The Dipole Moments of Molecules

Now use the strategy you have just learned to solve Problem 42. 

In Section 1.3, we saw that if a molecule has one covalent bond, then the dipole moment of the molecule is identical to the dipole moment of the bond. When molecules have more than one covalent bond, the geometry of the molecule must be taken into account because both the magnitude and the direction of the individual bond dipole moments (the vector sum) determine the overall dipole moment of the molecule. 

The dipole moment depends on the magnitude of the individual bond dipoles and the direction of the individual bond dipoles. 

Because the direction of the bond dipoles have to be taken into account, totally symmetrical molecules have no dipole moment. In carbon dioxide (CO2), for example, the carbon is bonded to two atoms, so it uses sp orbitals to form the two C—O tr bonds. The remaining two p orbitals on the carbon form the two C—O ir bonds. The sp orbitals form a bond angle of 180°, which causes the individual carbon-oxygen bond dipole moments to cancel each other. Carbon dioxide therefore has a dipole moment of 0 D. 

Another symmetrical molecule is carbon tetrachloride (CCI4). The four atoms bonded to the sp carbon atom are identical and project symmetrically out from the carbon atom. Thus, as with CO2, the symmetry of the molecule causes the bond dipole moments to cancel. Therefore, methane also has no dipole moment. 

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The leading tenn in the electrostatic interaction between the dipole moment of molecule A and the axial quadnipole moment of a linear, spherical or synunetric top B is... 

Table 6-3. Comparison of the dipoles of the isolated individual monomers (dipole M) compare to the dipole moments of molecules within the dimer (dipole D) via the interaction, calculated with different functionals. Units are atomic units, and we give as well the difference in length and orientation ...

Quantities that have both magnitude and direction are called vectors. Examples of vectors in chemistry include things like the dipole moments of molecules, magnetic and electric fields, velocities and angular momenta. It is convenient to represent vectors geometrically and the simplest example is... 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

In this chapter we will also focus on the dipole moment of molecules. With these, some of the most interesting phenomena are the molecules for which the electric moment is in the wrong direction insofar as the atomic electronegativities are concerned. CO is probably the most famous of these cases, but other molecules have even more striking disagreements. One of the larger is the simple diatomic BF. We will take up the question of the dipole moments of molecules like BF in Chapter 12. In this chapter we will examine in a more general way how various sorts of structures influence electric moments for two simple cases. For some of the discussion in this chapter we restrict ourselves to descriptions of minimal basis set results, since these satisfactorily describe the physics of the effects. In other cases a more extensive treatment is necessary. 

Contribution of Unshared Electron Pairs to the Electric Dipole Moments of Molecules.—In the preceding chapter we discussed the dipole moments of molecules, in relation to the partial ionic character of bonds, without considering the possible contribution of unshared electron pairs. A simple treatment based on hybrid orbitals provides some justification of this procedure. 

Fig. 12.5 Illustration of the orientation angles used in the Stockmayer intermolecular potential. Molecule j consists of atoms A and B, and molecule i consists of atoms C and D. The vector ry runs from the center of mass of molecule i to the center of mass of molecule j. The vector JTJ gives the orientation and magnitude of the dipole moment of molecule i, with a similar definition for JTj. A ghost copy of molecule j is shifted to left to more easily visualize the orientation angle ifr. See Eqs. 12.11 to 12.13 and accompanying text for definition and description of these angles.

In a ferroelectric material, the dipole moments of molecules remain aligned in the absence of an external field. This alignment gives the material a permanent electric polarization. 

The dipole moments of molecules are often treated as being equal to the vector sum of the bond dipoles of the various bonds in the molecules. It is almost impossible to measure the dipole moment of an individual bond within a molecule. For example, molecules such as methane, carbon tetrachloride, and p-dichlorobenzene have no dipole moments, whereas molecules such as methylene chloride and m-dichlorobenzene do. The vector sum treatment could be made to agree quantitatively with all known dipole moments if the bond moments were treated as variables that depend on the nature of the particular molecule in which the bonds were located. 

Again uq(R) is the hard sphere potential. This is necessary to keep the molecules from overlapping. The parameter is the dipole moment of molecule i. The factor D(i, j) is a term that depends on the orientation of the dipoles i and j and need not concern us here. We can call this potential the dipolar hard sphere potential. 

One of the purposes for which static permittivities of aqueous nonelectrolyte solutions have been determined, by Franks and his coUeagues, is for calculation of the dipole moments of molecules. There are molecules for whidi no studies can be made in the vapour phase or in solution in non-polar solvents however, sufficiently good comparisons of determinations of dipole moments in aqueous solution with other determinations can sometimes be made to allow an estimate of the limitations of the method. 

In a way that cannot be gone into here, it is possible to measure the dipole moments of molecules some of the values obtained are listed in Table 1.3. We... 

Spectroscopic studies of the Stark effect lead, through application of quantum-mechanical perturbation theory, to values for the dipole moments of molecules in particular stationary states.4 Very careful work, such as the microwave Stark studies of Scharpen, Muenter, and Laurie5 on OCS, NNO, and CD3 —C=C—H, and the molecular beam elec-... 

The dipole moments of molecules depend on both the molecular dimensions and the electron distribution. For example, Z-l,2-dichloroethene has a dipole moment of 1.90 D, whereas, owing to its symmetrical structure, the E isomer has no molecular dipole. 

Van der Waal s force the Van der Waal s Force is the attractive force between molecules, which is caused by the induced temporary polarisation of molecules by the dipole moments of molecules. 

The dipole moment p may be the resultant dipole moment of a molecule, many molecules, or a whole region. Polarization P [Cm/m = C/m ] is the electrical dipole moment per unit volume (dipole moment volume density). It is therefore a more macroscopic concept than the dipole moment of molecules or atoms. P is a space vector having the same direction as the E-vector in isotropic and linear materials ... 

Differences between gas phase molecules and molecules in condensed phases have been summarized previously [91]. Chemical reactivity can be highly influenced by the chemical environment and, therefore, chemical reactivity of an isolated molecule in vacuum is not always a good model for a molecule surrotmded by other active or solvent molecules. A first step to study solvent effects is to consider the dipole moment of molecules in gas phase as well as in condensed phase. 

The dipole moment of a molecule with more than one covalent bond depends on the dipole moments of all the bonds in the molecule and the geometry of the molecule. We will examine the dipole moments of molecules with more than one covalent bond in Section 1.16 after you learn about the geometry of molecules. 

Now we recognize that Qil = the dipole moment of molecule 1, and obtain eqn 11.16a. 

Molecular orbital calculations may be used to predict the dipole moments of molecules. 

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