© ESO, 2013

1. Introduction

Acetylene can be found in several astronomical environments: in molecular clouds (Lacy et al. 1989), in massive young stellar objects and planet forming zones (Lahuis & van Dishoeck 2000; Bast et al. 2013), in circumstellar envelopes of AGB stars (Ridgway et al. 1976; Matsuura et al. 2006; Fonfría et al. 2008), and it has been identified in cometary comae (Mumma et al. 2003) as well. This unsaturated hydrocarbon may react with radicals – atomic C, CN, and CH – to form complex molecules in starless cores (Herbst 2005), it plays a key role in the formation of circumstellar carbon chain molecules (Cherchneff & Glassgold 1993) and it is even a possible precursor of benzene in a carbon-rich PPN (Woods et al. 2002).

However, ¹²C₂H₂ does not have a permanent dipole moment and cannot be detected by (sub-)millimetre telescopes, therefore interstellar acetylene has been detected by observing its vibration-rotation bands. The only detectable sub-millimetre features could be those due to some P-branch high-J transitions of the ν₅ ← ν₄ difference band in the THz region (Yu et al. 2009). On the other hand, non-centrosymmetric isotopologues of acetylene, such as the subject of this paper ¹²C₂HD, do have a small permanent electric dipole moment. The first astronomical detection of ¹²C₂HD is recent, namely it has been observed in Titan’s atmosphere through the Composite InfraRed Spectrometer (CIRS) mounted on the Cassini spacecraft (Coustenis et al. 2008). From these observations it was possible to derive the D/H ratio on Titan, which was previously determined only through the transitions of the CH₄/CH₃D pair.

Molecules containing less abundant isotopes are very relevant from an astrophysical point of view. Several species containing D, ¹³C, ¹⁵N, ¹⁸O, among the most important, provide a tool to assess isotopic ratios in several astronomical environments (see for instance Herbst 2003; Caselli & Ceccarelli 2012; Bézard 2009). The D/H isotopic ratio is of particular interest for several reasons. It is an important experimental constraint on the Big Bang models, as deuterium was formed in abundance only in this event. It can also provide key information on the chemical processes that lead to the formation of complex organic molecules (Sandford et al. 2001). Although the cosmic D/H ratio is of the order of magnitude of 10^-5, abundances of a few percent with respect to their parent species can be produced in the interstellar medium through isotopic fractionation mechanisms (Herbst 2003). It is known that in cold dense interstellar clouds D-enrichment proceeds through gas phase ion-molecule exothermic reactions, but also through gas-grain chemistry (Sandford et al. 2001). Alternative routes for achieving D-H fractionation in more energetic environments and of interest for complex molecules are: a) gas phase unimolecolar photodissociation; and b) ultraviolet photolysis in D-enriched ice mantles (Sandford et al. 2001).

Laboratory rotational spectra have been observed in the past for several monodeuterated species of acetylene, including also ¹³C containing isotopologues (Wlodarczak et al. 1989; Matsumura et al. 1980; Cazzoli et al. 2008; Degli Esposti et al. 2013). Rotational transitions of ¹²C₂HD were measured up to 418 GHz for the ground vibrational state (GS) and for the v₄ = 1 and v₅ = 1 excited states, ν₄ and ν₅ being the trans and cis bending modes, respectively (Wlodarczak et al. 1989). Pure rotational transitions in the GS up to J′′ = 10, around 650 GHz, were observed for ¹²C₂HD, H¹²C¹³CD and H¹³C¹²CD (Cazzoli et al. 2008). In the same study, ab initio calculations were performed at various levels in order to predict the electric dipole moment for these species and the equilibrium structure of acetylene. The calculated dipole moment does not show sizable variations upon isotopic substitution of one carbon atom, and is approximately 0.01 D for all monodeuterated isotopologues in the GS. The ν₅ ← ν₄ difference band and associated hot bands for ¹²C₂HD have been recorded recently in the far-infrared (FIR) region, between 60 and 360  cm^-1, using the synchrotron radiation at the Canadian Light Source (Predoi-Cross et al. 2011). The same band for the H¹²C¹³CD and H¹³C¹²CD isotopologues was also detected and analysed.

