solid state nmr

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solid state nmr spectroscopy


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  • Solid State NMR Spectroscopy
  • Solid State NMR Applications The very powerful technique for amorphous solids, powder crystalline samples. Determination of local molecular environments. measurement of internuclear distances (dipolar recoupling) Structure Chirality Enzyme mechanisms Polymorphism
  • Organic complexes Inorganic complexes Zeolites mesoporous solids microporous solids aluminosilicates/phosphates minerals biological molecules Glasses cements food products wood ceramics bones semiconductors metals and alloys archaelogical specimens polymers resins surfaces Solid state NMR has been applied to
  • 6 13C NMR of glycine Adapted from M. Edn, Concepts in Magnetic Resonance 18A, 24. D. Lide, G. W. A. Milne, Handbook of Data on Organic Compounds: Compounds 10001-15600 Cha-Hex. (CRC Press, 1994). Solid Liquid Powder Spectra
  • Solid and Liquid 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 produces a rotating magnetic field as it precesses in the applied magnetic field Each spin has a static field component that influences Larmor frequency of neighbors - Range of frequencies that add to line-width Chemical shift anisotropy - Chemical shift varies with orientation relative to B0 Bo Solid-state (ordered structure) Solution-state (random-orientation) 9
  • Line-shape Broadening Factors for Solid Samples Direct Dipolar Coupling Between at least two nuclear magnetic moments Heteronuclear and Homonuclear Chemical Shift Anisotropy Orientation dependence of molecule relative to Bo Shorter Spin-Spin (T2*) Relaxation Larger linewidths at half-height Quadrupolar Interaction for Spin > Between nuclear charge distribution and electric field gradient in the solid Magnetic Susceptibility Differences of Ho (mag. flux) at solid / liquid interface
  • NMR Interactions in the Solid State 12 1-Zeeman interaction of nuclear spins 2-Direct dipolar spin interaction 3-Indirect spin-spin coupling (J- coupling), nuclear-electron spin coupling (paramagnetic), coupling of nuclear spins with molecular electric field gradients (quadrupolar interaction). 4-Direct spin-lattice interactions 3,5-Indirect spin-lattice interaction via electrons 3,6-Chemical shielding and polarization of nuclear spins by electrons 4,7-Coupling of nuclear spins to sound fields
  • Nuclear spin interactions The size of these external interactions is larger than internal
  • All NMR interactions are anisotropic - their three dimensional nature can be described by second-rank Cartesian tensors, which are 3 3 matrices. The NMR interaction tensor describes the orientation of an NMR interaction with respect to the cartesian axis system of the molecule. These tensors can be diagonalized to yield tensors that have three principal components which describe the interaction in its own principal axis system (PAS)
  • Zeeman interaction It can be described with a Hamiltonian or in ternsor form In the magnetic field the two spin states have different energies It is far the strongest interaction and all other types of interaction can be considered as corrections Order of the magnitude:
  • Chemical shielding is an anisotropic interaction characterized by a shielding tensor , which can also be diagonalized to yield a tensor with three principal components. Isotropic Chemical shielding
  • chemical shielding anisotropy gives rise to frequency shifts with the following orientation dependence: In order to calculate powder patterns (for any anisotropic NMR interaction), one must calculate frequencies for a large number of orientations of the interaction tensor with respect to the magnetic field - many polar angles over a sphere: ,
  • Chemical shifts in single crystals Shielding depends on molecular (i.e. crystal) orientation: s q 23
  • Powder patterns Spectra from powdered samples are sums over individual crystallite orientations: (Shape reflects probability of particular orientation) axial symmetry (h = 0) Well-defined powder patterns can analysed to determine chemical shift tensor components Loss of resolution (and sensitivity) is usually unacceptable 24
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  • , , = 0 Rossum, Solid State NMR and proteins (2009) J. Duer, Solid State NMR spectroscopy (2002) Chemical Shift Anisotropy More shielding -> lower chemical shift
  • More shielding -> lower chemical shift. Dependent on angular orientation More shielded , , Chemical Shift Anisotropy
  • 28 Chemical Shift Anisotropy
  • Powder Pattern 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 29
  • Why is the chemical shift orientation dependent? Molecules have definite 3D shapes, and certain electronic circulations (which induced the local magnetic fields) are preferred over others. Molecular orbitals and crystallographic symmetry dictate the orientation and magnitude of chemical shielding tensors.
  • Nuclear Pair Internuclear distance [] Dipolar coupling [] 1H,1H 10 120 1H,13C 1 30 1H,13C 2 3.8 Dipolar coupling causes huge line broadening J. Duer, Solid State NMR spectroscopy (2002) Dipole-Dipole Coupling
  • When two spins (nuclei I and S) are close (10 ) in a magnetic field ... One spin affects local magnetic field at another spin Changes frequency of paired nuclei Interaction depends on I-S distance and angle between I-S and Bo z y x 1H 13C qB0 r The degree by which spin I affects the magnetic field at spin S is determined by the dipolar coupling constant (d): zzIS SIdH 1cos3 2 q In solution, random motion averages dipolar coupling to zero In solids, orientations are static defined by crystal lattice
  • Direct dipole coupling Useful for molecule structure studies and provides a good way to estimate distances between nuclei and hence the geometrical form of the molecule
  • The dipolar interaction results from interaction of one nuclear spin with a magnetic field generated by another nuclear spin, and vice versa. This is a direct through space interaction.
  • Dipolar hamiltonian can be expanded into the dipolar alphabet, which has both spin operators and spatially dependent terms. Only term A makes a secular contribution for heteronuclear spin pairs, and A and B (flip flop) both make contributions for homonuclear spin pairs: HDD=A+B+C+D+E+F
  • In a solid-state powder sample every magnetic spin is coupled to every other magnetic spin; dipolar couplings serve to severely broaden NMR spectra. In solution molecules reorient quickly; nuclear spins feel a time average of the spatial part of the dipolar interaction +3cos2 2-1, over all orientations 2,N. The dipolar interaction tensor is symmetric and traceless, meaning that the interaction is symmetric between the two nuclei, and there is no isotropic dipolar coupling: For a heteronuclear spin pair in the solid state, the (3cos2 - 1) term is not averaged by random isotropic tumbling: the spatial term will have an effect on the spectrum!
  • So, for an NMR spectrum influenced only by the Zeeman and AX dipolar interaction, the frequencies for A can be calculated as: For a homonuclear spin pair, the flip flop term (B) is also important: So the frequencies of the transitions can be calculated as:
  • Presence of many dipolar interactions (e.g. between 1Hs) results in featureless spectra: B0 q r d r -( )3 1 2 3 cos2 q The dipolar interaction
  • In a single crystal with one orientation of dipolar vectors, a single set of peaks would be observed