Group electric dipole

Molecular point-group symmetry can often be used to determine whether a particular transition s dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states /ei and /ef do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components these symmetries can be read off the right most column of the character tables given in Appendix E), the matrix element will vanish. 

Forces Molecules are attracted to surfaces as the result of two types of forces dispersion-repulsion forces (also called London or van der Waals forces) such as described by the Lennard-Jones potential for molecule-molecule interactions and electrostatic forces, which exist as the result of a molecule or surface group having a permanent electric dipole or quadrupole moment or net electric charge. 

As shown in the Appendix (in Section V), in the C2h point group, the 1Ag - 1Bll (i.e. the monoelectronic r - jr excitation) possesses only an electric dipole moment, while in the C2V structure the electric and magnetic dipole moments, both non-vanishing, are orthogonal. In both cases the product in equation 1 leads to zero rotational strength. 

Let us now apply group theory again to determine the electric dipole (ED) allowed transitions. 

In the ideal case of free Eu + ions, we first must observe that the components of the electric dipole moment, e x, y, z), belong to the irreducible representation in the full rotation group. This can be seen, for instance, from the character table of group 0 (Table 7.4), where the dipole moment operator transforms as the T representation, which corresponds to in the full rotation group (Table 7.5). Since Z)° x Z) = Z) only the Dq -> Fi transition would be allowed at electric dipole order. This is, of course, the well known selection rule A.I = 0, 1 (except for / = 0 / = 0) from quantum mechanics. Thus, the emission spectrum of free Eu + ions would consist of a single Dq Ei transition, as indicated by an arrow in Figure 7.7 and sketched in Figure 7.8. 

Electric dipole n polarized emissions are those in which the electric field of the emitted light is parallel to z. Thus the selection rule for n emissions from level A1 are those defined by the direct product A1 x A2. By an inspection of the character table of group 1)3 (Table 7.6), we can easily prove that Ai x A2 = A2, so that only the A A2 emission is allowed by n polarized radiation (as shown in Figures 7.7 and 7.8). 

An interaction, either intermolecular or intramolecular, between molecules, groups, or bonds having a permanent electric dipole moment. The distance and relative orientation between the two dipoles governs the strength of this interaction. See also van der Waals Forces... 

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