(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)

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

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

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, 3096-3129

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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 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.

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

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