Essential Techniques in Solid-state NMR - Jeremy Titman, School of Chemistry, University of Nottingham
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Essential Techniques in Solid-state NMR
Jeremy Titman,
School of Chemistry, University of Nottingham
Solid-state NMR
1945
proton NMR of
paraffin wax
Felix Bloch Ed Purcell
nitrogen-15 NMR of
VPU ion channel from HIV
2005
structure from
solid-state NMR
Solid-state NMR
1945
proton NMR of
paraffin wax
Felix Bloch Ed Purcell
nitrogen-15 NMR of
VPU ion channel from HIV
“We were physicists. We knew all the answers; we just
didn’t know what the questions were.”
2005
structure from
solid-state NMR
Problems with NMR of solids
Poor Resolution
★ Anisotropic nuclear spin interactions result in powder patterns.
★ Powder patterns from inequivalent sites overlap.
★ Multiple anisotropic interactions result in broad featureless lineshapes.
Low Sensitivity
★ NMR is inherently insensitive.
★ Many useful nuclei, such as carbon-13, nitrogen-15 etc, have low natural abundance.
★ Inefficient spin-lattice relaxation results in long experiment times.
carbon-13 NMR
glycine
tyrosine
300 200 100 0 -100
ppm
Improving resolution
All internal Hamiltonians can be written as a product of two parts
★ A spatial part which contains the variation of the interaction with orientation with respect to the B0-
field.
★ A spin part which (in the secular approximation) contains angular momentum operators which are
parallel to the B0-field.
For example, the anisotropic part of the chemical shift Hamiltonian
⎧ 3 ⎫
∑( )
3
1⎪ ⎪
∑
H = ⎨ σj +
3⎪
3cos2 θ j −1 σ j ⎬ γIzB0
⎪⎭
⎩ j=1 j=1
contains a spatial term proportional to 3 cos2θ – 1 and a spin term proportional to Iz.Motional averaging
Molecular motions can result in a averaged Hamiltonian which can be evaluated from the average over time for
one spin or over orientation for many spins.
τ
Hint =
1
τ ∫ ( ( ))
Hint θ t dt
0
π
Hint = ∫ Hint (θ) sinθdθ
0
The techniques used to improve resolution in solid-state NMR subject the nuclear spins to some external
motion in order to average interactions.
low temperature
carbon-13 NMR of fullerene
room temperature
C60 tumbles isotropically
200 100 0
ppmTypes of external motion
Two types of motions can be used:
★ Motions in sample space. These require a mechanical rotation of the sample itself. This changes the
spatial part of the Hamiltonian. An example is magic angle spinning.
★ Motions in spin space. These require rotations of the magnetization by radiofrequency pulses. This
changes the spin part of the Hamiltonian. An example is decoupling.
Note that in either case motional averaging is only effective when the motional frequency is greater than the
broadening observed in the spectrum.Magic angle spinning
Magic angle spinning simulates the rapid isotropic tumbling motion of a molecule in solution by rotation of the
sample at a frequency νR (up to 70 kHz) around an axis inclined at βR to the B0-field.
★ βR is a constant which can be varied mechanically.
★ The axis zPAS moves on the surface of a cone with a half angle β at the apex.
★ In a powder all values of the angles β and θ are present.
The motionally averaged Hamiltonian is
π
∫( ) ( )( )
1
H∝ 3cos2 θ −1 sinθdθ = 3cos2 βR −1 3cos2 β −1
2
0
B0
zPAS
zRF
"
!
!RScaling anisotropic interactions with MAS
π B0
∫( ) ( )( )
1
H∝ 3cos2 θ −1 sinθdθ = 3cos2 βR −1 3cos2 β −1
2
0
The term in βR acts as a constant scaling factor on the !R
powder pattern. 90
★ If βR = 0 there is no effect on the spectrum.
★ If βR = 90° the width of the powder pattern is
scaled by a factor 1/2 and reversed in sign.
★ When βR = 54.7° (known as the “magic angle”) 54.7
the term in β is zero and MAS will scale the
anisotropic part of the interaction to zero.
0Magic angle spinning
!R Fluorine-19 MAS of KAsF6
1955
1958 8 kHz 19
F-75As J coupling
with MAS
at 5.5 kHz
Raymond Andrew 30 kHz
Lithium-7 MAS of
1990 15 KHz Li3Eu3Te2O12 garnet
Eu - 7Li electron-nuclear
dipolar coupling
1996 35 kHz
with MAS
at 20 kHz
2005 70 kHz
200 kHz
E. R. Andrew, A. Bradbury and R. G. Eades, Nature, 182, 1659 (1958); E. R. Andrew, L. F. Farnell and T. D. Gledhill, Phys. Rev. Lett., 19, 6 (1967).Fast spinning limit
When νR ≫ ζ
★ the anisotropic part of the chemical shift is averaged to zero.
