We discuss past and recent progress of our continuing project of submillimetre-wave spectroscopic investigations of H2D+ and D2H+. Three new lines of H2D+ in the 2.5–3.5 THz range are measured with a tunable far-infrared laser system. Since these molecules are very light asymmetric molecules, analysis based on a conventional effective Hamiltonian is not very useful in predicting the transition frequencies to the accuracy of the order of several MHz or better. In this respect, any addition of new accurate measurements of transition frequencies is important. In this paper, some discussions will be made on and its deuterated species as probable interstellar species in cold dark clouds. In particular, , which is predicted to be abundant in cold dark clouds, can be (indirectly) detected by observing .
Deuterated plays a crucial role in deuterium fractionation processes in the interstellar space. In extreme low-temperature clouds, where no background infrared sources are available, submillimetre-wave and/or terahertz transitions are the only means to detect H2D+ and D2H+. Spectra of these species were first investigated by infrared spectroscopy. Following the first spectroscopic identification of H2D+ by Shy et al. (1981), all of the three fundamental bands were recorded and reasonably accurate molecular constants were determined (Amano & Watson 1984; Amano 1985; Foster et al. 1986b). The high-resolution spectroscopic identification of D2H+ was made by Lubic & Amano (1984) by observing the ν1 fundamental band, followed by observation of the ν2 and the ν3 fundamental bands using the infrared diode laser technique by Foster et al. (1986a). Polyansky & McKellar (1990) later improved the molecular constants by reanalysing ν2 and ν3 fundamental bands with aid from high-level ab initio calculations. Details of such historic background have been described in one of our previous publications (Amano & Hirao 2005).
These infrared investigations provided good predictions for the rotational transitions. Laboratory observations of one of the relatively easily accessible millimetre- and submillimetre-wave transitions, J=110–111 around 372 GHz, were achieved by two groups independently at almost the same time (Bogey et al. 1984; Warner et al. 1984). During the very early stage of the development of astrochemistry, H2D+ was recognized as an important molecular ion in dark clouds (Dalgarno et al. 1973) and the accurate laboratory measurements were available; the interstellar identification had not been made until the detection of a submillimetre-wave emission line towards a young stellar object NGC 1333 IRAS 4A (Stark et al. 1999). Subsequently, Caselli et al. (2003) detected the H2D+ line in a pre-stellar core L1544, followed by detection towards another pre-stellar core 16293E (Vastel et al. 2003). In these sources, H2D+ turned out to be a major molecular ion as abundant as electrons.
The D2H+ and species had not been considered to be important and abundant interstellar species, owing to the small cosmic abundance of D. However, in view of the recent discoveries of the multiply deuterated species, they should also be regarded as important multiply deuterated species themselves and at the same time they might play a crucial role in deuteration processes, which leads to multiple deuteration of other molecules.
In our previous investigation, the 110–111 line of H2D+ and the 110–101 transition of D2H+ were measured to provide more accurate rest frequencies, which would lead to a more reliable determination of the velocities of the observed H2D+ and D2H+ in interstellar sources (Amano & Hirao 2005). The H2D+ ion is the lightest asymmetric top molecule and the effective Hamiltonian for asymmetric rotors fails to predict the rotational transition frequencies to the submillimetre measurement accuracy even for relatively low J lines. In this respect, any new addition of rotational lines will help to understand and improve the molecular constants. In this investigation, we report new measurements of H2D+ in the frequency region of 2.5–3.5 THz measured with a tunable far-infrared laser spectrometer system at Toyama University.
2. Experimental details
(a) Submillimetre-wave spectroscopy
In the long history of microwave spectroscopy, the submillimetre-wave region remained a difficult frequency region, primarily owing to the lack of powerful easy-to-use radiation sources. It is in relatively recent years that adequate submillimetre-wave radiation sources have become available. In the laboratory, submillimetre-wave spectroscopic techniques have advanced significantly by using more efficient multipliers (Drouin et al. 2005; Savage & Ziurys 2005) or backward-wave oscillators (BWOs) as radiation sources (Bogey et al. 1986; Petkie et al. 1997; Lewen et al. 1998; Krupnov 2001). However, submillimetre-wave spectroscopy for unstable molecular species such as ions and free radicals is still a challenging field.
The spectrometer at Ibaraki University (now moved to University of Waterloo, Canada) is a BWO-based system. The details are given in Amano & Maeda (2000) and only a brief description is given here. The outline of the system is given schematically in figure 1. Submillimetre-wave radiation of about several kilohertz frequency stability transmits through an extended negative glow discharge cell. The system has been developed specifically for the investigation of ions. The magnetic field was generated by applying an electric current to a three-layer solenoid coil wound over a stainless steel container of 10 cm diameter through which a 1.7 m long double-jacketed Pyrex absorption cell with 4 cm inner diameter is accommodated. Through the outer layer of the Pyrex cell, liquid nitrogen can be flowed for cooling the discharge.
