High Resolution Electron Energy Loss Spectroscopy - Selection Rules For Dipole Scattering From The Perspective of Vibrational Eigenmodes

Selection Rules For Dipole Scattering From The Perspective of Vibrational Eigenmodes

A microscopic theory makes it for example possible to approach the selection rule for dipole scattering in a more exact way. The scattering cross section is only none vanishing in the case of a nonzero matrix element . Where i denotes the initial and f the final vibrational mode of the adsorbed molecule and p_z the z component of its dipole moment.

As the dipole moment is something like charge times length p_z has the same symmetry properties as z, which is totally symmetric. Hence the product of i and f has to be a totally symmetric function, too, otherwise the matrix element would vanish. Hence

This is the surface selection rule for dipole scattering. Note that it says nothing about how big the intensity for scattering is and that not the displacement of the atoms of the adsorbate but its total dipole moment is the operator in the matrix element. This is important as a vibration of the atoms parallel to the surface can cause and vibration of the dipole moment normal to the surface, too. So the result in the section "dipole scattering" was not exactly correct.

When trying to gain information from selection rules it has to be carefully considered whether really a pure dipole or impact scattering region is investigated. Further symmetry breaking due to strong bindings to the surface must be considered. Another problem is that in cases of bigger molecules often many vibrational modes are degenerate, which could again be resolved due to strong molecule surface interactions. Those interactions can also generate completely new dipole moments which the molecule normally does not have. But when investigating carefully it is due to analysis of normal dipole modes mostly possible to get a very good picture of how the molecule adheres to the surface.