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
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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
Magnetic field (Gauss)
46360 46400 46440
Magnetic field (Gauss)
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
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