  The paper demonstrates possibility of giant enhancement of Surface Enhanced
Hyper Raman Scattering on the base of qualitative consideration of
electromagnetic field near some models of rough metal surfaces and of some
features of the dipole and quadrupole light-molecule interaction, such as it
was made in the dipole-quadrupole SERS theory. Consideration of symmetrical
molecules allows to obtain selection rules for their SEHR spectra and establish
such regularity as appearance of the bands, caused by the totally symmetric
vibrations, transforming after the unitary irreducible representation in
molecules with C2h,D and higher symmetry groups, which are forbidden in usual
HRS spectra. Analysis of literature data on trans-1,2-bis (4-pyridyle) ethylene
and pyridine molecules demonstrates that their SEHR spectra can be explained by
the SEHRS dipole-quadrupole theory, while analysis of the SEHR spectrum of
pyrazine reveals appearance of the strong forbidden bands, caused by vibrations
transforming after the unitary irreducible representation that strongly
confirms this theory which permits to interpret the whole SEHR spectrum in
detail. The results corroborate this common mechanism of Surface Enhanced
optical processes on molecules adsorbed on rough metal surfaces.
