NMR spectroscopy: Difference between revisions

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(→‎NMR spectroscopy: Observable parameters: introduce 'shielding' def)
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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 nuclear spin magnetic moment is  proportional to the nuclear spin angular momentum and the constant of proportionality is known as the magnetogyric ratio. The magnetogyric ratio may be either positive or negative. Therefore, the nuclear spin magnetic moment vector is either parallel or antiparallel to the nuclear spin angular momentum vector.
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 nuclear spin magnetic moment is  proportional to the nuclear spin angular momentum and the constant of proportionality is known as the magnetogyric ratio. The magnetogyric ratio may be either positive or negative. Therefore, the nuclear spin magnetic moment vector is either parallel or antiparallel to the nuclear spin angular momentum vector.
:<math> \scriptstyle
B_{induced} = - \sigma B_{applied}
B_{net} = B_{applied} + B_{induced}
</math>
where <math>\scriptstyle \sigma </math> is a tensor; however for molecules rotating rapidly in all directions, such as molecules in a gas, liquid or solutions, <math> \sigma </math> can be approximated by a scalar and is known as the shielding constant


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 a 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.    Electromagnetic radiation can efficiently cause transitions between the nuclear spin states if the frequency of the electromagnetic radiation, ν,  is equal to the energy difference &Delta;''E'' between the nuclear spin states divided by Planck's constant ''h''.   
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 a 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.    Electromagnetic radiation can efficiently cause transitions between the nuclear spin states if the frequency of the electromagnetic radiation, ν,  is equal to the energy difference &Delta;''E'' between the nuclear spin states divided by Planck's constant ''h''.   
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== NMR spectroscopy: Observable parameters ==
== NMR spectroscopy: Observable parameters ==
    
    
'''The Chemical shift'''<ref> W.G. Proctor, F.C. Yu  (1950) Phys.Rev. 77, 717. </ref><ref>N.F.Ramsey. (1950) Phys. Rev. 78, 699.</ref><ref>N.F.Ramsey. (1952) Phys. Rev. 86, 243. </ref>:  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.  This effect is called 'shielding', because the magnetic field induced by the circulation of charge is in opposite direction to field  (external) that was responsible for the circulation of charge. Therefore, the nuclei in a given molecule are subjected to a net magnetic field which is the sum of the applied magnetic field and the induced magnetic field.  The electron density as well as polarizability vary substantially depending upon the nature of the molecule, and the location of the nuclei within the molecule.  As a consequence, for a given value of the applied field, nuclei in different molecules and even nuclei in different parts of the same molecule may encounter different net values of  magnetic field - this results in a variations in the resonance frequency (because the resonance frequency is proportional to the magnetic field at the location of the nucleus).
'''The Chemical shift'''<ref> W.G. Proctor, F.C. Yu  (1950) Phys.Rev. 77, 717. </ref><ref>N.F.Ramsey. (1950) Phys. Rev. 78, 699.</ref><ref>N.F.Ramsey. (1952) Phys. Rev. 86, 243. </ref>:  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.  This effect is called 'shielding', because the magnetic field induced by the circulation of charge is in opposite direction to field  (external) that was responsible for the circulation of charge. Therefore, the nuclei in a given molecule are subjected to a net magnetic field which is the sum of the applied magnetic field and the induced magnetic field.   
 
The electron density as well as polarizability vary substantially depending upon the nature of the molecule, and the location of the nuclei within the molecule.  As a consequence, for a given value of the applied field, nuclei in different molecules and even nuclei in different parts of the same molecule may encounter different net values of  magnetic field - this results in a variation in the resonance frequency (because the resonance frequency is proportional to the magnetic field at the location of the nucleus).
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 for identification of functional groups in molecules.
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 for identification of functional groups in molecules.


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Nuclear Magnetic Resonance Spectroscopy[1][2] [3](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; it may also be used to obtain information regarding interactions between nuclear spins, to obtain information regarding interaction of the nuclear spins with their environment (lattice), to determine molecular structure, to obtain information regarding intermolecular interactions and to obtain information regarding motion and internal molecular dynamics.

Principles of Nuclear Magnetic resonance

Nuclear magnetic resonance is a consequence of a property possessed by the nucleus known as nuclear spin angular momentum. Some properties associated with nuclear spin angular momentum are similar to those of a spinning macroscopic body, however, 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—like the angular momentum of any other fundamental particle —is a quantized vectorial quantity[4]. 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. For a detailed list see http://en.citizendium.org/wiki/NMR_active_elements.

