Vector addition of bond moments

A most widely used method for the prediction of molecular dipole moments is the empirical vector addition of bond moments (45). It involves the concept of point dipoles situated in the directions of the individual bonds artd assumes that the magnitudes of the dipoles are transferable from one molecule to another. For allenes a somewhat modified approach has been established which is of relevance in connection with the discussion of influences of electrostatic field effects on spectroscopic properties of allenes (24 25) (Section III.D). This model uses fixed origines and Hxed orientations for all the different (point dipole) bond moments in substituted allenes. As the origins of the point dipoles the positions of the hydrogen atoms in allene (11) have been used (24). The directions of the dipole moments are assumed to make an angle of 40 with the C==C=C axis (Fig. 6) which represents an average value of experimental directions of dipole moments in differently substituted allenes (24). 

Dipole Moments While dipole moments are not generally useful with organic unknowns, occasionally they provide the best means of distinguishing among a few possible structures which would have differing dipole moments. Approximate moments can be calculated by vector addition of bond moments from the literature.K For example, rra is-l,4-dibro-... 

Experimentally, the molecular dipole can be measured. Individual bond dipoles cannot be measured but they have been inferred from experimental data for a variety of compounds. Estimates of the molecular dipole can be made by vector addition of individual moments. Such estimates (calculations) are indicative but may differ significantly from the measured values. The latter are recorded in Table 4.10. 

The vector addition of dipole moments is only permissible if the weights of the ionic states in the various bonds does not alter significantly in the various compounds, such as would be produced if molecular resonance occurred in these cases only is it possible to assign definite values for the contributions of the various valence bond structures. The data for the bonds OH, OR, NH, NR and SH are given in Table... 

Dichlorobenzene. Compare your experimental results with the values computed from a vector addition of carbon-chlorine bond moments obtained from the dipole moment of monochlorobenzene (5.17 X 10 ° C m, or 1.55 D). If they do not agree, suggest possible physical reasons for the disagreement. 

Favini applied the PPP method to vinyl azide. Here the delocalized tt system consists of 6 electrons and 5 atomic 2p orbitals. The calculated data include charge densities, bond orders and dipole moments (obtained by vector addition of the a and tt moments). Cis and trans isomers were considered... 

FIGURE 3.22 The total dipole moment of a molecule is obtained by vector addition of its bond dipoles. This operation is performed by adding the arrows when they lie pointing in the same direction, and subtracting the arrows if they lie pointing in different directions, (a) CO2. (b) OCS. (c) H2O. (d) CCI4. 

Use VSEPR theory to determine the geometry of the molecule. Assign bond dipoles to any polar bonds. Predict the overall dipole moment by estimating the result of vector addition of the bond dipoles. 

The molecular dipole moment can be estimated by vector addition of individual bond moments if the bond angles are known. The possession of a dipole moment permits direct interaction with electric fields or interaction with the electric component of radiation. 

Dipole moments of diatomic molecules can be calculated directly. In more complex molecules, vector addition of the individual bond dipole moments gives the net molecular dipole moment. However, it is usually not possible to calculate molecular dipoles directly from bond dipoles. Table 3.8 shows experimental and calculated dipole moments of chloro-methanes. The values calculated from vectors use C—H and C—Cl bond dipole moments of 1.3 X 10 ° and 4.9 X 10 C m, respectively, and tetrahedral bond angles. Clearly, calculating dipole moments is more complex than simply adding the vectors for individual bond moments. However, for many purposes, a qualitative approach is sufficient. 

Thus in a molecule containing more than one polar bond, the dipole moment of the molecule is given by vectoral addition of the dipole moments of the individual bonds. The dipole moment is zero in a symmetrical molecule. 

Each of the CO2 and HiO molecules contains two identical atoms bonded to a central atom and two polar bonds. However, only one of these molecules is polar. To understand why, think of each individual bond dipole as a vector. The overall dipole moment of the molecule is determined by vector addition of the individual bond dipoles. 

Figure 6.7 Vector addition of NLMO bond dipoles (light arrows) to give the total molecular dipole moment (heavy arrow) in the x-y plane of fmmamide, with nuclear positions shown in the same (principal) axis system for comparison. Note the large contribution of lone pairs (particularly /Iq to the total dipole, which lies roughly parallel to the N- -O axis in this species. 

The first complete formulation of vibrational intensities was put forward some fifty years ago by Volkenshtein et al. [39,63], and further develcqied by other authors [72,73] later. The formulation, known as die valence-optical dieory (VOT), is based on the assumption that the molecular dipole moment may be rqnesented as a vector-additive sum of bond moments... 

IR spectroscopy is not only useful for determining the chemical constitution of polymers. It additionally provides profound information on chain orientation and on the orientation of attached lateral substituents of polymers. In this case, polarized IR radiation is applied which is only absorbed by an IR-active bond if the plane in which the electrical field vector E of the IR beam oscillates is parallel to the transition dipole moment p of the vibration to be excited. If, on the other hand, the transition dipole moment p is perpendicular to the electrical field vector E of the IR beam no absorption is observed. Using this effect, the degree of orientation of a polymer sample (film, fiber) can be estimated by comparing the intensity at maximum /(11) and at minimum I ) absorption, i.e., the dichroic ratio. 

With the molecular angles given elsewhere, a C—Br bond dipole moment of 1.42 D and a furan molecular dipole of 0.661 D (either direction), even a rough vector addition gives results that leave no doubt that oxygen is at the negative end of the furan dipole (Figure 2). 

The overall dipole moment of a molecule is the vector sum of the individual bond dipoles. If the shape of a molecule is known, vector addition can be used to predict the direction of the dipole moment of that molecule. Several examples are shown in Figure 1.15. The predictions agree with experimental results. For example, C02 is found by experiment to have a dipole moment of zero. It is a nonpolar molecule. Because the bonds are polar, this is possible only if the bond dipoles cancel. Therefore, C02 must be a linear molecule. On the other hand, because water is polar, with a dipole moment of 1.8 D, it cannot be a linear molecule. A molecule that has only relatively nonpolar carbon-carbon and carbon-hydrogen bonds has only a small dipole moment, if any, and is said to be nonpolar. 

The individual bond dipoles of COj point in opposite directions.These cancel on vector addition, so this compound has a dipole moment of zero. 

Although it is more difficult to see, the individual bond dipoles of CCI4 also cancel on vector addition, and the overall dipole moment is zero. 

Dielectric studies have been applied principally to the problem of deciding between several possible structures. A typical H bonded example may be taken from one of Curran s papers (467) o-methoxy-phenol (guaiacol) has two possible planar configurations whose dipole moments, as calculated by the vector addition method, are widely different (Fig. 5-3). The measured value of 2.41 d indicates that the intra-molecularly H bonded form exists in the benzene and dioxane solutions used. A large number of phenols, aniline derivatives, and other disub-stituted aromatic compounds have been studied in a similar fashion, and the wide occurrence of the ortho effect has been demonstrated. If two adjacent positions of the ring have proper substituents, a H bond will form. 

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