EDP Sciences
Free Access
Issue
A&A
Volume 579, July 2015
Article Number A46
Number of page(s) 11
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201425478
Published online 25 June 2015

© ESO, 2015

1. Introduction

This paper is a continuation of a series of studies conducted in PhLAM Lille (France) that are devoted to the investigations of the spectra of different isotopic species of astrophysical molecules (Demyk et al. 2007; Margulès et al. 2009a,b, 2010; Carvajal et al. 2009; Tercero et al. 2012; Bouchez et al. 2012; Coudert et al. 2012, 2013; Richard et al. 2012, 2013; Haykal et al. 2013; Kutsenko et al. 2013; Nguyen et al. 2013). In particular, these works led to the first interstellar detection of HCOOCH2D (Coudert et al. 2013), HCOO13CH3 (Carvajal et al. 2009), HCO18OCH3, HC18OOCH3 (Tercero et al. 2012), and CH2DOCH3 (Richard et al. 2013). In the current paper we focus our attention on the 13C isotopologs of the ubiquitous interstellar molecule – acetaldehyde, which main isotopolog has been observed in the cold molecular clouds (Matthews et al. 1985), and translucent molecular clouds (Turner et al. 1999) toward hot cores (Nummelin et al. 1998) and star-forming regions (Charnley 2004). It was recently detected in the disk of a high redshift (z = 0.89) spiral galaxy located in front of the quasar PKS 1830-211 (Muller et al. 2011).

Rotational spectra of the parent acetaldehyde species was a subject of several investigations. The latest paper on this subject (Smirnov et al. 2014) covers the frequency range up to 1.6 THz and the range of rotational quantum numbers up to J ≤ 66 and Ka ≤ 22, providing a firm basis for producing reliable predictions of the acetaldehyde spectrum in the frequency range up to 1.9 THz. As concerns mono-labeled acetaldehyde isotopolog, the millimeter and submillimeter wave spectra were only studied for CH3CDO (Martinache et al. 1989; Elkeurti et al. 2010) with the upper frequency of 376 GHz. For other mono-substituted isotopologs CH2DCHO, 13CH3CHO, CH313CHO, and CH3CH18O, data available in the literature are very limited, covering the frequency range only from 8 to 40 GHz (Kilb et al. 1957; Turner & Cox 1976; Turner et al. 1981; Zaleski et al. 2012). In particular, for the 13CH3CHO and CH313CHO isotopologs of interest here, the dataset consisted of about 10 transitions for each of the 13C isotopologs, which are evenly distributed between A-type and E-type symmetry species of the ground torsional states (Kilb et al. 1957; Zaleski et al. 2012). It is evident that for producing reliable predictions of the 13CH3CHO and CH313CHO spectra, these datasets should be considerably extended and a new analysis should be performed. In this context we present a new study of the 13CH3CHO and CH313CHO spectra with measurements and analysis extended up to 945 GHz.

2. Experiments

2.1. Synthesis

The 1-13C and 2-13C acetyl chloride were purchased from Eurisotop and used without further purification. The 13CH3CHO and CH313CHO were synthesized following the preparation of Barbry and Couturier (Barbry et al. 1987), modified to isolate the product. In a 100 ml two-necked flask equipped with a stirring bar and a nitrogen inlet, and cooled at −20 °C were introduced under nitrogen (PPh3)4Pd (0.12 g, 0.1 mmol), xylene (15 ml), and 13C acetyl chloride (1g, 13 mmol). The flask was connected to a U-tube equipped with stopcocks and immersed in a −80 °C cold bath, and tributyl tin hydride (4.1 g, 14 mmol) was added in 2 min and the solution was then allowed to warm to room temperature. A gentle stream of nitrogen was then passed through the flask and the U-tube for 15 min. A mixture containing the labeled acetaldehyde (80%) and xylene (20%) was obtained. A very pure sample of 13C acetaldehyde (purity >96%) was obtained in a 78% yield (437 mg, 10 mmol) and in a 98% isotopic purity by a subsequent distillation of the solution in a vacuum line (0.1 mbar) equipped with a first U-tube cooled at −80 °C to remove the solvent and a second one immersed in a liquid nitrogen bath to selectively condense the expected product.

2.2. Lille – submillimeter spectra

The measurements in the frequency range under investigation (50–945 GHz) were performed using the Lille spectrometer (Alekseev et al. 2012). A quasi-optic dielectric hollow waveguide of 3-m length containing investigated gas at the required pressure was used as the sample cell in the spectrometer. The measurements were done at typical pressures of 10 Pa and at room temperature. The frequency ranges 50–315, 400–630, and 780–945 GHz were covered with various active and passive frequency multipliers where the Agilent synthesizer (12.5–17.5 GHz) was used as the source of radiation. Estimated uncertainties for measured line frequencies are 30 kHz and 50 kHz depending on the observed signal-to-noise ratio and the frequency range.

