Frontiers in Chemical Physics

1

Pulse EPR Spectroscopy

Stefan StollDepartment of ChemistryUniversity of Washington, Seattle Ohio State University

Mar 21, 2018

Spectroscopy over 15 order of magnitude

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Mößbauer 14 400 eV (57Fe)

XAS/XES 7 000 eV (Fe K-edge)

UV/Vis 2 eV (600 nm)

IR/Raman 0.01 eV (800 cm-1)

EPR 0.000 04 eV (10 GHz = 40 μeV)

NMR 0.000 006 eV (850 MHz = 3.5 μeV)

ENDOR etc. 0.000 000 004 eV (1 MHz = 4 neV)

Coupled spins

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Crystallography view:Nuclear geometry

Magnetic-resonance view:System of coupled spins

1 unpaired electron spin on Fe3+ (S = 1/2)all magnetic nuclei (1H, 2H, 14N, 15N, 13C, ...)nonmagnetic nuclei invisible (12C, 16O, 32S)

1H 1H1H 1H

1H1H

1H

1H

14N14N

14N

14N

14N14N

1H1H

1H1H

14N14Ne

Information from EPR

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14N14N

14N

14N

14N14N14N

14N e

1H1H 1H

1H

1H

1H 1H1H

1H

1H

1H

1H

CW EPR: low resolution- metal center, (ligands)- strongly coupled

magnetic nuclei

Pulse EPR: high resolution- weakly coupled magnetic

nuclei (1H, 14N, 13C, etc)- ligands in first and

second ligand sphere- hydrogen bonds- distances to other spin

centers

otherspin center

magnetic nuclei within a few Åelectron spins with a few nm

Pulse EPR: Set of high-resolution EPR techniques todetermine local structure around a spin center (metal ion, metal cluster, or radical)

Hidden details in CW EPR spectra

5

as recorded

integrated

Origins of static line broadenings1. anisotropies of g tensor,

A tensor, D tensor2. site-to-site structural heterogeneity

resulting in g, A, D heterogeneity3. unresolved splittings

- hyperfine coupling to magneticnuclei

- coupling to other electron spins

pulse EPR

Hidden structure

frozen solutionCW EPR "powder" spectrum

singleorientation(unresolvable with CW EPR)

Overview

6

CW vs. pulse EPR, samples, spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs, echoes, deadtime, relaxation

Nuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction

1. Fundamentals of pulse EPR

2. Molecular interactions

3. Pulse EPR experimentsField sweepsENDORESEEM, HYSCOREDEER

14N

1H

14N

14N

1H

1H

14N

14N

1H

1H14N

13C

Comparison CW and Pulse EPR

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CW (continuous-wave) EPR- continuous excitation- low microwave power (μW-mW)- absorption spectroscopy- measures steady-state response

during excitation- low resolution

Pulse EPR- pulse excitation- very high microwave power (W-kW)- emission spectroscopy- measures transient response

after excitation- high resolution

EPR unit conversions- Energy units: 30 GHz = 1.00 cm-1 = 0.124 meV = 1.20 J/mol- Field to frequency: 1 mT = 28 MHz @ g = 2- Field units: 1 mT (millitesla) = 10 G (gauss)

EPR frequencies and fields

How to make EPR samples

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Things to watch out for:(1) Unwanted dioxygen- oxygen-sensitive samples- dissolved dioxygen enhances relaxation- important for liquid samples- remove by freeze/pump/thaw, or Ar purging

(2) Other paramagnetic centers- avoid paramagnetic impurities- run controls on buffers and reagents- use quartz ("fused silica") tubes

(3) Aggregation- due to slow freezing, solvent crystallization- enhances relaxation, shortens Tm, T1- add glassing agent (glycerol, sucrose), freeze fast

(4) Dielectric constant- high εr solvents kill mw fields in resonator- sensitivity loss- worst: liquid water (static εr = 80 at 20°C)- frozen water: (εr = 3.15 at 0°C)

Sample quantity and positioning

Sample concentrationmagnetically dilutecw EPR: < 1 mMpulse EPR: ESEEM/ENDOR: max 5 mM

DEER: less than 200 μM

EPR measurement temperatures (approx)organic radicals 30-200 Kmononuclear metal centers 5-40 Koligonuclear metal clusters 2-10 K

- know O.D. and I.D. of EPR sample tube- fill no more than fits in the resonator

Too concentrated?- broadened spectra- enhanced relaxation

Too dilute?- Not enough signal.

