2009A&A...507..347V

Knowledge of the hyperfine structure of molecular lines is useful for estimating reliable column densities from observed emission, and essential for the derivation of kinematic information from line profiles. Deuterium bearing molecules are especially useful in this regard, because they are good probes of the physical and chemical structure of molecular cloud cores on the verge of star formation. However, the necessary spectroscopic data are often missing, especially for molecules which are too unstable for laboratory study. We have observed the ground-state (J=1-0) rotational transitions of DCO⁺, HN¹³C and DNC with the IRAM 30m telescope toward the dark cloud LDN 1512 which has exceptionally narrow lines permitting hyperfine splitting to be resolved in part. The measured splittings of 50-300kHz are used to derive nuclear quadrupole and spin-rotation parameters for these species. The measurements are supplemented by high-level quantum-chemical calculations using coupled-cluster techniques and large atomic-orbital basis sets. We find eQq=+151.12(400)kHz and C_I=-1.12(43)kHz for DCO⁺, eQq=272.5(51)kHz for HN¹³C, and eQq(D)=265.9(83)kHz and eQq(N)=288.2(71)kHz for DNC. The numbers for DNC are consistent with previous laboratory data, while our constants for DCO⁺ are somewhat smaller than previous results based on astronomical data. For both DCO⁺ and DNC, our results are more accurate than previous determinations. Our results are in good agreement with the corresponding best theoretical estimates, which amount to eQq=156.0kHz and C_I=-0.69 kHz for DCO⁺, eQq=279.5kHz for HN¹³C, and eQq(D)=257.6kHz and eQq(N)=309.6kHz for DNC. We also derive updated rotational constants for HN¹³C: B=43545.6000(47)MHz and D=93.7(20)kHz. The hyperfine splittings of the DCO⁺, DNC and HN¹³C J=1-0 lines range over 0.47-1.28km/s, which is comparable to typical line widths in pre-stellar cores and to systematic gas motions on ∼1000AU scales in protostellar cores. We present tabular information to allow inclusion of the hyperfine splitting in astronomical data interpretation. The large differences in the ¹⁴N quadrupole parameters of DNC and HN¹³C have been traced to differences in the vibrational corrections caused by significant non-rigidity of these molecules, particularly along the bending coordinate.