Solid-state nuclear magnetic resonance

Solid-state NMR spectroscopy is a kind of nuclear magnetic resonance

Nuclear magnetic resonance

Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...

(NMR) spectroscopy, characterized by the presence of anisotropic (directionally dependent) interactions.

Introduction

Basic concepts
A spin interacts with a magnetic

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

or an electric field

Electric field

In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

. Spatial proximity and/or a chemical bond

Chemical bond

A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

between two atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s can give rise to interactions between nuclei. In general, these interactions are orientation dependent. In media with no or little mobility (e.g. crystals, powders, large membrane vesicles, molecular aggregates), anisotropic interactions have a substantial influence on the behaviour of a system of nuclear spins. In contrast, in a classical liquid-state NMR experiment, Brownian motion

Brownian motion

Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

leads to an averaging of anisotropic interactions. In such cases, these interactions can be neglected on the time-scale of the NMR experiment.

Examples of anisotropic nuclear interactions
Two directionally dependent interactions commonly found in solid-state NMR are the chemical shift anisotropy (CSA) and the internuclear dipolar coupling. Many more such interactions exist, such as the anisotropic J-coupling

J-coupling

J-coupling is the coupling between two nuclear spins due to the influence of bonding electrons on the magnetic field running between the two nuclei. J-coupling contains information about dihedral angles, which can be estimated using the Karplus equation...

in NMR, or in related fields, such as the g-tensor in electron spin resonance. In mathematical terms, all these interactions can be described using the same formalism.

Experimental background Anisotropic interactions modify the nuclear spin

Spin (physics)

In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

energy levels (and hence the resonance frequency) of all sites in a molecule, and often contribute to a line-broadening effect in NMR spectra. However, there is a range of situations when their presence can either not be avoided, or is even particularly desired, as they encode structural parameters, such as orientation information, on the molecule of interest.
High-resolution conditions in solids (in a wider sense) can be established using magic angle spinning (MAS)

Magic angle spinning

In nuclear magnetic resonance, magic angle spinning is a technique often used to perform experiments in solid-state NMR spectroscopy.By spinning the sample at the magic angle θm In nuclear magnetic resonance, magic angle spinning (MAS) is a technique often used to perform experiments in...

, macroscopic sample orientation, combinations of both of these techniques, enhancement of mobility by highly viscous sample conditions, and a variety of radio frequency

Radio frequency

Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

(RF) irradiation patterns. While the latter allows decoupling of interactions in spin space, the others facilitate averaging of interactions in real space. In addition, line-broadening effects from microscopic inhomogeneities can be reduced by appropriate methods of sample preparation.

Under decoupling conditions, isotropic interactions can report on the local structure, e.g. by the isotropic chemical shift. In addition, decoupled interactions can be selectively re-introduced ("recoupling"), and used, for example, for controlled de-phasing or transfer of polarization to derive a number of structural parameters.

Solid-state NMR line widths
The residual line width (full width at half max) of ¹³C nuclei under MAS conditions at 5–15 kHz spinning rate is typically in the order of 0.5–2 ppm, and may be comparable to solution-state NMR conditions. Even at MAS rates of 20 kHz and above, however, non linear groups (not a straight line) of the same nuclei linked via the homonuclear dipolar interactions can only be suppressed partially, leading to line widths of 0.5 ppm and above, which is considerably more than in optimal solution state NMR conditions. Other interactions such as the quadrupolar interaction can lead to line widths of thousands of ppm due to the strength of the interaction. The first-order quadrupolar broadening is largely suppressed by sufficiently fast MAS, but the second-order quadrupolar broadening has a different angular dependence and cannot be removed by spinning at one angle alone. Ways to achieve isotropic lineshapes for quadrupolar nuclei include spinning at two angles simultaneously (DOR), sequentially (DAS), or through refocusing the second-order quadrupolar interaction with a two-dimensional experiment such as MQMAS or STMAS.

Anisotropic interactions in solution-state NMR
From the perspective of solution-state NMR, it can be desirable to reduce motional averaging of dipolar interactions by alignment media. The order of magnitude of these residual dipolar coupling

Residual dipolar coupling

The residual dipolar coupling between two spins in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings....

s (RDCs) are typically of only a few rad/Hz, but do not destroy high-resolution conditions, and provide a pool of information, in particular on the orientation of molecular domains with respect to each other.

Dipolar truncation
The dipolar coupling between two nuclei is inversely proportional to the cube of their distance. This has the effect that the polarization transfer mediated by the dipolar interaction is cut off in the presence of a third nucleus (all of the same kind, e.g. ¹³C) close to one of these nuclei. This effect is commonly referred to as dipolar truncation. It has been one of the major obstacles in efficient extraction of internuclear distances, which are crucial in the structural analysis of biomolecular structure. By means of labeling schemes or pulse sequences, however, it has become possible to circumvent this problem in a number of ways.

Chemical shielding

The chemical shielding is a local property of each nucleus, and depends on the external magnetic field.

Specifically, the external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that often vary across the entire molecular framework such that nuclei in distinct molecular environments usually experience unique local fields from this effect.

