Paramagnetic contributions

A common origin paramagnetic contribution can subsequently be obtained as the difference between the LORG total shielding tensor and the diamagnetic contribution from eq.(29), i.e. 

The data sets (above) with the large values of X are physical property measurements which presumably involve predominantly the pi electrons. For example, the F - and C -nmr shifts are dominated by paramagnetic contributions resulting from unbalanced pi orbitals (24). Ionization equilibria, on the other hand, are characterized by a much higher blend of polar effects (a blend which traditionally has been defined as X = 1.00 for the ionization of benzoic acid, H2O, 25 ). 

In addition to the standard constraints introduced previously, structural constraints obtainable from the effects of the paramagnetic center(s) on the NMR properties of the nuclei of the protein can be used (24, 103). In iron-sulfur proteins, both nuclear relaxation rates and hyperfine shifts can be employed for this purpose. The paramagnetic enhancement of nuclear relaxation rates [Eqs. (1) and (2)] depends on the sixth power of the nucleus-metal distance (note that this is analogous to the case of NOEs, where there is a dependence on the sixth power of the nucleus-nucleus distance). It is thus possible to estimate such distances from nuclear relaxation rate measurements, which can be converted into upper (and lower) distance limits. When there is more than one metal ion, the individual contributions of all metal ions must be summed up (101, 104-108). If all the metal ions are equivalent (as in reduced HiPIPs), the global paramagnetic contribution to the 7th nuclear relaxation rate is given by... 

This indicates that the deviations are due to systematic errors, for example deficiencies of the applied methods and basis sets. DFT-based methods, such as GIAO/DFT calculations are known to overestimate paramagnetic contributions to the chemical shielding. This results, for critical cases with small HOMO/LUMO separations, in overly deshielded competed chemical shifts. Notorious examples for these deficiencies are 29Si or 13C NMR chemical shift computations of silylenes, silylium ions or dienyl cation .(5/-54) Taking into account the deficiencies of the applied method, and bearing in mind very reasonable correlations shown in Figures 4 and 5, the computational results do support the structural characterization of the synthesized vinyl cations. 

The paramagnetic contribution again involves excited states... 

The paramagnetic contribution can be defined as the linear response function or polarization propagator [17]... 

The paramagnetic contribution can again be defined as a response function involving the terms linear in A. We write it as a sum of six terms... 

From this expression one can see now that the electronic contribution is related to the paramagnetic contribution to magnetizahility evaluated with the center... 

To this purpose, Fossheim et al. reported temperature sensitive liposomal Gd(III)-based probes (137-138). The composition of the liposomes was chosen in order to tune the temperature of transition between the gel-crystalline, where the liposome is water-impermeable, to the liquid-crystalline state, where water has free access to the interior of the liposome. This means that at temperatures below the transition, the relaxivity of the system is very low (paramagnetic contribution close to zero), whereas at higher temperature the Gd(III) complex ([GdDTPABMA(H20)] is the reference) is no longer silent... 

If the paramagnetic center is part of a solid matrix, the nature of the fluctuations in the electron nuclear dipolar coupling change, and the relaxation dispersion profile depends on the nature of the paramagnetic center and the trajectory of the nuclear spin in the vicinity of the paramagnetic center that is permitted by the spatial constraints of the matrix. The paramagnetic contribution to the relaxation equation rate constant may be generally written as... 

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