High Frequency Dynamic Nuclear Polarization · •Magic angle adjustment ... l The full system was modeled in HFSS l Internal Reflections Top View ... T=78 K, 13C{1H} CPMAS, 5.5 kHz

Biomolecular NMR Winter School Trapp Family Lodge January 7-12, 2018

High Frequency Dynamic Nuclear Polarization

Francis Bitter Magnet Laboratoryand

Department of ChemistryMassachusetts Institute of Technology

AMUPol

• Background and RationaleDNP, EPR, and Signal to NoiseDNP Enhancements of 100-400 in MAS Spectra @ 90 KDNP functions quite effectively in multiple classes of systems

• Instrumentation for DNPQuadruple Resonance, LT MAS ProbesSuperconducting Sweep CoilsGyrotron Microwave Oscillators and Amplifiers

• CW DNP Mechanisms and Polarizing AgentsSolid Effect — δ ~Δ << ω0I

two spins, without e- - 1H hyperfine couplingOverhauser Effect — δ ~Δ << ω0I

two spins, with e- - 1H hyperfine coupling Cross Effect — δ < ω0I < Δ

three spins, with e- -e--1H dipole coupling

• Time Domain DNPNOVEL — lab frame-rotating frame cross-polarizationIntegrated Solid EffectStretched Solid Effect

NEW

NEW

DNP Outline

Melanie Rosay








DNP Outline

What are the THREE most important parameters in magnetic resonance

Signal-to-noise Signal-to-noise

Signal-to-noise

4

Dynamic Nuclear Polarization

Nuclear Spin PolarizationTemperature and Field Dependence

1 10 100 300

0.01

0.1

100

Temperature (K)

10

1

0.001

0.0186 % 1H polarization @ 700 MHz / 90 K

POLARIZATION

• Current strategy -- increase the polarization by increasing B0 ! • Result -- “modest” increases in sensitivity and resolution ! Increases in magnet cost are non-linear !

P = n+ - n-

n+ + n- = tanh γ !B0

2kT⎛⎝⎜

⎞⎠⎟

500 MHz

900 MHz

P = γ !B0

2kT

Electron and Nuclear PolarizationTemperature and Field Dependence

12.24 % e- polarization @ 700 MHz / 90 K

0.0186 % 1H polarization @ 700 MHz / 90 K

POLARIZATION

• Much larger spin polarization is present in the electron spin reservoir •Transfer the electron polarization to the nuclear spins by irradiating the electrons with high frequency microwaves !

P = n+ - n-

n+ + n- = tanh γ !B0

2kT⎛⎝⎜

⎞⎠⎟

(γe/γ1H) ~ 660 P = γ !B0

2kT

Components of a DNP System

Barnes, et al. (2009) Bajaj, et al. (2007) Joye, et al., (2006)

Woskow, et al. (2005) Song, et al. (2006) Matsuki, et al. (2009)

Quadruple Resonance DNP/MAS Probew/ Optical Irradiation of the Sample

• Quadruple resonance -- 1H, 13C, 15N, and e-

• Routine low temperature spinning at 85-90 K, ωr/2π ~10 kHz• Optical irradiation (532/650 nm) of samples to generate photochemical

intermediates

Barnes, et. al. JMR (2009)

MAS and Sample Exchange

3D printed eject pipe

tapped waveguide

Barnes et al. JMR, 198(2), 261

custom 3.2 mm Lewis stator

• Changes samples in minutes • Reduces risk of damage

90° turn

80-100 K

Cambridge Instruments DNP Cryogenic MAS Probe

Challenges for cryogenic sample exchange:

•Magic angle adjustment•Limited space•Seals at low temperature•Physical restrictions under the magnet•Prevent damage to rotor

