  Star formation activity in molecular clouds is often found to be correlated
with the amount of material above a column density threshold of $\sim 10^{22}
\, {\rm cm^{-2}}$. Attempts to connect this column density threshold to a ${\it
volume}$ density above which star formation can occur are limited by the fact
that the volume density of gas is difficult to reliably measure from
observations. We post-process hydrodynamical simulations of molecular clouds
with a time-dependent chemical network, and investigate the connection between
commonly-observed molecular species and star formation activity. We find that
many molecules widely assumed to specifically trace the dense, star-forming
component of molecular clouds (e.g. HCN, HCO$^+$, CS) actually also exist in
substantial quantities in material only transiently enhanced in density, which
will eventually return to a more diffuse state without forming any stars. By
contrast, N$_2$H$^+$ only exists in detectable quantities above a volume
density of $10^4 \, {\rm cm^{-3}}$, the point at which CO, which reacts
destructively with N$_2$H$^+$, begins to deplete out of the gas phase onto
grain surfaces. This density threshold for detectable quantities of N$_2$H$^+$
corresponds very closely to the volume density at which gas becomes
irreversibly gravitationally bound in the simulations: the material traced by
N$_2$H$^+$ never reverts to lower densities, and quiescent regions of molecular
clouds with visible N$_2$H$^+$ emission are destined to eventually form stars.
The N$_2$H$^+$ line intensity is likely to directly correlate with the star
formation rate averaged over timescales of around a Myr.
