Solid-State NMR

1
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)
Solution-state (random-orientation)
Bo
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, 3096-3129
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
• 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

Angew. Chem. Int. Ed. 2002, 41, 3096-3129
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, 3096-3129
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) 121
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)
• 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

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

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, 3096-3129
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)
• 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

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

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 ?
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