solid-state nmr of quadrupolar nuclei · solid-state nmr of quadrupolar nuclei (the rest of the...

Solid-State NMR of Quadrupolar Nuclei(the rest of the periodic table)

P. J. Grandinetti

L’Ohio State Univ.

Jan. 10, 2018

P. J. Grandinetti (L’Ohio State Univ.) Solid-State NMR of Quadrupolar Nuclei Jan. 10, 2018 1 / 78

Most Abundant Isotope of Element with Odd Z is NMR ActiveGeneral rule: for element with even atomic number (Z) its most abundant isotopeis NMR active whereas for element with odd Z its most abundant isotope willhave nuclear spin of I=0 and be NMR inactive.

Hydrogen

Lithium

Sodium

Potassium

Rubidium

Berylium

Magnesium

Calcium

Strontium

Cesium Barium

87FrFrancium

Scandium Titanium Vanadium

Yttrium Zirconium

Lanthanum Hafnium

Praseodymium

Tantalum

Niobium

Tungsten

Molybdenum

Chromium

Neodymium

Rhenium

43TcTechnetium

Manganese

Osmium

Ruthenium

Iron Cobalt Nickel Copper Zinc

Rhodium Palladium Silver Cadmium

Iridium Platinium Gold Mercury

Boron Carbon Nitrogen Oxygen Fluorine Neon

Aluminum Silicon Phosphorus Sulfur Chlorine Argon

Helium

Gallium Germanium Arsenic Selenium Bromine Krypton

Indium Tin Antimony Tellurium Iodine Xenon

Thallium Lead Bismuth84Po

Polonium85AtAstatine

86RnRadon

88RaRadium

89AcActinium

Cerium61Pm

Promethium Samarium

Thorium Protactinium Uranium93Np

Neptunium

Europium Gadolinium Terbium Dysprosium Holmium Erbium

94PuPlutonium

95AmAmericium

96CmCurium

97BkBerkelium

98CfCalifornium

99EsEinsteinium

100FmFermium

101MdMendelevium

Thullium Ytterbium Lutetium

102NoNobellium

103LrLawrencium

IA

IIA

IIIB IVB VB VIB }VIIIBIB IIBVIIB

IIIA IVA VA VIA VIIA

VIIIA

Lanthanide Series

Actinide Series

1H1

3Li7

11Na23

19K3920Ca40

21Sc4522Ti48

23V5124Cr52

25Mn5526Fe56

27Co5928Ni58

29Cu6330Zn64

31Ga6932Ge74

33As7534Se80

35Br7936Kr84

12Mg2413Al27

14Si2815P31

16S32

17Cl3518Ar40

4Be95B

116C

127N

148O

169F

1910Ne20

2He499.9885%

92.41%

100%

93.2581%

37Rb85

55Cs13356Ba138

57La13972Hf180

73Ta181

58Ce140

74W18475Re187

76Os19277Ir193

78Pt19579Au197

80Hg20281Tl205

82Pb20883Bi209

38Sr8872.17% 82.58%

39Y89100%

40Zr9051.45%

41Nb93100%

42Mo9824.13%

44Ru10231.55%

45Rh103100%

46Pd10627.33%

47Ag10751.839%

48Cd11428.73%

49In11595.71%

50Sn12032.58%

51Sb12157.21%

52Te13034.08%

53I127100%

54Xe13226.89%

96.941% 100% 73.72% 99.750% 83.789% 100%

0%

100%

0% 0% 0%

71.698% 99.910% 35.08% 99.988%

88.450%

90Th232100%

91Pa231100%

92U23899.2745% 0% 0% 0% 0% 0% 0% 0% 0% 0%0%0%