LT dewar

Sample eject

Waveguide

Optic fiber

Alexander Barnes

Simulation of EM Coupling to Sample

l The full system was modeled in HFSS l Internal Reflections

Top View

Side View

Sapphire Rotor

EM Waves Launched

NMR Coil

• Modeling useful to optimize coupling of EM radiation to sample

8 mm

E. Nanni and R. Temkin, 2010

Frequency Calibration• NMR frequencies ---

– generally refer to 1H frequencies – 42.577 MHz/Tesla

• EPR frequencies --- – dealing with g=2 electrons – 28.0 GHz/Tesla

Magnetic Field (Tesla)

1H NMR Frequency (MHz)

g=2 EPR Frequency (GHz)

5 211 1408.93 380 25014.09 600 39516.44 700 46018.79 800 527

(γe/γH) = (2800/42.577) =657

(⅔)𝜈H(MHz)≈𝜈e(GHz)

460 GHz/ 700 MHz GyrotronOscillator

Hornstein,Kreischer, Temkin, et al (2004)

250/ 460 GHz GyrotronFunctional Details

A: Electron emission from an annular ring

B: Bunching in the cavity and emission of microwaves

C: Quasi optic coupling of the microwaves out to the sample. Electrons continue to the collector.

D: Electrons are collected in the collector

• Generates microwaves with a frequency of ~28 GHz/Tesla

Corrugated Waveguide

1.3 m

Wall thickness 300 microns

λ/4 Corrugation depth

•Very low insertion loss (0.01dB/m)

•Cryogenic Operation

•Excellent mode and polarization characteristics

Sample Preparation

• TOTAPOL is soluble in water and stable

• Cryoprotection is critical to minimize inhomogeneous broadening

• Polarization diffuses throughout the macromolecule

H2Oe

-

H2OH2Oe-

e-

e-

e-

e- H2O

H2O

H2O

H2O

H2O

H2Oe-

Purple membrane

Cryoprotected sample

Cryoprotectant (e.g. glycerol)

bacteriorhodopsin

1. Resuspension

2. centrifugation

TOTAPOL Sedimented Proteins

“DNP Juice”

d8-glycerol/D2O/H2O

60:30:10

DNP in Nonconducting Solids

♦ Requires microwaves and cryogenic temperatures

2H

2H

2H2H 2H

2H

2H2H

2H

2H

2H2H

2H

2H

2H

2H

2H2H

2H

2H

DNP Sensitvity Enhancement

♦ ε = 40: DNP – 1 Day; no DNP – 4.38 years

AMUPol Biradical Paul Tordo and Co.

Aux Marseille Universite

♦ ε = 420: DNP – 1 Day; no DNP – 483 years !

ε = 420

Qing Zhe Ni1M-13C-urea / 10 mM radical 60/30/10 (v/v/v)

380 MHz / 250 GHz - mw ~ 12 W

T=78 K, 13C{1H} CPMAS, 5.5 kHz

35 MHz e--e-

coupling

DNP WorldwideWS 2010 -- One student remarked that he/she “will not try DNP very soon” since ... there

will not be access to DNP hardware in the future !

Other efforts: A, Barnes, R. Tycko, Y. Matsuki, K. Zilm, M. Ernst, M. Levitt, C. Hilty, W. Koeckenberger, Dan Vigernon, etc.

400 MHz/263 GHz

H. Oschkinat/Berlin G. Bodenhausen/Lausanne

M. Baldus/Utrecht G. DePaepe/Grenoble x2

C. Glaubitz/Frankfurt M. Pruski/Iowa State

S. Han/ UCSB Kyoto and Tsukuba, Japan

600 MHz/395 GHz

A. McDermott/ Columbia V. Ladizhansky/Guelph

C. Greisinger/Goettingen J. Long, T. Cross/ Florida State

G. Debelouchina, S. Opella/UCSD V. Michaelis/ Alberta

C. Coperet/ETH-Zurich C.P. Jaroniec/OHio State

K, Frederik/ UTSW

800 MHz/527 GHz

M. Baldus, Utrecht Lesage, Pintacuda, Emsley/Lyon

G. Bodenhausen/Paris B. Reif/Munich

H. Oschkinat/Berlin H. Heise/ Dusseldorf

900 MHz/593 GHz L.Emsley/Lausanne

~17 Total

~13 Total

6 Total

1 Total

30-40

gyrotrons








DNP Outline

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect

Biradicals -- Cross Effect

AMUPol

EPR spectra and DNP Zeeman field profiles

• EPR spectra of polarizing

agents -- ~100 mT (1000 G)

