scattering amplitudes in the specular direction vanish for modes whose normal coordinates are odd under the reflection. When the axis normal to the surface is an axis of two-fold symmetry, and time reversal symmetry holds then the scattering amplitudes in the specular direction vanish for modes whose normal modes are odd under the twofold rotation. All those selection rules make it possible to identify the normal coordinates of the adsorbed molecules. Intermediate negative ion resonance In intermediate negative ion resonance the electron forms a compound state with an adsorbed molecule during the scattering process. However, the lifetime of those states are so short that this type of scattering is barely observed. All of these regimes can at once be described with the help of the single microscopic theory. Selection rules for dipole scattering from the perspective of vibrational eigenmodes A microscopic theory makes it possible to approach the selection rule for dipole scattering in a more exact way. The scattering cross section is only non-vanishing in the case of a non-zero matrix element . Where denotes the initial and the final vibrational energy level of the adsorbed molecule and the component of its dipole moment. As the dipole moment is something like charge times length, has the same symmetry properties as , which is totally symmetric. Hence the product of and must also be a totally symmetric function, otherwise the matrix element vanishes. Hence excitations from the totally symmetrical ground state of a molecule are only possible to a totally symmetric vibrational state. This is the surface selection rule for dipole scattering. Note that it says nothing about the intensity for scattering or 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 also cause a vibration of the dipole moment normal to the surface. Therefore, the result in the "dipole scattering" section above is not exactly correct. When trying to gain information from selection rules, one must carefully consider whether 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 larger 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