The nuclear spin angular momentum is characterized by a quantum number I known as the nuclear spin angular momentum quantum number (often briefly referred to as "nuclear 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 with quantum number I is,

where is Planck's reduced constant.

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 mh/(2π), 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.

For example,

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 nuclear spin magnetic moment is proportional to the nuclear spin angular momentum and the constant of proportionality is known as the magnetogyric ratio. The magnetogyric ratio may be either positive or negative. Therefore, the nuclear spin magnetic moment vector is either parallel or antiparallel to the nuclear spin angular momentum vector.

where is a tensor; however for molecules rotating rapidly in all directions, such as molecules in a gas, liquid or solutions, can be approximated by a scalar and is known as the shielding constant

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 a 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. Electromagnetic radiation can efficiently cause transitions between the nuclear spin states if the frequency of the electromagnetic radiation, ν, is equal to the energy difference ΔE between the nuclear spin states divided by Planck's constant h.

NMR spectroscopy: Observable parameters

The Chemical shift[5][6][7]: 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. This effect is called 'shielding', because the magnetic field induced by the circulation of charge is in opposite direction to field (external) that was responsible for the circulation of charge. Therefore, the nuclei in a given molecule are subjected to a net magnetic field which is the sum of the applied magnetic field and the induced magnetic field.

The electron density as well as polarizability vary substantially depending upon the nature of the molecule, and the location of the nuclei within the molecule. As a consequence, for a given value of the applied field, nuclei in different molecules and even nuclei in different parts of the same molecule may encounter different net values of magnetic field - this results in a variation in the resonance frequency (because the resonance frequency is proportional to the magnetic field at the location of the nucleus). 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 for 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 (Ramsey[8], Karplus[9]): J-coupling is due to the interaction between different nuclei in the same molecule that is mediated through electrons in chemical bonds. Usually, the J-coupling interaction is observable between nuclei that are separated from each other by three or fewer bonds. 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-coupling 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. In addition, the magnitude of the coupling constant provides information regarding the conformation of a molecule.

Relaxation time (Bloembergen[10]; Bloch [11]; Solomon[12]): 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. If this process is exponential, the rate constant 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. Similarly, T2 relaxation time characterizes the return to equilibrium of the transverse component of the magnetization of the collection of nuclei that are being studied. In a static homogeneous magnetic field, the transverse component of the net magnetization vector for a sufficiently large collection of nuclei is always zero, at equilibrium.

FTNMR and Multidimensional NMR

FTNMR: Fourier transform NMR spectroscopy (Ernst [13][14]) : 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.

Multidimensional NMR spectroscopy (Jeener [15]; Aue et al.[16]): The nuclei in a magnetic field are subjected to a series of pulses of electromagnetic radiation 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 (2D, 3D and 4D): COSY, NOESY, TOCSY, EXSY, HSQC, HNHA, HSQC-NOESY, HNCA, HNCO, HNCACO, HSQC-NOESY-HSQC. For a longer list of NMR experiments see http://en.citizendium.org/wiki/List_of_Nuclear_Magnetic_Resonance_experiments

Two dimensional correlation spectroscopy [17] [18](2D-COSY): Correlates chemical shifts of J-coupled nuclei.

Two dimensional nuclear overhauser effect spectroscopy[19] (2D-NOESY): correlates chemical shifts of nuclei that exhibit significant Nuclear Overhauser effect[20]. For molecules that experience free rotation along all three dimensions, the Nuclear Overhauser effect is generally observable between nuclei that are less than 5 angstroms apart.


Biomolecular NMR spectroscopy

NMR spectroscopy can be used to determine the structure of macromolecules[21] and to obtain information regarding their dynamics[22]. However, the NMR spectra of macromolecules are 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. The Sequential resonance assignment method was developed in order to associate specific nuclei in a protein with the observed resonance frequencies[23]. [24]Subsequently, the information obtained from quantitative and qualitative analysis of Nuclear Overhauser effects, J-coupling[25] and chemical shifts is converted into geometric restraints. These geometric restraints are then subsequently used to build a model of the molecule[26][27].

Applications of Magnetic resonance in Pharmacology, Physiology and Medicine

NMR spectroscopy is a useful tool in drug design and development. It is used to determine the structure of ligands and receptors; to study the interactions of ligands with receptors, even when the binding is weak and transient; and to build structure activity relationships.[28].

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[29][30] [31][32] (MRI) a tool that has found extensive applications in medical diagnostics.


Applications of Magnetic Resonance in Food technology[33]

Magnetic resonance has been used in studies of alcoholic beverages and to monitor the cheese production process.


Further reading

Fundamentals of Physics. Holliday, Resnick and Walker.

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.

