  It is generally argued that material classes with inversion symmetry do not
produce bulk dipole related second harmonic generation (SHG). So, SHG is then
either ascribed to surface effects or bulk related electric quadrupole or
magnetic dipole effects. Using symmetry and \emph{ab-initio} potentials we show
analytically that due to the fact of the decaying harmonic electric field
certain diamond crystal orientations, as e.g. Si(111), produce a bulk dipole
SHG response. For fcc and bcc lattices with a single atom basis, i.e. for the
most important metals, however, SHG can purely arise due to the disturbance
induced by the surface. Finally we propose an experiment, exploiting the
different dispersion for the fundamental as well as frequency doubled radiation
to determine this effect.
