Carbon atom displacement energy

The threshold energy of carbon atom displacement from CNS lattice in some cases can be considered as independent from the angle 5 (isotropic displacement). The integration of Equation 21.2 for these cases yields for the total displacement cross section the following expression ... 

The calculation of the threshold energy E of carbon atom displacement from the CNS lattice is usually carried out with use of tight-binding molecular-dynamics simulations (Crespi et al. 1996, Krasheninnikov et al. 2005, Zobelli et al. 2007). The total analysis of the collision process in calculations shows that the normal impulse to the lattice atom from the incident electron (8=0) leads... 

When an impacting particle transfers energy to a near sinface carbon atom in an amount sufficient to overcome the lattice bond energy or surface binding energy, some carbon atoms may be displaced and move in a direction defined by the angle... 

Cyclopentane is nonplanar, and the two minimum-energy geometries are the envelope and half-chair. In the envelope conformation, one carbon atom is displaced from the plane of the other four. In the half-chair conformation, three carbons are coplanar, vdth one of the remaining two being above the plane and the other below. The energy differences between the conformers are very small, and interconversion is rapid. All of the carbon atoms r idly move through planar and nonplanar positions. The process is called pseudorotation. 

It is clear that some information is lost as a result of our approximation, specifically regarding the individual bonds formed by sp carbon atoms, but the total of the F values in a molecule is expected to be generally reasonably accurate. The salient feature of ethylenic double bonds, namely, the inward displacement of tt orbital centroids on the C=C axis revealed by direct calculations, and its important role in energy calculations, can now be put in a clear perspective and efficiently tested for large collections of molecules. 

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