★ the isotropic part is retained.
⎧ 3 ⎫
∑( )
3
1⎪ ⎪
∑
H = ⎨ σj +
3⎪
3cos2 θ j −1 σ j ⎬ γIzB0
⎪⎭
⎩ j=1 j=1
carbon-13 NMR of tyrosine
with MAS
300 200 100 0 -100
ppmSlow spinning
When νR ≪ ζ the NMR precession frequency is modulated by the MAS
2
( ) ∑
ν t;Ω = ν
(m) (Ω ) exp (imν )
Rt
m=−2
As a consequence:
★ contributions from different orientations refocus after τR, resulting in “rotor echoes”.
★ rotational sidebands separated by νR appear in the spectrum.
★ sampling at the rotor echoes results in a spectrum of isotropic lines of restricted spectral width.
1.25 kHz
!R = 1.25 kHz Fourier
transform
0 5 10 15 20 300 200 100 0
ms ppm
"R = 800 µsSynchronous sampling
When νR ≪ ζ the NMR precession frequency is modulated by the MAS
2
( ) ∑
ν t;Ω = ν
(m) (Ω ) exp (imν )
Rt
m=−2
As a consequence:
★ contributions from different orientations refocus after τR, resulting in “rotor echoes”.
★ rotational sidebands separated by νR appear in the spectrum.
★ sampling at the rotor echoes results in a spectrum of isotropic lines of restricted spectral width.
1.25 kHz
!R = 1.25 kHz Fourier
transform
0 5 10 15 20 300 200 100 0
ms ppmSpinning sidebands
Measuring shift tensor parameters Simulated MAS sideband patterns
★ The envelope of the sideband intensities depends on
!/"R = 1 #=0
the anisotropy ζ and the asymmetry η.
★ This is the basis of the most common method for
measuring these parameters.
Identifying the isotropic line
★ The isotropic line corresponds to the chemical shift !/"R = 2
observed in solution.
★ Note that the isotropic line is not always the most
intense in the spectrum.
★ It can be identified as the sideband which does not
change frequency when the MAS rate changes. !/"R = 5
!/"R = 10
J. Herzfeld and A. E. Berger, J. Chem. Phys., 73, 6021 (1980); O. N. Antzutkin,Y. K. Lee, M. H. Levitt, J. Magn. Reson., 135, 144 (1998).Choosing the MAS rate
Measuring shift tensor parameters Simulated MAS sideband patterns
★ To produce a solution-like spectrum with only
!/"R = 1 #=0
isotropic lines the MAS rate must be greater
than the largest shift anisotropy.
★ To measure the shift anisotropy from the
sideband pattern with optimal precision
approximately 7 sidebands are required.
!/"R = 2
★ To measure the asymmetry more than 10
sidebands are required.
Other considerations
★ Molecular motions in the sample on a kHz
timescale will interfere with the MAS averaging !/"R = 5
and cause sidebands to broaden.
★ For abundant nuclei “rotational resonance
conditions” where Δδiso = nνR (n is a small
integer) should be avoided.
!/"R = 10
P. Hodgkinson and L. Emsley, J. Chem. Phys., 107, 4808 (1997).Choosing the MAS rate
Measuring shift tensor parameters carbon-13 NMR of bullvalene
with MAS at 5 kHz
★ To produce a solution-like spectrum with only
isotropic lines the MAS rate must be greater
isotropic shifts coalesce
than the largest shift anisotropy. 338 K
★ To measure the shift anisotropy from the
sideband pattern with optimal precision
358 K 3-fold jumps
approximately 7 sidebands are required.
★ To measure the asymmetry more than 10
temperature
sidebands are required. 318 K
Other considerations
★ Molecular motions in the sample on a kHz 295 K
sidebands coalesce
timescale will interfere with the MAS averaging interconversion of
and cause sidebands to broaden. 273 K
10!/3 tautomers
★ For abundant nuclei “rotational resonance
conditions” where Δδiso = nνR (n is a small
253 K
integer) should be avoided.
300 200 100 0 -100 ppm
J. J. Titman, Z. Luz and H. W. Spiess, J. Am. Chem. Soc., 114, 3765 (1992).Choosing the MAS rate
Measuring shift tensor parameters
★ To produce a solution-like spectrum with only
isotropic lines the MAS rate must be greater
than the largest shift anisotropy.
