  We present for the first time a detailed study of the properties of molecular
gas in metal-rich environments such as early-type galaxies (ETGs). We have
explored Photon-Dominated Region (PDR) chemistry for a wide range of physical
conditions likely to be appropriate for these sources. We derive fractional
abundances of the 20 most chemically reactive species as a function of the
metallicity, as a function of the optical depth and for various volume number
gas densities, Far-Ultra Violet (FUV) radiation fields and cosmic ray
ionisation rates. We also investigate the response of the chemistry to the
changes in $\alpha-$element enhancement as seen in ETGs. We find that the
fractional abundances of CS, H$_{2}$S, H$_{2}$CS, H$_{2}$O, H$_{3}$O$^{+}$,
HCO$^{+}$ and H$_{2}$CN seem invariant to an increase of metallicity whereas
C$^{+}$, CO, C$_{2}$H, CN, HCN, HNC and OCS appear to be the species most
sensitive to this change. The most sensitive species to the change in the
fractional abundance of $\alpha-$elements are C$^{+}$, C, CN, HCN, HNC, SO,
SO$_{2}$, H$_{2}$O and CS. Finally, we provide line brightness ratios for the
most abundant species, especially in the range observable with ALMA. Discussion
of favorable line ratios to use for the estimation of super-solar metallicities
and $\alpha$-elements are also provided.
