Direct dipolar interaction - utilization

Transcription

1 Direct dipolar interaction - utilization Two main uses: I: magnetization transfer II: probing internuclear distances Direct dipolar interaction - utilization Probing internuclear distances ˆ hetero D d H ( 3cos ) Iˆ zs ˆ z = θ with: d ( 3cos θ )[ 3I ˆ S ˆ I ˆ S ˆ ] ˆ homo D = z z H µ γ γ h d = 0 I S 3 4πr IS Information about internuclear distances in dipolar coupling constant (r IS -dependence) Dipolar coupling methods: methods to probe the strength of dipolar interactions to study internuclear distances Different spin-terms different response to pulse sequences!!!

2 Direct dipolar interaction - utilization Probing internuclear distances: second moments M Dipolar coupling methods: Probe the strength of dipolar interaction Measure for the strength of the dipolar interaction: the second moment M Possibly application: study of ion distribution in drdered systems (glasses, ) M M 6 r ij Type of ion distribution: - clustered/ phase-separated - statistical - homogeneous c(ion) 3 Direct dipolar interaction - utilization Determination of homonuclear M s Spin echo decay spectroscopy Based on a Hahn Echo: designed for I=/ nuclei Refocus (I=/ nuclei): - Field inhomogenities - Chemical shift antropy - Heteronuclear dipolar interaction (all interactions which are proportional to I z ) 4

3 Direct dipolar interaction - utilization Determination of homonuclear M s The Spin echo experiment t Echo t The Hahn Echo intensity is measured as a function of the evolution time t Echo t t the longer the evolution time the lower the echo intensity Reason for loss of signal: Homonuclear dipolar interaction 90 t 80 t Echo! Note: works only for spin-/ or pseudo spin-/ nuclei 5 Direct dipolar interaction - utilization Determination of homonuclear M s determination of M from a linear fit: I/I ln(i/i 0 ) t /us I(t ) (t) = exp I (0) homo M t /us 6 3

4 Direct dipolar interaction - utilization Determination of heteronuclear M s: SEDOR Iˆ Sˆ Z r ( 3 cos θ ) ˆ hetero Z D 3 H SEDOR Spin Echo SEDOR-Fit Spin Echo-Fit 0.6 I/I t /ms I(t ) F(t ) M = exp I(0) F(0) ( hetero t ) 7 Direct dipolar interaction - utilization Other dipolar coupling methods Homonuclear: % Heteronuclear: - REDOR (rotational echo double resonance): MAS version of the SEDOR experiment If the recoupled spin I>/: - Inverse REDOR If both nuclei I>/: -TRAPDOR (transfer of population in double resonance) - REAPDOR (rotational-echo adiabatic-passage double resonance) 8 4

5 theory Magnetic shielding/chemical shift = indirect magnetic interaction of the external magnetic field and the nuclear spins through the involvement of electrons B 0 Hˆ = Hˆ + Hˆ CS CS an CS - Chemical shift interaction is predominantly an intramolecular interaction Two step process: () External magnetic B 0 field induces currents in the electron clouds of the molecules () Circulating electronic currents generate an induced magnetic induced field B MS M. Levitt, spin dynamics, nd edition, Wiley & sons,(008) 9 Theory: magnetic shielding Hamiltonian - Strength of induced field increases linearly with B 0 : B induced MS = B 0 -Hamilton operator of the magnetic shielding interaction: with: magnetic shielding or chemical shift tensor = yx zx Hˆ CS xy zy xz yz matrix takes into account that the induced field is usually in a different direction to B 0 = γb induced Iˆ γ B Iˆ MS 0 z Energy correction term of them magnetic shielding: E = γh B m CS 0 (energy levels for each m are shifted by the value given by this equation) 0 5

