Contributions to the total electronic energy

Equation (A.22) is the energy of a single electron with spatial distribution given by the . Equation (A.21) is the total one-electron contribution to the total electronic energy. 

They are often taken directly as transitions between atomic or molecular orbitals (or band levels, in solids). This is an approximation because it ignores changes in the remaining contributions to the total electronic energy. In particular, it assumes that the remaioing orbitals are not affected in the process. 

As a consequence of these results, most of the individual integrals in the expansion will be zero. Nevertheless, it can be readily envisaged that there will still be an extremely large number of integrals to consider for all except the smallest problems. It is thus more convenient to write the energy expression in a concise form that recognises the three types of interaction that contribute to the total electronic energy of the system. 

Table 15.13 The contributions to the total electronic energy per electron (noEh). The atomic and molecular systems have been listed in order of increasing magnitude of the Hartree—Fock energy per electrm. All energies have bear calculated at the cc-pcV6Z level...

The relative impiHtance of the different contributions to the total electronic energy is illustrated in Table 15.14. Except fra- H2, the Hartree-Fock energy constitutes more than 99% of the total energy... 

This potential includes an unphysical repulsive interaction between the electron and itself (because the electron contributes to the total electron density). The energy associated with this unphysical interaction is the selfinteraction energy. 

The thermal internal energy function calculated at 298.15 K [E — 0] is also listed in Table 8.1. The translational and rotational contributions are found using Eqs. 8.80 and 8.82, respectively. The vibrational contributions (Eq. 8.84) are much less, as expected. Mode 2 makes a significant contribution to the total internal energy at this temperature. Vibrational modes 5 and 6 also make smaller, but nonnegligible, contributions. The electronic contribution was calculated directly from Eq. 8.76. Through application of Eq. 8.118, the total enthalpy is [H — Ho] - 11146.71 J/mole. 

The intermolecular electron correlation (the dispersion interaction) was calculated or estimated for some cation-ligand interactions using configuration interaction (Cl) calculations, perturbation theory or on the basis of a statistical model (see Table 4). Its contribution to the total interaction energy is less than 10% throughout. 

For the atomization of KCl, six bonds per atom pair must be broken. Since only eight electrons are available, however, these six are equivalent to only four normal covalent bonds, or n = 4. The observed bond length, Ro, is 3.14 A., whereas the covalent radius sum, Rc, is 2.95 A. The dissociation energy of K2 is 13.2 and of CI2, 58.2 kcal. per mole. The geometric mean of these is the square root of 13.2 x 58.2, or 27.7. The covalent contribution to the total bonding energy is then calculated as follows ... 

Because forces act on the nuclei in the FE conformation, the general statements of the virial theorem, which include the contributions of the virials of the nuclear forces to the total electronic energy, must be used (eqn (6.65)). The contribution of nucleus a to the virial of the forces acting on the electrons is equal to — Xj-F where X is the position vector of nucleus a and F = — the net force acting on it. When the forces on the nuclei vanish, one obtains the corresponding equilibrium statements of the virial theorem, T = — E and E = V. The general statement corresponding to T = — E is... 

The second chemical contribution to the total interaction energy is present if an ionic or a covalent chemical bond between the adsorbed molecule and the surface can be formed. Since covalent bonds also depend on the overlap between the wave functions of the subsystems, their distance dependence is exponential, see Table 1, as is that of the Pauli repulsion. In general, covalent bonds are only possible if at least one of the two partners possesses partially occupied valence orbitals. In contrast to the adsorption at metal or semiconductor surfaces, such a situation is rarely encountered at insulator and in particular at oxide surfaces. In most cases, the ions at the surface of an insulator try to adopt a closed shell electronic structure as they do in the bulk, as for instance the Na+ and Ck ions in NaCl or the Mg + and ions in MgO. Counterexamples are transition metal oxides in which the metal cations possess partially occupied d-shells which might form chemical bonds with the adsorbed molecule. One famous example is the interaction between NO and the NiO(lOO) surface where both the Ni + cations (d configuration with a A2g ground state) and the NO radical ( 11 ground state) have partially filled valence shells (see below). 

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