The presence of both acidic and basic adsorption sites on the surface of hydroxyapatite [${\mathrm{Ca}}_{10}{({\mathrm{PO}}_{4})}_{6}{(\mathrm{OH})}_{2}$; HAP] is an interesting property for catalytic applications. Here, we report a density functional theory investigation of the adsorption properties of $\mathrm{CO}, {\mathrm{CO}}_{2}, {\mathrm{C}}_{2}{\mathrm{H}}_{2}, {\mathrm{CH}}_{4}, {\mathrm{H}}_{2}, {\mathrm{H}}_{2}\mathrm{O}, {\mathrm{NH}}_{3}, {\mathrm{SO}}_{2}$, and ${\mathrm{BCl}}_{3}$ on the $\mathrm{HAP}(0001)$ surface. All probe molecules have a lower energy when they are adsorbed in the region between the most exposed ${\mathrm{Ca}}^{2+}$ ion (electron acceptor) and a neighboring $\mathrm{PO}{{}_{4}}^{3\ensuremath{-}}$ group, where the $\mathrm{O}$ atoms (electron donor) contribute to the stabilization of the adsorbed molecule. By evaluating the redistribution of the electron density and the change of the atomic charges, the ${\mathrm{Ca}}^{2+}$ and $\mathrm{PO}{{}_{4}}^{3\ensuremath{-}}$ sites were identified as Lewis acidic and Lewis basic adsorption sites, respectively, which indicates that simultaneous acid-base interactions occur upon adsorption of all studied probe molecules. All adsorbates interact with the surface via atoms of opposing charges, which enhances the ionic character of molecular bonds by increasing the distinction between cationic and anionic charges within the molecule. Furthermore, molecules with greater ionic character show stronger interaction with the substrate and greater geometric deformation. Although most adsorbed molecules ($\mathrm{CO}, {\mathrm{CO}}_{2}, {\mathrm{C}}_{2}{\mathrm{H}}_{2}, {\mathrm{CH}}_{4}, {\mathrm{H}}_{2}, {\mathrm{H}}_{2}\mathrm{O}$, and ${\mathrm{NH}}_{3}$) do not show substantial net charge transfer, polarization effects due to the redistribution of charge are observed upon adsorption of all probe molecules. The change in the work function increases linearly with the total change in the surface dipole moment for ${\mathrm{H}}_{2}\mathrm{O}, {\mathrm{NH}}_{3}, {\mathrm{SO}}_{2}$, and ${\mathrm{BCl}}_{3}$, while for the remaining systems, the magnitude of the work function change remains more uniform. By identifying the type of interaction between each probe molecule and the $\mathrm{HAP}(0001)$ surface, the present study contributes to the understanding of the acid-base properties of the $\mathrm{HAP}(0001)$ surface, which we elaborated in a short discussion based on the individual bond orders for the acidic and basic sites.