10 kHz
★ To measure the shift anisotropy from the
sideband pattern with optimal precision 13
C2-glycine
approximately 7 sidebands are required.
with MAS at 20 kHz
★ To measure the asymmetry more than 10
sidebands are required.
Other considerations
★ Molecular motions in the sample on a kHz with MAS at 10 kHz
timescale will interfere with the MAS averaging
and cause sidebands to broaden. 300 200 100 0 ppm
★ For abundant nuclei “rotational resonance
conditions” where Δδiso = nνR (n is a small
integer) should be avoided.
E. R. Andrew, A. Bradbury, R. G. Eades and V. T. Wynn, Phys. Lett., 4, 99 (1963).Sideband suppression with TOSS
TOSS (Total Suppression of Spinning Sidebands) uses a sequence of (five) carefully timed π pulses synchronized
with the MAS rotor.
★ The phases of the sidebands depend in a new way on orientation.
★ For an isotropic sample the sidebands from different orientations interfere destructively and cancel.
Note:
★ The TOSS centreband is not quantitative.
★ For small νR/ζ the centreband can have negative intensity.
Pulse sequence timing diagram centreband 1st sideband 2nd sideband
MAS
! ! ! ! !
90
TOSS
"R 180 0
#R 270
W. T. Dixon, J. Chem. Phys., 77, 1800 (1982); O. N. Antzutkin, Z. Song, X. Feng, and M. H. Levitt. J. Chem. Phys., 100, 130 (1994).MAS and homonuclear dipolar couplings
1
(
HD ∝ 3I1zI2z − I1.I2 = 2I1zI2z − I1+I−2 + I1−I+2
2 )
There are two parts to the homonuclear dipolar Hamiltonian:
★ an inhomogeneous part which shifts the energies of the Zeeman eigenstates
★ a homogeneous part which mixes degenerate Zeeman states and causes line broadening
The homogeneous term also causes energy conserving “flip-flop” transitions between degenerate states at a
rate which depends on the dipolar coupling.
proton NMR of glycine
E
500 ppm
inhomogeneous part
homogeneous partMAS and homonuclear dipolar couplings
The flip-flop transitions mean that the state of the spin system fluctuates and when νR/d is small this interferes
with the MAS averaging.
The spinning sidebands for a homogeneously broadened line behave very differently from those associated
with an inhomogeneous interaction.
proton NMR of glycine
!R / kHz
0
5
10
15
500 ppm
An isolated proton-carbon-13 dipolar interaction is inhomogeneous, but if the proton is part of a
homogeneous network then the overall behavior is homogeneous.Decoupling
Decoupling uses an enforced motion in spin space to average heteronuclear dipolar couplings.
HD = −
d
2( )
3cos2 θ −1 2Iz Sz
The spin part of the coupling Hamiltonian can be made to vary with time by continuous irradiation at the I-
spin (proton) Larmor frequency while the S-spin (carbon-13) signal is observed.
Magnetization Dipolar
Hamiltonian
z
Proton
magnetization Iz
y
1
H Decoupling
x !1 (Precession
frequency)
13
C B1 (Decoupling
field) z'
Rotating
Stationary
!1
y'
!1Decoupling
★ The radio-frequency radiation at the proton Larmor frequency causes the proton magnetization to
precess at a rate in the yz-plane.
★ In a rotating frame which follows the precessing magnetization the I-spin operator appears to rotate,
and the spin part of the dipolar Hamiltonian becomes
() (
HD t ∝ Iz cos 2πν1t + Iy sin2πν1t Sz )
★ The oscillating I-spin operator terms cause the dipolar Hamiltonian to average to zero.
Magnetization Dipolar
Hamiltonian
z
Proton
magnetization Iz
y
1
H Decoupling
x !1 (Precession
frequency)
13
C B1 (Decoupling
field) z'
Rotating
Stationary
!1
y'
!1Setting the decoupler power
Hardware considerations
★ To be effective the B1 field must cause the spins to precess at a rate ν1 which is large compared to the
IS dipolar coupling (about 20 kHz for 1H-13C).
★ When the I spins are homogeneous the rate must be comparable to the I spin homonuclear dipolar
coupling (about 60 kHz for 1H).
★ The amplitude of the decoupler B1 field is limited by the probe (60 kHz for 7.5 mm MAS probe; 140
kHz for 3.2 mm MAS probe). Note: an I-spin π/2 pulse of 2.5 µs corresponds to B1 = 100 kHz.
Sample considerations
★ Large B1 will cause sample heating.
★ Molecular motions in the sample on a kHz timescale will interfere with the decoupling and cause lines
to broaden.