59Pr141100%

60Nd14227.2%

62Sm15226.75%

63Eu15352.19%

64Gd15824.84%

65Tb159100%

66Dy16428.18%

67Ho165100%

68Er16633.61%

69Tm169100%

70Yb17431.83%

71Lu17597.41%0%

30.64% 40.78% 62.7% 33.832% 100% 29.86% 70.476% 52.4% 100% 0% 0% 0%62.60%

91.754% 100% 68.0769% 69.17% 48.63% 48.63% 36.28%

78.99% 100% 92.2297% 100%

100% 49.61% 50.69% 57.00%

94.93% 75.78% 99.6003%

100% 80.2% 98.93% 99.632% 99.757% 100% 90.48%

99.999863%

Most Abundant Isotope is NMR Active


NMR sensitivity increases with frequency

Hydrogen

Lithium

Sodium

Potassium

Rubidium

Berylium

Magnesium

Calcium

Strontium

Cesium Barium

87FrFrancium


Yttrium Zirconium

Lanthanum Hafnium

Praseodymium

Tantalum

Niobium

Tungsten

Molybdenum

Chromium

Neodymium

Rhenium

43TcTechnetium

Manganese

Osmium

Ruthenium






Helium





86RnRadon

88RaRadium

89AcActinium

Cerium61Pm

Promethium Samarium


Neptunium


94PuPlutonium

95AmAmericium

96CmCurium

97BkBerkelium

98CfCalifornium

99EsEinsteinium

100FmFermium

101MdMendelevium


102NoNobellium

103LrLawrencium

IA

IIA



VIIIA

Lanthanide Series

Actinide Series

1H1

3Li7

11Na23

19K3920Ca43

21Sc4522Ti48

23V5124Cr52

25Mn5526Fe57

27Co5928Ni61

29Cu6330Zn67

31Ga7132Ge73

33As7534Se77

35Br8136Kr83

12Mg2513Al27

14Si2915P31

16S33

17Cl3518Ar

4Be95B

116C

137N

158O

179F

1910Ne21

2He399.9885%

92.41%

100%

93.2581%

37Rb87

55Cs13356Ba137

57La13972Hf177

73Ta181

58Ce

74W18375Re187

76Os18977Ir193

78Pt19579Au197

80Hg19981Tl205

82Pb20783Bi209

38Sr8727.83% 7%

39Y89100%

40Zr9111.22%

41Nb93100%

42Mo9515.92%

44Ru9912.76%

45Rh103100%

46Pd10522.33%

47Ag10751.839%

48Cd11312.22%

49In11595.71%

50Sn1198.59%

51Sb12157.21%

52Te1257.07%

53I127100%

54Xe12926.4%

0.135% 100% 73.72% 99.750% 83.789% 100%

100% 11.232% 99.910% 18.6% 99.988%

90Th 91Pa231100%

92U23899.2745%

59Pr141100%

60Nd1458.3%

62Sm14714.99%

63Eu15147.81%

64Gd15715.65%

65Tb159100%

66Dy16118.91%

67Ho165100%

68Er16722.869%

69Tm169100%

70Yb17114.28%

71Lu1762.59%

14.31% 16.21% 62.7% 33.832% 100% 16.87% 70.476% 22.1% 100%62.60%

2.119% 100% 1.14% 69.17% 4.1% 39.892% 7.76%

10% 100% 4.683% 100%

100% 7.63% 49.31% 11.49%

0.75% 75.78%

100% 80.2% 1.11% 0.366% 0.038% 100% 0.27%

0.000137%

32-43 MHz/T

15-32 MHz/T

12-15 MHz/T

8-12 MHz/T

5-8 MHz/T

0-5 MHz/T

No stable NMR active isotope

Remember: Most abundant isotope of odd Z are NMR activeP. J. Grandinetti (L’Ohio State Univ.) Solid-State NMR of Quadrupolar Nuclei Jan. 10, 2018 3 / 78

