Bond densities

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

The energy dissipation per unit volume to fracture a network consisting of a bond density Nev = bonds per unit volume is... 

This equation predicts that the fracture stress increases with the square root of the number of bonds to be broken and is inversely proportional to M. The percolation parameter p is in effect, the normalized bond density such that for a perfect net without defects, p = 1 and for a net that is damaged or contains missing bonds. 

Figure 12.27 (a) Schematic representation of possible 3-centre islands of ti bonding above and belov. the ring plane for (NPXi)i. (b) experimental electron bonding density (see text). 

Electron densities, bond densities, and spin densities, as well as particular molecular orbitals may be displayed as graphical surfaces. In addition, the value of the electrostatic potential or the absolute value of a particular molecular orbital may be mapped onto an electron density surface. These maps provide information about the environment around the accessible surface of a molecule. Electrostatic potential maps show overall charge distribution, while orbital maps reveal likely sites for electrophilic and/or nucleophilic attack. Surface displays may be combined with any type of model display. 

The following bond density surface for hex-5-en-l-yne clearly allows you to see whicf atoms are connected. It does not, however, distinguish single, double and triple carbon-carbon bonds as clearly as a simple skeletal model. 

The usefulness of the bond density surface is more apparent in the following model o diborane. The surface shows that diborane is not flat. It also shows that there is relatively little electron density between the two borons. Apparently there is no boron-boron bonr in this molecule. This is information that we can extract from the bond density surfact model. We do not have to assume this information in order to construct a model. We would need it in order to construct a conventional model. 

Bond density surfaces are also superior to conventional models when it comes te describing chemical reactions. Chemical reactions can involve many changes in chemica bonding, and conventional formulas are not sufficiently flexible to describe what happen (conventional plastic models are even worse). For example, heating ethyl fonnate t( high temperatures causes this molecule to fragment into two new molecules, foraii( acid and ethene. A conventional formula can show which bonds are affected by ths reaction, but it cannot tell us if these changes occur all at once, sequentially, or in soms other fashion. 

On the other hand, the bond density surface is able to provide quantitative information The three surfaces shown below correspond, respectively, to the reactant, the transitioi state (a transition state is a molecule that is on the way to becoming the products an< its energy defines how fast the reaction can proceed), and the two products. 

Bond density surface for diborane locates bonds. 

Based on its structure and valence electron count, draw a Lewis structure or series of Lewis structures for diborane Examine the bond density surface. Does it substantiate 01 refute your speculation ... 

Draw a Lewis structure (or series of Lewis structures) foi 2-norbornyl cation which adequately describes its geometry, charge distribution and bond density surface, Relate this structure to your description of 3-methyl-1-butyl cation. 

Examine transition-state structures and bond density surfaces for the Diels-Alder, ene and Cope reactions. 

Bond density surface for transition state for ene reaction shows making and breaking of bonds. 

Finally, examine bond density surfaces for the lower-energy transition state for each reaction. Are all bonds broken and formed to roughly the same extent, or are some bonds made or broken to greater extent ... 

Bond density surface for 9-BBN-i4-methylpent-2-ene at C2 reveals to what extent bonds are formed in hydroboration transition state. 

Robertson has summarized the three recent classes of models of a-Si H deposition [439]. In the first one, proposed by Ganguly and Matsuda [399, 440], the adsorbed SiHa radical reacts with the hydrogen-terminated silicon surface by abstraction or addition, which creates and removes dangling bonds. They further argue that these reactions determine the bulk dangling bond density, as the surface dangling bonds are buried by deposition of subsequent layers to become bulk defects. 

In the literature, it is commonly postulated that glide occurs between the planes A and A" in Figure 5.8, but this seems most unlikely because the bond density is three times as large there compared with the region between A and A. ... 

That hydrogen is responsible for the large reduction of the dangling bond density in amorphous silicon is demonstrated by studies of films grown by sputtering of silicon with an inert gas (Paul et al., 1976). When hydrogen is added to the argon carrier gas, the spin density is reduced to 1016/cm3, and the films can be doped. In contrast, sputtered amorphous... 

Fig. 19. Hydrogen diffusion coefficient, measured at 240°C, as a function of phosphine and diborane gas phase doping level, deduced from the data in Fig. 17. The dependence on dangling bond density is indicated on the top horizontal scale (Street el al., 1987b).

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