Exchange repulsion overlap density

The exchange-repulsion energy is approximately proportional to the overlap of the charge densities of the interacting molecules [71, 72 and 73]... 

In order to obtain nonzero spin densities even on hydrogen atoms in tt radicals, one has to take the one-center exchange repulsion integrals into account in the eigenvalue problem. In other words, a less rough approximation than the complete neglect of differential overlap (CNDO) is required. This implies that in the CNDO/2 approach also, o and n radicals have to be treated separately (98). 

This section aims to illustrate the origin of the quantum mechanical exchange-overlap densities and their different behaviour in the case of the chemical bond in ground state H2 and the Pauli repulsion in He2. We choose as starting point for the 1Xg+ ground state of the systems the normalized Heitler-London (HL) wave functions (Magnasco, 2008) ... 

The exchange-repulsion term (Eer), which is always repulsive, can be taken as proportional to the overlap between the densities of the interacting molecules [28] ... 

The exchange-repulsion term is calculated by means of the charge density overlap following the Wheatley-Price overlap model (Wheatley and Price, 1990 Domene et al., 2001) ... 

We noted in Section 8.3 that, for two MOs i/// and i//y, there are two kinds of electron-electron repulsions to consider, namely the Coulomb repulsion and the exchange repulsion Kij. Tlic electron density distributions associated with i//,- and jjf are given by and respectively. As noted above these electron densities lead to J i (equation 8.18). On the other hand, it is the overlap density distribution that defines ATjy (equation 8.19). 

From these definitions, it follows that Kii=Jg. Also note that the Coulomb repulsion between two electrons is independent of their spins while the exchange repulsion vanishes unless their spins are the same.J,j- is repulsive (i.e., positive) and represents the electrostatic repulsion between electron fj, in orbital jfj and electron v in orbital j. It increases with increasing the overlap between the electron densities and... 

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