  This study examines the limitations of H$\alpha$ luminosity as a tracer of
star formation rates (SFR) in spatially resolved observations. We carry out
high-resolution simulations of a Milky Way-like galaxy including both supernova
and photoionization feedback, and from these we generate synthetic H$\alpha$
emission maps that we compare to maps of the true distribution of young stellar
objects (YSOs) on scales from whole-galaxy to individual molecular clouds
($\lesssim 100$ pc). Our results reveal significant spatial mismatches between
H$\alpha$ and true YSO maps on sub-100 pc scales, primarily due to ionizing
photon leakage, with a secondary contribution from young stars drifting away
from their parent molecular clouds. On small scales these effect contribute
significantly to the observed anti-correlation between gas and star formation,
such that there is noticeably less anti-correlation if we replace an
H$\alpha$-based star formation map with a YSO-based one; this in turn implies
that previous studies have underestimated the time it takes for young stars to
disperse their parent molecular clouds. However, these effects are limited in
dense regions with hydrogen columns $N_\mathrm{H} > 3 \times 10^{21}$
cm$^{-2}$, where the H$\alpha$- and YSO-based SFR maps show better agreement.
Based on this finding we propose a calibration model that can precisely measure
the SFR of large molecular clouds (mean radius > 100 pc) with a combination of
H$\alpha$ and CO observations, which provides a foundation for future study of
star formation processes in extragalactic molecular clouds.
