© ESO, 2013

1. Introduction

Glycolaldehyde (Fig. 1), the smallest sugar, is considered as a probable prebiotic molecule since its first detection in the interstellar medium (ISM) by (Hollis et al. 2000). In a recent paper (Jørgensen et al. 2012) the first detection of 13 transitions of glycolaldehyde around a solar-type young star was presented, which were made with the Atacama Large Millimeter Array (ALMA) observations of the Class 0 protostellar binary IRAS 16293-2422 at 220 GHz (six transitions) and 690 GHz (seven transitions). The order of magnitude increase in line density in these early ALMA data illustrates its huge potential to reveal the full chemical complexity associated with the formation of solar system analogs. Especially the constraints on the chemical formation of glycolaldehyde and other organic species have been discussed. According to Jørgensen et al. (2012), the relative abundances appear to be consistent with UV photochemistry of a CH₃OH – CO mixed ice that has undergone mild heating. This conclusion is consistent with previous published results (Bennett & Kaiser 2007) even if possible gas-phase pathways have also been proposed (Jalbout et al. 2007) and discussed (Simakov et al. 2011). In their article, Bennett & Kaiser (2007) paid special attention to the investigation of the glycolaldehyde formation process and its isomers (methyl formate and acetic acid), which obey the same empirical formula C₂H₄O₂. Their relative abundance, for example, was reported by Hollis et al. (2001) to be 52:2:1 (methyl formate:acetic acid:glycolaldehyde) in Sgr B2.

	Fig. 1 Schematic view of the most stable conformer of glycolaldehyde, stabilized by a weak hydrogen bond OH ... O = C binding the two functional groups.
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In addition to the ability of this hydroxyaldehyde diose to become involved in the production of important biomolecules (glycolaldehyde phosphates, amino acids, etc), the ¹³C isotopologs of glycolaldehyde are of special importance to astrophysicists. Detecting them in the future will enable us to measure the abundance ratio of ¹²C over ¹³C isotopes by measuring the ratio of the abundance of their respective isotopomers. Observating isotopic abundances in the interstellar medium provides an avenue for quantitatively assessing stellar nucleosynthesis and therefore Galactic chemical evolution. The ¹²C/¹³C isotope ratio is also considered an important tracer because it reflects the relative degree of primary to secondary processing in stars (Milam et al. 2005).

The present study investigates the rotational structure of the ground states and the three lowest vibrational modes for the two ¹³C isotopomers of glycolaldehyde. Although they are so important on the astrophysical scale, the two ¹³C-isotopologs of glycolaldehyde, ¹³CH₂OHCHO and CH₂OH¹³CHO, were studied only once in the past 40 years. Indeed, Marstokk & Møllendal (1973) reported the analysis of spectra recorded in the microwave range (12.4−36.3 GHz) with a spectral accuracy of 0.25 MHz. Ten and eighteen lines were observed in natural abundance and were identified to be ¹³CH₂OHCHO and CH₂OH¹³CHO, respectively. The data were fitted to a standard Watson Hamiltonian, providing a set of molecular parameters including the principal rotational constants and the quartic centrifugal distortion parameters. Marstokk & Møllendal (1973) also re-measured the permanent dipole moment of the parent species: μ_a = 0.2620 ± 0.002 D, μ_b = 2.330 ± 0.01 D, and μ_tot = 2.340 ± 0.01 D. Glycolaldehyde is a fairly light molecule (M = 60) whose typical μ_b type spectra have their maximum absorption at 820 GHz (at 300 K) and extend far beyond 1 THz. If glycoladehyde and its isotopic species are interesting objects for highly sensitive terahertz radio telescopes such as ALMA or Herschel, the results of Marstokk & Møllendal (1973) are insufficient to provide reliable frequency predictions in the terahertz range. Moreover, as we show below, the previous assignment of one of the ¹³C species is most probably erroneous and could not be used for astrophysical observations. The deuterated isotopologs of glycolaldehyde have recently been studied in the millimeter-wave region (150−630 GHz) by Bouchez et al. (2012). This spectroscopic study was motivated by a future comparison of the D/H ratios for better understanding the formation of glycolaldehyde in hot cores and hot corinos. According to the relative abundance of the ¹³C/¹²C and D/H ratios observed in the ISM, it is probably useful to be able to also identify in the future the two ¹³C-isotopologs of glycolaldehyde in the future. To this end we studied the spectroscopy of ¹³CH₂OHCHO and CH₂OH¹³CHO in the laboratory in the millimeter-wave and submillimeter-wave ranges. Precise molecular parameters were obtained for the ground and first three excited vibrational states of the two species, providing a line-list for a future detection, with an absolute frequency accuracy better than 30 kHz in the spectral ranges covered by the ALMA and Herschel telescopes.

