Atomic deformation polarization

Structural modifications brought about by an electric field can be of three kinds (a) orientation polarization, which can only take place for molecules having a permanent dipole moment, (b) atomic deformation polarization, (c) electronic deformation polarization. 

Hirshfeld (1971) was among the first to introduce atom-centered deformation density functions into the least squares procedure. Hirshfeld s formalism is a deformation model, in which the leading term is the unperturbed IAM density, and the deformation functions are of the form cos" 0jk, where 9jk is the angle between the radius vector r7 and axis k of a set of (n + l)(n + 2)/2 polar axes on each atom /, as defined in Table 3.8 (Hirshfeld 1977). The atomic deformation on atom j is described as... 

Oxalic acid dihydrate, studied by several laboratories as part of the HJCr oxalic acid project, contains a short hydrogen-bond of 2.481 AO O distance, linking the oxalic acid and water molecules. All experiments are in agreement that the lone-pair peak of the water-molecule oxygen atom is polarized into the short hydrogen bond. The deformation density in the plane perpendicular to the water-molecule plane, bisecting the H—O—H angle, for one of the experiments is shown in Fig. 12.6. 

In this discussion another type of interaction between the hydrogen atom and ion has been neglected to wit, the deformation (polarization) of the atom in the electric field of the ion. This has been considered by Dickinson,22 who has shown that it contributes an additional 10 kcal /mole to the energy of the bond. We may accordingly say that of the total energy of the one-electron bond in (61 kcal/mole) about 80 percent (50 kcal/mole) is due to the resonance of the electron between the two nuclei, and the remainder is due to deformation. 

Deformation polarization It can be divided into two independent types Electron polarization—the displacement of nuclei and electrons in the atom under the influence of an external electric field. Because electrons are very light, they have a rapid response to the field changes they may even follow the field at optical frequencies. 

The natural orbitals %2v and %3p are, in contrast to the hydrogenlike functions, localized within approximately the same region around the nucleus as the Is orbital. This means that the polarization caused by the long-range interaction is associated mainly with an angular deformation of the electronic cloud on each atom. If %2p and %3p are expanded in the standard hydrogen-like functions, an appreciable contribution will again come from the continuum. 

As at room temperature Bragg reflections contain both nuclear and magnetic structure factors, the nuclear structure was refined from a combination of polarized and unpolarized neutron data. Contrary to the ideal structure where only three atomic sites are present, it has been shown [11, 12] that some Y atoms were substituted by pairs of cobalt. These pairs, parallel to the c-axis are responsible for a structure deformation which shrinks the cobalt hexagons surrounding the substitutions. The amount of these substituted Y was refined to be 0.046 0.008. Furthermore, the thermal vibration parameter of Coi site appeared to be very anisotropic. The nuclear structure factors Fn were calculated from this refined structure and were introduced in the polarized neutron data to get the magnetic structure factors Fu. 

It must be mentioned that the attempt to discuss bond type in this roughly quantitative way without giving a complete quantum-mechanical treatment of the molecules cannot be rigorously justified. We have adopted the procedure of discussing the structure of molecules and the nature of chemical bonds as completely as possible with use of only the most stable of the atomic orbitals following this procedure, we are led to base our discussion on the simple structures M X, M+X and M X+ It is possible,19 on the other hand, to develop (at least in principle) a complete discussion of the structure of a molecule from either the purely ionic point of view (with extreme polarization or deformation of the ions) or the covalent point of view, provided that all the unstable atomic orbitals are used in the discussion. No treatment of either of these types has been carried out for molecules of any complexity, however, whereas the reasonable procedure that forms the basis of our argument has found extensive application to the problems of structural chemistry. 

As has been well established, piezoelectricity in a non-polar crystal is brought about by the internal strain in the crystal. The internal strain means the displacement of atoms which is not affine to the deformation of crystal lattice. In the case of a polymer film which is not electrically conductive and where the charges are possibly embedded, a description of piezoelectricity can be reached by considering not only the internal strain in the lattice but also the displacement of these charges which is not affine to the average deformation of the whole system. 

Nonempirical quantum-chemical calculations of acetylide molecules support the ready displacement of alkali metal cations to the bridge position (87IZV2777 88IZV1335, 88IZV1339). This naturally leads to the conclusion that the polarization and deformation of the ir-electronic shell of acetylene must depend on the atomic number of the cation attached to the acetylene anion. However, the acetylene activation in the reaction with ketoximes via acetylides suggests nucleophile attack at a carbanionlike complex, which is of course a week point of the hypothesis. Nevertheless, the electrophilic assistance from the alkali metal cation (Na+) to the... 

Simple cavity models have been used to study solvated electrons in liquid ammonia. In that case the dominant interactions arise from long range polarization effects, so that the energy of the localized state is not very sensitive to the fluid deformation in the vicinity of the localized charge. In the case of an excess electron in liquid helium, however, the electron-fluid interaction arises mainly from short range electron-atom interactions, and we shall show that the localized excess electron in a cavity in liquid helium lies lower in energy than the quasi-free electron. 

The semi-empirical bond polarization model is a powerful tool for the calculation of, 3C chemical shift tensors. For most molecules the errors of this model are in the same order of magnitude as the errors of ab initio methods, under the condition that the surrounding of the carbon is not too much deformed by small bond angles. A great advantage of the model is that bond polarization calculations are very fast. The chemical shift tensors of small molecules can be estimated in fractions of a second. There is also virtually no limit for the size of the molecule. Systems with a few thousand atoms can be calculated with a standard PC within a few minutes. Possible applications are repetitive calculations during molecular dynamics simulations for the interpretation of dynamic effects on 13C chemical shift distribution. 

For the more tight clusters SiO2 C70 and CS2 C7o, the local minimum of the PES corresponds to symmetric structure D h, the M(SiO) and R CS) distances are, respectively, 0.013 and 0.045 A shorter and their vstr frequencies experience a blue shift by 80 cm-1 (Si-O) and 145-245 cm-1 (C-S). As in the above clusters, the frequency of the deformation vibration nu e ) is red shifted by 78 (SiCA) and 145 (CS2) cm-1. Like the C-O and Be-F bonds, the Si-O bonds compressed in the cage become more polar. In the CS2 C7o cluster, a noticeable charge is transferred from the cage to the sulfur atoms, each of which acquires about 0.01 e (Table 11). 

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