Chemical shift pseudo-forces

Molecular force fields and chemical shift pseudo-forces 75... 

Fig. 10. The three best COSMOS-NMR force field results of a peptide-zinc complex obtained with NOE as well as chemical shift pseudo-forces. Zn-X bonds are shown if the distance is shorter than 2.5 A. The force field search for the most stable complex was run with a free Ziv ion.

These calculations demonstrate that it is possible to obtain highly refined structures using chemical shift pseudo-forces. The resulting differences between measured and calculated BPT chemical shifts are in the range of the experimental error. BPT pseudo-forces are in the same range as electrostatic interactions, and they act on all atoms that contribute to the chemical shift of a site. 

In geometry optimizations or molecular dynamics calculations the NMR data are used as target functions, by defining proper pseudo-energies as a function of measurements and calculated data. From these energies forces have to be derived that are used to drive the system into the desired direction. In the case of chemical shifts these pseudo-energies depend on the calculated values, hence we need to calculate the derivatives of the chemical shifts with respect to the molecular coordinates. 

These forces which drive the system under investigation into the direction of the minimum pseudo-energy contain derivatives of the theoretical chemical shifts with respect to the coordinates. As pointed out in Section 5, the calculation of chemical shift derivatives is even more time consuming than the calculation of the chemical shifts itself. The calculations should be performed at least on the same theoretical level as the chemical shifts. If theoretical or empirical chemical shift contour maps have been worked out in advance, their derivatives can be calculated numerically. If the contour maps are constructed as a function of the dihedral angles (see Sections 6.3-6.4), only the forces with respect to these inner coordinates are readily obtained. 

To predict proton chemical shifts, methods had been developed using theoretically derived formulae with an empirical parametrization (see Section 4.6). Despite the relatively large scatter of the predictions when plotted versus the experimental values, it was found that the deviations were reduced when calculating the shifts from better refined structures. Proton chemical shifts were thus included as target functions into force field calculations. Kuszewski et included a harmonic pseudo-energy term into XI LOR. " The ll... 

For the chemical shift it turns out that it can be expressed in terms of the atomic polarization energy. Expanding it with respect to the chemical shift tensor around the experimental value and taking the gradient, the BPT pseudo-force can be deduced... 

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