2. Experiment

The millimeter- and submillimeter-wave spectra of ¹³C-glycolaldehydes were recorded using the Lille spectrometer based on solid-state sources. The frequency source is a 20 GHz synthesizer (Agilent, model E8257D) that is stabilized on a global positioning system. The output frequency (12.5−18.4 GHz) is multiplied by six and amplified by an active sextupler (Spacek), providing an output power of +15 dBm in the W-band range (75−110 GHz). Passive Schottky multipliers (× 2,  × 3,  × 5,  × 3  ×  2,  × 3  ×  3, Virginia Diodes Inc.) are used in the last stage of the frequency multiplication chain to provide a useful signal in the 150−990 GHz spectral range. The commercial samples of ¹³CH₂OHCHO and CH₂OH¹³CHO (Omicron Biochemicals, Inc., 99% purity, in aqueous solution) were dehydrated and used without additional purification. It was found later that the two dehydrated commercial samples contained a mixture of the two ¹³C-glycolaldehydes in a ratio equal to ¹³CHO/¹³CH₂O = 0.59 and ¹³CH₂O/¹³CHO = 0.67, but without impurity. The absorption cell is a stainless-steel tube (6 cm diameter, 220 cm long). The sample pressure was equal to 20 × 10^-6 bars, and slightly increased up to 40 × 10^-6 bars in the 700−945 GHz region. To improve the signal sensitivity, the sources were frequency modulated at 10 kHz and lock-in detection with the second harmonic was used. Absorption signals were detected by an InSb liquid He-cooled bolometer (QMC Instruments Ltd.) and processed on a computer. Spectra of the two samples were recorded at room temperature (T = 294 K) in the 150−215, 230−315, 400−530, 500−630, and 700−945 GHz regions with a frequency step of 30, 36, 48, 54, and 76 kHz and with an acquisition time of 35 ms. The line frequencies were obtained by adjusting the second derivative of a Gaussian profile on the observed signals, knowing that the linewidths are limited by Doppler broadening (around 1 MHz at 600 GHz). The absolute accuracy of the line-center frequency is estimated to be better than 30 kHz (50 kHz above 700 GHz) for isolated lines, and can be as high as 100 kHz (150 kHz above 700 GHz) for blended or very weak lines.

3. Analysis

At first, the strongest lines associated with the ground state were considered for both ¹³CH₂OHCHO and CH₂OH¹³CHO. In previous spectroscopic works as well as in the present one, a standard asymmetric-top Hamiltonian with a Watson A-reduction in the I^r-representation was employed. Consequently, the rotational structure is characterized by the J_KaKc quantum numbers. The spectral data were fitted by means of the ASFIT¹ and ASROT¹ suite of programs. Final results are available at the CDS, using the formats of the program suite SPFIT and SPCAT (Pickett 1991), which are commonly used by astrophysicists (Pearson et al. 2010).

