Context. Deuteration has been suggested to be a reliable chemical clock of star-forming regions due to its strong dependence on density and temperature changes during cloud contraction. In particular, the H3+ isotopologues (e.g. ortho-H2D+) seem to act as good proxies of the evolutionary stages of the star formation process. While this has been widely explored in low-mass star-forming regions, in the high-mass counterparts only a few studies have been pursued, and the reliability of deuteration as a chemical clock remains inconclusive. Aims. We present a large sample of o-H2D+ observations in high-mass star-forming regions and discuss possible empirical correlations with relevant physical quantities to assess its role as a chronometer of star-forming regions through different evolutionary stages. Methods. APEX observations of the ground-state transition of o-H2D+ were analysed in a large sample of high-mass clumps selected from the ATLASGAL survey at different evolutionary stages. Column densities and beam-averaged abundances of o-H2D+ with respect to H2, X(o-H2D+), were obtained by modelling the spectra under the assumption of local thermodynamic equilibrium. Results. We detect 16 sources in o-H2D+ and find clear correlations between X(o-H2D+) and the clump bolometric luminosity and the dust temperature, while only a mild correlation is found with the CO-depletion factor. In addition, we see a clear correlation with the luminosity-to-mass ratio, which is known to trace the evolution of the star formation process. This would indicate that the deuterated forms of H3+ are more abundant in the very early stages of the star formation process and that deuteration is influenced by the time evolution of the clumps. In this respect, our findings would suggest that the X(o-H2D+) abundance is mainly affected by the thermal changes rather than density changes in the gas. We have employed these findings together with observations of H13CO+, DCO+, and C17O to provide an estimate of the cosmic-ray ionisation rate in a sub-sample of eight clumps based on recent analytical work. Conclusions. Our study presents the largest sample of o-H2D+ in star-forming regions to date. The results confirm that the deuteration process is strongly affected by temperature and suggests that o-H2D+ can be considered a reliable chemical clock during the star formation processes, as proved by its strong temporal dependence.

An estimate of the degree of CO-depletion (f D ) provides information on the physical conditions occurring in the innermost and densest regions of molecular clouds. A key parameter in these studies is the size of the depletion radius, i.e. the radius within which the C-bearing species, and in particular CO, are largely frozen onto dust grains. A strong depletion state (i.e. f D > 10, as assumed in our models) is highly favoured in the innermost regions of dark clouds, where the temperature is < 20 K and the number density of molecular hydrogen exceeds a few ×10 4 cm −3 . In this work, we estimate the size of the depleted region by studying the Infrared Dark Cloud (IRDC) G351.77-0.51. Continuum observations performed with the Herschel Space Observatory and the LArge APEX BOlometer CAmera, together with APEX C 18 O and C 17 O J=2→1 line observations, allowed us to recover the large-scale beam-and line-of-sight-averaged depletion map of the cloud. We built a simple model to investigate the depletion in the inner regions of the clumps in the filament and the filament itself. The model suggests that the depletion radius ranges from 0.02 to 0.15 pc, comparable with the typical filament width (i.e.∼0.1 pc). At these radii, the number density of H 2 reaches values between 0.2 and 5.5×10 5 cm −3 . These results provide information on the approximate spatial scales on which different chemical processes operate in high-mass star forming regions and also suggest caution when using CO for kinematical studies in IRDCs.