Theory of NMR

All nuclei that have an odd atomic number (number of protons) or odd mass number (protons + neutrons) possess a permanent magnetic dipole moment, and therefore behave like tiny bar magnets. This is because such neuclei are not perfect spheres, but are either oblate or prolate spheroids. When placed in a magnetic field, such nuclei absorb electromagnetic radiation in the radio-frequency (RF) region of the spectrum. The exact frequency depends upon various factors, but of critical importance to the chemist is the fact that this frequency (known as the frequency of resonance) varies with the chemical environment of the nucleus, and hence each nucleus in a molecule gives a characteristic signal. NMR therefore allows us to see the individual atoms that molecules are made of, and hence, to determine molecular structure. 

What atoms can we see by NMR It will be quite clear from the above definition that the nuclei of certain commonly occurring isotopes are not NMR active, e.g., For the case of carbon and oxygen, this 

In conclusion, and are the only two nuclei that are routinely used in the analysis of surfactant molecules by NMR. 

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I. Ando, G. A. Webb, Theory of NMR Parameters Academic Press, London (1983). 

A Reinvestigation of Ramsey s Theory of NMR Coupiing Let us define a transformed Hamiltonian as h. 

In the presence of both order-disorder and displacive, as in the KDP family, the two dynamic concepts have somehow to be merged. It could well be that the damping constant Zs becomes somewhat critical too (at least in the over-damped regime of the soft mode), because of the bihnear coupling of r/ and p. It would, however, lead too far to discuss this here in more detail. The corresponding theory of NMR spin-lattice relaxation for the phase transitions in the KDP family has been worked out by Blinc et al. [19]. Calculation of the spectral density is here based on a collective coordinate representation of the hydrogen bond fluctuations connected with a soft lattice mode. Excellent and comprehensive reviews of the theoretical concepts, as well as of the experimental verifications can be found in [20,21]. 

In a recent study (2(ia) Dreitlein and Kessemeicr developed more completely the theory of NMR absorption by a mechanically rotating solid. 

It is interesting to note that recently Pyykko published a short paper entitled Perspective on Norman Ramsey s theories of NMR chemical shifts and nuclear spin-spin couplings , where a concise and interesting account of the early development of the theory of high resolution NMR parameters is given.23... 

For these NMR experiments, the general theory of NMR must be understood and, on top of this, the theory of the electron-nucleus interaction and its consequences for the NMR parameters. Therefore, the field of NMR of paramagnetic molecules has its own niche in the entire scientific panorama. 

Ando,I. Webb,G. A. Theory of NMR Parameters, Academic Press, New York, NY, 1983. 

We shall shortly consider such fundamental concepts as density matrices and the superoperator formalism which are convenient to use in a formulation of the lineshape theory of NMR spectra. The general equation of motion for the density matrix of a non-exchanging spin system is formulated in the laboratory (non-rotating) reference frame. The lineshape of a steady-state, unsaturated spectrum is given as the Fourier transform of the free induction decay after a strong radiofrequency pulse. The equations provide a starting point for the formulation of the theory of dynamic NMR spectra presented in Section III. The reader who may be interested in a more detailed consideration of the problems is referred to the fundamental works of Abragam and... 

Practical applications of the theory of NMR lineshapes of dynamic spectra can be divided into two general groups. One concerns investigations of intra- and inter-molecular reaction mechanisms. The other deals with the determination of kinetic and thermodynamic parameters for equilibria. In the former case the verification of reaction mechanisms usually consists of qualitative comparisons between experimental spectra and those simulated for various values of the rate constants using either visual inspection or visual fitting. 

With the advances in experimental solid-state NMR and computational resources (both software and computing power), it is now possible to use both the experimental and computational results (sometimes in a complementary way) to study biologically important macromolecules such as proteins. The quantum-chemical computation (particularly by density functional theory) of NMR parameters in solids has found important application in protein structure determination.30-36 Tesche and Haeberlen37 calculated the proton chemical shift tensor of the methyl groups in dimethyl terephthalate and found the theoretical results were in good agreement with the multiple pulse experiment. 

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