• Variety of polarizing agents

allows for optimal DNP in

different situations

140 GHz EPR spectra

DNP Zeeman field profiles

Mn2+

Gd3+

NO• BDPAtrityl

DNP

0 200-200-400Frequency (MHz)

e1 e2

ωn

Δ 600 MHz

δ ~5 MHz

ω0I

• Mechanism determined by relative size of Δ, ω0I ,δ in EPR

•Cross effect -- three spins Δ> ω0I/2π> δ

•Solid effect -- two spins ω0I/2π > δ,Δ

•Overhauser effect - liquids, mobile electrons (?)

•Thermal mixing - many electrons, homogeneous EPR

• Time domain DNP — electron spin locking

DNP Mechanisms Δ, ω0I ,δ

CW Dynamic Nuclear Polarization Mechanisms

Solid Effect (SE) -- single electron,insulating solids (organic, biological systems) when .…

δ ~Δ << ωδ = homogeneous linewidth of the EPR spectrumΔ = breadth of the EPR spectrum ω = nuclear Larmor frequency (1H, 13C, 15N)

Overhauser Effect (OE) -- applicable to systems with mobile electrons -- i.e., metals, liquids, 1D conductors (Carver and Slichter, Li metal) and strong 1H hyperfine couplings

δ ~Δ << ω


Thermal Mixing (TM) -- multiple electrons, insulating solids, but ….

δ, Δ >> ω TM -- dominates when the g anisotropy is small, and/or the EPR line is homogeneously broadened, and ω is small

Cross Effect (CE) -- two electrons, insulating solids, but ….

Δ> ω>δ CE -- operative at high fields where Δg >> δ, the line is inhomogeneously broadened.


Solid Effect (SE) -- single electron,insulating solids (organic, biological systems) when .…

δ ~Δ << ωδ = homogeneous linewidth of the EPR spectrumΔ = breadth of the EPR spectrum ω = nuclear Larmor frequency (1H, 13C, 15N)

Overhauser Effect (OE) -- applicable to systems with mobile electrons -- i.e., metals, liquids, 1D conductors (Carver and Slichter, Li metal) and strong 1H hyperfine couplings

δ ~Δ << ω

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect -- Δ=25-60 MHz

9 GHz EPR spectra16 1H couplings 21 1H couplings

Can, et al, J. Chem. Phys. 141, 064202 (2014)

Paramagnetic Centers for DNP

BDPA

Galvinoxyl

TEMPO

49.949.849.749.649.5Field (kilogauss)

• EPR lineshapes are Dominated by g- anisotropy

• BDPA linewidth ~21 MHz ---- Solid effect

• TEMPO powder pattern~600 MHz ---- Thermal mixing or

cross effect

ωe/2π = 28 GHz/T

DNP with Gyrotrons

e- →1H→13C e- → 13Cεmax @ ωe ± ωn

ε~10 ε~40

1.5% efficient

(γe/γn) ~ 660

Trityl Radical Structure and FT EPR Spectrum

• Small g-anisotropy yields a solid effect enhancement mechanism

Dynamic Nuclear PolarizationSolid State EffectDNPDNPDNP

• Enhancement ~ (γ ε / γ n ) (ω1 /ω0 )2 (Ne / δ )T1n

• Irradiate the flip-floptransitionsW±

NuclearZeeman

Bath

ElectronZeeman

Bath

EquilibriumNegative

EnhancementPositive

EnhancementNo

Enhancement

νε−νn νε+νnνε

|--) + q |-+)

|+-) - q |++)|++)+ q* |+-)

WEPRWEPR

W±

|-+) - q* |--)Wnmr

Wnmr

Solid Effect @ 400 MHz/263 GHz

• Mediated by single electron-nuclear spin flips •Transitions are partially allowed due to state mixing.