Principles of Magnetic Resonance (1996) Charles P. Slichter. Springer Series in Solid-State Sciences.

Protein NMR spectroscopy: Principles and Practice. (2006) J.Cavanagh, W.J. Fairbrother, A6G. Palmer, N.J. Skelton, M.Rance. Academic Press.

Understanding NMR spectroscopy. (2005) J.Keeler. Wiley

Spectrometric Identification of Organic Compounds. (2005) Robert M. Silverstein, Francis X. Webster, and David Kiemle.

NMR in Drug Design. David J. Craik. (1995). Crc Series in Analytical Biotechnology.


References

  1. ↑ I. I. Rabi.(1937) Phys. Rev., 51 652
  2. ↑ N. Bloembergen, E. Purcell and R.V.Pound. (1948). Phys. Rev. 73, 679.
  3. ↑ F. Bloch, W. Hansen, and M.E. Packard, (1946) Phys. Rev. 69, 127.
  4. ↑ W. Gerlach and O. Stern. (1922) Zeit. f. Physik 9, 349
  5. ↑ W.G. Proctor, F.C. Yu (1950) Phys.Rev. 77, 717.
  6. ↑ N.F.Ramsey. (1950) Phys. Rev. 78, 699.
  7. ↑ N.F.Ramsey. (1952) Phys. Rev. 86, 243.
  8. ↑ N.F.Ramsey. (1953) Phys. Rev. 91, 303.
  9. ↑ M.Karplus (1963). J.Am.Chem.Soc. 30, 11.
  10. ↑ N. Bloembergen, E. Purcell and R.V.Pound. (1948). Phys. Rev. 73, 679.
  11. ↑ F. Bloch, W. Hansen, and M.E. Packard, (1946) Phys. Rev. 69, 127.
  12. ↑ I. Solomon. (1955). Phys. Rev. 99, 559.
  13. ↑ R.R.Ernst, Nobel lecture
  14. ↑ R.R. Ernst and W.A. Anderson, (1966) Rev. Sci. Instrum. 37, 93
  15. ↑ J. Jeener. (1971). Unpublished lectures at the Ampere International Summer School II, Basko polje, Yugoslavia.
  16. ↑ W.P.Aue, E. Bartholdi and R.R.Ernst. (1976). J. Chem. Phys. 64, 2229.)
  17. ↑ W.P.Aue, E. Bartholdi and R.R.Ernst. (1976). J. Chem. Phys. 64, 2229.)
  18. ↑ U.Piantini, O.W.Sorensen and R.R.Ernst. (1982). J.Am.Chem.Soc. 104, 6800.
  19. ↑ J.Jeener, B.H.Meier, P.Bachmann and R.R.Ernst. (1979). J.Chem.Phys. 71, 4546.
  20. ↑ A.W.Overhauser. (1953). Phys. Rev. 92, 411.
  21. ↑ K. Wüthrich, NMR of Proteins and Nucleic Acids, Wiley Interscience, New York, 1986.
  22. ↑ Z.L. Mádi, C. Griesinger, and R.R. Ernst, J. Am. Chem. Soc. 112, 2908 (1990).
  23. ↑ A. Dubs, G. Wagner and K. Wüthrich. (1979) Biochim. Biophys. Acta 577, 177.
  24. ↑ G. Wagner and K. Wüthrich (1982) J. Mol. Biol. 155, 347
  25. ↑ A. Pardi, M. Billeter and K. Wüthrich. (1984) J. Mol. Biol. 180, 741
  26. ↑ W. Braun, C. Bösch, L.R. Brown, N. Go¯ and K. Wüthrich (1981) Biochim. Biophys. Acta 667, 377
  27. ↑ Havel, T.F. and Wüthrich, K. (1984) Bull. Math. Biol. 46, 673
  28. ↑ S.B.Shuker, P.J.Hajduk, R.P.Meadows and S.W.Fesik (1996) Science 274, 1531
  29. ↑ P.C. Lauterbur, (1973) Nature 242, 190
  30. ↑ Anil Kumar, D. Welti, and R.R. Ernst, (1975) J. Magn. Reson. 18, 69 .
  31. ↑ W.A. Edelstein, J.M.S. Hutchison, G. Johnson, and T.W. Redpath, (1980) Phys. Med. Biol. 25, 751.
  32. ↑ P. Mansfield, A.A. Maudsley, and T. Baines, J. Phys. E9, 271 (1976).
  33. ↑ I. Farhat,P. Webb , G. Belton. Editors, Magnetic Resonance in Food Science: From Molecules to Man. Royal Society of Chemistry (RCS) 2007.
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