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Ion-molecule reactions involving HCO$^+$ and N$_2$H$^+$: Isotopologue equilibria from new theoretical calculations and consequences for interstellar isotope fractionation

$Aims$: We revisit with new augmented accuracy the theoretical dynamics of basic isotope exchange reactions involved in the $^{12}$C/$^{13}$C, $^{16}$O/$^{18}$O, and $^{14}$N/$^{15}$N balance because these reactions have already been studied experimentally in great detail. $Methods$: Electronic structure methods were employed to explore potential energy surfaces, full-dimensional rovibrational calculations to compute rovibrational energy levels that are numerically exact, and chemical network models to estimate the abundance ratios under interstellar conditions. $Results$: New exothermicities, derived for HCO$^+$ reacting with CO, provide rate coefficients markedly different from previous theoretical values in particular at low temperatures, resulting in new abundance ratios relevant for carbon chemistry networks. In concrete terms, we obtain a reduction in the abundance of H$^{12}$C$^{18}$O$^+$ and an increase in the abundance of H$^{13}$C$^{16}$O$^+$ and D$^{13}$C$^{16}$O$^+$. In all studied cases, the reaction of the ion with a neutral polarizable molecule proceeds through the intermediate proton-bound complex found to be very stable. For the complexes OCH$^+$...CO, OCH$^+$...OC, COHOC$^+$, N$_2$...HCO$^+$, N$_2$H$^+$...OC, and N$_2$HN$_2^+$, we also calculated vibrational frequencies and dissociation energies. $Conclusions$: The linear proton-bound complexes possess sizeable dipole moments, which may facilitate their detection.