NMR spectroscopy

Nuclear Magnetic Resonance Spectroscopy (NMR spectroscopy, MR spectroscopy, NMR)

NMR spectroscopy is the use of electromagnetic radiation to obtain information regarding transitions between different nuclear spin states in the presence of a magnetic field.

Principles of Nuclear Magnetic resonance: Nuclear magnetic resonance is a consequence of a property possessed by the nucleus known as 'Nuclear spin angular momentum' . It is important to remember that although some properties associated with 'Nuclear spin angular momentum' are similar to those of a spinning macroscopic body, Nuclear spin angular momentum is a fundamental property that CANNOT be explained in terms of any other fundamental property such as mass, charge, etc.

Nuclear spin angular momentum is a QUANTIZED VECTORial quantity. Its magnitude is restricted to certain fixed values AND its direction is also restricted to certain directions in the presence of a magnetic field. In the absence of a magnetic field, it is not possible to obtain ANY information regarding its direction.

Nuclei that have an even mass number and an even atomic number do not exhibit nuclear magnetic resonance, e.g., O-16, C-12. Some common nuclei that do exhibit nuclear magnetic resonance are: H-1, C-13, N-15, F-19.

The Nuclear spin angular momentum is characterized by a quantum number known as the Nuclear Spin Angular Momentum Quantum Number (often referred to as 'spin'). For example, the proton has a Nuclear Spin Angular Momentum Quantum Number of 1/2 and is known as a spin-1/2 particle. Similarly, the N-14 nucleus has a Nuclear Spin Angular Momentum Quantum number of 1 and is known as a spin-1 nucleus. The Magnitude of the Nuclear Spin Angular Momentum, | I |, is

                                   ( I * ( I + 1) )^(1/2) * h / (2*pi)

In the presence of an external homogeneous magnetic field (i.e., a magnetic field that has same magnitude everywhere in the space of interest; the magnetic field has no transverse components since the z-direction is chosen to point along the direction of the magnetic field), the z-component of the nuclear spin angular momentum vector is restricted to certain values ( m*h/(2*pi) )

where m is the spin magnetic quantum number, and can be any one of the values from +I to -I, that differ from each other in integral steps. 

e.g. If I=1, then m = +1, 0 or -1

      If I=1/2, then m = +1/2 or -1/2

(Note: Difference between different values of m should be integral; however, actual values of m may be integers or half-integers)

As a consequence of the restrictions on the magnitude of the z-component, the nuclear spin angular momentum vector can only point in certain (allowed) directions with reference to the external magnetic field. In the absence of other fields, there are no restrictions on the allowed directions in the x-y plane. The net result is that the spin angular momentum vectors of different nuclei point along the surface of cones that have a fixed angle with respect to the external magnetic field.

The different allowed values of m define the allowed orientations of the nuclear spin angular momentum and each of these spin states is associated with different energy. This is due to the fact that the energy of the spin states is proportional to the scalar product of the nuclear spin magnetic moment and the external magnetic field vectors. The nuclear spin magnetic moment is also proportional to the nuclear spin angular momentum. Electromagnetic radiation can efficiently cause transitions between the nuclear spin states if the frequency of the electromagnetic radiation, v, is equal to to the energy difference between the nuclear spin states divided by 2*pi.

Chemical aspects of NMR spectroscopy: Chemical shift, Areas and multiplicity.

The Chemical shift: The nuclei in molecules are surrounded by electrons. The applied magnetic field induces a circulation of electrons, which in turn produces an additional magnetic field. The nuclei in a given molecule sense not only the applied magnetic field but also the additional magnetic field due to the motion of the electrons. The electron density as well as polarizability varies substantially depending upon the nature of the molecule. As a consequence, the nuclei in different parts of the same molecule may be subjected to small differences in the total magnetic field - this results in a variation in the resonance frequency. The relative change in the resonance frequency is called the chemical shift. The chemical shifts of various functional groups are well characterized and provide a basis of identification of functional groups in molecules.

Signal area: The area of a signal is proportional to the total number of contributing nuclei.

J-coupling and multiplicity (Karplus, 1963): J-coupling is due to the interaction between different nuclei in the same molecule that is mediated through bonds. Usually, interaction between nuclei that are separated by 1, 2 or 3 bonds only is observable. The effect of this interaction on the observable spectrum is that the signals of a given nuclei are 'split' if the nucleus has a J-couling interaction with neighboring nuclei. If this coupling is weak, the resulting pattern can be used to deduce information regarding the number of neighboring nuclei. This information plays a critical role in structural elucidation of small organic molecules.

Relaxation time (Bloembergen, 1948; Bloch; Solomon, 1955): After a collection of nuclei in a magnetic field that is at equilibrium with its surroundings is perturbed in some manner (usually by a pulse of electromagnetic radiation) the system requires a certain amount of the time to return to equilibrium. The rate at which this process occurs is called relaxation rate. The relaxation rate is inversely proportional to relaxation time. T1 relaxation time characterizes the return to equilibrium of the longitudinal component of the magnetization of the collection of nuclei.

