power saturation experiments of P700+ in aerobic (●) and anaerobic (○ ) conditions

• In some cases, oxygen enhances relaxation of observed spin

P700+FX

-

P700+FA

-FB-

P700+

P700+FA

-

I(t) = Intensity of Saturation-

Recovery EPR Signal

= 1 - N õó

0

p

(e-{k1int + k1q}t) sinq dq

where: k1i = Intrinsic Rate isotropic

k1q = Dipolar Rate orientation dependent

s

f

H0

q

s

f

H0

q

Dipolar Model

6r/11k q

P1/2 (observed ) = P1/2 (intrinsic) + P1/2 (dipolar)

P1/2 (dipolar) = constant/r6

Hirsh and Brudvig (2007) Nature Protocols, 2, 1770.


P700+FX

-

P700+FA

-FB-

P700+

P700+FA

-

Progressive Power Saturation: The Charge-separated States of Photosystem I


P700+FA

-

P700+FB

-

P700+FX

-


P700

FX

FA

FB

32 Å

10 Å

22 Å


EPR Ruler

Tyrosine D

S2YZ

Progressive Power Saturation: The Tyrosine D and S2YZ

State Photosystem II


Signal Sample T (K) P1/2 (mW) S2YZ

• (YZ

• peak) acetate-inhibited 5.0 0.36 5.4 0.62 5.7 1.2 6.0 1.7 7.5 18 20 >100 S2YZ

• (55Mn hyperfine peaks) acetate-inhibited 6.0 6.7 YZ

• acetate-inhibited 293 >100 YZ

• Mn-depleted 293 12 S1YD

• acetate-inhibited 20 1.6 293 11 YD

• Mn-depleted 293 16

Progressive Power Saturation of Tyrosyl Radicals of Photosystem II

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Fundamentals and Applications of Electron …sites.psu.edu/bioinorganic/wp-content/uploads/sites/29389/2015/08/...Fundamentals and Applications of Electron Paramagnetic Resonance