Dipole moment magnitude

The next section in this chapter provides a brief comparison of the dipole moment (magnitude and direction) for a set of simple alcohols. Experimental gas phase dipole moments45 are compared to ab initio and as molecular mechanics computed values. It is important to note that the direction of the vector dipole used by chemists is defined differently in classical physics. In the former definition, the vector points from the positive to the negative direction, while the latter has the orientation reversed. 

Figure 3.3 Hypothetical distribution of dipole moment magnitudes from a simulation of liquid water. The dashed curve is generated by connecting the tops of histogram bins whose height is dictated by the number of water molecules found to have dipole moments in the range spanned by the bin. Note that although the example is illustrated to be symmetric about a central value (which will thus necessarily be (/z)) this need not be the case...

But with further development of the theory it became obvious that the effect of this displacement is negligible and that the dipole moment magnitude depends on the atomic dipole moments of the atoms O and N. 

For dipolar molecules in which the quantity is appreciably greater than 3a, the whole problem concerning the sensitivity of the anomaly magnitude on the precise forms of a ij) and a ijk) is absent, since the anomaly magnitude will depend entirely on the dipole moment magnitude in the absence of polarizability. Let us take the special case of nonpolarizable dipolar spheres for simplicity. Then the virial theorem yields... 

The effect of the dipole moment magnitude of the Hbrating molecxde on the intensity of Poley-type absorption was discussed in Ref. [55] for nonpolar liquids where it was found to be significwtly (by about an order of magnitude) lower than the observed intensities in the FIR spectra of polar liquids. In nonpolar liquids, the intensity of this absorption is usually related to the induced dipole momraits. 

Dipole moment Magnitude of the positive or negative charge constituting a dipole, multiplied by the spacing between the charges. 

Therefore, it has at most five independent components, and fewer if the molecule has some synnnetry. Syimnetric top molecules have only one independent component of 0, and, in such cases, the axial component is often referred to as the quadnipole moment. A quadnipolar distribution can be created from four charges of the same magnitude, two positive and two negative, by arranging them m the fonn of two dipole moments parallel to each other but pointing in opposite directions. Centro-syimnetric molecules, like CO2, have a zero dipole moment but a non-zero quadnipole moment. 

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15))... 

Our discussion of elecfronic effects has concentrated so far on permanent features of the cliarge distribution. Electrostatic interactions also arise from changes in the charge distribution of a molecule or atom caused by an external field, a process called polarisation. The primary effect of the external electric field (which in our case will be caused by neighbouring molecules) is to induce a dipole in the molecule. The magnitude of the induced dipole moment ginj is proportional to the electric field E, with the constant of proportionahty being the polarisability a ... 

Fi E- Zi eri F2 >. Here erj is the one-eleetron operator deseribing the interaetion of an eleetrie field of magnitude and polarization E with the instantaneous dipole moment... 

The compounds FCl and ICl have dipole moments p, that are similar in magnitude (0 9 and... 

The calculated magnitude of the dipole moment of water (2 39 D) is displayed at the bottom of the screen The calculated direction is indicated by a yellow arrow... 

The molecular dipole moment is perhaps the simplest experimental measure of charge density in a molecule. The accuracy of the overall distribution of electrons in a molecule is hard to quantify, since it involves all of the multipole moments. Experimental measures of accuracy are necessary to evaluate results. The values for the magnitudes of dipole moments from AMI calculations for a small sample of molecules (Table 4) indicate the accuracy you may... 

The permanent dipole moment of an isolated molecule depends on the magnitude of the charge and on the distance separating the positive and negative charges. It is defined as... 

In the examples shown in Figures 4.18(a)-4.18(g) all the molecules clearly have a charge asymmetry and, therefore, a non-zero dipole moment. Since a dipole moment has magnitude and direction it is a vector quantity and, if we wish to emphasize this, we use the vector symbol /x, whereas if we are concerned only with the magnitude we use the symbol /r. 

Although symmetry properties can tell us whether a molecule has a permanent dipole moment, they cannot tell us anything about the magnitude of a non-zero dipole moment. This can be determined most accurately from the microwave or millimetre wave spectrum of the molecule concerned (see Section 5.2.3). 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

The magnitude of the induced dipole moment depends on the electric field strength in accord with the relationship = nT, where ]1 is the induced dipole moment, F is the electric field strength, and the constant a is caHed the polarizabHity of the molecule. The polarizabHity is related to the dielectric constant of the substance. Group-contribution methods (2) can be used to estimate the polarizabHity from knowledge of the number of each type of bond within the molecule, eg, the polarizabHity of an unsaturated bond is greater than that of a saturated bond. 

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