1. (random-orientation)
Solid-State NMR
Impact of Structural Order on NMR Spectrum
Factors that average to zero in solution due to random motion are now factors in solid state NMR
T1 is long  lack of motion and modulation of dipole-dipole interaction
T2 is short  mutual spin flips occurring between pairs of spins
Each nucleus is “fixed” in the crystal lattice
Each nucleus produces a rotating magnetic field as it precesses in the applied magnetic field  lifetime of spin state is reduced
Each spin has a static field component that influences Larmor frequency of neighbors
Spin directions vary randomly
Range of frequencies that add to line-width
Chemical shift anisotropy
Chemical shift varies with orientation relative to B0
Contributes to line broadening
Solid-state
(ordered structure) Bo
Solution-state
(random-orientation)

2. Solid-State NMR Broad Structureless Resonances
Requires Different Approaches Compared to Solution State NMR
Contains Unique Information Relative to Solution State NMR
Peak width is caused by dipole-dipole interaction which is distance related
Solid state NMR spectrum can be used to obtain internuclear distances
Peak width can monitor motion within the crystal lattice
Slowly increase temperature
Line-width transactions indicates introduction of motion
13C NMR of glycine
solution-state
solid-state
Angew. Chem. Int. Ed. 2002, 41,

3. Solid-State NMR Powder vs. Crystal
Crystal – regular uniform and repeat lattice structure
Powder – consists of very many crystals all with different orientations

4. Solid-State NMR Powder Pattern z r q B0 y x Dipolar coupling
Interaction of nuclear magnetic moments of two different nuclear spins (I & S)
The local magnetic field at spin S will be affected by spin I
Changes resonance frequency of spin S
The degree by which spin I affects the magnetic field at spin S is determined by the dipolar coupling constant (d):
where q is the angle between Bo and the internuclear distance (r)
The dipolar constant is dependant on the distance between the nuclear spins and their gyromagnetic ratios
Through space interaction  structural information
In solution, random motion averages dipolar coupling to zero
In solids, orientations are static  defined by crystal lattice z y x 1H
13C q B0 r
Angew. Chem. Int. Ed. 2002, 41,

5. Solid-State NMR Powder Pattern Dipolar coupling
Contains structural information ( r, q)
Dipolar coupling provides distance information
Orientation relative to B0
Angew. Chem. Int. Ed. 2002, 41,

6. Solid-State NMR Powder Pattern Chemical Shift Anisotropy
Chemical shift is dependent on orientation of nuclei in the solid
Distribution of chemical shifts
Averaged to zero for isotropic tumbling
Leads to extensive line-width broadening in solid-state NMR
Progress in Nuclear Magnetic Resonance Spectroscopy 6 46 (2005) 1–21

7. Solid-State NMR Temperature Dependence
Crystal Lattice Mobility Changes with Temperature
Changes in bond rotations
Large changes in line-shape depending on mobility in lattice
Rotation about C-N bond
Rotation of NMe3
Whole molecule rotates and diffuse within crystal

8. Solid-State NMR Magic Angle Spinning (MAS) z r q B0 y x
Nucleus with magnetic moment (m) will create a field at a second nucleus at a distance r away
Magnetic field will have a z component (Bz) in direction of Bo direction
Influences the frequency of the second nucleus
Couples the two spins
Magnitude of Bz will depend on the angle of the magnetic moment relative to B0 z y x 1H
13C q B0 r

9. Solid-State NMR Magic Angle Spinning (MAS)
Zero z component (Bz) if the angle (q) relative to B0 is 54.44o
All dipolar interactions disappear at this angle
All chemical shift anisotropy disappear at this angle
Quadrupole broadening is also reduced
Simulate a uniform distribution of magnetic moments in a powder by spinning the sample very fast at 54.44o
Bz = 0

10. Solid-State NMR Magic Angle Spinning (MAS)
Spin Samples at 54.44o to reduce line-width
Spinning speed must be greater than static line-width to be studied (powder pattern width)
Normal speed limit is 35 kHz
rotor at MAS
Sample holder
rotor
Sample holder at MAS
MAS probe

11. Solid-State NMR Magic Angle Spinning (MAS)
Impact of Spinning Speeds at MAS
13C NMR of glycine powder
Similar to Solution Spectrum
Number of lines are reduced with increase in spinning speed as it approaches static line-width
Increasing Spinning Speed
Lines are separated by spinning speed
Powder Pattern
Angew. Chem. Int. Ed. 2002, 41,