6 E m Theory: impact on the energy eigenstates Effect on energy levels Zeeman m = ω 0 m = E = γh (θ ) B m MS 0 Zeeman + MS ( θ ) > 0, γ > 0 ω 0 + ω MS E m m = ω 0 m = Zeeman + MS ( θ ) < 0, γ > 0 ω 0 + ω MS ω 0 ω ω 0 ω ω 0ωMS ω ω MS ω MS Theory: definition of the chemical shift Definition of the chemical shift BUT contains structural information (shielding/deshielding due to electronic environment) - depends on B 0 field makes comparn between different instruments difficult - depends on sign of γ confusing, since direction of the frequency shift is switched for nuclei with positive and negative γ SOLUTION Chemical shift: ω ωref = ω ref = lab lab ( ( ref ) ) lab ( ref ) 6

7 Theory: the chemical shift tensor The chemical shift tensor magnetic shielding tensor = yx zx xy zy xz yz elements are replaced by αβ = ( ( ref ) ) αβ αβ αβ ( ref ) chemical shift tensor = yx zx xy zy xz yz Very often the chemical shift tensor is represented and characterized in its principal axis frame () 0 0 x() = 0 0 φ 0 0 B 0 (z(lab)) θ z () 3 Theory: the principal axis frame What is the principal axis frame ()? The principal axis example: carboxylate group -For each nuclear site: 3 special directions of the external magnetic field for which the induced field is parallel to the external field = principal axis of the chemical shift tensor -The PA are always perpendicular to each other! Every nuclear site in a molecule Has, in general, cs-tensors with different M. Levitt, spin dynamics, nd edition, Wiley & sons,(008) 4 7

8 Theory: the cs tensor in Properties of the chemical shift tensor represented in Isotropic chemical shift: ( + + ) equation is valid in any frame! = 3 sum of tensor diagonal elements is always the same Determines the position of peaks in tropic liquids chemical shift antropy (CSA): an = Quantifies the deviation from tropy of the CS tensor (solids only) asymmetry (biaxiality): η = 0 η an Quantifies the difference between the other two principal values (solids only) convention for assigning principal values and principal axis of cs tensor: 5 Theory: properties of the tropic chemical shift - chemical shift (cs) range: Main influence on the cs from low-lying electronic excited states. Trend: the heavier the tope the more low-lying electronic excited states Increasing cs ranges with increasing tope mass ( H: 0 ppm, 3 C: 00 ppm, 05 Pb several thousands ppm cs range) - cs values: correlates with the electronegativity of neighboring groups Electronegative atoms like O, Cl, F, etc. withdraw electron density of neighboring nucleus increasing local fields increased cs values - Measured tropic chemical shift is an average over rapid molecular motion (important if fast exchange reactions are present) -Chemical shifts can be influenced by neighboring molecules (important for solids, for example different signals for molecules in an asymmetric cell of a crystal) 6 8

9 Theory: chemical shift interaction in solids Chemical shift frequency: ω = γ ( ( θ, )) cs B + 0 φ Example: a single crystal: the chemical shift depends on the orientation of the solid with respect to B 0 M. Levitt, spin dynamics, nd edition, Wiley & sons,(008) 7 Theory: chemical shift interaction in solids A Powder spectrum - Usually the sample is not single-crystal, but a powder Molecules have all possible orientations M. Levitt, spin dynamics, nd edition, Wiley & sons,(008) 8 9

10 Theory: chemical shift interaction in solids Lineshapes of a Powder spectrum Position of the center of gravity of the powder spectrum is determined by the tropic chemical shift Lineshape of the powder spectrum is determined by asymmetry of chemical sift tensor η Broadening of the powder pattern an is determined by CSA 9 Utitlization: tropic chemical shifts Interpretation of tropic chemical shifts: like in solution state NMR Assignment of chemical environments Example: 3 C chemical shift ranges: 0 0

11 Utitlization: tropic chemical shifts In solids: Chemical shift is influenced by neighboring molecules Chemically identical molecules may have different chemical shifts depending on their structural order: Crystalline - amorphous Polymorphs: Crystall lattice (orthorhombic, monoclinic ) Experimental approach: MAS Utitlization: CSA and asymmetry Characterization of structural order H-decoupled static 3 C spectrum for frozen acetic anhydride Determination of CSA and η by static powder pattern (if magnetic shielding is dominant interaction) M. Levitt, spin dynamics, nd edition, Wiley & sons,(008)