Image dipoles

When an atom or molecule approaches a surface, the electrons in the particle - due to quantum fluctuations - set up a dipole, which induces an image dipole in the polarizable solid. Since this image dipole has the opposite sign and is correlated with fluctuations in the particle, the resulting force is attractive. In the following we construct a simple model to elucidate the phenomenon. 

There is also the normal dipole selection rule in operation, as illustrated in Figure 5.48, due to Liith (1981). Any dipole at a surface induces an image charge within the surface. If the dipole orientation is normal to the surface, the effect is enhanced by the image dipole. If, however, the orientation is parallel to the surface, the effect is annihilated by the image dipole. This orientation selection rule thus strongly favours normally oriented dipoles. 

Furthermore, as mentioned above the screening of the dipole field by the conduction electrons can be represented by an image dipole inside the metal. This complex of the chemisorbed molecule and its image has a vibration frequency different from that of the free molecule. The electrodynamic interaction between a dipole and its image has been discussed in many works. The theoretical problem is that the calculated frequency shift is extremely sensitive to the position of the image plane (Fig. 3a). One can with reasonable parameter values obtain a downward frequency shift of the order of 5-50 cm S but the latest work indicates that the shift due to this interaction is rather small. 

Ideal gas, standard state, 936 Ilkovic equation, 1246 Ilkovic, D., polarography, 1424 Image dipole, 896... 

Fig. 6.73. (a) The interaction between a water molecule and a metal can be computed by (b) replacing the metal with an image dipole. 

Define the following terms used in Section 6.7 (a) image forces, (b) image dipole, (c) dispersion forces, (e) chemical forces, (f) saturated dielectric, (g) water monomers and water dimers, (h) configurational entropy, (i) libration entropy, and (j) vibrational entropy. (Gamboa-Aldeco)... 

Figure 6. Dependence on distance d from image plane of the image dipole sum V for the ( /TX " / 3)-30o structure ( = 1/3) of CO on Cuflll). Also shown is the frequency shift, = 0 - = 1/3, which depends strongly on the displacement of the singleton frequency to lower values by the self-image.

On metal surfaces, two additional selection mles apply. The first is that only vibrations perpendicular to the surface are HREELS active. This mle follows from two phenomena unique at metal surfaces " (i) Electromagnetic waves polarized perpendicularly to the plane of incidence (parallel to the plane of the surface) undergo a 180° phase shift upon reflection. That is, at the metal surface, the out-of-phase electric-field vectors of the incident and reflected waves cancel each other as a result, no field exists that can couple with dipoles that oscillate parallel to the surface, (ii) The dynamic dipole moment generated by an oscillator that vibrates in the surface-parallel direction is cancelled by that of its image dipole (Figure 1) hence, there the net dynamic dipole moment is zero. On the other hand, if the real dipole is oriented perpendicularly to the surface, its dynamic dipole moment is reinforced by that of its image dipole. This selection mle is the same as that for infrared reflection-absorption spectroscopy (1RAS).°... 

Figure 1 The dynamic electric moment of the dipole oriented parallel to the metal surface is cancelled by that of its image dipole. In the vertical orientation, the dynamic electric moments of the surface and image dipoles reinforce each other...

Campion, A., Gallo, A., Harris, C., Robota, H. J., and Whitmore, P. (1980) Electronic energy transfer to metal surfaces A test of classical image dipole theory at short distances. Chem. Phys. Letts. 73 447-450. 

Solution of Eq. (5.8) for the operator b, and then determination of n t) by first-order perturbation theory yields a formula similar to Eq. (5.7) and the results in Fig. 28. A number of assumptions must be made to obtain quantitative agreement with experiment, including two critical ones. First, the energy of the n level as a function of the distance of the molecule from the surface is written in the image-dipole form ... 

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