Electronic density overlap

As the donor and acceptor molecules approach each other closely so that their regions of electron density overlap, electrons can be exchanged between the two molecules. This mechanism is therefore called the exchange mechanism. The electron-exchange mechanism requires a close approach (1-1.5nm), though not necessarily actual contact,... 

Still another form of the electron tunneling factor can be recast in terms of the electrode-molecule electronic density overlap, M(ii), rather than electronic wave function overlap/ ... 

A carbon atom must provide four equal-energy orbitals in order to form four equivalent a bonds, as in methane, CH4. It is assumed that the four equivalent orbitals are formed by blending the 2s and the three 2p AO s give four new hybrid orbitals, called sp3 HO s (Fig. 2.5). The shape of an sp3 HO is shown in Fig. 2.6. The larger lobe, the head, having most of the electron density, overlaps with an orbital of its bonding mate to form the bond. The smaller lobe, the tail, is often omitted when HO s are depicted (see Fig. 2.11). However, at times the tail plays an important role in an organic reaction. 

When two molecules approach one another their electron densities overlap to some extent. In principle, this overlap should be treated as a partially bonding effect, but Pixel preserves the identity of two separate electron clouds, so that when pixels overlap, singularities in the R dependence may result for very short pixel-pixel distances. As a practical countermeasure, all pixel-pixel distances below half the stepsize of the pixel mesh are reset at half the stepsize (the collision avoidance procedure). 

Kim Y S, Kim S K and Lee W D 1981 Dependence of the closed-shell repulsive interaction on the overlap of the electron densities Chem. Phys. Lett. 80 574... 

The structure of ethylene and the orbital hybridization model for its double bond were presented m Section 2 20 and are briefly reviewed m Figure 5 1 Ethylene is planar each carbon is sp hybridized and the double bond is considered to have a a component and a TT component The ct component arises from overlap of sp hybrid orbitals along a line connecting the two carbons the tt component via a side by side overlap of two p orbitals Regions of high electron density attributed to the tt electrons appear above and below the plane of the molecule and are clearly evident m the electrostatic potential map Most of the reactions of ethylene and other alkenes involve these electrons... 

Syn- and anti-orientations are possible and there is evidence that the anti-orientation does not favor orbital overlap such an orientation is favored with larger branched-chain substituents. A C-nmr study found that the TT-electron density on the vinyl P-carbon is lower as the reactivity of the monomer increases (20). Methyl vinyl ether exists almost entirely ia the syn-stmcture, a favorable orbital overlap situation, and MVE for this reason is less reactive to both polymerization and hydrolysis (21). 

Figure 2.4 uses electrostatic potential maps to show this build-up of electron density in the region between two hydrogen atoms as they approach each other closely enough for their orbitals to overlap. 

Strong sp -sp a bonds are not possible for cyclopropane, because the 60° bond angles of the ring do not permit the orbitals to be properly aligned for effective overlap (Figure 3.10). The less effective overlap that does occur leads to what chemists refer to as bent bonds. The electron density in the carbon-carbon bonds of cyclopropane does not lie along the internuclear- axis but is distr-ibuted along an arc between the two carbon atoms. The r-ing bonds of cyclopropane are weaker than other carbon-carbon a bonds. 

The graph brings up a problem for chemists seeking to define atomic and molecular size. The electron cloud lacks a clear boundary. While electron density decays rapidly with distance from the nucleus, nowhere does it fall to zero. Therefore, when atoms and molecules rub up against each other , their electron clouds overlap and merge to a small extent. 

The only way to solve the boundary problem is to make an arbitrary decision abou which part of the electron cloud to pay attention to and which part to ignore. For example we see that when two electron clouds overlap there is a point where both clouds havi the same electron density. This is a logical place to mark each molecule s boundary ... 

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