Frozen solutions – lab and molecular frames

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Very common in bioinorganic/biological EPR: frozen aqueous solutions of paramagnetic molecules.

B0

Molecular frames- fixed in molecules- most commonly molecular

symmetry frame or g tensorframe

Euler angles 𝜑𝜑,𝜃𝜃,𝜒𝜒

z(lab)

x(lab)y(lab)

Lab frame- fixed in laboratory- z(lab) along static field B0- x(lab) along oscillating

microwave field B1

z(mol)

x(mol)y(mol)

Relative orientation

B1

Frozen solution =random uniform distribution of static orientations of the molecules, like a dilute powder.

molecules

Pulse EPR spectrometer

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N

sampleresonatorcryostat

magnet

S

B0

circulator

mw2 PFU

0-60dB

cw sources pulse formers

mw1 PFU

12

high-poweramplifier

high-powerattenuator

mw

tran

smitt

er

3

protectionswitch

low-noiseamplifier (LNA)

mixer

digitizercomputer

amplifiers

phase

mw

rece

iver

rf1

high-poweramplifier

ENDOR transmitter

PFU att.

low mw power high mw power video signal

Why use a resonator?

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cw EPR: high sensitivity→ high Q, critically coupled

pulse EPR: large bandwidth→ high Q + overcoupled, or

low Q + critically coupled

𝑄𝑄 =𝜈𝜈0∆𝜈𝜈

Types of resonators1. dielectric (ring, split-ring)2. cavity (rectangular, cylindrical)3. loop-gap resonators

Resonator Q factor and bandwidth

Why to use a resonator?(1) concentrates microwave magnetic

field (B1) on sample; higher signalintensity

(2) separates microwave electric fieldfrom sample; lower sample heating

Downside: works only for a verynarrow range of frequencies, limitedbandwidth

resonator frequency

bandwidth (undercoupled)

Q factor; range: 100 - 10000

∆𝜈𝜈

Irradiation reorients spins

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Resonance condition:

precession

nutation

mw frequency = precession frequency(Larmor or Zeeman frequency)

ℎ𝜈𝜈mw = 𝑔𝑔𝜇𝜇B𝐵𝐵

magnetic field71.447732

𝜈𝜈mwGHz

= 𝑔𝑔𝐵𝐵

mT1 mT = 10 G

rotating frame:follow precession( = running alongwith the merry-go-round)

mw frequencyg factor

equilibrium non-equilibrium

𝑩𝑩0

Bohr magneton9.274·10-24 J/T 1 G = 2.8 MHz @ g = 2

Planck constant6.626·10-34 J s

Pulses and excitation bandwidth

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Pulse excitation bandwidth- excitation bandwidth = approx.

distance between zeroes: 2/tp(for pi and pi/2 pulses)

- example: 10 ns pulse → 200 MHz

Microwave pulses (for electron spins)frequency 9-10 GHz, 34-36 GHz, 95 GHzshort 5-20 nsmedium 20 ns-200 nslong 200 ns-several μs

RF pulses (for nuclear spins)frequency 1-200 MHzshort 10 μslong 100 μs

π/2, 90°

pulse length

flip angle

tp

Rectangular pulse

carrierfrequency

pulse amplitude

Spin gymnastics and energy level diagrams

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B0

Energy level diagram

E

E

Classical description: Bloch equations (limited to a isolated spins)Quantum description: Liouville-von Neumann equation (general)

Spectral width and pulse excitation bandwidth

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EPR

abs

orpt

ion

inte

nsity

frequency (GHz)

g =1.83

g =2.55

g =2.00

pulse hits spins within10-100 MHz of mw frequency

mw pulse at 9.5 GHz

spectral width: several GHz

• Only a small fraction of spins in the sample are excited.• They have resonance frequencies close to the mw frequency.• They have specific orientations → orientation selection

Orientation selection

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Resonance frequency depends onorientation relative to field.

