Nuclear magnetic shielding contributions

Medium effects include that of bulk susceptibility, which depends on the geometry of the sample and the composition of the solution. For a perfectly spherical sample, the nuclear magnetic shielding contribution a of the bulk susceptibility is zero. For other shapes a susceptibility correction is needed because of polarization of the sample near the liquid surface. For an infinitely long cylinder, oriented with the cylindrical axis perpendicular to the direction of the magnetic field as in an electromagnet, the frequency shift due to bulk susceptibility of a pure solvent (as for a molecule observed in infinite dilution) is related to the molecular magnetic susceptibility x, or the volume susceptibility Xv of the solvent by... 

The third-rank diamagnetic and paramagnetic contributions to electric field dependent magnetic susceptibility and nuclear magnetic shielding, to first order in... 

Theoretical bases of continuum models including their mathematical formulation and numerical implementation have already been discussed in the previous chapter of this book. We have therefore restricted our review to the environment effects on the NMR observables, without going into the theory of continuum models. This contribution is divided into five sections. After the Introduction, the definitions of the NMR parameters are recalled in the second section. The third section is focused on methodological aspects of the calculation of the NMR parameters in continuum models. The fourth section reviews calculations of the solvent effects on the nuclear magnetic shielding constants and spin-spin coupling constants by means of continuum models, and the final section presents a survey on the perspectives of this field. 

Table 15. Diamagnetic and paramagnetic contributions, (r and to the germanium nuclear magnetic shielding constants (rand their analyses into core and valence MO contributions (in ppm)... 

Calculated Rovibrational Contributions, Temperature Corrections, and Nuclear Magnetic Shielding Constants at 300 K [<7(300 K)] in Comparison with Corresponding Shielding Constants Derived from Experimental Spin-Rotation Constants" ... 

Even though the contributions to the absolute value of the nuclear magnetic shielding of the heavy nucleus are very large, they are almost insensitive to the change in chemical environment from HX to CH3X. 

It is possible to visualize flow of current directly from calculations of the induced current density for the molecule in an external magnetic field, from which accurate values of magnetizability of the molecule and nuclear magnetic shielding of selected nuclei may be calculated by integration. Contributions to the integral properties can be analyzed using property densities, such as the... 

In the spirit of the Geertsen method. Smith et al. [26] proposed a sum-over-state expression for the diamagnetic contribution to the nuclear magnetic shielding tensor. They used the commutator... 

The change in the 11 contributions to the nuclear magnetic shieldings in the translation (61) of the origin of the coordinate system is... 

In the same way, the contribution of the nuclear magnetic shielding tensor to the energy can be obtained. The final expression for the energy of a polarizable charge and current distribution in the presence of a magnetic induction B and M nuclear magnetic moments, m then reads (Lazzeretti, 1989)... 

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