One of the drawbacks of the conventional frequency modulation technique is baseline distortion, which often limits the detection sensitivity. To alleviate such a problem, we developed a high-sensitivity frequency/magnetic field double modulation technique (Amano & Maeda 2000). The magnetic field was switched on and off at a frequency of typically 32 Hz, resulting in ion concentration modulation. An InSb hot electron bolometer cooled with liquid helium is used for detection of the submillimetre-wave radiation. As shown in figure 1, two lock-in amplifiers were used in series. The first one demodulated the frequency-modulated signals at typically 34 kHz, and the second lock-in amplifier demodulated the magnetically sensitive signals. The time constant for the first lock-in amplifier was chosen to allow the magnetically modulated signal components to pass through. In this scheme, magnetically insensitive components, such as the baseline distortion and the signals from species that are not sensitive to the magnetic field, can mostly be eliminated.
The optimum mixing ratios for the production of H2D+ and D2H+ were found to be H2/D2/Ar∼4/2/17 mTorr and approximately 3/2/17 mTorr for H2D+ and D2H+. The optimum mixing ratio of H2 to D2 for the production of D2H+ was found to be about 3 : 2 rather than the statistical 1 : 2 ratio. As pointed out in our previous paper (Hirao & Amano 2003), the liquid nitrogen cooling might favour tilting the reactions towards deuterations owing to exothermicity, albeit small, of the deuteration reactions, resulting in the optimum mixing ratio of 3 : 2. Details have been described in Amano & Hirao (2005) and will not be reproduced here.
(b) Tunable far-infrared spectroscopy
The tunable far-infrared spectrometer at Toyama University consists of two frequency-stabilized CO2 lasers and a microwave sweeper. Two CO2 laser lines from two CO2 lasers, either 9 or 10 μm bands, are mixed together with the microwave radiation at a metal–insulator–metal diode. By sweeping the microwave frequency, tunable far-infrared or terahertz radiation can be generated. A schematic diagram of the system is given in figure 2. Details of the spectrometer are described in Matsushima et al. (1994, 1997, 1998).
The ions were generated in a glow discharge in a 2 : 1 mixture of H2 and D2 with a total pressure of approximately 50 Pa. The cell had a triple-jacketed construction and the middle layer allowed a flow of liquid nitrogen to cool the discharge. The inner diameter of the cell was 1.6 cm and the discharge current was 500 mA–1 A. All the measurements were made at liquid N2 temperature. The signals were detected by using either frequency modulation or velocity modulation method. The polarity of the discharge voltage was switched at the frequency of 1.2 kHz for the velocity modulation scheme.
The transition frequencies for lines in the terahertz region were estimated prior to search by using calculated transition frequencies obtained from the molecular constants determined by the infrared and microwave spectroscopies (Amano & Hirao 2005). So far, three transitions were detected for H2D+ near the predicted frequencies, and the measured transition frequencies are listed in table 1. The measurement accuracies are about 1, 0.4 and 0.5 MHz for the 202–101, 211–110 and 313–212 lines, respectively. In addition, the identification and the assignments were confirmed by deriving the transition frequencies by using the combination differences derived from the infrared measurements listed in table 1 of Amano & Hirao (2005) and the known submillimetre lines. Figure 3 depicts the schemes of deriving the transition frequencies from the combination differences. The observed transition frequencies are in good agreement with those derived values confirming the assignments.
3. Spectroscopic results
With new measurements for H2D+ in the terahertz region, we carried out a least-squares analysis. We included all of the combination differences of the ground state from the available infrared data for the three fundamental bands as given in table 1 of Amano & Hirao (2005). They were subject to least-squares analysis with the Watson effective Hamiltonian to obtain the best-fit molecular constants for the ground state. It was found that the inclusion of these three lines in the fit deteriorated the quality of the fit. The identification of the lines and the assignments have been confirmed by comparing the estimated values derived from the combination differences as described above. We had to add three higher order centrifugal distortion constants to attain a satisfactory fit. This is an indication that the effective Hamiltonian is not quite adequate to describe this light asymmetric top molecule. However, we maintained using this formulation here to compare new results with all of the previous ones.
Table 1 lists the residuals of the fit for the combination differences and the millimetre- and submillimetre-wave lines for H2D+. Table 2 summarizes the molecular constants thus determined for H2D+. The molecular constants obtained here are in good agreement with those determined previously.
