Born distortion

The first non-linear polarizability is a tensor of rank 3 and possesses non-vanishing elements only in the case of molecules without a centre of symmetry. This Born distortion tensor was resorted to by Piekara for explaining the non-linear dielectric behaviour of nitrobenzene. In the case of axially symmetric molecules, the tensor of the first non-linear distortion (hyperpolarizability ) can be written as follows ... 

Quantum mechanical studies of the three-dimensional reaction have recently begun to appear. Quantum studies based upon the Born, distorted-wave Born, and infinite-order-sudden approximations have emphasized the energy dependence of cross sections and relative product yields into different v j states. In addition, closecoupling calculations of the 3D reaction have been reported by Redmon and Wyatt. Quantum mechanical probabilities for the 0-> 2 and... 

W.C. Chew and Y.M. Wang. Reconstruction of two-dimensional permittivity distribution using the distorted born iterative method. IEEE Transaetions on Medical Imaging, 9, 1990. 

A number of improvements to the Bom approximation are possible, including higher order Born approximations (obtained by inserting lower order approximations to i jJ into equation (A3.11.40). then the result into (A3.11.41) and (A3.11.42)), and the distorted wave Bom approximation (obtained by replacing the free particle approximation for the solution to a Sclirodinger equation that includes part of the interaction potential). For chemical physics... 

It was shown by several workers that in this case the first-order Jahn-Teller distortion is due to an ej vibration, and that the second-order distortion vanishes. Therefore, in terms of simple Jahn-Teller theoi, the moat around the symmetric point should be a Mexican hat type, without secondary minima. This expectation was borne out by high-level quantum chemical calculations, which showed that the energy difference between the two expected C2v structures ( A2 and Bi) were indeed very small [73]. 

The X-ray crystallographic analysis of the unsymmetrical BisP shows a strong distortion of the five-membered chelation ring as compared to that of symmetric BisP [32]. The large difference in the steric repulsions between the bulky substituent borne on one phosphorus atom and the neighboring atoms on the one hand and the other (different) bulky substituent borne on the other phosphorus atom and the same neighboring atoms on the other hand is believed to be responsible for better steric matching with some substrates. 

To obtain an estimate for the energy of reorganization of the outer sphere, we start from the Born model, in which the solvation of an ion is viewed as resulting from the Coulomb interaction of the ionic charge with the polarization of the solvent. This polarization contains two contributions one is from the electronic polarizability of the solvent molecules the other is caused by the orientation and distortion of the... 

As already noted, in the Born-Oppenheimer approximation, the nuclear motion of the system is subject to a potential which expresses the isotope independent electronic energy as a function of the distortion of the coordinates from the position of the transition state. An analysis of the motions of the N-atom transition state leads to three translations, three rotations (two for a linear molecule), and 3N - 6 (3N- 5 for a linear transition state) vibrations, one which is an imaginary frequency (e.g. v = 400icm 1 where i = V—T), and the others are real vibrational frequencies. The imaginary frequency corresponds to motion along the so-called reaction... 

Structure at high temperatures. A distorted perovskite would be expected to transform to the cubic structure at high temperatures. The Born model of ionic solids with the appropriate repulsive and van der Waals parameters can explain the relative stabilities of crystal structures in partly covalent solids, an ionicity parameter would have to be used to predict the preferred crystal structure (see Chapter 1, Section 1.3). 

For both cis- and Irans-dianthrylethylenes, the degree of deconjugation, which parallels the degree of deviation from coplanarity of the ethylene and anthracene ir-systems, is borne out in the shape of the electronic absorption spectra. Thus, the long-wavelength absorption of cis-dianthrylethylene 38a is characterized by the fine structure pattern which is typical of the anthracene chromophore, while the bathochromically shifted spectrum of the transisomer 39a is virtually structureless (see Figure 7). Substitution of the ethylene double bond is absorption spectroscopically noticeable for the cis-isomers 38b-f by distortion of the anthracene absorption. The absorption... 

Distorted-wave Born Qualitative agreement with quasiclassical ... 

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