At the initial stage of the line assignment, we used predictions based on the principal rotational constants from Marstokk and Møllendal (Marstokk & Møllendal 1973) while the value of the quartic and sextic distortion parameters were fixed to the corresponding values of the CH₂OHCHO parent molecule (Widicus Weaver et al. 2005). We first searched for the intense R-branch lines of the low K_a quantum number (K_a = 0,1) with respect to the selection rule associated with the μ_b type transitions (ΔK_a =  ± 1, ΔK_c =  ± 1). Their doublet structure helped us to recognize them, cf. Fig. 2. Following the systematic decrease of the splitting within the doublets and the increase of the line intensity with the increase of the J quantum number, we collected doublets up to J = 21 for CH₂OH¹³CHO and J = 20 for ¹³CH₂OHCHO in the 150−215 GHz frequency range. Meanwhile, the observed minus calculated frequency shift increased quickly, reaching 5.5 MHz at J = 21 for CH₂OH¹³CHO and 43 MHz at J = 20 for ¹³CH₂OHCHO. Consequently, the new millimeter-wave lines of each isotopomer were fitted together with the microwave lines measured by Marstokk and Møllendal (Marstokk & Møllendal 1973). The initial set of parameters was refined and new and more accurate predictions were generated. However, we had to exclude four microwave lines from the fit for CH₂OH¹³CHO because their observed-calculated residuals did not satisfy the 3σ criteria (where σ is the experimental measurement uncertainty). We found that the A rotational constant obtained by Marstokk and Møllendal for ¹³CH₂OHCHO (Marstokk & Møllendal 1973) could not be associated with the ground state. Therefore all microwave transitions (Marstokk & Møllendal 1973) were omitted from our analysis. The next step was to proceed with the assignment by increasing the K_a quantum number. In this frequency range for (CH₂OH¹³CHO) and for (¹³CH₂OHCHO) were reached. Afterward, we searched for the Q type transitions and gathered them up to J′,K_a′ = 64,14 (CH₂OH¹³CHO) and J′,K_a′ = 66,15 (¹³CH₂OHCHO), cf. Fig. 2. Pursuing the analysis up to 950 GHz, we assigned R and Q transitions up to and J′ = 93 following the same strategy. At the end the weak lines associated with the μ_a type of transitions (ΔK_a = 0, ΔK_c =  ± 1) were assigned. We finally determined a set of 20 molecular parameters for each molecule, including centrifugal distortion parameters up to the octic terms, by fitting a total of 4218 assigned lines for CH₂OH¹³CHO and 4655 for ¹³CH₂OHCHO, with a relevant root mean square deviation (rms) of 31 and 29 kHz. The final sets of molecular parameters are presented in Tables 1 and 2. The number of assigned lines and the maximal values of the observed quantum numbers are also given.

	Fig. 2 a) Strong R-line doublets associated with Ka = 0,1, observed in the 191 GHz range with a sample containing the two 13C-glycolaldehydes and b) weak Q-lines of 13CH2OHCHO associated with Ka = 22, observed in the 557 GHz range. All signals are assigned to the ground states and are labeled (JKaKc)′ ←  − (JKaKc)′′.
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The good quality of the spectra provided by our spectrometer and the high signal-to-noise ratio allowed us to proceed with assigning of the rotational structure of the three lowest excited vibrational modes (Fig. 3). The calculated vibrational energies for the parent molecule are approximately 213 cm^-1 (ν₁, the C−C torsion mode), 294 cm^-1 (ν₂, the C−C−O bending mode), and 426 cm^-1 (ν₃, the O-H torsion mode) (Senent 2004). To start the analysis of ν₁ = 1, the rotational constants were roughly predicted using the vibration-rotation constants α of the parent molecule (β = A,B,C) (Widicus Weaver et al. 2005):

This relation also served to predict the first set of rotational constants for ν₂ = 1 and ν₃ = 1. At the beginning of the analysis, the quartic, sextic, and octic distortion parameters values were fixed to those of the ground state (see Tables 1 and 2). This first set of parameters supplied the preliminary predictions. Taking into account the decrease of the Boltzmann distribution and following the same assignment strategy as for the ground state, we could assign the rotational structure up to 630 GHz. The rotational constants and the centrifugal distortion parameters up to the sextic terms were determined for the three lowest excited modes of the two isotopomers. They are presented in Tables 1 and 2, for CH₂OH¹³CHO and ¹³CH₂OHCHO. Finally, a full list of assigned lines is given in Tables 3 and 4 for CH₂OH¹³CHO and ¹³CH₂OHCHO. The tables contain the rotational assignments, the vibrational assignement, the observed frequencies, the observed-calculated frequency residuals, and the experimental uncertainties.

