Polarizable bonds

The molecular polarizability can be considered to be the cumulation of individual bond polarizabilities. The bond polarizability is known (in simple cases) to be an approximately linear function of bond length for small amplitudes of vibration. That is, polarizability is essentially a bond property and consequently is independent of direction along any axis (or independent of sense ). 

The antisymmetric stretching vibration. The molecule loses its original symmetry during the vibration. At the two extrema of the vibration the shapes of the molecule will be identical. Because the molecular polarizability is essentially the summation of all bond polarizabilities and is independent of direction along the internuclear axis, it will have identical values at the extrema. Consequently, the vibration is Raman inactive. 

Raman intensities of the molecular vibrations as well as of their crystal components have been calculated by means of a bond polarizibility model based on two different intramolecular force fields ([87], the UBFF after Scott et al. [78] and the GVFF after Eysel [83]). Vibrational spectra have also been calculated using velocity autocorrelation functions in MD simulations with respect to the symmetry of intramolecular vibrations [82]. 

Two different methods for estimating the probable value of force constant have so far been proposed in estimating the second term in braces in Eq. (11), Binsch et have used the bond-bond polarizabilities, while Nakajima et have made an extensive use of... 

Using a simple bond polarizability theory of ROA for the case of a molecule composed entirely of idealized axially symmetric bonds, the relationships j3(G )2 = j3 (A)2 and a G = 0 are found (Barron and... 

MM3(2000) has also included a new approach to obtain bond polarizabilities and induced dipole moments.69 A general formula based on the original MM3 force constants and bond polarizabilities was derived and is used to compute bond polarizabilities, and then molecular polarizabilities by an additive model. 

Isotope superlattices of nonpolar semiconductors gave an insight on how the coherent optical phonon wavepackets are created [49]. High-order coherent confined optical phonons were observed in 70Ge/74Ge isotope superlattices. Comparison with the calculated spectrum based on a planar force-constant model and a bond polarizability approach indicated that the coherent phonon amplitudes are determined solely by the degree of the atomic displacement, and that only the Raman active odd-number-order modes are observable. 

The rationalization of the conformational anomeric effect solely based on electrostatic interactions fails to account for these solvent effects. Another interpretation based on bond polarizability in 1,1-dialkoxyalkyl systems calls electronic transfer from a non bonding electron pair of one oxygen atom to the empty cr c 0 orbital from the other alkoxy substituent (Fig. 10).16... 

Interpretation of the v(CO) Raman intensities of a variety of carbonyls using a bond polarizability model... 

The Raman line shape is calculated with the bond polarizability model as described above. The unpolarized Raman line shape computed from the sum of the VV and VH line shapes is shown in Fig. 3. One again sees fair agreement between theory and experiment, with excellent peak position and evidence of a... 

Figure 7. Differences A8 between -y -SCS(F) values at C(9) and C(4) in 93 plotted against C(4)-Y bond polarizabilities 6,. ...

The entire set of molecules contained 782 bonds out of which 111 a-bonds were selected. The parameters were calculated by our methods to build a reactivity space with electronegativity difference, resonance effect parameter, bond polarizability, bond polarity, a-charge distribution, and bond dissociation energy as six coordinates. 

Band intensity in Raman spectra depends on bond polarizability rather than molecular dipole changes. 

Carbon-fluorine bonds also have unusual electrooptical properties. Fluoropolymers are often used to provide favorable electrical properties such as low dielectric constants. The low dielectric constants are another consequence of the relatively low polarizability of C—F bonds. Polarizability a is related to index of refraction n through the following equation ... 

By assuming the additivity of bond polarizabilities, a formal expression is derived for the difference Ay in principal polarizabilities of a real polymer chain having constant end-to-end distance r. An expression in a matrix form is derived for Ay of the PE chain. 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

Experimental results on the characteristic ratio, 0lnP- = 6.6, and on the temperature coefficient, d (In 0) / d T = - 0.28 10 3 K 1, are reproduced within limits of 0.2 and 0.15 x 1O 3, respectively. The effect of a 10° change in other hand, both Aa and its temperature coefficient are much greater than calculated from RIS theory assuming additivity of bond polarizabilities. The disparity (more than tenfold for Act) cannot be relieved by any rational adjustment of the structural parameters. 

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