Spin 1/2 Nuclei are easy

Hydrogen

Lithium

Sodium

Potassium

Rubidium

Berylium

Magnesium

Calcium

Strontium

Cesium Barium

87FrFrancium


Yttrium Zirconium

Lanthanum Hafnium

Praseodymium

Tantalum

Niobium

Tungsten

Molybdenum

Chromium

Neodymium

Rhenium

43TcTechnetium

Manganese

Osmium

Ruthenium






Helium





86RnRadon

88RaRadium

89AcActinium

Cerium61Pm

Promethium Samarium


Neptunium


94PuPlutonium

95AmAmericium

96CmCurium

97BkBerkelium

98CfCalifornium

99EsEinsteinium

100FmFermium

101MdMendelevium


102NoNobellium

103LrLawrencium

IA

IIA



VIIIA

Lanthanide Series

Actinide Series

1H1

3Li

11Na

19K 20Ca 21Sc 22Ti 23V 24Cr 25Mn 26Fe5727Co 28Ni 29Cu 30Zn 31Ga 32Ge 33As 34Se77

35Br 36Kr

12Mg 13Al 14Si2915P31

16S 17Cl 18Ar

4Be 5B 6C13

7N15

8O 9F19

10Ne

2He399.9885%

37Rb

55Cs 56Ba 57La 72Hf 73Ta

58Ce

74W18375Re 76Os187

77Ir 78Pt19579Au 80Hg199

81Tl20582Pb207

83Bi

38Sr 39Y89100%

40Zr 41Nb 42Mo 44Ru 45Rh103100%

46Pd 47Ag10751.839%

48Cd11112.80%

49In 50Sn1198.59%

51Sb 52Te1257.07%

53I 54Xe12926.44%

0% 0% 0%

90Th 91Pa 92U

59Pr 60Nd 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm169100%

70Yb17114.28%

71Lu

14.31% 1.96% 33.832% 16.87% 70.476% 22.1%

2.119%

4.6832% 100%

7.63%

1.07% 0.368% 100%

0.000137%High Abundance > 50%

Low Abundance < 50%

14N (I=1) 99.634%15N (I=1/2) 0.366%


Nuclei with Spin > 1/2 have electric quadrupole moments

NuclearSpin

Allowed Nuclear Multipole Moments as a function of Nuclear Spin I

Electric Quadrupole Moment, describes shape of nucleus

Prolate SpheroidOblate SpheroidSphere


Nuclei with Spin > 1/2 have electric quadrupole moments


Nuclei with electric quadrupole moments couple with surroundingelectric field gradient

nuclear quadrupolemoment tensor

electric field gradient tensor

InteractionEnergy

The electric field gradient is to the nuclear electric quadrupole moment asthe magnetic field is to the nuclear magnetic dipole moment.


Nuclei with electric quadrupole moments precess in electric fieldgradient

The nuclear electric quadrupole moment interacts with surrounding electric field gradients.

These electric field gradients are generated by

orbiting electrons as well as neighboring nuclei.

nuclear electric quadrupole moment precesses

in an electric field gradientnuclear magnetic dipole moment precesess in a magnetic field


Electric field gradient at the nucleus


How big is the electric field gradient at the nucleus?

0

two useful parameters

NMR can’t measure efg directly – instead it measures...


Unpaired e− in single p orbital generates substantial efg at nucleus

In a closed subshell the efg tensors arising from each atomic orbital sum to zero


Examples of Quadrupolar couplings in solids


Relationships between EFG and StructureLets try a simple point charge model for predicting the EFG of a Cl− ion with theapproach of a point charge

0.0000 0.0002 0.0004 0.0006 0.0008 0.00100

100

200

300

400

500

1/d3 / (1/Å3)

10Å11Å12Å13Å14Å20Å

Cl- +

d

electric fieldgradient of

a point charge

quadrupole couplingconstant generated by

point charge

simple point charge



0.0000 0.0002 0.0004 0.0006 0.0008 0.00100

100

200

300

400

500

1/d3 / (1/Å3)

10Å11Å12Å13Å14Å20Å

Cl- +

d


a point charge


point charge

Gaussian input file

Except, point charge model incorrectly predicts

Gaussian gives a value ofA factor of ~140 times larger!

Why?simple point charge

full electro

nic structure + point c

harge



0.0000 0.0002 0.0004 0.0006 0.0008 0.00100

100

200

300

400

500

1/d3 / (1/Å3)

10Å11Å12Å13Å14Å20Å

Cl- +

d


a point charge


point charge

Gaussian input file

Except, point charge model incorrectly predicts

Gaussian gives a value ofA factor of ~140 times larger!

Why? - “Sternheimer anti-shielding effect”an amplification of the efg caused by induced

polarization of core electrons by the external charge

simple point charge

full electro

nic structure + point c

harge


EFG in HCl : Gaussian Calculation

z

xyH

Cl

Z-Matrix

For Deuterium

For Chlorine-35

- 1st atom defines origin- 2nd atom defines z axis


Effect of bond length on EFG in HCl Gaussian Calculation

1.20 1.24 1.28 1.32 1.36 1.4050

60

70

80

1.20 1.24 1.28 1.32 1.36 1.40-350

-300

-250

-200

-150

-100

H Cl

note: NOT proportional to 1/d3


EFG in H2O : Gaussian Calculation

z

x

yO

H

H

Z-Matrix

Need to find principal axis system for each efg tensor


Diagonalizing a 2x2 matrix


EFG in H2O : Gaussian CalculationLets focus on Oxygen

z

xyO

H

H

Z-Matrix


EFG in H2O : Gaussian Calculation

yy

xx

zz OH

H


NMR Transition Frequencies


The (Chemical) Shift Frequency Contribution

60

40

20

0

0 45 90 135 180-20

frequency / µHz/Hz-20-40-60 0 20 40 60 80 100

θ,ϕ

Single Crystal Calcium Carbonate Polycrystalline Calcium Carbonate

Larmor Frequency

IsotropicShielding

ShieldingAnisotropy

Frequency dependence on the orientation of the shielding tensor PAS relative to B0

Spatial symmetry function


Associated Legendre Polynomials and their roots.Highlighted are the polynomials associated with the sectoral harmonics.