•Maximum and minimum enhancements at ω =ωe ± ωn

Trityl Radical triphenyl methyl radical

Magne&cField

Polarizeωe±ωn

C. Can, M.Caporini, F. Mentink-Vigier , S. Vega and M. Rosay, JCP (2014)

Dynamic Nuclear PolarizationSolid State EffectDNPDNPDNP

• Enhancement ~ (γ ε / γ n ) (ω1 /ω0 )2 (Ne / δ )T1n

• Irradiate the flip-floptransitionsW±

NuclearZeeman

Bath

ElectronZeeman

Bath

EquilibriumNegative

EnhancementPositive

EnhancementNo

Enhancement

νε−νn νε+νnνε

|--) + q |-+)

|+-) - q |++)|++)+ q* |+-)

WEPRWEPR

W±

|-+) - q* |--)Wnmr

Wnmr

State Mixing+ + S+ − − = + − S+ − + = 0 !

• Electron-nuclear transitions are forbidden

Perturbation Theory Notes 1

ψ n1 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠n∑ Ψm

0 !

En1 = ψ n

0 ′H ψ n0 !

En2 =

ψ m0 ′H ψ n

0 ψ n0 ′H ψ m

0

En0 − Em

0 =m≠n∑ ′Hmn ′Hnm

En0 − Em

0m≠n∑ !

•Hamiltonian of interest is the electron-nuclear dipolar coupling

Electron-Nuclear Dipole Coupling

• C and D (C’) terms mix adjacent states

HIS =

γ Iγ Sr3 (A + B + C + D + E + F) !

A=(1− 3cos2θ) SZ IZ[ ]B = −

14

(1− 3cos2θ) S−I+ + S+I−[ ]

C = −32

sinθ cosθe− iφ S+IZ + SZ I+[ ]

D = C† = −32

sinθ cosθeiφ S−IZ + SZ I−[ ]

E = −34

sin2θe−2iφ S+I+[ ]

F = −34

sin2θe2iφ S−I−[ ]


• Only terms with the nuclear frequency survive in the expansion

ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0 ψ 10 +

ψ 20 ′H ψ 3

0

E30 − E2

0 ψ 20 +

ψ 40 ′H ψ 3

0

E40 − E1

0 ψ 40

E30 − E1

0 =12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟−

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= γ IB0 = ω0 I

E30 − E2

0 =12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟− −

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= γ SB0 = ω0S

E40 − E1

0 = −12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟−

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= −γ SB0 + γ IB0 ≈ −ω0S

!

ω 0S / 2π = 140 GHz ω 0 I / 2π = 211 MHz


• Only terms with the nuclear frequency survive

ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0 ψ 10 +

ψ 20 ′H ψ 3

0

E30 − E2

0 ψ 20 +

ψ 40 ′H ψ 3

0

E40 − E1

0 ψ 40

E30 − E1

0 =12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟−

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= γ IB0 = ω0 I

E30 − E2

0 =12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟− −

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= γ SB0 = ω0S

E40 − E1

0 = −12γ SB0 +

12γ IB0

⎛⎝⎜

⎞⎠⎟−

12γ SB0 −

12γ IB0

⎛⎝⎜

⎞⎠⎟

= −γ SB0 + γ IB0 ≈ −ω0S

!

ω 0S / 2π = 140 GHz ω 0 I / 2π = 211 MHz



ψ 31 =

ψ m0 ′H ψ n

0

En0 − Em

0m≠3∑ ψ m

0 =ψ 1

0 ′H ψ 30

E30 − E1

0 ψ 10 +

ψ 20 ′H ψ 3

0

E30 − E2

0 ψ 20 +

ψ 40 ′H ψ 3

0

E40 − E1

0 ψ 40

q = −γ Iγ S

r3

32ω0 I

sinθ cosθe− iφ + + SZ I+ + −

ψ 3= + − − q + +



q = −γ Iγ S

r3

32ω0 I

sinθ cosθe− iφ + + SZ I+ + −

ψ 3= + − − q + +

ψ 1= + + + q * + −ψ 2 = − + − q * − −ψ 4 = − − + q − +

!

