Hyperfine structure in the J = 1–0 transitions of DCO⁺, DNC, and HN¹³C: astronomical observations and quantum-chemical calculations

¹ SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen, The Netherlands e-mail: vdtak@sron.nl
² Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³ I. Physikalisches Institut der Universität, Zülpicher Straße 77, 50937 Köln, Germany
⁴ Institut für Physikalische Chemie, Universität Mainz, 55099 Mainz, Germany
⁵ Department of Chemistry and Biochemistry, University of Texas, Austin, TX 78712, USA

Received: 17 July 2009
Accepted: 27 August 2009

Abstract

Context. 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.

Aims. 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.

Methods. We have observed the ground-state () rotational transitions of DCO⁺, HN¹³C and DNC with the IRAM 30 m telescope toward the dark cloud LDN 1512 which has exceptionally narrow lines permitting hyperfine splitting to be resolved in part. The measured splittings of 50–300 kHz 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.

Results. We find  kHz and  kHz for DCO⁺,  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  kHz and C_I = -0.69 kHz for DCO⁺,  kHz for HN¹³C, and eQq(D) = 257.6 kHz and eQq(N) = 309.6 kHz for DNC. We also derive updated rotational constants for HN¹³C: B = 43 545.6000 (47) MHz and D = 93.7 (20) kHz.

Conclusions. The hyperfine splittings of the DCO⁺, DNC and HN¹³C lines range over 0.47–1.28 km s^-1, which is comparable to typical line widths in pre-stellar cores and to systematic gas motions on ~1000 AU 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.