Inner repulsion energy

In the next section, the basic features of decomposition schemes for bond energies will be discussed. In particular, we wish to stress the importance of other interactions than the charge-transfer type HOMO-LUMO interactions commonly employed in frontier orbital considerations. Important contributions arise also from polarization of the interacting units, "especially in the highly polarizable metallic substrates, and from repulsive interaction with occupied (sub-)valence shells contributing to the steric repulsion. The latter interaction in fact determines the bond distances as it is responsible for the inner, repulsive, part of the potential energy curves. 

The total EH energy is taken as the sum of the one-electron energies. For methane, this is 2 X (-0.8519) + 6 x (-0.5487), or -4.9963 a.u. There is some ambiguity as to how this energy is to be interpreted. For instance, does it include any of the intemuclear repulsion energy Also, what problems will arise from our neglect of inner-shell... 

The total energy of repulsion between charge cloud 2 and electron 1 at r is the sum of inner and outer repulsive energies. But electron 1 is not always at r. Therefore, we must finally integrate over all positions of electron 1, weighted by the frequency of their occurrence ... 

Figure 4.8 Comparison of quantal, solid curve, vs. classical, dashed, calculation of l 9), on a logarithmic scale, for the same realistic potential at the same collision energy. The classical differential cross-section diverges at e = 0 and at the rainbow angle while the oscillatory quantal cross-section is everywhere finite. In the backward direction, where there is only one classical trajectory, there is close agreement between the classical and quantal results. The backward scattering results from low b collisions, and these sample the inner repulsive core of the potential. The backward angular distribution is therefore hard-sphere-like, see Eq. (4.11).

The conformation of an isolated polyelectrolyte chain can be envisaged as a stretched object set up of coiled subunits. A coiled subunit forms for a sequence of n monomeric units for which the electrostatic energy arising from the inner repulsive forces, / , equals the thermal energy, i.e.,... 

Electron-electron repulsion integrals, 28 Electrons bonding, 14, 18-19 electron-electron repulsion, 8 inner-shell core, 4 ionization energy of, 10 localization of, 16 polarization of, 75 Schroedinger equation for, 2 triplet spin states, 15-16 valence, core-valence separation, 4 wave functions of, 4,15-16 Electrostatic fields, of proteins, 122 Electrostatic interactions, 13, 87 in enzymatic reactions, 209-211,225-228 in lysozyme, 158-161,167-169 in metalloenzymes, 200-207 in proteins ... 

The surface molecule model has been used to study chemisorption of hydrogen 47) and nitrogen 48) on tungsten (100). The parameters used in these calculations are collected in Table IV. Preliminary calculations on the diatomic molecules WH and WW showed that inclusion of tungsten 5 p orbitals is essential to produce a minimum in the energy/ distance curves. However, the repulsion due to inner electrons could be calculated by the empirical relationship ... 

We discuss briefly the factors that determine the intensity of the scattered ions. During collision, a low energy ion does not penetrate the target atom as deeply as in RBS. As a consequence, the ion feels the attenuated repulsion by the positive nucleus of the target atom, because the electrons screen it. In fact, in a head-on collision with Cu, a He+ ion would need to have about 100 keV energy to penetrate within the inner electron shell (the K or Is shell). An approximately correct potential for the interaction is the following modified Coulomb potential [lj ... 

---