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Photoionization cross sections and rate coefficients have been calculated forall bound vibrational levels of the 1s$\sigma_{\mathrm{g}}$ state ofH$_{2}^{+}$, HD$^{+}$, and D$_{2}^{+}$. The Born-Oppenheimer approximation isemployed in our calculation of vibrationally-resolved photoionization crosssections. Vibrationally-resolved and local thermal equilibrium photoionizationrate coefficients are presented for photon temperatures less than $50\,000$ Kand are found to be several orders of magnitude larger than previous results inthe literature. Analytic fits for the vibrationally-resolved and local thermalequilibrium photoionization rate coefficients are provided. Near thresholdoscillations in the vibrationall-resolved photoionization are observed. Abenchmark set of photoionization cross sections are presented. Fixed-nucleiphotoionization cross sections are calculated using two-center true continuumwave functions and are verified by comparison with previous calculations andare found to be in excellent agreement in all cases. Data files for our set ofbenchmark cross sections, rate coefficients, and fitting parameters forH$_{2}^{+}$, HD$^{+}$, and D$_{2}^{+}$ are available on Zenodo under anopen-source Creative Commons Attribution license:https://doi.org/10.5281/zenodo.8304060 .

Photoionization from the ground and excited vibrational states of H+2 and its deuterated isotopologues