Bond moment model

The bond moment model, first formulated by Barron (1979), was reformulated by Polavarapu (1983) to compare it to the charge flow model. His expression for the rotatory strength of a vibrational transition is then ... 

P. L. Polavarapu and D. F. Michalska, /. Am. Chem. Soc., lOS, 6190 (1983). Vibrational Circular Dichroism in fSJ-(-)-Epoxypropane. Measurement in V por Phase and Verification of the Perturbed Degenerate Mode Theory. P. L. Polavarapu and D. F. Michalska, Mol. Phys., 52, 1225 (1984). Mid Infrared Vibrational Cin r Dichroism in fS)-(-)-Epoxypropane Bond Moment Model Predictions and Comparison to the Experimental Results. P. L. Polavarapu and D. F. Michalska, Mof. Phys., 55, 723 (1985). Errata Mid Infrared Vibrational Circular Dichroism in f5J-(-)-Epoxypropane Bond Moment Model Predications and Comparison to the Experimental Results. P. L Polavarapu, B. A. Hess, and L. J. Schaad, /. Chem. Phys., 82, 1705 (1985). Vibrational Spectra erf Epoxypropane. 

Generalizing, two different approaches — the first based on analysis of contributions of the LCAO composite dipole terms, and the second based on studies of properties of the electron charge-density function reveal a complex picture of intramolecular electronic effects determining band intensities in infiared q>ectia. The application of a bond-moment model in describing this particular molecular property is fru- from straightforward. 

In order to compensate for some of die above difficulties of the bond moment modeL Sverdlov et al. [73,91] have proposed a modification of the oiigiiial formuladoa In their treatment certain adjustments of die physical pimequisites are made by allowing the presence of bond moment componeiits popendicular to bond directions. The additive representation for the molecular dipole moment is retained ... 

It should be emphasized that the charge-flux effects are implicidy included in electro-optical parameters of the type dpj dRj that appear in the first-order bond moment model [72]. Thus, in standard applications to various molecules it does not seem necessary to extend the original formulation since this would result in further increase in intensity parameters. 

Some of the problems and difficulties associated widi plying die bond moment model will be seen from the exanqiles of application described next... 

In Eqs. (3.51) through (3.53) M is the C-Cl bond moment and p die C-H bond moment. Bond moments are in Debye units, eop s of the type dpj /arj are in units D A while apif/ayi with Yi an angular internal coordinate are in units D rad The total number of electro-optical parameters is 13 while the number of observables that can be used in dieir evaluation is just 7. It is evident that to solve the sets of linear equations some eop s have to be put equal to zero. Another difficult problem is how to decompose p, into particular bond moment values. Even if p and M are assigned particular values [73] a number of different solutions are obtained depending on which electro-optical parameters are ignored. It is, dierefore, of particular importance to discuss in detail the approximations adopted in calculations employing the bond moment model. 

FIGURE 6.1 The vector model used to calculate dipole moments from bond moments. 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

Consequently, the bond is fully saturated for A sp = 0 with a bond order of 1, but it is only partially saturated by the time the gap closes for AEap/2 h = 1 (cf eqn (7.92)) when the bond order equals 0.76. This simple second moment model has been extended to include the compound semiconductors. The resultant values of the bond order are given in Table 7.2. We see that the bonds in tetrahedral carbon and silicon are almost fully saturated, but those in zinc selenide and cadmium telluride are only about 75% saturated due partly to the mismatch in the sp orbitals between chemically distinct atoms. 

Correlation and solvation effects on heterocyclic equilibria in aqueous solution were analyzed with the use of SM2/AM1 and Onsager models. It was found that the Onsager model was inferior to SM2/AM1,because it underestimates the solvation of the syn -form. Local bond moments, as shown by SM2/AM1, had significant effects on the bulk electric polarizaton, even when they largely cancel in the net dipole moment. Moreover, the equilibrium shifts calculated with SM2 /AMI, due to the effects of methyl substitution on the isoxazole ring, were consistent with the available experimental data [79]. 

The LSER approach relates a bulk property, P, to molecular parameters thought to account for cavity formation, dipole moment/polarizability, and hydrogen-bonding effects at the molecular level. The cavity term models the energy needed to provide a solute molecule-sized cavity in the solvent. The dipole moment/polarizability terms model dipole and induced dipole interactions between solute and solvent these can be viewed as related to dispersion interactions. The hydrogen-bonding terms model HBA basicity and EIBD acidity interactions. 

Since charge compensation requires a modification of the charge density, changes of covalency at the surface are often assumed to heal the polarity. With the help of the bond transfer model, one can show that this statement is incorrect, as far as semi-infinite polar surfaces are concerned. It is useful to make a distinction between weakly polar surfaces, in which the dipole moment in the repeat unit is entirely due to covalent effects, and truely polar surfaces whose dipole moment contains an integer contribution. As already said, in the fully ionic limit, the first ones are considered as nonpolar, while the second ones are recognized as polar. 

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