Overlapping charge distributions, energies

The second two-electron integral is a little more difficult to understand formally, it represents the mutual potential energy of the overlap charge distribution -eiAff(r]) s(ri) due to electron 1 with an identical density -eifRi 2) l s0 2) due to electron 2. 

The situation is not so simple with K R). The overlap charge distribution is shown in Fig. 2.7 and is far from spherical. The upshot of the differences is that the k2 R) integral is the self-energy of the overlap distribution and is more dependent upon its charge than upon its size. In addition, at any distance there is in ki R) a portion of the distribution that surrotmds the point charge, and, again, the distance dependence is decreased. The overall effect is thus that shown in Fig. 2.4. 

If the charge distributions of the D and A overlap than a new class of interactions has to be considered, namely the exchange interaction between the electrons on D and on A. This type of energy transfer is called Dexter transfer [80, 96,98], Here we briefly outline the physical principles involved. 

Comparison of the Gibbs energies of Na -alkylammonium exchange in different clay minerals with their charge distribution from CNDO (complete neglect of differential overlap)... 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

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