	Fig. 3 Example of strong lines of 13CH2OHCHO, i.e. JKaKc = 200,20 − 191,19 (I) and JKaKc = 201,20 − 190,19 (II), observed simultaneously in the ground state and in the first three excited vibrational states in the 200 GHz range at 294 K.
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The tabulated values for the ¹³C-glycolaldehydes partition function are given in Table 5, with Q(T)_tot = Q(T)_vibQ(T)_rot. Various temperatures are considered. Q(T)_rot was calculated as

where A,B, and C represent the rotational contants of the ground state in MHz. As noted by Widicus Weaver et al. (2005), the glycolaldehyde partition function increases significantly when taking into account the vibrational contribution. This is mainly because of the low-frequency vibrational modes. Unfortunately, no experimental or theoretical data are available for the ¹³C-glycolaldehydes. Meanwhile, regarding the weak differences in atomic and molecular masses (one ¹²C atom is replaced by one ¹³C atom and M_tot = 61 instead of M_tot = 60), we estimated the vibrational partition function using the observed or calculated frequencies for the main species. The three lowest calculated frequencies (ν₁, ν₂, ν₃) were taken from Senent (2004), the observed band centers (ν₅, ν₆, ν₈, ν₁₀–ν₁₈) in the infrared region were taken from Jetzki et al. (2004) and the others (ν₄, ν₇, ν₉) from Carbonniere & Pouchan (2012). Indeed, these last authors performed a high-level ab initio calculation limited to the mid-infrared region. Their results agree well with the few experimental data (Jetzki et al. 2004). Putting the zero energy at the ground state level, the vibrational partition function was calculated using the expression

4. Conclusions

The rotational structure of the two ¹³C-isotopologs of glycolaldehyde was characterized in the laboratory for the ground state and the first three excited vibrational modes up to 945 and 630 GHz. High-quality spectra were continuously recorded with an absolute frequency accuracy better than 30 kHz. The sets of molecular parameters we determined can be used to generate predictions in the range of one to several hundred GHz at the experimental accuracy, without bias. These isotopologs of glycolaldehyde are relevant targets for the ALMA interferometers owing to their high sensitivity and spatial resolution.

Acknowledgments

The authors gratefully acknowledge Jean-Claude Guillemin (Ecole Nationale Supérieure de Chimie de Rennes, France) for his help in conditioning the samples. This work was supported by the French ANR agency under contract ANR-08-BLAN-0054, by the French CNRS-INSU programme “Action sur Projet Physico-Chimie du Milieu Interstellaire” and by the Centre National d’Etudes Spatiales (CNES).

References

All Tables

All Figures

	Fig. 1 Schematic view of the most stable conformer of glycolaldehyde, stabilized by a weak hydrogen bond OH ... O = C binding the two functional groups.
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In the text

	Fig. 2 a) Strong R-line doublets associated with Ka = 0,1, observed in the 191 GHz range with a sample containing the two 13C-glycolaldehydes and b) weak Q-lines of 13CH2OHCHO associated with Ka = 22, observed in the 557 GHz range. All signals are assigned to the ground states and are labeled (JKaKc)′ ←  − (JKaKc)′′.
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In the text

	Fig. 3 Example of strong lines of 13CH2OHCHO, i.e. JKaKc = 200,20 − 191,19 (I) and JKaKc = 201,20 − 190,19 (II), observed simultaneously in the ground state and in the first three excited vibrational states in the 200 GHz range at 294 K.
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In the text