Coulomb repulsion energy, interelectronic

As indicated in Equation 4.21, the interelectronic Coulomb repulsion energy functional J[p is written as the classical expression... 

The third term, describing the interelectronic Coulomb repulsion energy, is given in density functional theory as ... 

We note that three spin-allowed electronic transitions should be observed in the d-d spectrum in each case. We have, thus, arrived at the same point established in Section 3.5. This time, however, we have used the so-called weak-field approach. Recall that the adjectives strong-field and weak-field refer to the magnitude of the crystal-field effect compared with the interelectron repulsion energies represented by the Coulomb term in the crystal-field Hamiltonian,... 

The most localized MOs are those that are most separated from one another by this we mean that set of MOs for which the interelectronic repulsion between the different MOs viewed as charge clouds is a minimum. The energy of repulsion between the charge clouds of electron 1 in the MO (/>, and electron 2 in the MO j is a Coulomb integral of the form (9.100). The total interorbital charge-cloud repulsion energy is then... 

We conclude that interelectronic coulomb repulsion will tend to cause the A states to attain lower energy than the B states. 

Electrons in molecules and crystals repel each other according to Coulomb s law, with the repulsion energy depending on the interelectron distance as This interaction creates a correlation hole around any electron, i.e. the probabihty to find any pair of electrons at the same point of spin-coordinate space is zero. Prom this point of view only the Hartree product of molecular or crystalline spin-orbitals... 

This chapter describes the new features that appear when we deal with systems having more than one electron. One of these features, interelectron repulsion, is easy to understand in its manifestation as operators in the hamiltonian and as coulomb repulsion integrals, J, in the average energy expression. Another feature, antisymmetry for... 

The Hamiltonian as well as all following formulas are given in atomic units. The subscripts c and V denote core and valence, respectively, and the Hamiltonian is given for a molecule with valence electrons and N cores with effective core charges Q. ry and denote interelectronic and internuclear distances, respectively. The individual terms of equation 6.1 are the kinetic energy of the valence electrons, the Coulomb interaction between the valence electrons, the superposition of N atomic ECPs point charge Coulomb repulsion... 

Finally, we must remember that just as a d-d spectrum is not properly described at the strong-field limit - that is, without recognition of interelectron repulsion and the Coulomb operator - neither is a full account of the energies or number of charge-transfer bands provided by the present discussion. Just as a configuration... 

Since only Coulomb potentials are involved, the matrix T v, v turns out to be energy independent. Its elements are pure numbers that depend only on N, the number of electrons, and are independent of the nuclear charge Z. The roots lK of the energy-independent interelectron repulsion matrix T v, v are also pure numbers (Table 1). In the large-Z approximation, the generalized Sturmian secular equation (41) reduces to the requirement ... 

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