Pm𝓁 (cos 𝜃) Polynomial Roots

P00(cos 𝜃) 1

P01(cos 𝜃) cos 𝜃 90◦

P11(cos 𝜃) − sin 𝜃 0◦ 180◦

P02(cos 𝜃) 1

2(3 cos2 𝜃 − 1) 54.73561◦ 125.2644◦

P12(cos 𝜃) −3 cos 𝜃 sin 𝜃 0◦ 90◦ 180◦

P22(cos 𝜃) 3 sin2 𝜃 0◦ 180◦

P03(cos 𝜃) 1

2(5 cos2 𝜃 − 3) cos 𝜃 39.23152◦ 90◦ 140.7685◦

P13(cos 𝜃) − 3

2(5 cos2 𝜃 − 1) sin 𝜃 0◦ 63.43495◦ 116.56505◦ 180◦

P23(cos 𝜃) 15 cos 𝜃 sin2 𝜃 0◦ 90◦ 180◦

P33(cos 𝜃) −15 sin3 𝜃 0◦ 180◦

P04(cos 𝜃) 1

8(35 cos4 𝜃 − 30 cos2 𝜃 + 3) 30.55559◦ 70.124281◦ 109.87572◦ 149.44441◦

P14(cos 𝜃) − 5

2(7 cos2 𝜃 − 3) cos 𝜃 sin 𝜃 0◦ 49.10660◦ 90◦ 130.89340◦ 180◦

P24(cos 𝜃) 15

2(7 cos2 𝜃 − 1) sin2 𝜃 0◦ 67.79235◦ 112.20765◦ 180◦

P34(cos 𝜃) −105 cos 𝜃 sin3 𝜃 0◦ 90◦ 180◦

P44(cos 𝜃) 105 sin4 𝜃 0◦ 180◦


Variable- and Magic-Angle Spinning

0 010

5

10

15

2030405060708090

100110

1 2 3 4 5 6 7 8 9 10Rotor Outer Diameter / mm

Max

. Rot

or S

peed

/ kH

z

0 1 2 3 4 5 6 7 8 9 10Rotor Outer Diameter / mm

Transition symmetry function

is the angle between the rotor axis and B0, and and give the orientation of the tensor relative to the rotor frame


Legendre Polynomials

0 10 20 4030 6050 90 100 110 120 130 140 150 160 170 1808070

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

30.56˚ 54.74˚ 70.12˚


Variable-Angle Spinning of Shift Anisotropy

0°

90°

45°

15°

60°

30°

75°

54.74°

frequency/kHz200-20

frequency/kHz200-20

rotor angle


Magic-Angle Spinning of Shift Anisotropy

2.5 kHz

5 kHz

7.5 kHz

static

10 kHz

12.5 kHz

15 kHz

17.5 kHz

20 kHz

frequency/kHz frequency/kHz200-20 200-20

spinning speed


Which way is the Quantization Axis?


Quadrupolar Frequency ContributionThe battle between the EFG and B0

Increasing external magnetic field strength

Series expansion of the NMR transition frequency about the high magnetic field limit

Zeroth-OrderContribution

First-OrderContribution

Second-OrderContribution


First-Order Quadrupolar Frequency Contribution

QuadrupolarSplitting

Frequency

where

transition symmetry function

spatial symmetry function

Polycrystalline SampleSpin I=1 case, e.g., 2D


First-Order Quadrupolar Anisotropy: 2H NMR in Oriented Samples

Membrane Bilayersoriented on glass slides

CH3

D

D

θ

CH3

D

D

All Trans

CH3

D

D

g+

θ

CH3

D

D

θ

tiltCH3

D

D

g+, t+, g- kink

θ

Membrane Surface

B0

40 30 20 10 0 -10 -20 -30 -40Frequency / kHz

90°

78°

67°

54.7°

48°

27°

0°

θ

M. F. Brown and coworkers, J. Chem. Phys., 110:8802,1999, and Colloids and Surfaces A: Physicochem. Eng. Aspects}, 158:281-298, 1999.


Measuring the ensemble average distribution of the bond order SCD

Frequency / kHz segment position30 20 10 -10 -20 -300 2

0.0

0.1

0.2

0.3

0.4

0.5

4 6 10 12 148

DMPC-d54 cholesterol (l/l)

DMPC-d54

DMPC-d54 cholesterol (l/l)DMPC-d54

M. F. Brown and coworkers, J. Chem. Phys., 110:8802,1999, and Colloids and Surfaces A: Physicochem. Eng. Aspects}, 158:281-298, 1999.