★ At high MAS rates the averaging by MAS interferes with the averaging by decoupling and the
decoupling efficiency can fall.Improved decoupling schemes
A number of decoupling schemes have been proposed which give increased decoupling efficiency relative to
CW for the same B1 amplitude, especially at high νR.
These include TPPM (Two Pulse Phase Modulation) and XiX.
7 O
5 4
phase: 0° 180° (CH3)3C(CH3)2Si 6 NH
5'
XiX O O N 2
4' 1' O
3'
2'
O O
P
MeO
#R
MeO
5
~! pulses 4 2 =CH
4'
62 1' 3' 5'
CH= 2'
phase: " "+~10°
TPPM
150 100 50 0
ppm
1
H Decoupling CW
13
C XiX
A. E. Bennett, C. M. Reinstra, M. Auger, K. V. Lakshmi and R. G. Griffin, J. Chem. Phys., 103, 6951 (1995);
A. Detken, E. H. Hardy, M. Ernst and B. H. Meier, Chem. Phys. Lett., 356, 298 (2002).Problems with NMR of solids
Poor Resolution
★ Anisotropic nuclear spin interactions result in powder patterns.
★ Powder patterns from inequivalent sites overlap.
★ Multiple anisotropic interactions result in broad featureless lineshapes.
Low Sensitivity
★ NMR is inherently insensitive.
★ Many useful nuclei, such as carbon-13, nitrogen-15 etc, have low natural abundance.
★ Inefficient spin-lattice relaxation results in long experiment times.Improving sensitivity
Sensitivity can be improved by:
★ increasing magnetization by polarization transfer from neighboring spins of higher magnetogyric ratio.
★ increasing the repetition rate of successive scans, so that more signal averaging can take place, by
polarization transfer from neighboring spins with more efficient spin-lattice relaxation.
Alex PinesCross polarization
★ Polarize the I spins at high field (B0 = MHz).
★ Cool the I spins to a low “spin temperature” in the rotating frame (B1 = kHz).
E
population depletion
#HB1(1H)
1
H Decoupling
B1(1H)E
Hartmann-Hahn matching population depletion
#HB1(1H)
1
H Decoupling
B1(1H)Choosing CP parameters
Experimental parameters
★ The I and S B1 field are matched by observing maximum signal intensity for a suitable sample e.g
adamantane or hexamethylbenzene for carbon-13, kaolinite for silicon-29, glycine for nitrogen-15 etc.
★ Choose the contact time which gives the highest overall intensity, since different chemical sites have
different TIS and different I-spin T1ρ.
Sample considerations
★ Quarternary carbon sites require long contact times.
★ Mobile systems can have short I-spin T1ρ.
polymethylmethacrylate
signal intensity
time
constant: T1!
time
constant: TIS
contact time / ms
J. Schaefer, E. O. Stejskal and R. Buchdal, Macromolecules, 8, 291 (1975).CPMAS
The combination of cross polarization, MAS and heteronuclear decoupling is now the routine experimental
method for recording high resolution NMR spectra of spin-1/2 nuclei.Cross polarization and rapid MAS
MAS averages the heteronuclear dipolar coupling.
★ When νR is rapid compared to dIS the Hartmann-Hahn matching condition splits into a set of spinning
sidebands.
★ The central matching condition has a slower TIS than the sideband matches.
adamantane
no MAS
Carbon-13 signal intensity
central matching band
with MAS at 5 kHz
-2 -1 0 1 2
!IB1(1H) - !SB1(13C)
2"#R
0 1 2 3 4 5
Contact time /msVariable amplitude CP
This problem can be overcome by ramping the amplitude of the cross polarization B1 field.
For optimal signal:
★ the ramp size should be approximately twice νR
★ the step size should be as small as possible
with ramp CP
Carbon-13 signal intensity
1
H Decoupling
13
C Ramp
-1 0 1
!IB1(1H) - !SB1(13C)
2"#R
G. Metz, X. Wu and S. O. Smith, J. Magn. Reson. A, 110, 219 (1994).Summary Anisotropic nuclear spin interactions cause loss of resolution in NMR spectra of solids. Magic angle spinning can be used to average inhomogeneously broadened interactions, such as the chemical shift anisotropy. MAS uses a mechanical rotation in sample space to average the interaction. For homogeneous interactions, averaging is best achieved by rotations in spin space using radiofrequency pulses. For example to remove the heteronuclear dipolar interaction between carbon-13 and a proton which is itself part of a dipolar-coupled network heteronuclear decoupling is required. Solid-state NMR spectroscopy is insensitive because of long spin-lattice relaxation times. Cross polarization can be used to enhance sensitivity by transferring polarization from neighboring spins with higher magnetogyric ratio and more efficient spin-lattice relaxation.
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