  We have carried out extensive and detailed photoionization modeling to
successfully constrain the locations of different emission-line galaxies in
optical and mid-infrared diagnostic diagrams. Our model grids cover a wide
range in parameter space for the active galaxy continuum and starburst galaxies
with different stellar population laws and metallicities. We compare the
predicted AGN and star-formation mid-infrared line ratios [Ne III]15.56mm/[Ne
II]12.81mm and [O IV]25.89mm/[Ne III]15.56mm to the observed values, and find
that the best fit for the AGN is via a two-zone approximation. This two-zone
approximation is a combination of a matter-bounded component, where [Ne III]
and [O IV] are emitted efficiently, and a radiation-bounded component that
maximizes [Ne II] emission. We overlay the predictions from this two-zone
approximation onto the optical [O III]l5007/Hbeta and [N II]l6583/Halpha
diagnostic diagram derived from the Sloan Digital Sky Survey, to find that the
high-density and low-ionization radiation-bounded component in our two-zone AGN
approximation model provides a good lower limit for [N II] emission. This
establishes a new theoretical demarcation line for the minimum AGN contribution
in this diagram. This new classification results by a factor of ~1.4 in a
higher AGN population than predictions derived from previous divisions of
star-forming galaxies. Similarly, we define a maximum AGN contribution in the
[O III]/Hbeta and [N II]/Halpha diagram by using a two-zone approximation
within a parameter range typical of the narrow-line region.
