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The Physical Methods in Inorganic Chemistry (Fall Term, 2004) Department of Chemistry National Sun Yat-sen University

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##### The Physical Methods in Inorganic Chemistry (Fall Term, 2004) Department of Chemistry National Sun Yat-sen University

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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**CRAMPS (combination of rotation and multi-pulse spectroscopy****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