Under sufficiently fast magic angle spinning

Magic angle spinning

, or in solution-state NMR, the directionally dependent character of the chemical shielding is removed, leaving the isotropic chemical shift

Chemical shift

In nuclear magnetic resonance spectroscopy, the chemical shift is the resonant frequency of a nucleus relative to a standard. Often the position and number of chemical shifts are diagnostic of the structure of a molecule...

J-coupling

The J-coupling

J-coupling

or indirect nuclear spin-spin coupling (sometimes also called "scalar" coupling despite the fact that J is a tensor quantity) describes the interaction of nuclear spins through chemical bonds.

Dipolar coupling

Main article: Dipolar coupling (NMR)

Magnetic dipole-dipole interaction

Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. The potential energy of the interaction is as follows:...

Nuclear spins exhibit a dipole moment

Nuclear magnetic moment

The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic dipole moment; the quadrupole moment does cause some small shifts in the hyperfine structure as well....

, which interacts with the dipole moment of other nuclei (dipolar coupling). The magnitude of the interaction is dependent on the spin species, the internuclear distance, and the orientation of the vector connecting the two nuclear spins with respect to the external magnetic field B (see figure). The maximum dipolar coupling is given by the dipolar coupling constant d,

where r is the distance between the nuclei, and γ₁ and γ₂ are the gyromagnetic ratios of the nuclei. In a strong magnetic field, the dipolar coupling depends on the orientation of the internuclear vector with the external magnetic field by

Consequently, two nuclei with a dipolar coupling vector at an angle of θ_m=54.7° to a strong external magnetic field, which is the angle where D becomes zero, have zero dipolar coupling. θ_m is called the magic angle

Magic angle

The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, P_2=0 \,, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle...

. One technique for removing dipolar couplings, at least to some extent, is magic angle spinning

Magic angle spinning

Quadrupolar interaction

Nuclei with a spin greater than one-half have a non spherical charge distribution. This is known as a quadrupolar nucleus. A non spherical charge distribution can interact with an electric field gradient caused by some form of non-symmetry (e.g. in a trigonal bonding atom there are electrons around it in a plane, but not above or below it) to produce a change in the energy level in addition to the Zeeman effect

Zeeman effect

The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...

. The quadrupolar interaction is the largest interaction in NMR apart from the Zeeman interaction and they can even become comparable in size.
Due to the interaction being so large it can not be treated to just the first order, like most of the other interactions. This means you have a first and second order interaction, which can be treated separately. The first order interaction has an angular dependency with respect to the magnetic field of

(the P2 Legendre polynomial), this means that if you spin the sample at

(~54.74°) you can average out the first order interaction over one rotor period (all other interactions apart from Zeeman, Chemical shift, paramagnetic and J coupling also have this angular dependency). However, the second order interaction depends on the P4 Legendre polynomial, which has zero points at 30.6° and 70.1°. These can be taken advantage of by either using DOR (DOuble angle Rotation) where you spin at two angles at the same time, or DAS (Double Angle Spinning) where you switch quickly between the two angles. Specialized hardware (probe) has been developed for such experiments. A revolutionary advance is Lucio Frydman's multiple quantum magic angle spinning (MQMAS) NMR in 1995 and it has become a routine method for obtaining high resolution solid-state NMR spectra of quadrupolar nuclei. A similar method to MQMAS is satellite transisition magic angle spinning (STMAS) NMR proposed by Zhehong Gan in 2000.

History

See also: nuclear magnetic resonance

Nuclear magnetic resonance

Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...

or NMR spectroscopy

NMR spectroscopy

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of atoms or the molecules in which they are contained...

articles for an account on discoveries in NMR and NMR spectroscopy in general.

History of discoveries of NMR phenomena, and the development of solid-state NMR spectroscopy:

Purcell, Torrey and Pound: "nuclear induction" on ¹H in paraffin 1945, at about the same time Bloch et al. on ¹H in water.

Basic example

A fundamental RF pulse sequence and building-block in most solid-state NMR experiments starts with cross-polarization (CP) [Waugh et al.]. It can be used to enhance the signal of nuclei with a low gyromagnetic ratio (e.g. ¹³C, ¹⁵N) by magnetization transfer from nuclei with a high gyromagnetic ratio (e.g. ¹H), or as spectral editing method (e.g. directed ¹⁵N→¹³C CP in protein spectroscopy). To establish magnetization transfer, the RF pulses applied on the two frequency channels must fulfill the Hartmann–Hahn condition [Hartmann, 1962]. Under MAS, this condition defines a relationship between the voltage through the RF coil and the rate of sample rotation. Experimental optimization of such conditions is one of the routine tasks in performing a (solid-state) NMR experiment.

CP-MAS is a basic building block of most pulse sequences in solid-state NMR spectroscopy. Given its importance, a pulse sequence employing direct excitation of ¹H spin polarization, followed by CP transfer to and signal detection of ¹³C, ¹⁵N) or similar nuclei, is itself often referred to as CP experiment, or, in conjunction with MAS, as CP-MAS [Schaefer and Stejskal, 1976]. It is the typical starting point of an investigation using solid-state NMR spectroscopy.

