Coulomb energy electron repulsion

This rule is a consequence of the energy required for pairing electrons in the same orbital. When two electrons occupy the same part of the space around an atom, they repel each other because of their mutual negative charges with a Coulombic energy of repulsion, n, per pair of electrons. As a result, this repulsive force favors electrons in different orbitals (different regions of space) over electrons in the same orbitals. 

As explained in Section 2-2-3, the energy of pairing two electrons depends on the Coulombic energy of repulsion between two electrons in the same region of space, II., and the purely quantum mechanical exchange energy,. The relationship between the... 

Our evaluation of the Fundamental Integral cannot proceed further than (18) unless we now specify the two-electron function f(x). We are now in a position to consider some of the integral types which arise in quantum chemical calculations overlap, kinetic-energy, electron-repulsion, nuclear-attraction and anti-coulomb. 

There is one very obvious pitfall in all that we have said so far the Coulomb energy of repulsion of a density with itselT includes the interaction of each electron with all the others plus the interaction of that electron with itself. This self-interaction energy is clearly spurious in the MO method it is automatically cancelled by the diagonal exchange terms... 

Each of these corresponds to a state having a particular energy. State (1) involves Coulombic energy of repulsion, because it is the only one that pairs electrons in the same orbital. The energy of this state is higher than that of the other two by 11 as a result of electron-electron repulsion. 

Coulombic energy of repulsion 11 is a consequence of repulsion between electrons in the same orbital the greater the number of such paired electrons, the higher the energy of the state. ... 

The first two tenns in Eq. (2) represent the kinetic energy of the nuclei and the electrons, respectively. The remaining three terms specify the potential energy as a function of the interaction between the particles. Equation (3) expresses the potential function for the interaction of each pair of nuclei. In general, this sum is composed of terms that are given by Coulomb s law for the repulsion between particles of like charge. Similarly, Eq. (4) corresponds to the electron-electron repulsion. Finally, Eq. (5) is the potential function for the attraction between a given electron (<) and a nucleus (j). 

The GEM force field follows exactly the SIBFA energy scheme. However, once computed, the auxiliary coefficients can be directly used to compute integrals. That way, the evaluation of the electrostatic interaction can virtually be exact for an perfect fit of the density as the three terms of the coulomb energy, namely the nucleus-nucleus repulsion, electron-nucleus attraction and electron-electron repulsion, through the use of p [2, 14-16, 58],... 

Coulombic energy transfer is a consequence of mutual electrostatic repulsion between the electrons of the donor and acceptor molecules. As D relaxes to D, the transition dipole thus created interacts by Coulombic (electrostatic) repulsion with the transition dipole created by the simultaneous electronic excitation of A to A (Figure 6.9). 

Like atomic orbitals (AOs), molecular orbitals (MOs) are conveniently described by quantum mechanics theory. Nevertheless, the approach is more complex, because the interaction involves not simply one proton and one electron, as in the case of AOs, but several protons and electrons. For instance, in the simple case of two hydrogen atoms combined in a diatomic molecule, the bulk coulombic energy generated by the various interactions is given by four attractive effects (proton-electron) and two repulsive effects (proton-proton and electron-electron cf figure 1.20) ... 

The first term on the right in equation 1.141 is repulsion between the two nuclei, the second term represents electron-electron repulsion, and the third and fourth terms are attraction effects between electrons and nuclei. If we subtract the coulombic energies of separate atoms from equation 1.141 ... 

As described in Chapter 1, the first term on the left-hand side describes the kinetic energy of the electron, V is the potential energy of an electron interacting with the nuclei, VH is the Flartree electron-electron repulsion potential, and Vxc is the exchange-correlation potential. This approach divides electron-electron interactions into a classical part, defined by the Flartree term, and everything else, which is lumped into the exchange-correlation term. The Flartree potential describes the Coulomb repulsion between the electron and the system s total electron density ... 

The only term in this expression that can be derived directly from the charge distribution is the Coulombic energy. It consists of nucleus-nucleus repulsion, nucleus-electron attraction, and electron-electron repulsion terms. For a medium of unit dielectric constant,... 

---