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無機物理方法（核磁共振部分） The Physical Methods in Inorganic Chemistry(Fall Term, 2004)Department of ChemistryNational Sun Yat-sen University Chapter 7
Introduction to Solid State NMR • 7.0 Summary of internal interactions in solid state NMR • 7.1 Typical lineshapes for static samples • 7.2 Magic-angle-spinning (MAS) • 7.3 Cross polarization (CP) and CPMAS • 7.4 Homonuclear decoupling pulse sequences • 7.5 Multi-quantum MAS (MQMAS) of quadrupole spins
Spin 1 creates a tiny magnetic field at spin 2 and vise versa, introducing direct magnetic coupling between them.
The magnetic field produced by spin 1 at the position of spin 2 is 2 r1,2 (unit vector) 1 Which causes an energy of amount This is the same energy that the spin 1 gains from the magnetic field produced by the spin 2.
Expressing the energy in quantum mechanics, we have the direct dipolar interaction Hamiltonian as which can be written in compact form [with ] Z j Y i X
Z j Y i X
where D is called dipolar coupling tensor. It is symmetric It is traceless (see the reason?)
Principal-Axis System (PAS) In the principal-axis system (PAS), only the diagonal elements of D are non-zero and j i
Spherical Coordinates (x,y,z)
HD in Spherical coordinates Zero-quantum terms Single-quantum terms Double-quantum terms
Expressed with irreducible tensors (dipolar tensor in PAS) and spin part (operator tensor) : The most important terms are those commuting with
Why irreducible tensors? • Rotation is treated most conveniently by means of irreducible tensors • No matter how many rotations you have, the calculation is straightforward if the Hamiltonian is expressed in terms of irreducible tensors. PASRotorLAB
Electric quadrupolar interaction For a quadrupolar nucleus (spin>=1), the electric field gradient (EFG) at the nucleus may cause energy shift for the nucleus. The general form for EFG is a tensor (like dipolar coupling tensor).
The quadrupolar Hamiltonian can be derived as In the principal axis-system (PAS), it is given by
In arbitrary coordinate systems, electric quadrupolar interaction is given by γ β with spatial part (quadrupolar tensor in PAS): α and spin part (operator tensor)
Secular term (First order) For many quadrupolar nuclei, higher orders may become appreciable and need to be removed.
Chemical shift interaction The most significant term is
J-coupling interaction The expression of J tensor is complicated and is not discussed here. Unlike direct dipolar interaction, J-coupling tensor has non-zero isotropic component and in most cases, it is the only term to be considered.
The most important internal interactions in NMR spectroscopy are • Chemical shift interaction • J-coupling interaction • Dipolar coupling interaction • Quadrupolar interaction • Spin-rotation interaction (for rotating molecules, not studied here) All of them can be written in the form of where R is a rank-2 tensor (matrix), varying with the type of interactions.
Coordinate Systems Lab Frame(XYZ)
How to calculate a solid NMR spectrum More generally,
Direct Dipole-Dipole Coupling ~80 kHz Many coupled spins Spin Pair
Decoupling Sequences • Hetronuclear decoupling: CW TPPM • Homonuclear decoupling WAHUHA MREV HR CORY etc
Indirect Spin-Spin Coupling • In contrast to the direct, through space dipole-dipole coupling of two nuclear magnetic moments, the indirect spin-spin coupling interaction is mediated by the electrons of the intervening bonds. • The isotropic J coupling constant is familiar from solution NMR. We are also interested in anisotropies in the indirect spin-spin coupling tensor, denoted as J. This anisotropy can be measured by a few different techniques; solid-state NMR is especially useful in certain cases. • Wasylishen J. Am. Chem. Soc. 2000, 122, 3197. • "Anisotropy in the 199Hg-31P Indirect Spin-Spin Coupling Tensor of a 1:2 Mercury-Phosphine Complex. A Phosphorus Single-Crystal NMR Study", Michael D. Lumsden, Roderick E. Wasylishen, and James. F. Britten J. Phys. Chem. 1995, 99, 16602.
Dipolar-Chemical Shift NMR (1D) • The interplay of chemical shift anisotropy and spin-spin coupling interactions results in complex line shapes. • The dipolar-chemical shift method is useful in the case of isolated spin pairs. Many other cases where more than one interaction are involved.
Cross polarization • CP condition: The nutation frequency must be the same for the two coupled spins: • CP incorporated with MASCPMAS—one of the most important solid state NMR techniques. • CP contact time: several hundred microseconds to tens of milliseconds. • Purpose: To enhance the sensitivity of the lower γ spins such as carbon-13. maximal enhancement factor: γI/γS • Other advantages: Shorter recycle delay time • Distinguish the interconnectivity of nuclear spins such as the protonation of a certain carbon nucleus.
Separation of Local Fields Chemical shift correlation Chemical shift -dipolar correlation Chemical shift-quadrupolar correlation Interaction A Interactions B,A Mixing I t1 t2 tm S
3/2 1/2 -1/2 -3/2 Multiple Sites Dig EFGs From This Spectrum! Quadrupolar Coupling May Be Very Strong! m In A Powder Zeeman Quadrupolar (first-order) Quadrupolar (second-order) Energy Levels of a Spin-3/2 Nucleus in a Static Magnetic Filed
Second Order Quadrupolar Frequency Both The EFG Information And High Resolution Can Be Achieved. 2D Solution:Keep AND Remove
Multi-Quantum Magic-Angle Spinning (MQMAS) Excitation Evolution Conversion Acquisition P1 t1 P2t2 Magic Angle (54.7 ) Spinning MQC SQC o θM θM
MQMAS Signal Enhancement • S.Ding,C.A.McDowell, Chem. Phys. Lett. 1997, 270, 81-86.
Other Topics • Multiple pulse for homonuclear decoupling (WAHUHA, MREV, HR, CORY etc) • Combination of rotation and multiple pulses (CRAMP) • Recoupling (Rotational Resonance, REDOR, RFDR etc) • Other multi-dimensional solid state NMR (HETCOR, CSA/Q correlation, D/Q correlation, 3D correlation spectra) • Single-Crystal NMR