FTNMR: Fourier transform NMR spectroscopy (Ernst) : A pulse (or a pulse train) of electromagnetic radiation (usually radiofrequency electromagnetic radiation is abbreviated as RF) is used to cause a perturbation in the sytem. The time dependent response of the system is recorded. A fourier transform of the response gives information regarding the frequency response. In the case of a single pulse perturbation, the fourier transform of the time dependent response is equivalent to a 1D NMR spectrum.

Biological aspects of NMR spectroscopy:

   NMR spectroscopy can be used to determine the structure of macromolecules and to obtain information regarding their dynamics.  However, the NMR spectra of macromolecules are very much more complicated than those of small molecules and it is usually necessary to use multidimensional NMR spectroscopy in order to obtain data that can be used for structural analysis.

Multidimensional NMR spectroscopy (Jeener, 1971; Aue et al., 1976): The nuclei in a magnetic field are subjected to a series of pulses of electromagnetic radation separated by delays. The time dependent response of the system is recorded. The delays between the pulses may be fixed or incremented systematically between different repetitions of the experiment. The number of variable delays determines the dimensionality of the experiment. A multidimensional Fourier Transform of the entire data set characterizes the frequency responses of the system and enables a correlation between different NMR parameters.

  Different combinations of the pulses and delays known as 'pulse sequences' enable us to correlate and measure different types of NMR parameters.  Some common examples of multidimensional NMR spectroscopy experiments are COSY, NOESY, TOCSY, EXSY, HSQC, HNHA, HSQC-NOESY, HNCA, HNCO, HNCACO.

2D-COSY (Aue et al., 1976; Piantini et al. 1982): Correlates chemical shifts of J-coupled nuclei.

2D-NOESY (Jeener et al. 1979): correlates chemical shifts of nuclei that exhibit significant Nuclear Overhauser effect. For molecules that experience free rotation along all three dimensions, Nuclear overhause effect is generally observable between nuclei that are less than 5 angstroms apart.

2D-HSQC: Heteronuclear single quantum coherence spectroscopy. Correlates the chemical shifts of two different types of nuclei, that have strong J-coupling. e.g. H-1 with N-15 or H-1 with C-13

HNCA: A three dimensional NMR spectroscopic experiment that correlates the chemical shifts of the proton, N-15 and C-13 nuclei, when the proton is J-coupled to N-15 and the N-15 is J-coupled to the C-13. e.g. In a polypeptide or protein, the chemical shift of the Hydrogen atom attached to the peptide nitrogen atom can be correlated with the chemical shifts of the peptide N and the adjacent C-alpha atoms.

Applications of NMR spectroscopy in Pharmacology, Physiology and Medicine:

    NMR spectroscopy is a useful tool in drug design and development, due to its ability to characterize the interactions of ligands with receptors, even when the binding is weak and transient.  
    MR spectroscopy can be used to monitor physiological changes in a non-invasive manner due to its ability the quantify the changes in a large set of metabolites simultaneously.  Metabonomics is an attempt to characterize the physiological changes by quantifying the entire set of metabolites in an organism or its components.  
  Information regarding spatial distribution of NMR parameters may be obtained using of magnetic field gradients.  This is the basis of Magnetic Resonance Imaging (MRI) a tool that has found extensive applications in medical diagnostics.

Applications of NMR spectroscopy in Food technology:

    MR has been used to monitor the quality of wine and to monitor the cheese production process.

Textbooks:

Fundamentals of Physics. Holliday, Resnick and Walker.

Spectrosocpy of organic compounds. Silverstein.

Biophysical Chemistry. Cantor and Schimmel.

Principles of Nuclear Magnetic Resonance spectroscopy in one and two dimensions. (1987). R.R.Ernst, G. Bodenhausen and A.Wokaun. Clarendon Press. Oxford.

NMR of proteins and nucleic acids. K.Wuthrich. Wiley.

Quantum description of high resolution NMR in liquids. M.Goldman. Oxford.

Key references: N. Bloembergen, E. Purcell and R.V.Pound. (1948). Phys. Rev. 73, 679. E.L.Hahn. (1950). Phys. Rev. 80, 480. A.W.Overhauser. (1953). Phys. Rev. 92, 411. H.Y.Carr and E.Y.Purcell. (1954). Phys. Rev. 94, 630. I. Solomon. (1955). Phys. Rev. 99, 559. M.Karplus (1963). J.Am.Chem.Soc. 30, 11 J. Jeener. (1971). Unpublished lectures at the Ampere International Summer School II, Basko polje, Yugoslavia. W.P.Aue, E. Bartholdi and R.R.Ernst. (1976). J. Chem. Phys. 64, 2229 J.Jeener, B.H.Meier, P.Bachmann and R.R.Ernst. (1979). J.Chem.Phys. 71, 4546. G.A.Morris and R.Freeman. (1979) J.Am.Chem.Soc. 101, 760. U.Piantini, O.W.Sorensen and R.R.Ernst. (1982). J.Am.Chem.Soc. 104, 6800. K.Wuthrich, G.Wagner, G. Wider and W.Braun. (1982). J.Mol.Biol. 155, 311.