  Intermediate-mass black holes (IMBHs) with masses between $100 -
10^5M_{\odot}$ are crucial to our understanding of black hole seed formation
and are the prime targets for LISA, yet black holes in this mass range have
eluded detection by traditional optical spectroscopic surveys aimed at finding
active galactic nuclei (AGNs). In this paper, we have modeled for the first
time the dependence of the optical narrow emission line strengths on the black
hole mass of accreting AGN over the range of $100-10^8M_{\odot}$. We show that
as the black hole mass decreases, the hardening of the spectral energy
distribution from the accretion disk changes the ionization structure of the
nebula. The enhanced high energy emission from IMBHs results in a more extended
partially ionized zone compared with models for higher mass black holes. This
effect produces a net decrease in the predicted [OIII]/H$\beta$ and
[NII]/H$\alpha$ emission line ratios. Based on this model, we demonstrate that
the standard optical narrow emission line diagnostics used to identify massive
black holes fail when black hole mass falls below $\approx10^4M_{\odot}$ for
highly accreting IMBHs and for radiatively inefficient IMBHs with active star
formation. Our models call into question the ability of common optical
spectroscopic diagnostics to confirm AGN candidates in dwarf galaxies, and
indicate that the low-mass black hole occupation fraction inferred from such
diagnostics will be severely biased.
