Lone-pair orbitals distribution

The square cell is convenient for a model of water because water is quadrivalent in a hydrogen-bonded network (Figure 3.2). Each face of a cell can model the presence of a lone-pair orbital on an oxygen atom or a hydrogen atom. Kier and Cheng have adopted this platform in studies of water and solution phenomena [5]. In most of those studies, the faces of a cell modeling water were undifferentiated, that is no distinction was made as to which face was a lone pair and which was a hydrogen atom. The reactivity of each water cell was modeled as a consequence of a uniform distribution of structural features around the cell. 

To explain the stereochemistry of the photoaddition, Buchi proposed that the reaction of electron-rich olefins and excited ketone involves an interaction of the electron-deficient carbonyl lone-pair orbital with the electron-rich 7r-olefin orbitals to form a diradical intermediate which could subsequently close to give the observed products. Indeed, reaction to yield the most stable diradical intermediate usually does nicely rationalize the observed product distribution. Examples of this are as follows11005 ... 

Removal of an electron from a hydrazine unit changes the lone pair orbital occupancy from four to three, which has a large effect on the preferred geometry with respect to the nitrogens. The formation of a three-electron bond has also been demonstrated in the cation radical of octamethyl-l,2,4,5-tetra-aza-3,6-disilacyclohexane. In this cation radical, the spin density is distributed between only two of the four nitrogen atoms. There is a pronounced interaction of the unpaired electron with protons of the methyl groups joined to these two nitrogen atoms. 

The latter effect is explained by the fact that the point at which the potential is calculated lies outside the plane and is therefore asymmetrically placed with respect to these two lone pairs. The large difference between the two contributions suggests a strong directionality of the two lone-pair orbitals in fact, as will be seen later, in a multipole expansion of the potential due to the charge distribution of such groups,... 

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