Bond expansion

There are many expansions of the total many-electron wave function which may be used in discussing the properties of an electronic system. For the present discussion, we assume a resonating valence bond expansion, which is represented by... 

The electric conductivity of carbon nanotubes is largely influenced by the presence of defects. Even effects as modest as axial strain with bond expansion change the band structure. Stone-Wales defects and other imperfections diminish the electric conductivity as well. This effect is especially pronounced for defects with two adjacent vacancies. The resistance of a 400 nm long SWNT, for example, increases by a factor of 1000 if the tube bears as little as 0.03% of these double vacancies. Single vacancies, on the other hand, do not cause such dramatic changes. In any case, however, the free path of the electrons is reduced considerably by the defects (in parts down to a few nanometers). Still, due to the multitude of existing conduction channels, this has no large influence on the overall conductivity. 

A comparison of Eq. (106) and Fig. 11 with Eq. (103) and Fig. 9 shows immediately that the/ bond expansion of (T%) corresponds to those terms in Us+i)a that do not have a white articulation circle. An articulation circle is defined as a circle that, if removed, would cause the graph to fall apart into two or more pieces, at least one of which contains black circles but no white circles. Equation (108) is then equivalent to the following graphical prescription ... 

It is, however, well-known that the dissociation energies cannot be computed very accurately using the SDCI + Q level of theory as this method ignores electron-correlation effects from other reference configurations. This method is also not a size-consistent method. Dolg et al. found that relativistic effects lead to a bond expansion of 0.016 A and lowering of by 0.44 eV. Relativistic effects also increase the... 

Two possible geometries for the activated complex are considered. At each geometry the first value is based upon a 30% bond expansion the values in parentheses are based upon no bond expansion. The experimental value for A in the temperature range 300-700 K is 2 X 10 cm mol sec. ... 

Some interesting points emerge. The calculation is insensitive to the amount of bond expansion assumed. The temperature dependence of A for the two geometries is quite small, which is a general feature so that any temperature in the experimental range can be used in these calculations. 

Recalculate the -factors in Problems 9.2 and 9.3 assuming no bond expansion in the activated complex. Does this alter your choice for the more probable geometry ... 

If these bond expansion coefficients are used, computer modelling of the structures of various end members of the high-quartz-type and keatite-type alumino-silicates yields coefficients of thermal expansion in reasonable qualitative agreement with the measured ones. 

For rubber there is slow, viscous motion to reach the changed conformations, steel expands by affine bond expansion (speed of sound). 

Figure 4 Relationship between C ,e-C (

However, exceptional cases exist. Based on the fine structure of boron and carbon /T-edges in EELS and TEM, Lu et al. [56] found local C-C bond expansion at sites with local high B content in the diamond grain. 

H-H dissociation in H2 and 0-0 single- and double-bond dissociation in the H2O2 and O2 molecules. For these three cases we derived adiabatic QM bond expansion/compression energies, where the expansion was taken all the way to the dissociative limit. Most weight was put on the QM-data close to the equilibrium and to the dissociation energies. Figure 6.1(a-c) shows the QM and ReaxFF results for these cases. 

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