The Bond Moment Model

The transformation of vibrational absorption intensities of binary overtone and combination bands in terms of bond moments and derii ves has been formulated by Gribov [72,155]. The transition dipole moment is expressed in terms of first and second dipole moment derivatives with respect to normal coordinates as shown in Eq. (6.3). Further expansion of (dp/dQiJo (d p/dQ (dQ )o terms ipearing in the expansion in terms of Ixmd moments and derivatives with respect to internal coordinates is 

Lj is the i row of the L matrix. The analogous expression for the second dipole moment derivatives is much more elaborate [155]  

The matrix M consists of bond moment values arranged as the matrix [ q. (6.58)] while the array d e JdR dR, has a form analogous to matrix [Eq. (6.57)]. 

The procedure for evaluating elements of the matrix d dRadR is quite elaborate and will not be presented. It is described in die book of Gribov and Orville-Thomas [155]. 

Three types of intensity parameters oiter Eq. (6.59). These are die bond dipole moments Pk, die first derivatives of bond moments widi respect to internal coordinates, and second derivatives d pk/dR dR],. The latter quantities are termed electro-optical anharmonic parameters. These toms reflect the non-linear dependence of Pk on the vibrational coordinates Bj and are determined by die electrical anharmonicity of molecular vibrations. As in the charge flow formulation, harmonic terms miter the expressions for intensities of binary overtone and combination bands. 

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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 ... 

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 ... 

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. 

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. 

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. 

CH2CI2 is similar to CH4 in that it has an overall tetrahedral shape, as predicted by the VSEPR model. Not aU the bonds are identical, however, so there are three different bond angles H—C—H, H—C—Cl, and Cl—C—Cl. These bond angles are close to, but not equal to 109.5°. Because chlorine is more electronegative than carbon, which is more electronegative than hydrogen, the bond moments do not cancel, and the molecule possesses a nonzero dipole moment ... 

L. D. Barron, in Molecular Light Scattering and Optical Activity, Cambridge University Press, Cambridge, U.K., 1982, pp. 317-321. P. L. Polavarapu, Mol. Phys., 49, 645 (1983). A Comparison of Bond Moment and Charge Flow Models for Vibrational Circular Dichroism Intensities. J. R. Escribano, T. B. Freedman, and 1- A. Nafie, /. Phys. Chem., 91, 46 (1987). A Bond-Origin-Independent Formulation of the Bond Dipole Model of Vibrational Circular Dichroism. 

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. 

As early as 1972 it was recognized that an explicit inclusion of terms associated with the charge-flux effects accompanying molecular vibrations may offer an opportunity for better understanding of the physical significance of parameters in infi-ared intensity models based on the bond moment concept [42]. 

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... 

I is the bond length. The experimental quadrupole moment is consistent with a charge, q, of approximately 0.5e. In fact, a better representation of the electrostatic potential around the nitrogen molecule is obtained using the five-charge model shown in Figure 4.20. 

STRATEGY In each case, we must decide on the shape of the molecule by using the VSFPR model and then decide whether the symmetry of the molecule results in the cancellation of the dipole moments associated with the bonds. If necessary, refer to Fig. 3.7. 

One important stracture in molecules are polar bonds and, as a result, polar molecules. The polarity of molecules had been first formulated by the Dutch physicist Peter Debye (1884-1966) in 1912, as he tried to build a microphysical model to explain dielectricity (the behaviour of an electric field in a substance). Later, he related the polarity of molecules to the interaction between molecules and ions. Together with Erich Hiickel he succeeded in formulating a complete theory about the behaviour of electrolytes (Hofimann, 2006). The discovery of the dipole moment caused high efforts in the research on physical chemistry. On the one hand, methods for determining the dipole momerrt were developed. On the other hand, the correlation between the shape of the molectrle and its dipole moment was investigated (Estermanrr, 1929 Errera Sherrill, 1929). 

Stimulated by these observations, Odelius et al. [73] performed molecular dynamic (MD) simulations of water adsorption at the surface of muscovite mica. They found that at monolayer coverage, water forms a fully connected two-dimensional hydrogen-bonded network in epitaxy with the mica lattice, which is stable at room temperature. A model of the calculated structure is shown in Figure 26. The icelike monolayer (actually a warped molecular bilayer) corresponds to what we have called phase-I. The model is in line with the observed hexagonal shape of the boundaries between phase-I and phase-II. Another result of the MD simulations is that no free OH bonds stick out of the surface and that on average the dipole moment of the water molecules points downward toward the surface, giving a ferroelectric character to the water bilayer. 

Fig. 5.7. Simplified schematic flow chart for the optimization of the parameters of the bond length and bond angle potentials. The input parameters from the chemically realistic model are the moments (L), (L2), ( ), (02), (LG) taken from the bond length and bond angle distributions, and the reduced effective barrier (W) from the torsion potentials. From Tries [184]... 

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