Angular deformation parameters

Dumont and Bougeard (68, 69) reported MD calculations of the diffusion of n-alkanes up to propane as well as ethene and ethyne in silicalite. Thirteen independent sets of 4 molecules per unit cell were considered, to bolster the statistics of the results. The framework was held rigid, but the hydrocarbon molecules were flexible. The internal coordinates that were allowed to vary were as follows bond stretching, planar angular deformation, linear bending (ethyne), out-of-plane bending (ethene), and bond torsion. The potential parameters governing intermolecular interactions were optimized to reproduce infrared spectra (68). 

FIGURE 21. Scatter plot of pyramidality coefficient PN.% versus the angular out-of-plane deformation parameter x for the sample of 474 enamine fragments... 

The extensional deformation extremal (eq. 48) is compared with its affine counterpart (eq. 50) in Figure 5 for uniaxial tension with cl = 2.5, and a parameter Y = 6. The same comparison is made in Figure 6 for uniaxial compression with Cl = 0.56 (equivalent to biaxial tension in the xy plane with ccx = ccy = 1.31). The corresponding comparisons of the angular deformation extremal (eq. 49) and affine behavior (eq. 51) are given in Figures 7 and 8. Additional values of a have been investigated and it is found that the extremals approach affine behavior as cc tends toward unity. 

Here are Luttinger parameters, and me is an electron effective mass, av, b, d and ac are Bir-Pikus deformation potentials. As0 is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lf, LJ is defined as [Lf, LJ = (LjLj + LjLj)/2. The summation of i,j runs through x, y, z. 

Deformation density can also be fit by Equation 9.4. The shape of the valence shell electron density is represented by a parameter k which is a scale factor for a radial function. " An expanded spherical harmonic function Yprovides the angular aspects of the model ... 

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