Solid-State NMRImpact 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 randomlySpin directions vary randomly- Range of frequencies that add to line-widthRange of frequencies that add to line-width

Chemical shift anisotropy- Chemical shift varies with orientation relative to BChemical shift varies with orientation relative to B00

- Contributes to line broadeningContributes to line broadening

BBooSolid-state(ordered structure)

Solution-state(random-orientation)

Solid-State NMRBroad 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 distancesSolid state NMR spectrum can be used to obtain internuclear distances

Peak width can monitor motion within the crystal lattice- Slowly increase temperatureSlowly increase temperature- Line-width transactions indicates introduction of motion Line-width transactions indicates introduction of motion

13C NMR of glycine

solution-state solid-state

Angew. Chem. Int. Ed. 2002, 41, 3096-3129

H2N

O

OH

glycine

Solid-State NMRPowder vs. Crystal

• Crystal – regular uniform and repeat lattice structure

• Powder – consists of very many crystals all with different orientations

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 SChanges 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 where is the angle between is the angle between BoBo and the internuclear and the internuclear

distance (r)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

Solid-State NMR

zzIS SIdH 1cos3 2

z

y

x

11HH

1313CC

BB00

r34 IS

SIo

rd

Angew. Chem. Int. Ed. 2002, 41, 3096-3129

34 IS

SIo

rd

Solid-State NMR

Powder Pattern• Dipolar coupling

Contains structural information ( r, )

Dipolar coupling provides distance informationDipolar coupling provides distance information

zzIS SIdH 1cos3 2

Orientation relative to BOrientation relative to B00

Angew. Chem. Int. Ed. 2002, 41, 3096-3129

Solid-State NMRPowder Pattern

• Chemical Shift Anisotropy Chemical shift is dependent on orientation of nuclei in the solid

- Distribution of chemical shiftsDistribution of chemical shifts- Averaged to zero for isotropic tumblingAveraged to zero for isotropic tumbling- Leads to extensive line-width broadening in solid-state NMR Leads to extensive line-width broadening in solid-state NMR

Progress in Nuclear Magnetic Resonance Spectroscopy 6 46 (2005) 1–21Progress in Nuclear Magnetic Resonance Spectroscopy 6 46 (2005) 1–21

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 bondRotation about C-N bond

Rotation of NMeRotation of NMe33

Whole molecule rotates Whole molecule rotates and diffuse within crystaland diffuse within crystal

Solid-State NMR

Magic Angle Spinning (MAS)• Nucleus with magnetic moment () 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 nucleusInfluences the frequency of the second nucleus- Couples the two spinsCouples the two spins

Magnitude of Bz will depend on the angle of the magnetic moment relative to B0

1cos3 23

r

KBZ

z

y

x

11HH

1313CC

BB00

r

Solid-State NMR

Magic Angle Spinning (MAS)• Zero z component (Bz) if the angle () 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

BBzz = 0 = 0

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 kHzNormal speed limit is 35 kHz

Sample holderSample holder rotorrotor

Sample holder at MASSample holder at MAS MAS probeMAS probe

rotor at MASrotor at MAS

Angew. Chem. Int. Ed. 2002, 41, 3096-3129

Solid-State NMR

Magic Angle Spinning (MAS)• Impact of Spinning Speeds at MAS

Incr

easi

ng S

pinn

ing

Spe

ed

Powder Pattern

13C NMR of glycine powder

Similar to Solution Spectrum

Lines are separated by spinning speed

Number of lines are reduced with increase in spinning speed as it approaches static line-width

H2N

O

OH

glycine

Solid-State NMR

MAS reduces linewidth MAS reduces linewidth from 5000 Hz to 200 Hzfrom 5000 Hz to 200 Hz

High power decoupling High power decoupling reduces linewidth from reduces linewidth from 5000 Hz to 450 Hz5000 Hz to 450 Hz

Increase in sensitivity Increase in sensitivity (NOE, spin-splitting)(NOE, spin-splitting)

MAS & high power MAS & high power decoupling reduces linewidth decoupling reduces linewidth from 5000 Hz to 2 Hzfrom 5000 Hz to 2 Hz

Similar to liquid state sampleSimilar to liquid state sample

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 TLong T1 1 requires slow pulse rates to avoid saturation of signalrequires slow pulse rates to avoid saturation of signal- Low sensitivity of nuclei requires long acquisition times Low sensitivity of nuclei requires long acquisition times

Solid-State NMR

Cross-polarization combined with MAS (CP-MAS)• Exchange polarization from 1H to 13C

Similar in concept to INEPT experiment

2 ms 50 ms

• 11H 90H 90oo pulse generates xy magnetization (B pulse generates xy magnetization (B1H1H))• Spin-lock pulse keeps magnetization in xy planeSpin-lock pulse keeps magnetization in xy plane precessing atprecessing at::

HHBB1H1H/2/2 Hz Hz • 1313C pulse generates xy magnetization that precesses C pulse generates xy magnetization that precesses at:at:

CCBB1C1C/2/2 Hz Hz• Polarization transfer occurs if:Polarization transfer occurs if:

HHBB1H1H// Hz Hz = CCBB1C1C/2/2 Hz Hz

Hartmann Hahn matching conditionHartmann Hahn matching condition

E = h Bo / 2

C

C

HHBB1H1H//22 CCBB1C1C//

22

Polarization transferPolarization transfer

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 H/C

HHBB1H1H// Hz Hz = CCBB1C1C/2/2 Hz Hz

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 H/C

Increases signal sensitivity

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

Solid-State NMR

Static Spectrum with Static Spectrum with Broad Line-widthsBroad Line-widths

MAS with increasing MAS with increasing spinning ratesspinning rates

CRAMPSCRAMPS

1H NMR of aspartic acid powder

Spin ½ Nuclei with High Magnetogyric ratios (1H, 19F)• Example of CRAMPS

Resolution on the order of 180 Hz is possible

NH2 O

OH

O

HO

aspartic acid

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 Exchange between Methylsbetween Methyls

Solid-State NMR

Two-Dimensional NMR Spectrum• 2D HETCOR

Correlates closely spaced 1H and 13C resonances

• Similar to HSQC and HMQC experiments

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

The integral of the dipolar The integral of the dipolar coupling averages to zero for coupling averages to zero for each rotation each rotation

Magnitude of dipolar couplingMagnitude of dipolar coupling

Apply 180Apply 180oo pulses at regular pulses at regular intervals that disrupts the intervals that disrupts the trajectory of the dipolar trajectory of the dipolar coupling so the integral is no coupling so the integral is no longer zero during a complete longer zero during a complete rotation. rotation.

Solid-State NMR

Two-Dimensional NMR Spectrum• 2D REDOR

A reference spectra is collected without the pulses (S0) A series of spectra are collected with increasing mixing time (m) Measure magnetization decay (S) as a function of m

Dipolar coupling is measured by fitting the S/So vs. m plot

A distance can be measured from:

34 IS

SIo

rd

d = 195 Hz, 13C-15N = 2.47 Ǻ

H2N

O

OH

glycine

Solid-State NMR

Two-Dimensional NMR Spectrum• 2D REDOR

Can also be used to generate chemical shift correlations- Similar to HSQC, HMQC experimentsSimilar to HSQC, HMQC experiments- HETCOR: MAS effectively removes HETCOR: MAS effectively removes 1313C-C-1515N couplings N couplings

13C-15N correlations for a peptide

15N

13C