Different orientation →different resonance frequency

frequency (GHz)

Free-induction decay

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90°

FID

spins in thermalequilibrium

pulse rotates spins by90 degrees

spins precess withdifferent frequencies

deadtime

B0

all are in phase dephasing

fast spins

slow spins

Dead time

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Dead time:- time after pulses during which power

levels are too high to openthe sensitive receiver

- due to 1) ringdown in cavity2) reflections in spectrometer3) recovery of receiver protection

- typical value: 100 ns at X-bandshorter at higher frequencies

- affects all pulse EPR experiments

τ τ

τ τ

dead time

signal cannotbe measured!

Consequences- short values of τ cannot be accessed- loss of broad lines- phase distortions in spectrum- spurious features in spectrum

kW kW μW

kW kW μW

1 kW = 1 mile1 μW = 0.0016 mm

Two-pulse echo

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90°pulse

180°pulse

two-pulse echo( = 2x FID)

FID

thermalequilibrium

rotated by 90o

precessing anddephasing

dephased rotated by 180o

precessing andrephasing

refocused

τ τ

also called primary echo or Hahn echo

B0

Three-pulse echo

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90°pulse

three-pulseecho

FID

thermalequilibrium

rotated by 90o

precessing anddephasing

dephased precessingand rephasing

refocused

τ τ

also called stimulated echo

90°pulse

90°pulse

T

"stored"along -z,

precessing

complexmotion

(approximate)

B0

Relaxation

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Relaxation constantsT1: longitudinal relaxation (spin-lattice relaxation)T2: transverse relaxation (spin-spin relaxation)Tm: phase memory time (similar to T2)

Spectral diffusion- spin center randomly changes

frequency during pulse sequence- leads to dephasing and loss of signal- contributes to Tm

cw EPR- choose low mw power that avoids saturation- choose scan rates, modulation amplitudes and

frequencies that avoid passage effects

pulse EPR- fast relaxation prevents long pulse experiment- slow relaxation prevents fast repetition

Overview

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CW vs. pulse EPR, samples, spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs, echoes, deadtime, relaxation

Nuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction

1. Fundamentals of pulse EPR

2. Molecular interactions

3. Pulse EPR experimentsField sweepsENDORESEEM, HYSCOREDEER

14N

1H

14N

14N

1H

1H

14N

14N

1H

1H14N

13C

Magnetic nuclei and their interactions

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Nuclear Zeeman interactionMagnetic interaction withexternal applied magnetic field(static or oscillating)

Hyperfine interactionMagnetic interaction ofnucleus with field dueto electron spin

Two contributions:1. through-bond

(isotropic; "Fermi contact")2. through-space

(anisotropic; dipolar)

Nuclear quadrupole interactionElectric interaction betweennonspherical nucleus andinhomogeneous electric field

Only for nonsphericalnuclei (spin > 1/2)!

ℋnuc = −𝑔𝑔n𝜇𝜇N𝑩𝑩 � 𝑰𝑰 + ℎ 𝑺𝑺 � 𝑨𝑨 � 𝑰𝑰 + ℎ 𝑰𝑰 � 𝑷𝑷 � 𝑰𝑰

Nuclear spin Hamiltonian (for one nuclear spin coupled to one electron spin):

B magnetic fieldS electron spinI nuclear spin

Nuclear Zeeman interaction

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Nucleus Spin % gn1H 1/2 99.99 +5.585692H 1 0.01 +0.85743814N 1 99.6 +0.40376115N 1/2 0.4 - 0.56637813C 1/2 1.1 +1.4048217O 5/2 0.04 - 0.75751631P 1/2 100 +2.2632

no spin: 12C, 16O, 32S, etc.

