Vector addition, dipole moments

Additionally, the scalar magnitude of the magnetic dipole moment vector is given by [43]... 

Four thiourea molecules at sites are the building blocks of the unit cell of the crystal of the space group >2. The point group which is relevant for the selection rules is found by deleting the superscript, which yields >2a- Table 2.7-4 lists the details and results of the application of Eqs. I and II from Table 2.7-1. As shown in Fig. 2.7-8, the results are assigned to the components of the polarizability tensor and the dipole moment vector of the crystal, with x and y = a, b, c, which explains the Raman and infrared activity. We see that in addition to the translations of the whole crystal most... 

The electric field is calculated through the addition of a non-interacting particle at the desired position, and the sum of the dipole moment vectors divided by the polarizability of each particle is taken at this point. The enhancement of the electric field, M, is calculated by ... 

An alternative would retain the number of centers at three, but extend the expansion around each center beyond monopole, to include dipoles, quadrupoles, or perhaps even higher moments. One may, for example, place dipole moment vectors on each of the three atoms, as illustrated in Fig. 2g, to supplement the atomic charges in 2e. This scheme would not, however, provide for any charge distribution above or below the molecular plane. On the other hand, one can account for this aspect by adding a perpendicular component of a quadrupole moment to each atomic center, as indicated in Fig. 2h. This addition could add an important, and qualitatively correct, out-of-plane component to this molecule s interaction with another and help to model the O lone pairs. 

Here, is the dipole moment vector of the zth particle and n, is a unit vector along Rg — Ri. For any given configuration of the three particles, we have in this case the exact relation of additivity... 

The O—H bond lengths in the water molecule (H2O) are 0.96 A, and the H -O - H angle is 104.5°. The dipole moment of the water molecule is 1.85 D. (a) In what directions do the bond dipoles of the O— H bonds point In what direction does the dipole moment vector of the water molecule point (b) Calculate the magnitude of the bond dipole of the O—H bonds. (Note You will need to use vector addition to do this.) (c) Compare your answer from part (b) to the dipole moments of the hydrogen halides (Table 8.3). Is your answer in accord with the relative electronegativity of oxygen ... 

The CF4 and CFIF3 molecules have very similar polarizabilities, but CFIF3 is polar and CF is not. The dipole moment vector of CFIF3 is represented by the blue arrow. The difference in the dipole moments manifests itself as a dramatic difference in boiling point. As discussed, the intermolecular attractions between CHF3 molecules include additional contributions—namely, dipole-dipole and dipole-induced dipole interactions— that are not present between pairs of CF4 molecules. 

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. 

The dipole moment of 1,10-phenanthroline was first measured by Fielding and Le Fevre,18 who obtained a moment of 4.1 D, close to the value of 3.8 D expected for the hypothetical m-2,2 -bipyridyl. Since then the dipole moments of the phenanthrolines have been studied by other groups.16,17,64 The experimental values are recorded in Table I. They were found to be in good agreement with values computed by the vector addition of the moments of the individual pyridine nuclei. The molecular polarizability of 1,10-phenanthroline has been further studied and its molar Kerr constant determined.65... 

The dipole moments of the two conformers 146 and 147 of 1-rm-butyl-piperidine-4-spiro-4 (l, 3 -dioxolan) were calculated by vector addition of the moments of 1-fert-butylpiperidine and 4,4-dimethyl-1,3-dioxolan, making reasonable assumptions regarding geometries. This gave 1.15 and 1.93 D as the moments of the two conformers. The observed moment of 1.47 D gave AG° of 0.37 kcal mol-1 in favor of the axial oxygen conformer 146 in cyclohexane solution. AG%2- of 0.26 kcal mol-1 was estimated from low-temperature H-NMR studies.121 The differences between the piperidine and... 

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 measured dipole moments for (258-261) (Figure 3) (70AK(32)217, 75JHC615) agree closely with predicted values (75JHC615) based on vector addition of dipole moments for reference constituent compounds (benzo[6 ]thiophene, quinoline, isoquinoline). 

The observed dipole moments of a number of pyranopyrandiones also differ from the values calculated by vector addition. However, CNDO/2 calculated moments show a much closer agreement with the experimental values, as indeed does the value for pyran-4-one itself (76JHC609). 

The dipole moment of xanthone (21) (2.95 D) is considerably higher than that predicted by vector addition (1.85 D) of the moments of benzophenone (3.0 D) and diphenyl ether (1.15 D). Whilst this may be attributed to contributions from dipolar structures such as (183), it was concluded that there is but a small contribution from such species (37JCS196). 

A dipole moment study of the conformational equilibrium in some halogenotetrahy-dropyrans has been carried out (80JPR429). Comparison of the observed moments with those calculated by CNDO/2 and by vector addition for the pure conformers indicated that a halogen in the 3-position is preferably equatorially disposed. On the other hand, an axial arrangement is favoured by a 4-halogen atom. 

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 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. 

Dipole moments have been measured for four of the parent thienopyridines. Experimentally obtained data were similar to the predictions based upon vector addition using model compounds. The data are summarized in Table 34 <75JHC615>. 

---