Coulomb exclusion energy

Electron correlation in the triplet is a consequence of the Pauli exclusion principle, which is embodied mathematically in the antisymmetrization of the electronic wave function. Anti-symmetrization results in zero probability for two electrons of the same spin simultaneously being in the same AO in an LCAO-MO wave function. This obviously reduces the Coulomb repulsion between these electrons from the value, Jxy, that is calculated by computing the Coulomb repulsion energy between a pair of uncorrelated electrons, one in f/x and the other in ffy. 

This is the difference in interaction energy, for the solvent molecules in given positions, of the solvent with the reactant and product [31], In the simplest case of no geometric size changes accompanying the ET, AE will be exclusively determinated by the Coulombic interactions between the solute and the solvent molecules. We will assume this to be the case in all that follows. We make the further restriction that the solute intramolecular vibrations play no key role. 

The XC energy represents the correction to the Coulomb energy for the self-energy of an electron in a many-electron system. The latter is due to both the direct self-energy of the electron as well as the redistribution of electronic density around each electron because of the Pauli exclusion principle and the Coulomb interaction. As an example, we now discuss the case of Fermi hole and the exchange energy in Hartree-Fock (HF) theory [16]. For brevity, we restrict ourselves to closed-shell cases. 

According to these considerations three subregions are defined as depicted in Fig. 1. The inner and outer parts of the QM region are termed the QM core and QM layer zone, respectively. As discussed solutes in the QM core do not require the application of non-Coulombic potentials—composite species with complex potential energy surfaces can be treated in a straightforward way, while complex potential functions are required in the case of classical and even conventional QM/MM simulation studies. Interactions at close solute-solvent distances are treated exclusively via quantum mechanics and account for polarization, charge transfer, as well as many-body effects. The solute-solvent... 

In papers on the Walden inversion, Ingold s group (Harvey et al., 1960) established that electrostatic forces do not contravene the normal stereochemistry of SN2 reactions. Even in the favorable case of negative nucleophile (azide) and positive substrate (sulfonium salt), exclusive inversion occurs. Obviously, the quantal forces of orbital symmetry and energy obliterate the coulombic factor here. 

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