Shielding chemical

This equation splits the contributions related to chemical shielding and susceptibility effects. This distinction is somewhat arbitrary as they are both a result of the response 

The orientational dependence is present in the chemical shielding tensor which in its principal axis system (PAS) is diagonal with principal components axx, o yy and ctzz-In a crystalline powder sample all orientations of the PAS system of the shielding tensor are present and for most orientations the PAS does not coincide with the laboratory (LAB) frame where the z-axis is aligned with the direction of the applied magnetic field Bq. Hence the tensor representation gives in the PAS 

The tensor components are distinguished by capital subscripts in the PAS and lower case subscripts in the laboratory frame. The two frames are related by rotation of the axes using matrices with the Euler angles defining the rotation to give 

Then the field at the nucleus, including both the main field and the shielding, gives 

It is only the zz-component that is of interest since after this transformation this is the component that is aligned with Bq, CTxz and cjyz make only second-order contributions. Hence the Hamiltonian representing the chemical shielding is now given by 

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Chemical shielding G So 102-10 Alteration of the magnetic field by the electrons... 

Champmartin D and Rubini P 1996 Determination of the 0-17 quadrupolar coupling constant and of the C-13 chemical shielding tensor anisotropy of the CO groups of pentane-2,4-dione and beta-diketonate complexes in solution. NMR relaxation study/norg. Chem. 35 179-83... 

However, because of chemical shielding anisotropy (CSA) and quadnipolar and dipolar effects, the Lamior... 

Kaupp, M., Malkina, O. L., Malkin, V. G., 1997, The Calculation of 170 Chemical Shielding in Transition Metal Oxo Complexes. I. Comparison of DFT and Ah Initio Approaches, and Mechanisms of Relativity-Induced Shielding , J. Chem. Phys., 106, 9201. 

The difference in resonance NMR frequency of a chemically shielded nucleus measured relative to that of a suitable reference compound is termed chemical shift [164,165], and is a measure of the immediate electromagnetic environment of a nucleus. While the chemical shift depends on the Bo field, J does not. Chemical shifts, which cover a range of about 10 ppm for protons (i.e. 600 Hz in case of a 14.1 kG magnetic field) and 250 ppm for 13C, are the substance of NMR. 

Several calculations of the chemical shielding tensor have been carried out by different methods for simple model disilenes. For H2Si=SiH2, calculated values of 300,44 291,43 and 195 ppm46 have been obtained for Act, the CSA spread. A value of 255 ppm has been calculated for Me2 Si=SiMe2,46 and a value of 120 ppm was obtained for (CH2=CH)2Si=Si... 

Chesnut, D. B., and C. G. Phung. 1991. Ab Initio Determination of Chemical Shielding in a Model Dipeptide. Chem. Phys. Letters 183, 505-509. 

Csaszar, A. G. 1992. Conformers of Gaseous Glycine, J. Am. Chem. Soc. 114,9568-9575. de Dios, A. C., J. G. Pearson, and E. Oldfield. 1993. Chemical Shifts in Proteins An Ab Initio Study of Carbon-13 Nuclear Magnetic Resonance Chemical Shielding in Glycine, Alanine, and Valine Residues, J. Am. Chem. Soc. 115, 9768-9773. 

Fundamental constants (Cx), spatial tensors in the principal axis frame ((fi3 m,)F), and spin tensors (Tjm) for chemical shielding (a), J coupling (J), dipole-dipole (IS), and quadrupolar coupling (Q) nuclear spin interactions (for more detailed definition of symbols refer to [50])... 

Theoretical calculation of NMR chemical shifts is usually done by first considering the electronic current density which is induced by the external magnetic field. Once this current has been calculated the chemical shift can be obtained by application of the Biot-Savard law, which describes the magnetic field created by it. The strength of this field at the position of an atom represents the NMR chemical shielding of this atom. 

Under the assumption that the induced field is much smaller than the external one, and that the latter is still small on the atomic energy scale, the induced field will be proportional to the external field. Both assumptions are valid for experimentally accessible field strenghts, i.e. up to more than 10 Tesla. The proportionality coefficient between them depends on the chosen position in space, and is called chemical shielding, commonly denoted by aafi(R) ... 

The chemical shieldings were then recalculated in this same system using the QM/MM method [10], To this end, each molecule was considered individually. The water molecule of interest and its first solvation shell were treated quantum mechanically, whereas the surrounding water molecules were taken into account with an empirical force field representation (MM molecules). The first solvation shell was defined via a distance criterion on the oxygen-oxygen distance. As a threshold, the first minimum of the O-O pair correlation function was taken this occurs at 3.5 A [93]. All... 

These QM/MM calculations are in contrast to a standard evaluation of chemical shielding for gas phase water clusters where the classical point charge environment is omitted entirely. The same solvation shell criterion as before was applied, and the system was treated purely quantum mechanically. 

Figure 1.4 shows a significant deviation between the isolated cluster calculations and the full calculation. The situation is, however, considerably improved by the presence of the classical point charges in the QM/MM calculation. Here the whole bandwidth of chemical shielding constants is present, and correlation with the reference values is excellent. 

This shows that the second and further solvation shells still have a non-negligible effect on NMR chemical shielding constants through the long-range electrical field they create. The approximation of an isolated molecular cluster in vacuo is valid for large clusters only this eventually makes determination of the shieldings of all protons computationally much more expensive than the fully periodic ab initio calculation. 

For a water molecule with its first solvation shell only, chemical shielding differs considerably from the complete ab initio calculation. Although this discrepancy is not completely removed by the inclusion of the electrical field of the remaining molecules through the QM/MM approach, it is strongly reduced. 

Facelli, J. C., Molecular Structure and Carbon-13 Chemical Shielding Tensors Obtained from Nuclear Magnetic Resonance, 19, 1. 

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