Bond compression/extension

Although further work on polyatomic molecules is now in progress it can already be concluded that for an experimenal chemist electronic and nuclear Fukui fimctions offer complementary information on a molecule s fate upon attack by a nucleophile or electrophile. Whereas the electronic Fukui function indicates the preferential site of attack (site selectivity - see also 3.2.2.), the nuclear Fukui function foresees nuclear rearrangements (bond compression or extension) at the reactive site. 

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

Vibrational energy, which is associated with the alternate extension and compression of die chemical bonds. For small displacements from the low-temperature equilibrium distance, the vibrational properties are those of simple harmonic motion, but at higher levels of vibrational energy, an anharmonic effect appears which plays an important role in the way in which atoms separate from tire molecule. The vibrational energy of a molecule is described in tire quantum theory by the equation... 

Rg. 13J1 Extension and compression of the Fe—O bonds in [PefH OV,]1 and [FedMMJ2. respectively. to form an activated complex in which all metal-hgand distances are identic, a prsequisile for electron transfer between the two complexes. [From Lems,... 

Thus, for example, if we apply equation (7.46) to describe the periodic vibrational motion in a diatomic molecule, x represents time, and positive and negative values for y correspond to bond extension and compression, respectively. Finally, we can see that equation (7.46) is an eigenvalue equation in which y is the eigenfunction and —n2 is the eigenvalue (see Section 4.3.1). 

Thus obtained results show that the polyamorphic transitions occur not only at compression (Si02, H20, etc.) but at extension as well (C) in the systems having stable or metastable crystal analogs with a different density and a different coordination number z. At the minimal z=2 (chain structures) the transitions may occurs only at compression, at the maximal z=12 (close-packed structures) - only at extension, at the intermediate z (2structure-sensitive properties change and new metastable phases can appear. Amorphization under radiation (crystal lattice extension) can be associated with a softening of phonon frequencies. The transitions in the molecular glasses consisted from the molecules with unsaturated bonds are accompanied by creation of atomic or polymeric amorphous systems. 

In a diatomic molecule, the masses mv and m2 vibrate back and forth relative to their centre of mass in opposite directions, as shown in the following figure. The two masses reach the extremes of their respective motions at the same time. The diatomic molecule has only one vibrational degree of freedom, i.e., it has only one frequency, called the fundamental vibrational frequency. During vibrational motion, the bond of the molecule behave like a spring and the molecule exhibits a simple harmonic motion provided the displacement of the nuclei from the equilibrium configuration is not too much. At the two extremes of motion which correspond to extension and compression of the chemical bond between the two atoms, the potential energy is maximum. On... 

In layered misfit structures of the type we are discussing, bonds at the layer surfaces (within and between the layers) will be strained periodically along a non-commensurate lattice direction parallel to the layers after a certain number of subcells there is a near match of the layers. Clapp has pointed out that, for a simple case, layer mismatch will cause tension in one layer type and compression in the other. The resulting strain energy may be relieved by the introduction of periodic antiphase boundary (apb) planes so that alternate contraction and extension occurs in all layers (Fig. 22) and hence cancels out (at the price of a small deformation of coordination polyhedra). 

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