NMR: gyromagnetic ratio 𝛾𝛾 = 𝑔𝑔n𝜇𝜇N/ℏ

𝜈𝜈I = − 𝜇𝜇N/ℎ ⋅ 𝑔𝑔n𝐵𝐵0

Nucleus Spin % gn63Cu 3/2 69 +1.48465Cu 3/2 31 +1.58853Cr 3/2 9.5 - 0.314755Mn 5/2 100 +1.381957Fe 1/2 2.1 +0.180659Co 7/2 100 +1.31861Ni 3/2 1.1 - 0.5000

no spin: 56Fe, 58Ni, 60Ni, etc.

magneticfieldnuclear

g factor

nuclear Bohrmagneton5.0508·10-27 J/T

Nuclear precession/Larmor/Zeeman frequency:

×6.5

oppositesign

Example: 1H with 𝐵𝐵0 = 0.350 T → 𝜈𝜈𝐼𝐼 = 14.9 MHz (electron: 9.8 GHz)

Hyperfine coupling 1: Fermi contact coupling

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Simple interpretation:spin population in atom-centered orbitals relativeto 100% orbital occupancy via reference Aiso

𝐴𝐴iso =𝜇𝜇0𝜇𝜇B𝜇𝜇N

3ℎ𝑆𝑆𝑧𝑧 −1𝑔𝑔e ⋅ 𝑔𝑔n ⋅ 𝜎𝜎𝛼𝛼−𝛽𝛽

Nucleus Spin Aiso(100%) 1H 1/2 1420 MHz14N 1 1811 MHz, 1538 MHz15N 1/2 -2540 MHz, -2158 MHz13C 1/2 3777 MHz, 3109 MHz

Electron-nucleus magnetic interaction due tosmall, but finite, probability of finding an unpairedelectron at position of nucleus (s orbitals only!)

Reasons for non-zero Aiso(1) ground-state open s shell(2) valence-core spin polarization

(e.g. 3d→2s, 2p →1s)

spin density atposition of nucleus

scales with 𝑔𝑔n

Example: Aiso(1H) = 20 MHz → 20/1420 = 1.4%

alternative: compare to quantum-chemical estimates

conventional units:MHz

What you can learn from Aiso(1) spin delocalization(2) proximity of nucleus to metal ion

Hyperfine coupling 2: through-space dipolar

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Be, Bhfelectron

nucleusmagnetic dipolefield of electron

rme

mn

Bn

magnetic dipolefield of nucleus

θ

B0

𝑻𝑻 = 𝑇𝑇⊥−1 0 00 −1 00 0 +2

𝑇𝑇⊥ =𝜇𝜇04𝜋𝜋ℎ

𝜇𝜇B𝜇𝜇N �𝑔𝑔e𝑔𝑔𝑛𝑛𝑟𝑟3

+2𝑇𝑇⊥−𝑇𝑇⊥

electron spin nuclear spin

T = dipolar hyperfine matrixeigenvalues: principal values

ℋ = ℎ 𝑺𝑺 � 𝑻𝑻 � 𝑰𝑰

- orientation dependence- distance dependence

This assumes electron is localized.In delocalized systems, integrate over electron spin density.

Zeeman + Hyperfine: local fields

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B0

Bhf

Btot

electron

nucleus

B0

hyperfine fielddue to electronspin

Zeeman field

total field

at equilibrium, nuclear spinaligns along total field

Zeeman + Hyperfine

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B0Bhf

Btot

electron

nucleus

B0

hyperfine field dueto electron spin

Zeeman field

total field

flipped!

changed!

Hyperfine + Zeeman

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component of hyperfine fieldperpendicular to external field(nonsecular)

component of hyperfine fieldparallel to external field(secular)

B0

Bhf

Btot

external (Zeeman)magneticfield

total field actingon the nucleus

hyperfinefield line

Nuclear frequencies:

Iν

𝐴𝐴 = 𝐴𝐴||cos2𝜃𝜃 + 𝐴𝐴⊥sin2𝜃𝜃= 𝐴𝐴iso + 𝑇𝑇⊥(3cos2𝜃𝜃 − 1)

𝐵𝐵 = 𝐴𝐴|| − 𝐴𝐴⊥ sin𝜃𝜃 cos𝜃𝜃= 3𝑇𝑇⊥sin𝜃𝜃 cos𝜃𝜃

𝜈𝜈 𝑚𝑚𝑆𝑆 = (𝜈𝜈I + 𝑚𝑚𝑆𝑆𝐴𝐴)2+(𝑚𝑚𝑆𝑆𝐵𝐵)2

𝜈𝜈I = −𝑔𝑔n𝜇𝜇N𝐵𝐵0/ℎ 𝑚𝑚𝑆𝑆 = ±1/2

can be neglected at high fieldfor small hfc

𝑚𝑚𝑆𝑆𝐵𝐵

𝑚𝑚𝑆𝑆𝐴𝐴

Hyperfine + Zeeman: Three regimes

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Weak coupling Strong couplingIntermediate coupling