As far as the infrared (IR) region is concerned, several papers have been published on ¹²C₂HD. The most recent are the investigations of the bending states up to v₄ + v₅ = 3 (Fusina et al. 2005a) and of the stretching-bending bands in the 1800–4700  cm^-1 spectral region (Fusina et al. 2005b). In both cases the spectra were recorded by Fourier transform infrared spectroscopy (FTIR). A study of the integrated band intensities in the 25–2.5 μm window was also published (Jolly et al. 2008).

In the present paper we report on the observation of the pure rotational transitions of ¹²C₂HD up to 657 GHz, that is in bands 3, 6, 7, 8 and 9 of the Atacama Large Millimeter Array (ALMA). A total of 168 transitions were assigned in the GS and in various excited vibrational bending states. The rotational lines detected in this work were fitted together with the FIR (Predoi-Cross et al. 2011) and IR lines (Fusina et al. 2005a). The spectroscopic parameters obtained from the final global fit are determined with an excellent accuracy.

The high accuracy of the millimetre- and submillimetre-wave data presented in this paper, together with the increasing sensitivity of new observation systems, such as ALMA, will favour the observation of transitions belonging to this species.

It should also be stressed that the dipole moment of ¹²C₂HD is strongly enhanced by the bending vibrations. Therefore, considering that some chemically rich regions, e.g. IRC+10216 (Cernicharo et al. 2011), show a high degree of vibrational excitation, this will facilitate the detection of emission lines in the bending states ν₄ or ν₅ of ¹²C₂HD. In Sect. 3.1, the dipole moment variation in excited bending states is discussed.

2. Experimental details

The sample of ¹²C₂HD was purchased from CDN Isotopes (98.9% purity). The rotational spectra of ¹²C₂HD were observed in selected frequency regions between 100 and 700 GHz, using a source-modulation mm-wave spectrometer which employs Gunn oscillators (RPG Radiometer Physics GmbH and J. E. Carlstrom Co.) as main radiation sources covering the fundamental frequency range 75–124 GHz. Higher frequencies were generated using three different frequency multipliers (VDI – Virginia Diodes, Inc. and RPG). The Gunn oscillators were phase-locked to the suitable harmonic of the frequency emitted by a computer-controlled frequency synthesizer (Schomandl), referenced to an external rubidium frequency standard (SRS Stanford Research System). This guaranteed an absolute accuracy of ca. 20 Hz to the frequency scale. A liquid-helium-cooled InSb detector (QMC Instr. Ltd.) was employed. The Gunn oscillators were frequency modulated at 6 kHz, and the detected signals were demodulated by a lock-in amplifier tuned at twice the modulation frequency, so that the second derivative of the actual spectrum profile was detected by the computer-controlled acquisition system.

Transition frequencies were recovered from a line-shape analysis of the spectral profile (Dore 2003); their accuracy, estimated by repeated measurements, was in the range 5–30 kHz depending on the signal-to-noise ratio of the recorded lines.

The absorption cell was a 3.5 m long, 10 cm in diameter glass tube equipped with polyethylene windows. A double pass arrangement based on a wire grid polarizer and a roof mirror (Ziurys et al. 1994; Dore et al. 1999) was employed to increase the absorption path. Sample pressures of a few tens of mTorr were employed during the measurements.

3. Results and discussion

3.1. Rotational analysis

Fig. 1 The J = 5 ← 4 transition of 12C2HD in the v5 = 1, ground, and v4 = 1 vibrational states. The low-frequency components of each ℓ-doublet are displayed. Fourteen scans are co-added, the total integration time is 850 s.

