  We report spatial distributions of the Fe-K$\alpha$ line at 6.4 keV and the
CO($J$ = 2--1) line at 230.538 GHz in NGC 2110, which are respectively revealed
by $Chandra$ and ALMA at $\approx$ 0.5 arcsec. A $Chandra$ 6.2--6.5
keV-to-3.0--6.0 keV image suggests that the Fe-K$\alpha$ emission extends
preferentially in a northwest-to-southeast direction out to $\sim$ 3 arcsec, or
500 pc, on each side. Spatially-resolved spectral analyses support this by
finding significant Fe-K$\alpha$ emission lines only in northwest and southeast
regions. Moreover, their equivalent widths are found $\sim$ 1.5 keV, indicative
for the fluorescence by nuclear X-ray irradiation as the physical origin. By
contrast, CO($J$ = 2--1) emission is weak therein. For quantitative discussion,
we derive ionization parameters by following an X-ray dominated region (XDR)
model. We then find them high enough to interpret the weakness as the result of
X-ray dissociation of CO and/or H$_2$. Another possibility also remains that CO
molecules follow a super-thermal distribution, resulting in brighter emission
in higher-$J$ lines. Further follow-up observations are encouraged to draw a
conclusion on what predominantly changes the inter-stellar matter properties,
and whether the X-ray irradiation eventually affects the surrounding star
formation as an AGN feedback.
