The Physical Methods in Inorganic Chemistry (Fall Term, 2004) Department of Chemistry National Sun Yat-sen University 無機物理方法（核磁共振部分） 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

Single Crystal or Polycrystalline (Powder) Samples

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 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. (unit vector) r 1,2 1 2

Expressing the energy in quantum mechanics, we have the direct dipolar interaction Hamiltonian as [with ] which can be written in compact form i j X Y Z

i j X Y Z

It is symmetric It is traceless (see the reason?) where D is called dipolar coupling tensor.

Principal-Axis System (PAS) In the principal-axis system (PAS), only the diagonal elements of D are non-zero and i j

Spherical Coordinates (x,y,z)

H D in Spherical coordinates Zero-quantum terms Single-quantum terms Double-quantum terms

Principal-Axis System (PAS)

(dipolar tensor in PAS) and spin part (operator tensor) The most important terms are those commuting with : Expressed with irreducible tensors

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. PAS  Rotor  LAB

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 with spatial part (quadrupolar tensor in PAS): and spin part (operator tensor) β α γ

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,

Chemical shit anisotropy interaction

Direct Dipole-Dipole Coupling Spin Pair ~80 kHz Many coupled spins

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, "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,

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 MAS  CPMAS—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: γ I /γ S 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 t1t1 tmtm t2t2 I S Interaction A Interactions B,A Mixing

Chemical Shift Correlation Spectrum

3D CSA-D Correlation (with One Quadrupolar Spin)

MQMAS

Under rapid magic angle spinning (MAS):

Dig EFGs From This Spectrum! Energy Levels of a Spin-3/2 Nucleus in a Static Magnetic Filed m 3/2 1/2 -1/2 -3/2 ZeemanQuadrupolar (first-order) Quadrupolar (second-order) Quadrupolar Coupling May Be Very Strong! Multiple Sites Multiple Sites In A Powder

Both The EFG Information And High Resolution Can Be Achieved. Second Order Quadrupolar Frequency 2D Solution:Keep AND Remove

Excitation Evolution Conversion Acquisition P 1 t 1 P 2 t 2 θ M θ M MQC SQC Magic Angle (54.7 ) Spinning o Multi-Quantum Magic-Angle Spinning (MQMAS)

L.Frydman, J.S.Harwood, JACS, 1995.

2D- 17 O-DAS spectrum of the silicate coesite

MQMAS Signal Enhancement S.Ding,C.A.McDowell, Chem. Phys. Lett. 1997, 270, S.Ding,C.A.McDowell, Chem. Phys. Lett. 1997, 270,

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

Effect of MAS on dipolar coupling

Proton Decoupling

Pulsed decoupling (WAHUHA, MREV-8)

Correlation experiment

Homonuclear correlation

Homonuclear correlation : establishing connectivities

Let us have a tour of solid state NMR following Professor Malcolm H. Levitt.