The very small dipole moment of ¹²C₂HD was first determined by Matsumura et al. (1980), who performed Stark-effect measurements on the J = 2 ← 1 rotational transition of ¹²C₂HD in the v₄ = 1,3 and v₅ = 1,3 states. The obtained dipole moment values are: − 0.02359(5) D for v₄ = 1, 0.05601(9) D for v₅ = 1, − 0.09077(26) D for v₄ = 3 and 0.1472(21) D for v₅ = 3. These experimental values led to extrapolate a GS moment of 0.01001(15) D, since the dipole moments of the v₄ = 1 and v₄ = 3 states have opposite sign with respect to that of the GS. The increase of the dipole moment values due to vibrational excitation causes a considerable intensity enhancement of the excited state rotational lines, so that their detection is much easier than expected from an evaluation of the population factors. At room temperature (kT = 207  cm^-1), the population factors are N₄/N₀ = exp ( − 518/kT) = 0.0819 and N₅/N₀ = exp ( − 677/kT) = 0.0378, which should reduce the intensity of the rotational lines by a factor of 12 for v₄ = 1 and of 26 for v₅ = 1. It should be noticed that the bending states are doubly degenerate. However, the factor 2, which doubles the population of v₄ = 1 and v₅ = 1, has no effect on the intensity of the rotational lines. In fact, the ℓ-type doubling removes the degeneracy of the levels and rotational transitions are allowed only within each set. On the other hand, from the experimental μ values one can calculate the following ratios: (μ₄/μ₀)² ≃ 5.6 and (μ₅/μ₀)² ≃ 31, which partly compensate the unfavourable population factors of the excited states. The intensity ratio between rotational lines in the excited bending states and in the GS can be calculated as (1)The rotational transitions in v₄ = 1 are expected to be less intense than those of the GS by only a factor 12/5.6 ≃ 2, whereas the lines in v₅ = 1 should be even stronger than those in the GS by a factor 31/26 ≃ 1.2. Figure 1 shows a 250 MHz frequency scan in which the J = 5 ← 4 transitions of v₅ = 1, ground, and v₄ = 1 states are simultaneously present. The experimental intensity ratios nicely agree with the predicted ones. Anyway, for any combination of bending vibrational quanta, the dipole moment can be calculated by applying the usual expression for the vibrational dependence (2)as reported in Eq. (11) of Matsumura et al. (1980). The values of the parameters δμ_i are: δμ₄ = − 0.03360(13) D and δμ₅ = 0.04600(17) D, as given in Table 3 of the same reference. For mixed excitations of ν₄ and ν₅ there is a less significant enhancement on the dipole moment, and therefore on the intensity, since δμ₄ and δμ₅ have opposite sign and comparable magnitude. Indeed, only transitions in the combination v₄ + v₅ could be detected, whereas in higher-order mixed vibrational excitations they were too weak to be observed.

A summary of the intensity predictions at 300 K and 500 K for rotational lines of some vibrationally excited bending states is reported in Table 1. It is evident a large temperature effect, therefore at 500 K the transitions in vibrational states up to the doubly excited ν₄ and ν₅ are stronger than the ground-state ones.

A very limited number of excited-state transitions of ¹²C₂HD have previously been observed only for v₄ = 1,3 (Π) and v₅ = 1,3 (Π) (Wlodarczak et al. 1989; Matsumura et al. 1980). We have considerably enlarged the previous data-set by measuring more than 150 new line frequencies, spanning J values from 1 to 10, corresponding to transitions in the ground state, in the first excited vibrational bending states v₄ = 1 and v₅ = 1 (Π), in the doubly excited v₄ = 2 and v₅ = 2 states (Σ⁺ and Δ), in the combination state v₄ = v₅ = 1 (Σ⁻, Σ⁺ and Δ) and in the triply excited v₄ = 3 and v₅ = 3 states (Π and Φ). The search of the rotational lines was guided by predictions based on the spectroscopic constants determined in a previous analysis of 4888 IR and FIR data and 21 rotational transitions available at that time (Predoi-Cross et al. 2011). On average, the newly observed lines were found some hundreds of kHz away from the initial predictions. The measured transition frequencies are listed in Table 2, along with predictions of unobserved low-J transitions and of the ones occurring at higher frequency up to 1 THz.