Transition Probabilities

ψ 1 S+ ψ 42

= + +( ) + q + −( ) S+ − −( ) + q − +( ) 2= 2q = 4q2 !

ψ 2 S− ψ 32

= − +( ) − q − −( ) S− + −( ) + q + +( ) 2= 2q = 4q2 !

Double Quantum

Zero Quantum

q2 ω0 I

−2 !

• Solid effect scales as ω 0−2 !

Solid Effect with Trityl Radical

• Soluble in aqueous media

• Frequency dependence shows a well resolved solid effect

• Peaks in the enhancement curves at ω e±ω n

δe < ω n90 MHz < 211 MHz• Enhancements are significant but modest only ±15 ! L !

K. Hu et. al (2004)

Solid Effect DNP

•Sta&cHamiltonian: Huet.al.,JCP(2011)CorziliusJCP(2012)

•Hcanbediagonalizedin2subspaces

CodyCan(2012)

Solid Effect Field Profile

• Resolved solid effect at 5 T

• Unresolved solid effect at 0.35 TCan et al., J. Chem. Phys. 141, 064202 (2014)

• 3-spin mechanism

• Enhancement up to ~100 at 0.35 T

Experiment by Dr. Kong Tan

ω1S ± 2ω0I

9.72 9.74 9.76 9.78 9.8 9.82 9.84250

200

150

100

50

0

50

100

150

200

250

uw / GHz

Sign

al In

tens

ity

170423_trityl_80k_3484G_eldorsweep_SE_2MHz

ωe-2ωn

ωe-ωn

ωe+ωn

ωe+2ωn

deBoer, J. Low Temp. Phys. 22, 185(1976)

Trityl radical3-Spin Solid Effect

Zeeman Field Profile

3-Spin Solid Effect

• 3-spin mechanism

• Enhancement up to ~100 at 0.35 T

Simulation by Dr. Chen YangExperiment by Dr. Kong Tan

ω1S ± 2ω0I

• Background and RationaleDNP, EPR, Signal to Noise and bRDNP Enhancements of 100-400 in MAS Spectra @ 90 KDNP functions quite effectively in multiple classes of systems





• Time Domain DNP — NOVELNOVEL — lab frame-rotating frame cross-polarization


NEW

DNP Outline

LessonsfromSolu9onNMR๏Overhausereffectsrequiremobileelectronsornuclei....Metals,1Dconductors,NainNH3,solu&onNOE’s

๏ HeteronuclearOverhausereffectsscale~B0-n.... Transla&onalandrota&onalspectraldensi&es Heteronuclear(1H-13C)NOE’sareaKenuated>2.3T

Shouldnotdo13CproteinNMRabove>60-100MHz

๏ TimeDomainExperimentsarenotfielddependent.... INEPTfor1H-13C/15Npolariza&ontransfers

OverhauserDNPininsulators—newmechanism!

OverhauserDNPscalesasB0+n!

PulsedDNPexperimentsarenotfielddependent!

Overhauser Effect vs. ω0

• Overhauser effects commonly scale ~ω0-n

•13C NMR in proteins — only at <100 MHz

Hauser and Stehlik Adv in Mag. Res 1970

Oldfield, Norton and Allerhand J. Biol. Chem. 1975

electron-nuclear 1H-13C NOE’s in proteins

7Li w/ DNP @ 84 MHz

7Li w/o DNP

1H glycerol

• 7Li NMR @ ω0/2π= 50 kHz (30.3 Gauss)

• EPR @ ω0/2π= 84 MHz

ε ~ 100

• Initial demonstration of the Overhauser effect -- DNP • Nuclear Overhauser effect is important in solution NMR !