Decoupling

Nuclear spin interactions must be removed (decoupled

Nuclear magnetic resonance decoupling

Nuclear magnetic resonance decoupling is a special method used in nuclear magnetic resonance spectroscopy where a sample to be analyzed is irradiated at a certain frequency or frequency range to eliminate fully or partially the effect of coupling between certain nuclei...

) to increase the resolution of NMR spectra and isolate spin systems.

A technique that can substantially reduce or remove the chemical shift anisotropy, the dipolar coupling is sample rotation (most commonly magic angle spinning

Magic angle spinning

, but also off-magic angle spinning).

Homonuclear RF decoupling decouples spin interactions of nuclei that are the same as those being detected. Heteronuclear RF decoupling decouples spin interactions of other nuclei.

Recoupling

Although the broadened lines are often not desired, dipolar couplings between atoms in the crystal lattice can also provide very useful information. Dipolar coupling are distance dependent, and so they may be used to calculate interatomic distances in isotopically labeled molecules.

Because most dipolar interactions are removed by sample spinning, recoupling experiments are needed to re-introduce desired dipolar couplings so they can be measured.

An example of a recoupling experiment is the Rotational Echo DOuble Resonance (REDOR) experiment
which also can be the basis of an NMR crystallographic study of e.g. an amorphous solid.

Biology

Membrane protein

A membrane protein is a protein molecule that is attached to, or associated with the membrane of a cell or an organelle. More than half of all proteins interact with membranes.-Function:...

s and amyloid

Amyloid

Amyloids are insoluble fibrous protein aggregates sharing specific structural traits. Abnormal accumulation of amyloid in organs may lead to amyloidosis, and may play a role in various neurodegenerative diseases.-Definition:...

fibrils, the latter related to Alzheimer's disease

Alzheimer's disease

Alzheimer's disease also known in medical literature as Alzheimer disease is the most common form of dementia. There is no cure for the disease, which worsens as it progresses, and eventually leads to death...

and Parkinson's disease

Parkinson's disease

Parkinson's disease is a degenerative disorder of the central nervous system...

, are two examples of application where solid-state NMR spectroscopy complements solution-state NMR spectroscopy and beam diffraction methods (e.g. X-ray crystallography, electron microscopy).

Chemistry

Solid-state NMR spectroscopy serves as an analysis tool in organic and inorganic chemistry. SSNMR is also a valuable tool to study local dynamics, kinetics, and thermodynamics of a variety of systems.

Advanced readings

Books and major review articles

McDermott, A, Structure and Dynamics of Membrane Proteins by Magic Angle Spinning Solid-State NMR Annual Review of Biophysics, v. 38, 2009.
Mehring, M, Principles of High Resolution NMR in Solids, 2nd ed., Springer, Heidelberg, 1983.
Slichter, C. P., Principles of Magnetic Resonance, 3rd ed., Springer, Heidelberg, 1990.
Gerstein, B. C. and Dybowski, C., Transient Techniques in NMR of Solids, Academic Press, San Diego, 1985.
Schmidt-Rohr, K. and Spiess, H.-W., Multidimensional Solid-State NMR and Polymers, Academic Press, San Diego, 1994.
Dybowski, C. and Lichter, R. L., NMR Spectroscopy Techniques, Marcel Dekker, New York, 1987.
Ramamoorthy, A., NMR Spectroscopy of Biological Solids, Taylor & Francis, New York, 2006.

General

References to books and research articles

Andrew, E. R., Bradbury, A. and Eades, R. G., "Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation," Nature 183, 1802, (1959)
Ernst, Bodenhausen, Wokaun: Principles of Nuclear Magnetic Resonance in One and Two Dimensions
Hartmann S.R., Hahn E.L., "Nuclear Double Resonance in the Rotating Frame" Phys. Rev. 128 (1962) 2042.
Pines A., Gibby M.G., Waugh J.S., "Proton-enhanced NMR of dilute spins in solids" J. Chem. Phys. 59, 569-90, (1973)
Purcell, Torrey and Pound (1945).
Schaefer, J. and Stejskal, E. O., "Carbon-13 Nuclear Magnetic Resonance of Polymers Spinning at the Magic Angle," Journal of the American Chemical Society 98, 1031 (1976).
Gullion, T. and Schaefer, J., "Rotational-Echo, Double-Resonance NMR," J. Magn. Reson., 81, 196 (1989).
MacKenzie, K.J.D and Smith, M.E. "Multinuclear Solid-State NMR of Inorganic Materials", Pergamon Materials Series Volume 6, Elsevier, Oxford 2002.

External links

SSNMRBLOG Solid-State NMR Literature Blog by Prof. Rob Schurko's Solid-State NMR group at the University of Windsor
www.ssnmr.org Rocky Mountain Conference on Solid-State NMR

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Introduction

Chemical shielding

J-coupling

Dipolar coupling

Quadrupolar interaction

History

Basic example

Decoupling

Recoupling

Biology

Chemistry

Suggested readings for beginners

Advanced readings

General

External links