The term values of the observed rotational levels in the ground and excited vibrational states are in the range 2 − 2140  cm^-1. With the exception of the ground state, multiplets of rotational lines were always observed for each J + 1 ← J transition, because of ℓ-type resonance effects. Before performing the final ro-vibrational global analysis (see Sect. 3.2), a series of state-by-state least-squares fits were done to check the consistency of the MW measurements. The pure rotational spectra have been analysed using the formalism originally developed by Yamada et al. (1985) and already employed to fit the excited-state rotational spectra of a large number of linear carbon chains (see for example Bizzocchi & Degli Esposti 2008, and references therein). The model is slightly different from the one used to perform the global ro-vibrational analysis (see Sect. 3.2 for a detailed description), because the vibrational dependence of the various parameters is neglected, so that effective constants for each vibrational state were determined by these preliminary fits. Briefly, rotational and vibrational ℓ-type resonance effects have been treated by diagonalization of ro-vibrational matrices with off-diagonal elements which include q_t, , r_tt′ and spectroscopic parameters (t and t′ being equal to 4 or 5). The vibrational energy differences between the interacting ℓ sublevels (Δℓ_t = ± 2) of each doubly or triply excited vibrational state have been expressed through the effective values of the constants g₄₄, g₅₅ and g₄₅, which produce ℓ-dependent energy contributions. In addition, the ℓ-dependence of rotational and quartic centrifugal distortion constants have been taken into accounts trough the γ^tt′ and δ^tt′ parameters, respectively. Generally, not all of the required constants can be statistically determined from the rotational transitions of a single vibrational state, and some assumptions had to be necessarily made. The ℓ-type doubling parameters q_t and were fitted for the v_t = 1 (t = 4 or 5) and v_t = 3 states (where degenerate ℓ = ± 1 levels do exist), but constrained to interpolated values for the v_t = 2 states, in order to avoid high correlations with the g₄₄ and g₅₅ constants. The latter constant has a rather large value (ca. 5.2  cm^-1), so that rotational ℓ-type resonance effects are weak in the v₅ = 3 state, where no splitting of the | ℓ | = 3 lines could be observed. As far as the v₄ = v₅ = 1 combination state is concerned, where rotational and vibrational ℓ-type resonance effects are simultaneously present, q_t and constants were held fixed at the values determined for the singly excited bending states, while the parameters involved in the vibrational ℓ-type resonance, namely g₄₅, r₄₅ and were refined. The various state-by-state fits were repeated iteratively in order to achieve full consistency of the obtained parameters. The results of the eight least-squares fits performed are collected in Tables 3 and 4.

3.2. Global ro-vibrational analysis

Ro-vibrational transitions involving the vibrational states presently studied, except the v₄ = 3 state (Φ), were already observed in the FIR and IR regions (Predoi-Cross et al. 2011; Fusina et al. 2005b). They have been fitted together with the rotational transitions presently measured. The model Hamiltonian adopted for the global analysis represents an extension up to three quanta of the bending excitation, i.e. v₄ + v₅ = 3, of the Hamiltonian for a molecule with two bending vibrations which has been described in detail by Herman et al. (1991). It was already used for ¹³C₂HD (Degli Esposti et al. 2013) and ¹²C₂HD (Fusina et al. 2005a) itself. The term values of the ro-vibrational levels of the transitions were obtained by diagonalizing the appropriate energy matrix containing the following vibrational (G⁰) and rotational (F) diagonal contributions: with M = J(J + 1) and k = ℓ₄ + ℓ₅.

Vibrational and rotational ℓ-type resonances are expressed by off-diagonal matrix elements (Herman et al. 1991) containing the following parameters: The global fit included 5317 IR and 168 MW transitions. Overlapping lines were given zero weight. The uncertainty for the FIR and IR data was in the range 5.0 × 10^-5 − 2.0 × 10^-4 cm^-1, and 1.0 × 10^-7 cm^-1 for the MW data. The MW blended lines were given an uncertainty of . Finally, 489 IR transitions, 9.2%, were excluded in the final fit because they were overlapping (271) or their observed-calculated values (218) were larger than 5 times their estimated experimental uncertainty.

