Ionic self energy

The electron gas model would give exact results if an exact density functional were used for the interaction energy, the ionic densities were fully variable so that any total density could be obtained by summing the ionic densities, and the calculation ofthe ionic self-energies were exact. In practice these conditions cannot be met and approximations must be used. 

The P3 approximation to the self-energy was applied to the atoms Li through Kr and to neutral and ionic molecular species from the G2 set [47]. For the atoms, a set of 22 representative basis sets was tested. Results for the molecular set were obtained using standard Pople basis sets as described below. 

For polar solvents like water, DMSO, or 100% sulfuric acid, D l is quite small compared to unity (Table 13.1) so the electrostatic self-energy of a gaseous ion is almost entirely eliminated on transferring the ion to a polar solvent. For an ionic compound to be freely soluble in a given solvent, the solvation energies of its anions and cations must outweigh the lattice energy sufficiently, otherwise an ionic solid results instead. Ionic solids are therefore not usually very soluble in solvents of low D. 

The first and second terms on the right are self-energies of the central ion and the ionic atmosphere, and the third contains the interaction energies of the central ion with its ionic cloud and vice versa. According to Green s reciprocal theorem, these energies are equal and are given by... 

In this section we shall particularly study the dynamic properties of a core hole in terms of its self-energy and spectral function15 19,23,27 32). This is a kind of model problem because one does not discuss by which physical mechanism the core hole is created. The hole is simply created in the system at a specific instant of time and destroyed at a later time. By studying the development of the core hole during this interval one gets a picture of how the core level strength becomes distributed over the various possible levels of the ionic system. Nevertheless, since the creation of the core hole is sudden, the resulting spectral function is very closely connected to the X-ray photoelectron spectrum (XPS) as already briefly discussed in Sect. 2.2, Eq. (6). 

As discussed in Sect. 5, our approximation scheme for the self-energy 2j(E) is designed for a situation where the main ionic excitation strength lies in the continuum. However, from Fig. 2516 it is obvious that this situation is not at hand in Ba because the main ionic excitation strength (in this approximation) has become concentrated to the 4dav(4d 4f P) level. The approximation will then have to be improved in typically two ways ... 

Fig. 28a-h. 4 p self-energy diagrams in a case where a 4d24f ionic excited level dominates the excitation spectrum (see text and compare with Figs. 10, 17-19)... 

Im. Z i(E) can be considered as a product of an ionic excitation density of states and an energy-dependent coupling constant. In model calculations one can independently vary the shape and the band with of the denstiy of states and the strength of the coupling constant. In the present case we can only vary these parameters indirectly by changing the atomic number Z. Since the self-energy involves the polarizability of the ionic system there must be an oscillator-strength sum rule such that... 

From the previous discussion we have a reasonable idea about the positions of the nn excitations relative to the ionic ground state, and we now simply transfer this picture to the valence hole levels. Fig. 44 a shows a typical, schematic picture of the self-energy for... 

This tensor, in a lowest order calculation, is the familiar relativistic Lindhard-type function. The other self-energies appearing in the above equations expressed in terms of the functional Bj are in the functional scheme, whereas those expressed in terms of F have their origins in the -derivable scheme. In both formulations, the contributions due to electronic, ionic, and electromagnetic interactions are incorporated into the respective functionals mentioned above. A direct comparison of the two procedures should be illuminating to see how... 

Diffusion coefficients provide two kinds of information. First, their absolute magnitudes, combined with membrane sodium ion concentrations, are useful indicators of the temperature dependence of ionic self-diffusion and thereby they yield the activation energy for diffusion. They thereby provide insight into the nature of the diffusion mechanism (16). When activation energies are measured for various types of related membranes, the influence of different membrane structural design features can thus be separated and determined directly. 

---