Shift Derivatives

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. 

There is also an immediate interest in coordinate derivatives of chemical shifts in situations where temperature effects, isotope chemical shifts, vibrational or rotational corrections are investigated. For these purposes chemical shielding hyper-surfaces have been calculated using ab initio methods (for a discussion see Jameson, Bennett and Raynes, Raynes and Bennett, Chesnut and Wright, de Dios et Sundholm et Sundholm and Gauss,and Auer et and the slope with respect to any internal 

For polyatomic molecules the computational burden grows rapidly, since for every combination of internal coordinates a single point calculation has to be performed. Moreover, there are two other problems (i) the ab initio calculations have to be performed for non-equilibrium states, and (ii) strong environmental influences on the chemical shifts will change the hyper-surfaces so that only weakly interacting molecules can be discussed on the basis of a hyper-surface of a single molecule. Therefore, it would be much more desirable to calculate the analytical shift derivatives directly. 

In proteins the main influence on the C and chemical shifts is exerted by the type of amino acid and the backbone dihedral angles (, V ). In this case it is possible to limit the calculation of the derivatives to these relevant effects. 

A special case occurs for macroscopically oriented samples, when the change of the shift along the field direction is monitored as a function of the sample tilt angle  

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Is as follows Apply the Pt-Pt phase shift (derived from Pt metal) to the 1st forward transform of Pt02 This will partially smear the Pt-0 peak. Then take the back transform of this smeared Pt-0 peak. Extract a new phase shift from this back transform using the known Pt-0 distance, 2.07 X. This phase shift can now be used on the catalysts to focus the Pt-0 peak region. 

Isomer Shift Derived from NFS (Including a Reference Scatterer)... 

In order to analyze these data, the frequency shift of geffectivecan be calculated by averaging over all orientations the anisotropic shift derived from a static spin Hamiltonian [67]. This treatment is based on the assumptions that molecular motion neither changes the spin precession rate nor perturbs the states and, thus, that the center of gravity of the spectrum is invariant even in presence of some motional averaging. For the allowed 11/2) <-> <-l/2 transition under perturbation theory, with expressions valid up to the third order, this shift is given by [47] ... 

Similarity Translation (shift) Derivative Symmetry Complex conjugate... 

Nieuwpoort, W. C., D. Post, and P. Th. van Duijnen (1978). Calibration constant for Fe Mdssbauer isomer shifts derived from ab initio self-consistent-field calculations on octahedral FeFj, and Fe(CN)s clusters. Phys. Rev. B17, 91-98. 

Most double resonance measurements of proton shifts have been homonuclear studies of hidden and unresolved lines (e.g. refs. 107 and 366). However, in NMR, measurements of proton shifts using the correlation of C and spectra by off-resonance decoupling is common. While the aim is usually to assign the signals, it can also be to assign proton signals, as in the case of the N-methylene protons of amides (367) and the methyl signals of valine. (368) H shifts derived from similar experiments can be used as trial parameters for the iterative analysis of complex H spectra this technique was demonstrated for [l,l,3- H3]indene. (369)... 

Measure and spectra processing (Spectrum module), this module applies different models, compares them and choose the most appropriate for the studied sample. Moreover, the module allows different spectrum calculation (spectrum shift, derivative, spectra addition, spectra subtraction),... 

Since analytical expressions for the simple one center integrals in Eq. (45) have been worked out, their derivatives can be obtained in a straightforward manner. As for the chemical shift, when the charges are known the computational cost of the chemical shift derivative calculation is proportional to N. Most time consuming is the charge calculation which goes with N. ... 

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. 

PZC was found to be linearly correlated with DO + DM, where DO and DM are oxygen and metal chemical shifts derived from XPS specira of metal oxides [825,3097]. The following correlation was found in [3071] ... 

The coupling of the unpaired electrons with the nucleus being observed generally results in a shift in resonance frequency that is referred to as a hyperfine isotropic or simply isotropic shift. This shift is usually dissected into two principal components. One, the hyperfine contact, Fermi contact or contact shift derives from a transfer of spin density from the unpaired electrons to the nucleus being observed. The other, the dipolar or pseudocontact shift, derives from a classical dipole-dipole interaction between the electron magnetic moment and the nuclear magnetic moment and is geometry dependent. 

The formulae for the level shifts derived from the relativistic calculations are given on p. 50. They are taken from Bethe, Brown and Stehn [8] where the computation of the average excitation energy for the 22S level in hydrogen is to be found. Calculations of the average excitation energy ir0, for the levels Is to 4p inclusive have been made by Harriman [56]. As anticipated (p. 47). these quantities are not very sensitive to n. 

The constitution is often desired, however, for all non-repetitive biomolecules or synthetic compounds although, for the latter, the chemist mostly has some preknowledge about the compound in question. HSQC [29], COSY [7], TOCSY [9], and HMBC [31] experiments are the experiments of choice for such molecules. They reflect the connectivities of atoms in the molecule from which the constitution can be derived. With correlation spectra as discussed in Sect. 2.2, connectivity information is obtained. With an intelligent structure builder like Cocon [53], an especially powerful program, that takes the connectivity information and the rules of bonding between atoms into account, all constitutions that are in agreement with the provided correlation data are proposed. These are frequently more than one. Chemical-shift information can be used in addition to single out the most probable constitution. To use chemical shift information, data bases, ab initio calculations, or neuronal networks are available. As an example, the ascididemin constitution has been derived from connectivity information as well as with chemical shifts derived from neuronal networks Fig. 22) [25]. 

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