For the 3ν₄(Φ) state, the J′′ = 3 e/f components were not resolved. For the 3ν₅(Φ) state, all the e/f components of the rotational lines were not resolved. The couples of overlapping lines were identified by the same frequency (see Table 2) and their observed-calculated values were derived from the comparison of the experimental frequency with the average of the frequencies calculated for the two components. Sixty nine statistically well determined parameters, which are collected in Table 5, were refined with a final rms value of 3.06 × 10^-4 cm^-1 for the IR data and 19 kHz for the MW data. A few parameters in the model not reported in Table 5 were nevertheless allowed to vary during the fitting procedure but they resulted statistically undetermined and were constrained to zero. Some of the parameters are highly correlated, i.e. , and y₄₄₄, and , γ⁴⁴ and . The results in Table 5 can be compared with those obtained from the previous analysis, see Table 2 of Predoi-Cross et al. (2011). Sixty two parameters are common to both sets. The inclusion of the MW data allowed the determination of 7 additional constants. Three of these are related to the ν₄ bending states, partly because experimental data for the v₄ = 3(Φ) state have been obtained for the first time. Values and signs of all the common parameters are consistent in both sets: the differences between new and old values being in the range 0–1% (31 parameters), 1–10% (18 parameters), 10–50% (7 parameters), 50–100% (5 parameters) and 1 parameter, h₄, differs by 306%. The inclusion of the MW data also yields a significant improvement of the precision of the main constants which contribute to the rotational energy. For example, the values of B₀, α_t, and constants are ca. 5 times more precise than those determined previously (Predoi-Cross et al. 2011). It should be pointed out that in the present global analysis 60 additional IR transitions were discarded in the final fit, compared with the previous fit (Predoi-Cross et al. 2011), adopting the same rejection limits. The discarded lines are scattered over most of the bands. Considering the high accuracy of the assigned MW transitions, this result is particularly pleasing since it confirms the validity of the calibration of the IR data, which span a wide wavenumber range, from about 90 to 2100 cm^-1.

4. Conclusions

Rotational lines of ¹²C₂HD were detected in the range 100–700 GHz. They were analysed together with the IR transitions reported in the literature in a global fit. Sixty nine parameters (rotational, vibrational, ro-vibrational, and ℓ-type interaction) were determined with high precision. The analysis of the ℓ-type resonances which affect the pure rotational spectra allows the determination of the small vibrational energy differences ΔG between different ℓ-sublevels of a given vibrational state, which can be directly calculated using the effective values of the fitted g_tt′, r₄₅ and B_v constants in Tables 3 and 4.

The reliability of these results can be checked by comparison with the corresponding values from the global analysis. Table 6 shows that the agreement between the two sets of ΔG values is very good, differences being mostly less than one percent, thus confirming that an accurate treatment of ℓ-type resonances in the pure rotational spectra can provide precise information on the vibrational energy. The set of spectroscopic constants determined in this work is the most accurate and consistent available in the literature. From these constants it is possible to derive very accurate predictions for IR and MW spectra useful for astronomical searches. An extensive list of rotational frequencies up to 1 THz is reported in Table 2 for all the observed vibrational states, whose energies are reported in Table 1. The line strength of each transition can be calculated by the simple formula (Lafferty & Lovas 1978): (3)

Acknowledgments

The authors acknowledge the Università di Bologna and the Ministero della Ricerca e dell’Università for financial support under the grant PRIN09 “High-resolution Spectroscopy for Atmospherical and Astrochemical Research: Experiment, Theory and Applications”. The authors also thank Prof. G. Di Lonardo for helping the analysis of the infrared spectra.

References

All Tables

All Figures

	Fig. 1 The J = 5 ← 4 transition of 12C2HD in the v5 = 1, ground, and v4 = 1 vibrational states. The low-frequency components of each ℓ-doublet are displayed. Fourteen scans are co-added, the total integration time is 850 s.
In the text