1st-order quadrupolar frequency is invariant under 𝜋 pulse

General effect of π pulse on a transition

Effect of π pulse on transition symmetry functions


Two pulse pathways in Deuterium

01

-1

01

-1

rf

01

-1

01

-1

rf

Hahn Echo Sequence Solid Echo Sequence


Two pulse pathways in Deuterium

01

-1

01

-1

rf

01

-1

01

-1

rf

No Echo Sequence Hahn-Solid Echo Sequence


Simultaneous Hahn Solid Echo Sequence on Deuterium

01

-1

01

-1

rf

Both 𝕕I and 𝕡I refocus into echo at same time.P. J. Grandinetti (L’Ohio State Univ.) Solid-State NMR of Quadrupolar Nuclei Jan. 10, 2018 39 / 78

Static 2H NMR: p-d correlation on CuCl2⋅2D2O

Shifting d echo sequence Walder et. al., J. Chem. Phys., 142, 014201 (2015)

01

-1

01

-1 00

100 200 300 400

100

200

300

400

/ µs

/ µs

Experimental 2D raw time domain spectrum

p removed d removed

First-Order Shift Contribution

First-Order Quadrupole Coupling


Separating and correlating shift and first-order quadrupolar anisotropiclineshapes

Paramagnetic Shift Anisotropy / ppm

Qua

drup

olar

Ani

sotro

py /

kHz

0

40

80

120

-40

-80

-120

0

40

80

120

-40

-80

-120

0

40

80

120

-40

-80

-1200100200300 -100 -200-300 0100200300 -100 -200-300 0100200300 -100 -200-300 0100200300 -100 -200-300


Static 2H NMR: p-d correlation on CuCl2⋅2D2O

01

-1

01

-1

1

10

0

1

112

21 1

1

Qua

drup

olar

Ani

sotro

py /

kHz

Qua

drup

olar

Ani

sotro

py /

kHz

Shift / ppm from D2O0200 -200

0

40

80

120

-40

-80

-120400

Shift / ppm from D2O0200 -200

0

40

80

120

-40

-80

-120400

“shifting d” transition pathwayCuCl2 • 2 D2O

Experiment

Best Fit

Walder et. al., J. Chem. Phys., 142, 014201 (2015)


Spin I > 3∕2 : Solomon Echoes (multiple d echoes at different times)

rf

10

-1

24

0-2-4

24

0-2-4

24

0-2-4

Assignment


The Centra Transition


The Central Transition of Half-Integer Quadrupolar Nuclei

Whats so special about it?

m = -1/2 -3/2

m = 1/2 -1/2

m = 3/2 1/2

ZeemanInteraction

QuadrupoleInteraction

1st order quadrupolarfrequencycontributionvanishes.

transition symmetry functions

True for any symmetric (m → −m) transition


NMR spectrum of I=3/2 nucleus in polycrystalline sample

Frequency / MHz0 -0.5 -1.0 -1.50.51.01.5

Intensity X 46

Frequency / kHz010 -1020 -20

2

Frequency / MHz0 -0.5 -1.0 -1.5 -2.00.51.01.52.0

Frequency / kHz010 -1020 -20

static sample magic-angle spinning sample

Much narrower linewidthbut still has anisotropic broadening under MAS.

Why?

centraltransition central

transition


Central Transition Nutation Behavior

-1.00

-0.50

0.00

0.50

1.00

0 5 10 15 20I=3/2

Cq = 1 kHz

Cen

tral T

rans

ition

Inte

nsity

Pulse Duration (microseconds)

ν1 = 50 kHz



-1.00

-0.50

0.00

0.50

1.00

0 5 10 15 20I=3/2

Cq = 1 kHz 1000 kHz

Cen

tral T

rans

ition

Inte

nsity


ν1 = 50 kHz

In the limit that the effective central transition nutation frequency becomes ...



-1.00

-0.50

0.00

0.50

1.00

0 5 10 15 20I=3/2

Cq = 1 kHz 25 kHz 50 kHz

100 kHz 250 kHz

1000 kHz

Cen

tral T

rans

ition

Inte

nsity


ν1 = 50 kHz

In the limit that the effective central transition nutation frequency becomes ...

A one-pulse (two-dimensional) nutation experiment should be one of the first experiments you do on any quadrupolar nucleus to determine nutation behavior

t1 t2 Do a proper 2D experiment,not paropt.


Second-Order Quadrupolar Frequency Contribution

2nd-order spatial symmetry functions

...adds to the isotropic chemical shift. Resonance positions are not field independent. In units of frequency, the 2nd-order isotropic shift decreases with the inverse of the B0.

...in the liquid state has a different nature than the isotropic chemical shift. When the inverse correlation time for reorientational motion exceeds the Larmor frequency the 2nd-order isotropic shift averages to zero.