For both H2D+ and D2H+, only one spin modification (ortho-H2D+ and para-D2H+) has been detected in the interstellar space. The lowest lying rotational transitions (101–000 for para-H2D+ and 111–000 for ortho-D2H+), which are yet to be detected in interstellar space, were measured in the laboratory by Jennings et al. (unpublished work) to the estimated accuracy of 0.3 MHz. We plan new measurements of these transition frequencies with better accuracy and the results will be published in the near future.
Vastel et al. (2004) reported slightly different velocities (vLSR) of 3.55±0.02 and 3.76±0.03 km s−1 for H2D+ and D2H+, respectively, by using the laboratory frequencies (Bogey et al. 1984; Warner et al. 1984; Hirao & Amano 2003). It was our main motivation to remeasure the transition frequencies for these two lines (Amano & Hirao 2005). Our new measurements for H2D+ at 372 421.385(10) MHz and D2H+ at 691 660.483(20) MHz now revise their vLSR of H2D+ and D2H+ to 3.51 and 3.74 km s−1, respectively, and the difference of vLSR still remains 0.23 km s−1.
It is very interesting to note that the hyperfine structure may shift the line centre and the shift may be significant at extremely low temperature, as indicated by a theoretical calculation by Jensen et al. (1997). According to the calculation, the stronger hyperfine structure components are located at about 50 kHz lower than the line centre for the 110–111 transition of H2D+, while a much smaller shift is expected for the 110–101 line of D2H+. There is a possibility that the line peak observed at extremely low temperature coincides more or less with the strongest component. On the other hand, under laboratory conditions, the line peak is given as a weighted average of all the components, resulting in the shift of the apparent line centre frequency. Nevertheless, this difference may not be significant as the velocity resolution of the astronomical measurement was 0.101 km s−1 (Vastel et al. 2004). It is not conclusive from the observation whether the velocities of H2D+ and D2H+ are really different and their spatial distributions do not coincide. However, it is very interesting to explore whether the spatial distributions for these ions can be mapped and the difference in the distributions are revealed. Such observations will become possible in the near future when high-spatial resolution millimetre/submillimetre-wave arrays, such as Atacama large millimetre array, are commissioned.
The first spectroscopic identification of was made by Okumura et al. (1988) by observing the vibrational bands in the H–H stretching vibrational mode region. Bae (1991) extended the measurements to a higher frequency to observe the overtone bands by using a similar technique. This cluster is the first and most stable member of possible higher clusters, . In addition, there is indirect evidence that is formed in the liquid nitrogen-cooled hollow cathode discharge (Amano & Chan 2000). In their extensive theoretical work, Yamaguchi et al. (1987) identified 10 low lying conformers and obtained the relative energies, the vibrational harmonic frequencies and the molecular structures. Since then, the ion has been subjected to extensive theoretical activities; for example, one of most recent works by Xie et al. (2005) and references cited therein. Špirko et al. (2006) investigated the vibrational predissociation processes by using the recent most accurate potential surfaces and concluded that the broad features observed by Okumura et al. (1988) are owing to state congestion rather than the vibrational predissociations.
Formations of molecular clusters in the interstellar space were theoretically investigated by Duley (1996) and the equilibrium abundances were predicted. However, it is not quite certain whether can be formed under interstellar conditions in abundance owing to the lack of experimental and observational evidence. Nevertheless, spectroscopic characterization of the rotational structure of and its isotopic species should be a very important and challenging task for laboratory spectroscopists. In particular, may provide indirect evidence of interstellar , as has no permanent dipole moment and therefore it is very unlikely to be detected in cold molecular clouds by observing the rotational transitions. The conformer 1-C2v is the global minimum, but the structure should be delocalized among the four low lying conformers, 1-C2v, 2-D2d, 3-C2v and 4-D2h. Here, the geometry of the conformers should be referred to figure 2 of Xie et al. (2005). Theoretical calculation of the rotational structure is essential for attempting the search for the rotational transitions, which is one of the most challenging tasks left to submillimetre-wave spectroscopy.
The author thanks Prof. Matsushima for sending him his data and for his contributions in tunable far-infrared spectroscopy. Valuable discussions with and various suggestions from Dr Špirko are gratefully acknowledged. This research was supported in part by grants from the Japan Society for Promotion of Science (JSPS) and from the Ministry of Education, Science and Culture of Japan.
↵† Present address: Department of Chemistry, University of Waterloo, Waterloo, ON N2L 3G1, Canada (firstname.lastname@example.org).
One contribution of 26 to a Discussion Meeting Issue ‘Physics, chemistry and astronomy of ’.
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