Electric field gradient principles

The dependence of the dipolar couplings on the orientation of the internuclear vector in the principle axis system of the electric field gradient has Inherent information about the molecular geometry of the relevant and sites. For example, in a peptide bond, where two carbons are bound to the same nitrogen, the dipolar coupling of each depends on the orientation of its respective internuclear vector with respect to the common coordinate system of the nitrogen electric field gradient principle axis system. Thus, the NMR spectrum is analyzed in terms of the relative orientation of the internuclear vectors, In principle, this can lead to an independent determination of the conformation of the peptide bond. 

P. Blaha, K. Schwarz and P. Herzig, First-principles calculation of electric field gradient of LisN. Phys. Rev. Lett., 1985, 54,1192-1195. 

Although 1 is one of the best investigated molecules, there is, apart from data concerning its electron density distribution, very little information available on its one-electron properties. In principle, accurate data could be obtained by correlation-corrected ab initio methods, but almost nothing has been done in this direction, which of course has to do with the fact that experimental data on one-electron properties of 1 are also rare, and therefore, it is difficult to assess the accuracy and usefulness of calculated one-electron properties such as higher multipole moments, electric field gradients, etc. 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

Further evidence for pi bonding is provided by the temperature coefficients of the resonance frequencies of these complex ions (see Table 6). The temperature coefficient is normally expected to be negative because of the decrease in the effective electric field gradient with increasing molecular bending vibrations (36,68, 69). Stretching vibrations do not reduce the principle electric field gradient (70). From Table 6... 

Hartree-Fock-Roothaan methods have often been quite successful in the calculation of properties despite the fact that the variational principle upon which they are based ensures only the best total energy. In particular, other energetic properties such as force constants and charge-distribution properties such as electron-density distributions and electric-field gradients are well reproduced. 

For nuclei with /> 1, the quadrupole coupling constant is defined as the product of the nuclear quadruple moment eQ and the maximum principle value of electric field gradient tensor q. 

The magnitude of the electric field gradient tensor is determined in principle by several factors ... 

In principle, it should also be possible to add a semi-loced potential to the non-relativistic all-electron Hamiltonian to eirrive at a quasi-rela-tivistic all-electron method. One such suggestion has been made by Delley [76], but the resulting method has only been tested for valence properties, which could also have been obtained by valence-only methods. Effective core potential methods have the advantage of a reduced computational effort (compared to all-electron methods) and are a valuable tool as long as one is aware of the limited domain of valence-only methods. Properties for which density variations in the atomic core are important should not be calculated this way. Examples are the electric field gradient at the nucleus or the nuclear magnetic shielding. 

Figure 19.7 shows two different principles for measuring the protection level. The potential measurement level is obtained by measuring the actual potential on the structure relative to a reference electrode. The electrical field gradient measurements are the potential difference between two reference electrodes mounted with a constant distance. The first principle is the most frequently used, and Figures 19.8 through 19.11 show pictures of different methods that are used for measuring potential level. 

FIGURE 19.7 Principle of potential measurements and electrical field gradient measurements [5]. 

It is worth noting that the linewidth of this resonance decreases with increasing Tc This behavior is in sharp contrast to the situation described by Eq. (2) and to the dipolar relaxation process, where the linewidth increases with increasing VqTc. From the field dependence of the chemical shift and linewidth described in Eqs. (3) and (4), the values of 7 and for spin 5/2 nuclei in the slow motion limit can be obtained. As the parameter % provides a measure of the coupling between the nuclear quadrupole and the electric field gradient at the nucleus, it reflects the symmetry of the local environment of the nucleus and thus can give information on the nature of the colloidal species, ic is a measure of the mobility of the species involved and, in principle, can provide information on the magnitude of the particle size when Eq. (1) is used. 

---