2nd-order isotropic shift...


Second-Order Quadrupolar Frequency Contribution

Anisotropy is described by spatial symmetry functions

Remember 4th-rank Legendre polynomials?


Legendre Polynomials

0 10 20 4030 6050 90 100 110 120 130 140 150 160 170 1808070

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

30.56˚ 54.74˚ 70.12˚


There is no single spinning axis angle that can eliminate both 2nd- and4th-rank anisotropies.

η = 0.0 0.3 0.5 0.7 1.0

00.00°

90.00°

63.43°

30.56°

70.12°

37.38°

79.19°

54.74°

rotorangle

What can we do?


Buy a bigger magnet

14 T

19.6 T

25 T

40 T

100 0 -50-2550 2575Frequency / µHz/Hz

27Al central transition MAS of aluminoborate 9 Al2O3 + 2 B2O3

2nd-order contributionsdecreases with increasing

magnetic field strength


Try to buy (or build) a Double Rotation probe

Under double rotation at speeds faster than the anisotropic part of the 2nd-order frequency averages to

where now gives the orientation of the efg tensor relative to the inner rotor axis. Under DOR the central transition averages to


23Na central transition spectra of polycrystalline Na4P2O7

** *

**

*

**

*

νL = 158.7 MHz

νR = 1420 Hz

νL = 211.6 MHz

νR = 1250 Hz

νL = 105.8 MHz

νR = 850 Hz

**

* **

**17.6 T

14.1 T

9.4 T

14.1 T

9.4 T

1020 0 -10 -20 -30 -40 -50 -60 -70 -80Frequency / µHz/Hz

102030 0 -10 -20 -30 -40 -50 -60 -70Frequency / µHz/Hz

18.8 T

1

1

1,2

2

2

3

3

3

4

4

4

Magic-Angle Spinning Double Rotation


Try to buy (or build) a Dynamic-Angle Spinning probe

The DAS solution is hidden in the variable-angle spinning spectra below. Can yousee it?

η = 0.0 0.3 0.5 0.7 1.0

00.00°

90.00°

63.43°

30.56°

70.12°

37.38°

79.19°

54.74°

rotorangle


DAS uses simultaneous D0 and G0 echoes to refocus residualanisotropy

isotro

pic

dimensio

n

54.74°

79.19°

37.38°

Need probe that can flip rotor angle during experiment.

Chmelka et al., Nature, 339, 42 (1989).

Llor and Virlet, Chem. Phys. Lett., 152, 248 (1988).


17O DAS of coesite (crystalline polymorph of silica, SiO2)

0.0 –50.050.0

Frequency / µHz/Hz (from H217O)0.0 –50.050.0

Magic-Angle Spinning

Dynamic-Angle Spinning


Dynamic-Angle Spinning is a 2D NMR experiment correlating isotropicto anisotropic frequencies

O4

O3

O5O3

δiso = 29 ppmCq = 6.05 MHzηq = 0.0O1: 180.0°,1.595Å

δiso = 41 ppmCq = 5.43 MHzηq = 0.166O2: 142.56°, 1.612Å

δiso = 53 ppmCq =5.52 MHzηq = 0.169O4: 149.5°,1.608Å

δiso = 57 ppmCq = 5.45 MHzηq = 0.168O3: 144.5°, 1.614Å

δiso = 58 ppmCq = 5.16 MHzηq = 0.292O5: 137.2°,1.620Å

MAS dimension (ppm)

0 -20 -40 -60 -80204060

0

-10

-20

-30

10

20

30

0 -40 -8040MAS dimension (ppm)

isot

ropi

c di

men

sion

(ppm

)

O1

O2

O4

O3

O5

17O 2D DAS of coesite (crystalline polymorph of silica, SiO2)


You dont have a bigger magnet, a DOR, nor a DAS probe.MAS alone eliminates 𝔻 anisotropy but leaves 𝔾0 anisotropy

If we can’t remove the last term by eliminating G0, what about the transition symmetry functions?

a little intimidating, but depend only on and

where


Make tables of transition symmetry function values, stare, and think!

1

3

3

1

1

3

3

1

1

3

3

1

1

3

3

1

3

9

9

3

27

27

21

21

8

6

6

8

72

114

114

72

15

27

27

15

135

303

303

135

24

54

54

24

216

546

546

216

Transition

Values in black filled circles are negative

SymmetricTransitions

Centraltransitionwith pI=-1



1

3

3

1

3

9

9

3

27

27

21

21

Transition




Just think about the spin I=3/2 case



1

3

3

1

3

9

9

3

27

27

21

21

Transition




Just think about the spin I=3/2 caseLike DAS, design a two-dimensional experiment that refocuses c4 into an echo modulated only

by isotropic frequencies.



