Symmetry and dipole moments

All bonds between equal atoms are given zero values. Because of their symmetry, methane and ethane molecules are nonpolar. The principle of bond moments thus requires that the CH3 group moment equal one H—C moment. Hence the substitution of any aliphatic H by CH3 does not alter the dipole moment, and all saturated hydrocarbons have zero moments as long as the tetrahedral angles are maintained. 

Since the dipole moment is a vector in a particular direction it has the same symmetry species as a translation of the molecule in the same direction. Figure 6.21 shows this for FI2O in which the dipole moment and the translation in the same direction have the same symmetry species, the totally symmetric dj species. In general. 

Conformational populations of cyanomethylphosphine oxides (136) have been estimated from dipole moments and indicate a preference for the tra/15-conformation. The moments of the o-, m- and p-chloro- and tolyl-derivatives of triaryl phosphites (137, Y = ) and triaryl phosphates (137 Y = O) indicate that the oxygen atom in the latter series causes the aryl rings to rotate further away from a position in which their planes all meet along the molecular symmetry axis. Conformational studies have also been carried out on the dioxaphosphorinanes. The moments of the isomeric series (138a) and (138b) were in the ranges 3.7—4.2 and 5.4—5.5 D respectively. ... 

The operators for the potential, the electric field, and the electric field gradient have the same symmetry, respectively, as those for the atomic charge, the dipole moment, and the quadrupole moment discussed in chapter 7. In analogy with the moments, only the spherical components on the density give a central contribution to the electrostatic potential, while the dipolar components are the sole central contributors to the electric field, and only quadrupolar components contribute to the electric field gradient in its traceless definition. 

The melting points in the data set can be explained as equally due to the influence of Ncu the dipole moment, and the molecular symmetry, but with very little influence from Alp. 

One requirement for second-order non-linearity in optical molecules is that they exhibit non-centrosymmetric symmetry, i.e. they must be dipolar in nature and all point in the same direction. Hence, materials suitable for electro-optical uses should have high figures for the multiplier where p is the dipole moment and P the molecular second order optical non-linearity parameter. ... 

One of the most useful features of a QM model is its ability to provide information about the molecular charge distribution. It is a general rule of thumb that even very low quality QM methods tend to give reasonable charge distributions. For neutral molecules, the dominant moment in the overall charge distribution is the usually dipole moment (unless symmetry renders the dipole moment zero). For a 125-molecule test set including H, C, N, O, F, Al, Si, P, S, Cl, Br, and I functionality, Stewart found mean unsigned errors in dipole moments... 

Symmetry also plays an important part in the determination of the structure of molecules. Here, a great deal of the evidence comes from the measurement of crystal structures, infra-red spectra, ultra-violet spectra, dipole moments, and optical activities. All of these are properties which depend on molecular symmetry. In connection with the spectroscopic evidence, it is interesting to note that in the preface to his famous book on group theory, Wigner writes ... 

At the end of this chapter we will show that knowledge of symmetry can lead us directly to predict whether a molecule can have a dipole moment and whether it can exhibit optical activity. 

It is a remarkable fact that the translational transitions of virtually all supermolecules are infrared active - even if the individual molecules are not. The only exceptions are supermolecules that possess a symmetry which is inconsistent with the existence of a dipole moment. Pairs of like atoms, e.g., He-He, have inversion symmetry, implying a zero dipole moment and, hence, infrared inactivity. But dissimilar atomic pairs, e.g., He-Ar, or randomly oriented molecular pairs, e.g., H2-H2, generally lack such symmetry. As a consequence, more or less significant collision-induced dipoles exist for the duration of the interaction which generate the well known collision-induced spectra. 

Since a molecule with a center of symmetry, such as one belonging to point groups D h (n even). Cntl (n even). Dtlll (n odd), O, and //, cannot have a dipole moment, no matter how polar the individual bonds (Chapter 3), dipole moments have proved to be useful in distinguishing between two structures Much of the classic chemistry of square planar coordination compounds of the type MA2B2 was elucidated on the basis of cis isomers having dipole moments and traps isomers having none (see Chapter 12). ... 

Symmetry is a fundamental concept of paramount importance in art, mathematics, and all areas of natural science. In the context of chemistry, once we know the symmetry characteristics (i.e., point group) of a molecule, it is often possible for us to draw qualitative inferences about its electronic structure, its vibrational spectra, as well as other properties such as dipole moment and optical activity. 

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