ξ ξ ξ

nucleus

Btot(α)Btot(β)

Btot(α)

Btot(β)

Btot(α)

Btot(β)matching fields

𝑩𝑩0 ≫ 𝑩𝑩hf 𝑩𝑩0 ≈ 𝑩𝑩hf 𝑩𝑩0 ≪ 𝑩𝑩hf

angle between twototal field vectors: sin2𝜉𝜉 =

𝜈𝜈I𝐵𝐵𝜈𝜈𝛼𝛼𝜈𝜈𝛽𝛽

2

= 𝑘𝑘 k = modulation depth parameter(important in ESEEM)

βαββ

αααβ

βαββ

αu αv

βαββ

αα αβ

Nuclear frequencies and powder spectra

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Weak coupling regime Strong coupling regime

𝜈𝜈 𝑚𝑚𝑆𝑆 ≈ |𝜈𝜈I + 𝑚𝑚𝑆𝑆𝐴𝐴|

𝜈𝜈I = −𝑔𝑔n𝜇𝜇B𝐵𝐵0/ℎ

𝜈𝜈I ≫ |𝑚𝑚𝑆𝑆𝐴𝐴| 𝜈𝜈I ≪ |𝑚𝑚𝑆𝑆𝐴𝐴|

neglecting 𝑚𝑚𝑆𝑆𝐵𝐵 term(valid for weak and strong coupling only)

centered at νI, split by A centered at A/2, split by 2νI

𝜈𝜈 𝑚𝑚𝑆𝑆 = (𝜈𝜈I + 𝑚𝑚𝑆𝑆𝐴𝐴)2+(𝑚𝑚𝑆𝑆𝐵𝐵)2

Nuclear quadrupole interaction

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torque

Nucleus Spin Quadrupole moment (b)2H 1 +0.0028614N 1 +0.0204433S 3/2 - 0.067863Cu 3/2 - 0.2217O 5/2 - 0.0255855Mn 5/2 +0.33

- Nnonspherical spape, described by an electric quadrupole moment Q.

Q > 0prolate nucleus

egg shaped

−

−

1 b (barn)= 100 fm2

highest energy

−

−

+ +

(2) Inhomogeneous electric fields in molecules: electric field gradient (EFG) at nuclei

(1) Nuclei with spin>1/2 have electric quadrupole moment

−

−

lowest energy

+

+

(3) Quadrupole nuclei haveorientation-dependentenergy

+

++ +

Q < 0oblate nucleusburger shaped

- Spin is tied to nuclear shape!

electric, notmagnetic interaction!

(4) This leads to additionalsplittings in spectra.

Nuclear quadrupole interaction

33

Electric field gradient (EFG) at nucleus

sign of q ambiguousfor 𝜂𝜂 = 1

Spin Hamiltonian term

ℋ = ℎ 𝑰𝑰 � 𝑷𝑷 � 𝑰𝑰

𝑷𝑷 =𝑒𝑒2𝑄𝑄𝑄𝑄/ℎ4𝐼𝐼(2𝐼𝐼 − 1)

−(1 − 𝜂𝜂) 0 00 −(1 + 𝜂𝜂) 00 0 +2

quadrupole tensor

Rhombicity

e2Qq/h and η

Largest component

Principal valuesEFG is a 3x3 matrix V Interaction of quadrupole moment with EFG

EFG asymmetryEFG strength

quadrupolemoment

Experimental parameters:

nuclear spin vector

𝑉𝑉𝑧𝑧𝑧𝑧 = 𝑒𝑒𝑄𝑄

𝑉𝑉𝑥𝑥𝑥𝑥 + 𝑉𝑉𝑦𝑦𝑦𝑦 + 𝑉𝑉𝑧𝑧𝑧𝑧 = 0

0 ≤ 𝜂𝜂 ≤ 1

𝑉𝑉𝑧𝑧𝑧𝑧 ≥ 𝑉𝑉𝑦𝑦𝑦𝑦 ≥ 𝑉𝑉𝑥𝑥𝑥𝑥

𝑉𝑉𝑥𝑥𝑥𝑥, 𝑉𝑉𝑦𝑦𝑦𝑦, 𝑉𝑉𝑧𝑧𝑧𝑧

𝜂𝜂 =𝑉𝑉𝑥𝑥𝑥𝑥 − 𝑉𝑉𝑦𝑦𝑦𝑦

𝑉𝑉𝑧𝑧𝑧𝑧

D2O: e2Qq/h = 0.213 MHz, η = 0.12Imidazole ligands: EFG at 14N depends on electron populations of 2px,y,z orbitals

Nuclear quadrupole interaction

34

2H

J. Biol. Chem. 2012 287 4662 link

𝐾𝐾 = 𝑎𝑎 −𝑏𝑏

𝑟𝑟O−D3

Length of H-bonds to semiquinones

mCoM reductase, 33S HYSCOREJACS 2005 127 17744 link

Aconitase, 17O ENDORJ. Biol. Chem. 1986 261 4840 link

strong hf couplingsmall nq splitting

33S

17O I = 5/2 gives 2𝐼𝐼 = 10 lines

I = 1 gives 2𝐼𝐼 = 4 lines

EFG depends on electron populations Nx,y,z of 2px,y,z orbitals

14N

very useful for imidazole ligands!

Overview

35

CW vs. pulse EPR, samples, spectrometerResonators and bandwidthsPulses, excitation widthOrientation selectionFIDs, echoes, deadtime, relaxation

Nuclear Zeeman interactionHyperfine interactionCoupling regimesNuclear spectraQuadrupole interaction

1. Fundamentals of pulse EPR

2. Molecular interactions

3. Pulse EPR experimentsField sweepsENDORESEEM, HYSCOREDEER

14N

1H

14N

14N

1H

1H

14N

14N

1H

1H14N

13C

Types of pulse EPR spectra

36

Field echo-detected field sweepFID-detected field sweep

RF frequency

MW frequency

Pulse delays

Pulse EPR measures spin echo (or FID) amplitude as a function of…

inversion recoverytwo-pulse ESEEMthree-pulse ESEEMHYSCORE

Quantity Experiment name Result

EPR spectrum

relaxation timesnuclear spectrumnuclear spectrum

nuclear spectrumnuclear spectrum

Davies ENDORMims ENDOR

ELDOR-detected NMRDEER

nuclear spectrumdistance between spin centers

Field-sweep spectra

37

Distortions due to tau-dependent nuclear modulation of echo amplitude

FID-detected field sweep

FID

two-pulse echotau = 140 ns

90°

τ τ

180° echotwo-pulse echotau = 300 ns

90°

FID

integrate

Echo-detected field sweep

- works only if FID is longer than dead time- use long microwave pulse

deadtime

Relaxation measurements

38

T1: Inversion recovery

T2, Tm: Two-pulse echo decay

180°

τ

invertedecho

90° 180°

τt

measure echo intensity as a function of t

𝑉𝑉 𝑡𝑡𝑉𝑉 0

= 1 − 2exp(−𝑡𝑡/𝑇𝑇1)

measure echo intensity as a function of τ

90°

τ τ

180°

Other methods for T1: saturation recovery, three-pulse echo decay

𝑉𝑉 𝑡𝑡𝑉𝑉 0

≈ exp(−2𝜏𝜏/𝑇𝑇2)

- approximately exponential decay- phase memory, Tm, rather than T2 is obtained- best with small flip angles (avoids instantaneous diffusion)

echo

Nuclear spectra: Mims ENDOR

3939

90°

τ

90° 90°

trf

τ

echo

Mims ENDOR: rf pulse frequency is varied

rf

mw

180°

Basics- use short hard mw pulses- acquire echo intensity asfunction of rf pulse frequency

Blind spots- intensity is modulatedwith τ-dependent sawtoothpattern, centered at Larmorfrequency and with period 0.5/τ("Mims holes")

- central hole at Larmor frequency!