1

3

3

1

3

9

9

3

27

27

21

21

Transition




Just think about the spin I=3/2 caseLike DAS, design a two-dimensional experiment that refocuses c4 into an echo modulated only

by isotropic frequencies.

pulse pulse


MQ-MAS uses a c4 echo to refocus residual anisotropy

Frydman and Harwood, J. Am. Chem. Soc., 117, 5367 (1995)

Medek, Harwood, and Frydman, J. Am. Chem. Soc. 117, 12779 (1995)

Pulse Pulse

-20 -30 -40 -50 -60 -70Frequency / µHz/Hz (from 1M RbNO3)

-20 -30 -40 -50 -60 -70Frequency / µHz/Hz (from 1M RbNO3)

MAS

MQ-MAS


In MQ-MAS the isotropic frequency is a weighted average of triplequantum and central transition isotropic frequencies.

I=3/2 case:

I=5/2 case:

difference between isotropic shielding and chem. shift reference in central transition spectrum


Shear Transformation in DAS and MQ-MAS

Echo appears in t2 at k t1.

“Symmetry Pathways in Solid-State NMR”, Prog. NMR Spect. 59, 121-196 (2011)

shear shearω2

ω2

isot

ropi

c di

men

sion


Field Dependance of Isotropic Shift

7.0 T

9.4 T

Frequency (ppm from 1M 87RbNO3)-10 -30 -50 -70 -90

11.7 T

4.2 T

Isotropic frequency of quadrupolar nucleus is sum of isotropic (1) chemical shift and (2) 2nd order quadrupolar shift.

0.01 0.02 0.03 0.04 0.05 0.06

-60

-50

-40

-30

η = 0.12 siteη = 0.48 siteη = 1.00 site

1 / B02 ( Tesla-2 )

δ obs

( pp

m )

87Rb DAS Spectra of RbNO3

3 Rb sites

CB

Azyx

Warning: Avoid labeling spectrum axis of quadrupolar nuclei in solids as"Chemical Shift". Only true in limit that 𝜈q∕𝜈0 goes to zero.


Comparison of high-resolution methods for quadrupolar nuclei

Advantages DisadvantagesDOR • Quantitative

• High sensitivity (despite low filling factor)• Low rf power• One dimensional experiment - Quick experiment (In principle)

• Quantitative• High sensitivity, even with nuclei having large quad. couplings• Low rf power• works well for dilute quadrupolar nuclei

• Easiest to implement (no special probe)• Works well for abundant nuclei • Works well for nuclei with short longitudinal relaxation

• Special probe required• Stable spinning requires finesse• Slow spinning speeds - (large # of sidebands)• Large coil ... low rf power - poor decoupling.

• Special probe required• Fails in presence of strong homonuclear dipolar couplings• long hop times (30 ms) limits use to samples with long longitudinal relaxation (rare problem).

DAS

MQ-MAS • Not always quantitative• requires high rf power for excitation and mixing• Poor sensitivity for large Cq• Complex spinning sideband behavior


Enhancing Sensitivity


Population Transfer from Satellites to Central Transition

If you only plan to excite and detection the central transition, why not stealpolarization from the satellites?

mI

3/2

1/2

-1/2

-3/2

Enhance Central Transition by Selective Saturation of Satellite TransitionsIdea first described by Pound in 1950Nuclear electric quadrupole interations in crystals, Phys, Rev., 79, 685-702 (1950)

If all satellites are saturated the central transition is enhanced by a factor of (I+1/2)-3/2, -1/2 -1/2, 1/2 1/2, 3/2

-3/2, -1/2

-1/2, 1/2

1/2, 3/2

Significant enhancement and easy to implement


Population Transfer from Satellites to Central TransitionIf you only plan to excite and detection the central transition, why not stealpolarization from the satellites?

mI

3/2

1/2

-1/2

-3/2

Enhance Central Transition by Selective Saturation of Satellite Transitions

Enhance Central Transition by Selective Inversion of Satellite Transitions

Idea first described by Pound in 1950Nuclear electric quadrupole interations in crystals, Phys, Rev., 79, 685-702 (1950)

mI

3/2

1/2

-1/2

-3/2

Described by Vega and Naor in 1980.Triple quantum NMR on spin systems with I=3/2 in Solids, J. Chem. Phys., 75, 75-86 (1981)

If all satellites are saturated the central transition is enhanced by a factor of (I+1/2)