12. Solid-State NMR
Spin ½ Nuclei with Low Magnetogyric ratios (13C, 15N, 29Si, 31P, 113Cd)
Combine MAS with high power 1H decoupling
Double resonance technique
High power is required because of very large 1H line-widths
Long T1 requires slow pulse rates to avoid saturation of signal
Low sensitivity of nuclei requires long acquisition times
MAS reduces linewidth from 5000 Hz to 200 Hz
MAS & high power decoupling reduces linewidth from 5000 Hz to 2 Hz
Increase in sensitivity (NOE, spin-splitting)
High power decoupling reduces linewidth from 5000 Hz to 450 Hz
Similar to liquid state sample

13. Solid-State NMR Cross-polarization combined with MAS (CP-MAS) 2 ms
Exchange polarization from 1H to 13C
Similar in concept to INEPT experiment
1H 90o pulse generates xy magnetization (B1H)
Spin-lock pulse keeps magnetization in xy plane
precessing at:
gHB1H/2p Hz
13C pulse generates xy magnetization that precesses at:
gCB1C/2p Hz
Polarization transfer occurs if:
gHB1H/2p Hz = gCB1C/2p Hz
Hartmann Hahn matching condition
2 ms
50 ms
Polarization transfer
1Hb
13Cb
gHB1H/2p
gCB1C/2p
1Ha
13Ca
DE = g h Bo / 2p

14. Solid-State NMR Cross-polarization combined with MAS (CP-MAS)
Simultaneously pulse 1H to 13C
Use RF energy to equilibrate energy states
The increase in the 13C signal depends on the strength of the dipolar interaction and the duration of the mixing or contact time
Maximum enhancement is gH/gC
gHB1H/2p Hz = gCB1C/2p Hz

15. Solid-State NMR Cross-polarization combined with MAS (CP-MAS)
Example of CP-MAS 13C spectrum
Cross-polarization increases the 13C population difference by the factor gH/gC
Increases signal sensitivity

16. Solid-State NMR Spin ½ Nuclei with High Magnetogyric ratios (1H, 19F)
Homonuclear interactions are very strong
Difficult to remove by MAS
Highest field strength and spinning rates can reduce a 10 kHz line-width to 1500 Hz
Static line-widths are very large and chemical shifts are small
Obtaining resolution is challenging
Simulate MAS spinning by a series of RF pulses (MREV-8)
Shift magnetization quickly between the three orhogonal axes
Hop around magic angle and reduce dipole-dipole interaction
Does not affect CSA or heteronuclear interactions
MAS can be used to remove CSA
CRAMPS – combines MAS with MREV-8

17. Solid-State NMR Spin ½ Nuclei with High Magnetogyric ratios (1H, 19F)
Example of CRAMPS
Resolution on the order of 180 Hz is possible
1H NMR of aspartic acid powder
CRAMPS
MAS with increasing spinning rates
Static Spectrum with Broad Line-widths

18. Solid-State NMR Two-Dimensional NMR Spectrum
Can run similar solution state 2D NMR experiments
Have to account for larger band-width, higher energy longer T1 and shorter T2
Example of 2D 1H EXSY experiment using CP-MAS 13C spectrum
[(Me3Sn)4Ru(CN)6]
Six unique methyl resonances, two distinct SnMe3 groups, exchange identifies which methyls belong to which group
Exchange between Methyls

19. Solid-State NMR Two-Dimensional NMR Spectrum 2D HETCOR
Correlates closely spaced 1H and 13C resonances
Similar to HSQC and HMQC experiments

20. Solid-State NMR Two-Dimensional NMR Spectrum 2D REDOR
Dipolar coupling contains distance information
MAS yields sharps lines, but eliminates dipolar coupling
Reintroduces dipolar coupling information while maintaining sharp lines
Can not turn spinning on and off
Can synchronize spinning with RF to reintroduce dipolar coupling
Magnitude of dipolar coupling
The integral of the dipolar coupling averages to zero for each rotation
Apply 180o pulses at regular intervals that disrupts the trajectory of the dipolar coupling so the integral is no longer zero during a complete rotation.

21. Solid-State NMR Two-Dimensional NMR Spectrum 2D REDOR
A reference spectra is collected without the p pulses (S0)
A series of spectra are collected with increasing mixing time (tm)
Measure magnetization decay (S) as a function of tm
Dipolar coupling is measured by fitting the S/So vs. tm plot
A distance can be measured from:
d = 195 Hz, 13C-15N = 2.47 Ǻ

22. Solid-State NMR Two-Dimensional NMR Spectrum 2D REDOR
Can also be used to generate chemical shift correlations
Similar to HSQC, HMQC experiments
HETCOR: MAS effectively removes 13C-15N couplings
13C-15N correlations for a peptide
15N
13C