Spectrum- echo intensity decreaseswhenever rf frequency isresonant with a nucleartransition

- upside-down representation

works best for small hyperfine couplings less than about 1/τ(typically 2H, 13C)

rf frequency

Nuclear spectra: Davies ENDOR

40

180°

τ

invertedecho

Davies ENDOR: rf frequency is varied

rf

mw

180°

90° 180°

τ

trf

Basics- based on inversion recovery- use medium/long mw pulses- acquire echo intensity as functionof rf pulse frequency

Spectrum- fully inverted echo is baseline- decrease in echo intensity whenrf frequency is resonant withnuclear transition

Blindspots- no τ-dependent blindspots- central hole at Larmor frequency- width proportional to 1/tp- suited for larger hf couplings- for small couplings, use long pulses(narrower central hole)

tp rf frequency

Nuclear spectra: ESEEM

41

90°

τ τ

180°

Two-pulse ESEEM: τ is varied

- modulation of echo amplitude as a function of interpulse delay(s)- modulation with nuclear resonance frequencies and their combinations- modulation due to hyperfine coupling of electron spin with surrounding nuclei- modulation depth depends on hyperfine coupling, quadrupole coupling, nuclear Zeeman

90°

τ

90° 90°

T τ

stimulatedecho

primary (Hahn)echo

Three-pulse ESEEM: T is varied

τ

τ + T

V3p

V2p

V2p

V3p

modulationdepth/amplitude

modulationdepth/amplitude

electron spin echo envelope modulation

ESEEM: Vector model

42

B0

Bhf(α)

Btot(α)

B0

Bhf(β)

Btot(β)

suddenelectronspin flip

- Electron spin flip inverts hyperfine field at nucleus.- This changes the total local field and the quantization direction of the nucleus.- The change is sudden on the timescale of the nucleus.- The nucleus will precess around the new field direction.

nuclear spinprecession!

"forbidden" transition!

stationarynuclear spin

(1) Electron spin flip induces nuclear precession

ESEEM: Vector model

43

B0

Bhf(β)

Btot(β)

ΔB(t)

- precessing nucleus causes a time-dependentfield along z felt by the electron

- electron precession frequency becomestime dependent

B0

time-dependentprecession frequency!

precession

L. G. Rowan, E. L. Hahn, W. B. Mims, Phys. Rev. A 137, 61-71, 1965D. Grischkowsky, S. R. Hartmann, Phys. Rev. B 2, 60-74,1970S. A. Dikanov, Yu. D. Tsvetkov, ESEEM Spectroscopy, CRC Press, 1992

ESEEM: Data processing

44

ENDOR vs ESEEM

45

Two-pulse ESEEMENDOR

equal intensities Tm decay (fast)sum and difference frequenciesno blind spots

/ 2k / 2k

/ 4k−/ 4k−

Three-pulse ESEEM

T1 decay (slower)no sum and difference frequenciesblind spotsτ adds to dead time

( )β1 cos4k ω τ−

( )α1 cos4k ω τ−

𝜈𝜈𝛼𝛼 + 𝜈𝜈𝛽𝛽

𝜈𝜈𝛽𝛽𝜈𝜈𝛼𝛼𝜈𝜈𝛽𝛽𝜈𝜈𝛼𝛼

𝜈𝜈𝛼𝛼 − 𝜈𝜈𝛽𝛽

𝜈𝜈𝛽𝛽𝜈𝜈𝛼𝛼

ENDOR vs ESEEM

46

ENDOR:- maximum intensity at θ = 90°- mimimum intensity at θ = 0°ESEEM:- no intensity along principal axes- maximum intensity off-axis

Situations for best intensitiesESEEM enhanced by nuclear statemixing; most intense in matchingregime, i.e. low nuclear frequencies

ENDOR enhanced by hyperfineenhancement, most intense forhigh nuclear frequencies

difficult to measurebroad lines with ESEEM!only central part visible!