If all satellites are inverted (outermost to innermost)the central transition is enhanced by a factor of 2I

-3/2, -1/2 -1/2, 1/2 1/2, 3/2

-3/2, -1/2

-1/2, 1/2

1/2, 3/2

-3/2, -1/2 -1/2, 1/2 1/2, 3/2

-3/2, -1/2

-1/2, 1/2

1/2, 3/2

Significant enhancement and easy to implement

Greatest enhancement but difficult to implement


Rotor Assisted Population Transfer (RAPT) from Satellites to CentralTransitionLet the rotor bring the satellites to you

mI3/21/2-1/2-3/2

τ(π/2)CT

01

-1p

54.74°B0

τ1x x_Recycle

Delay

n

t

RAPTSelective Saturation of Satellite Transitions

Spectrum Frequency

νoff (RAPT Offset Frequency)

0 -Cq/2Cq/2

0 -Cq/2Cq/2

CT

STST

93Nb (I=9/2)Central Transition

in NaNbO3

0 -40 -80 -1204080120Frequency (ppm)Frequency (ppm)Frequency (ppm)

0 -20 -40 -60204060

59Co(I=7/2)Central Transitionin Na3[Co(NO2)6]

3.02.687Rb (I=3/2)

Central Transitionin RbClO4 1.96

0 -25 -50 -75255075

Yao et al., Chem. Phys. Lett., 327, 85-90 (2000), Prasad et al., J. Am. Chem. Soc., 124(18), 4964-4965 (2002)


Multiple Rotor Assisted Population Transfers

Frequency (ppm)100 80 60 40

1.02.05

3.02No RAPT

Single RAPT

Multi-RAPT

No RAPT

Single RAPT

Multi-RAPT

27Al (I=5/2) in Albite

Frequency (ppm)0 -200 -400 -600200400600

1.0

5.76

3.05

93Nb (I=9/2) in NaNbO3

τ(π/2)CT

01

-1p

τ1x xx_ _

RecycleDelay

n m

54.74°B0

t

Kwak, et al, Solid-State NMR, 24, 71-77 (2003)


RAPT Enhanced Central Transition

Use Low Power Central Transition Pulse for Highest Enhancement

pw = 1.93 μs

1.49

pw = 3.53 μs

1.75

pw = 9.20 μs

1.89

pw = 16.1 μs

1.96

Frequency (ppm)0 -25 -50 -75255075

Frequency (ppm)0 -25 -50 -75255075

Frequency (ppm)0 -25 -50 -75255075

Frequency (ppm)0 -25 -50 -75255075

ν1 = 65 kHz ν1 = 7.8 kHzν1 = 35 kHz ν1 = 14 kHz

87Rb in RbClO4RAPT-Saturated SatellitesEquilibrium

Trease et al., J. Magn. Reson., 200, 334-339 (2009).Optimum Excitation of Enhanced Central Transition Populations


Acknowledgments

"Quadrupole" CollaboratorsAlex Pines, Jay Baltisberger, Antoine Llor, Margaret Eastman, Young Lee, Boqin Sun, Yue Wu, Jonathan Stebbins, Ian Farnan, Ulrike Werner-Zwanziger, Sheryl Gann, Josef Zwanziger, Joe Sachleben, Maurice Goldman, Zbigniew Olejniczak, Andrew Kolbert, Lucio Frydman, Gerry Chingas, Raz Jelinek, Brad Chmelka, Jacek Klinowski,

Dominique Massiot, Joseph Virlet, Thomas Vosegaard, Zhehong Gan, Lyndon Emsley, Dimitri Sakellariou, Michael Deschamps, Franck Fayon, Stefan Steuernagel, Guido Pintacuda

Past Group MembersProf. Jay Baltisberger

Dr. Pierre FlorianDr. Alex Klymachyov

Prof. Ted ClarkDr. Subramanian Prasad

Dr. Mike DavisDr. Karl Vermillion

Dr. Ping ZhangDr. Hyung-Tae Kwak

Dr. Jason AshDr. Nicole Trease

Dr. Krishna DeyDr. Brennan Walder

Zhi YaoTravis Sefzik

Antonio PaulicRamesh SharmaDerek KasemanKim ShookmanJacob Sillaman

Eric KeelerKevin Sanders

Pyae Phyo

RMN

Multidimensionalsignal processing on MacOS(ask for a free promo code)

Current Group MembersDr. Daniel Jardón-Álvarez

Deepansh SrivastavaJose Lorie Lopez

Brendan WilsonMark BoveeSam Atkins


solid-state nmr of quadrupolar nuclei · solid-state nmr of quadrupolar nuclei (the rest of the...

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