Carver and Slichter, Phys. Rev. 92, 212-213 (1953) Phys. Rev. 102, 975-980 (1956)

Water soluble BDPA

• Improved Solid Effect

performance with MAS 40 mM in d8-Glycerol/D2O/H2O (60:30:10) 4 mm rotor spinning at 5 kHz, 80 K 5 W cw microwave irradiation

Olesya Haze, Tim Swager, et al. JACS (2012)

Solid and Overhauser Effects @ 400 MHz/263 GHz

•Small Overhauser enhancement for SA-BDPA •Well developed transition for BDPA •Trityl cannot make up its mind !

SolidEffectSolidEffect

+Overhauser


Solid + Overhauser Effect @ 600 MHz/395 GHz

• Overhauser enhancement for BDPA and SA-BDPA

• SA-BDPA -- 40 % of the SE enhancement

• g-anisotropy evident on the SE lineshape

• 800 and 1200 MHz ?

Abragam, A. Phys. Rev. 1955, 98, 1729–1735.Can, et al, J. Chem. Phys. 141, 064202 (2014)

DNP Polarizing AgentsMonoradicals -- Solid and Overhauser Effect -- Δ=25-60 MHz

9 GHz EPR spectra16 1H couplings 21 1H couplings


Solid + Overhauser Effect HYperfine Coupling Zero Quantum

• Overhauser and solid effect enhancements

• Two spin model -- 5 MHz 1H-e- couplings

• Zero quantum relaxation mediates the OE enhancementCan, et al, J. Chem. Phys. 141, 064202 (2014)

Solid + Overhauser Effect


• Two spin model, 1H hyperfine coupling

• Zero quantum relaxation mediates the OE enhancementCan, et al, J. Chem. Phys. 141, 064202 (2014)

Solid + Overhauser Effect HYperfine Coupling Zero Quantum

58


• Two spin model -- 5 MHz 1H-e- couplings

• Zero quantum relaxation mediates the OE enhancement


Solid + Overhauser Effect Simulations

F. Mentink-Vigier and S. Vega

• Overhauser enhancement for BDPA and SA-BDPA

• Two spin model, 1H hyperfine coupling

• BDPA’s have 1H’s ! Trityl e--1H coupling weak !


Overhauser Effect Power Dependence F. Mentink-Vigier and S. Vega

• Zero quantum relaxation OE enhancement

• High frequency sources (400-1000 GHz), <5 watts


Solid + Overhauser Effect Dipolar Coupling Double Quantum


• e- -1H dipolar coupling

• Double quantum relaxation mediates the OE enhancementCan, et al, J. Chem. Phys. 141, 064202 (2014)

Solid + Overhauser Effect


• Two spin model, 1H hyperfine or dipolar coupling

• Zero or double quantum relaxation OE enhancement

e- -1H dipolar --DQe- -1H Hyperfine -- ZQ


Overhauser Effect vs. ω0

• Overhauser effects commonly scale ω0-n

• Solid effect scales ℇ0 ~ω0-2

• Overhauser effect scales ~(ℇ0 +k’ω0) [rather than ω0-n]

Marc Baldus Utrecht Univ.

BDPA/ortho-terphenyl at 14.1 T

• Ortho-terphenyl forms a excellent glass

• A factor of ~ 5 improvement compared to polystyrene

• Stable narrow line radicals with large 1H hyperfine couplings

Can, et al, (submitted) (2015)

65

OverhauserDNPEnhancement@[email protected]

600MHz/395GHz T=1.2K

• Factor of ~ 5 improvement compared to polystyrene

• T=1.2 K eliminates many molecular fluctuations that could mediate the OE enhancement.

OverhauserDNPEnhancement@800MHz,ωr/2π=40KHz

66

•BDPA in OTP (95% 2H)

• 13C enhancement =105

•No depolarization effects

• ℇ increases with ωr/2π

• Long build-up time — 40 s

•ω0/2π=800 MHz !

105

•Higher ωr/2π and ω0/2π yield larger the Overhauser enhancements !

43 s

High Frequency Dynamic Nuclear Polarization · •Magic angle adjustment ... l The full system was modeled in HFSS l Internal Reflections Top View ... T=78 K, 13C{1H} CPMAS, 5.5 kHz

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