HYSCORE: a 2D ESEEM experiment

47

90°

τ

90° 90°

t1 τ

HYSCOREecho

HYSCORE: t1 and t2 is varied

V(t1,t2)

180°

t2

echo intensity as afunction of t1 and t2

2D time domain (TD)

1st quadrant2nd quadrant

3rd quadrant(identical to 1st)

4th quadrant(identical to 2nd)

2D frequency domain (FD)

π pulse should beas short as possible

only 1st and 2nd quadrant are shown

HYSCORE = hyperfinesublevel correlation

HYSCORE data processing

48

Time-domain data

Spectrum

t2 baseline correction t1 baseline correction

2D windowing

2D zero filling2D Fourier transform

2x

2x

12

3 4

tapertowardszero

HYSCORE: Spectral patterns

49

Powder spectra

𝜈𝜈α

𝜈𝜈β

Weak coupling

𝜈𝜈α𝜈𝜈β

𝜈𝜈α

𝜈𝜈β

first quadrant

𝜈𝜈α

𝜈𝜈β

Strong coupling

−𝜈𝜈α −𝜈𝜈β

𝜈𝜈α

𝜈𝜈β

second quadrant

Quadrupole splittings

HYSCORE: blindspots

50

Blind spots:- τ-dependent intensity factor: sin(𝜋𝜋𝜈𝜈1𝜏𝜏)sin(𝜋𝜋𝜈𝜈2𝜏𝜏)- intensity drops to zero at frequenciesthat are multiples of 1/𝜏𝜏

- both dimensions, all quadrants

1/𝜏𝜏

2/𝜏𝜏

Example: 𝜏𝜏 = 120 ns1/𝜏𝜏 = 8.33 MHz

1/𝜏𝜏 2/𝜏𝜏

0

0

Consequences:- peaks are missing- peaks are distorted- danger of wrong assignment

Remedies:- acquire spectra with severaldifferent tau values

- use blind-spot free advancedtechniques3/𝜏𝜏

3/𝜏𝜏

−3/𝜏𝜏 −2/𝜏𝜏 −1/𝜏𝜏

ESEEM/ENDOR at higher frequencies

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Advantages- separation of isotopes- weak coupling regime forlarge hyperfine couplings

- increased sensitivity forlow-gamma nuclei

- larger spin polarization- larger orientation selectivity

Disadvantages- less signal for stronglyanisotropic systems

- less available power- longer pulses

Pulse EPR powerX-band 9-10 GHz 1000 WQ-band 34-36 GHz 300 WW-band 95 GHz 2 WD-band 130 GHz 0.125 WG-band 263 GHz 0.020 W

ENDOR/ESEEM frequency ranges for common isotopes:

DEER – double electron-electron resonance

52

90°

τ1

180°

τ2

refocusedtwo-pulse

echo

4-pulse DEER: t is varied180°

t

mw1

mw2

τ1 τ2180°

two-pulseecho

Echo modulation

DEER = double electron-electron resonance(also called PELDOR = pulse electron double resonance)

B

A

𝜈𝜈ee =𝜇𝜇0𝜇𝜇B2

4𝜋𝜋ℎ𝑔𝑔𝐴𝐴𝑔𝑔𝐵𝐵

1𝑟𝑟3

Dipolar coupling betweentwo electron spins analogousto dipolar hyperfine coupling

B0

mw2

mw1

A = probe spin, mw1B = pump spin, mw2

pump spin up pump spin down

DEER data analysis

53

Echo modulation

Dipolar spectrum

Distance distribution

Fourier transformation

Least-squares fit(Tikhonov regularization)

called formfactor afterbackgroundcorrection

What you can learn from EPR data

54

g tensorhyperfine couplingszero-field splittingsrelaxation times

Fieldsweeps

ENDORESEEM

DEER dipolar coupling distance between spin centersprotein conformations

type of spin center (metal, radical)spin quantum numberdelocalization of spincoordination geometryoxidation state, spin multiplicity

nuclear Zeeman frequencyisotropic hyperfine couplinganisotropic hyperfine coupingnuclear quadrupole coupling

EPR parameters Structural information

type of ligand nucleiprotonation stateslocation of protonsoxidation state assignmentcoordination mode of ligands

A new textbook about EPR spectroscopy

55

648 pages27 chapters

available April 2018