  It has been generally accepted that there are significant quadrupolar and
bulk contributions to the second harmonic generation (SHG) reflected from the
neat air/water interface, as well as common liquid interfaces. Because there
has been no general methodology to determine the quadrupolar and bulk
contributions to the SHG signal from a liquid interface, this conclusion was
reached based on the following two experimental phenomena. Namely, the broken
of the macroscopic Kleinman symmetry, and the significant temperature
dependence of the SHG signal from the neat air/water interface. However,
because sum frequency generation vibrational spectroscopy (SFG-VS) measurement
of the neat air/water interface observed no apparent temperature dependence,
the temperature dependence in the SHG measurement has been reexamined and
proven to be an experimental artifact. Here we present a complete microscopic
analysis of the susceptibility tensors of the air/water interface, and show
that dipolar contribution alone can be used to address the issue of broken of
the macroscopic Kleinman symmetry at the neat air/water interface. Using this
analysis, the orientation of the water molecules at the interface can be
obtained, and it is consistent with the measurement from SFG-VS. Therefore, the
key rationales to conclude significantly quadrupolar and bulk contributions to
the SHG signal of the neat air/water interface can no longer be considered as
valid as before. This new understanding of the air/water interface can shed
light on our understanding of the nonlinear optical responses from other
molecular interfaces as well.