3. Theoretical model

Like the parent species, 13C acetaldehydes represent the case of near prolate (κ ≈ −0.95) nonrigid molecules with the large amplitude torsional motion of the methyl top. The molecules have a plane of symmetry that means that the G6 permutation-inversion group will be appropriate for them if internal rotation of the methyl group is taken into account. The torsional large amplitude motion of the methyl top in the molecules splits rotational transitions into two components that correspond to nondegenerate (A1/A2) and degenerate (E) symmetry species in G6. Corresponding AE splittings may already reach hundreds of MHz in the ground vibrational state. Combination of rather large rotational constants (A ≈ 56 GHz, B ≈ 10 GHz, C ≈ 9 GHz) with an intermediate barrier height to internal rotation of the methyl group (V3 ≈ 407 cm-1) and considerable dipole moment (μ ≈ 2.734 D) leads to an intense complex rotational spectrum expanding in THz region. The ratio of the methyl top moment of inertia to that of the rest of the molecule is rather high in these molecules, which leads to a relatively large coefficient for the coupling term between internal rotation and global rotation (ρ ≈ 0.32). This means that the principle axis method will experience serious problems with fitting spectra of 13C acetaldehydes since its convergence strongly depends on the ρ value (Kleiner 2010).

Table 1

Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.

The Hamiltonian used in the present work is the so-called RAM (rho axis method) internal-rotation Hamiltonian based on the work of Kirtman (Kirtman 1962), Lees and Baker (Lees & Baker 1968), and Herbst et al. (Herbst et al. 1984). Since rather complete descriptions of this method, which takes its name from the choice of axis system, have been presented several times (Hougen et al. 1994; Kleiner 2010) we do not repeat this general description here. The main advantage of the RAM Hamiltonian is its general approach that simultaneously takes into account the A- and E-symmetry species and all the torsional levels, intrinsically taking the intertorsional interactions into account within the rotation-torsion manifold of energy levels. This method was successfully applied to a number of molecules containing a C3v rotor and Cs frame, including the main isotopolog of acetaldehyde (Smirnov et al. 2014). As for the main isotopolog (Smirnov et al. 2014) we employed the RAM36 (rho-axis-method for 3- and 6-fold barriers) code that uses the RAM approach for the molecules with the C3v top attached to a molecular frame of Cs or C2v symmetry and having 3- or 6-fold barriers to internal rotation, respectively (Ilyushin et al. 2010, 2013). The Hamiltonian in the RAM36 program is presented by the following expression: (1)where the Bknpqrst are fitting parameters; pα is the angular momentum conjugate to the internal rotation angle α; and Px,Py,Pz are projections on the x,y,z axes of the total angular momentum P. In the case of a C3v top and Cs frame (as is appropriate for acetaldehyde), the allowed terms in the torsion-rotation Hamiltonian must be totally symmetric in the group G6 (and also must be Hermitian and invariant to the time reversal operation). Since all individual operators pα,Px,Py,Pz,P2,cos(3) and sin(3) used in Eq. (1) are Hermitian, all possible terms provided by Eq. (1) will automatically be Hermitian. The particular term to be fit is represented in the input file with a set of k,n,p,q,r,s,t integer indices that are checked by the program for conformity with time reversal and symmetry requirements, to prevent accidental introduction of symmetry-forbidden terms into the Hamiltonian.

The RAM36 computer code uses the two-step diagonalization procedure of Herbst et al. (1984). In the first step, a set of torsional calculations is performed with a relatively large torsional basis set for each symmetry species and for each value of K in the range JmaxK ≤ +Jmax. In the current fit we used 21 torsional basis functions at the first stage. In this step only the main torsional-rotation Hamiltonian matrix elements diagonal in K are considered. In the second step a reduced torsional basis set is used, which is obtained by discarding all but the lowest several torsional eigenfunctions for a given K and symmetry species obtained from the first stage. In the current fit we used 9 torsional basis functions at the second stage. In the second step, all desired asymmetric-rotor and torsion-rotation K mixing effects are taken into account. At both stages a non-degenerate symmetry submatrix is not split into A1/A2 parts, which are instead treated together. A conventional weighted least-squares fit is carried out to determine the Hamiltonian parameter values with a special treatment of blends where an intensity-weighted average of calculated (but experimentally unresolved) transition frequencies is put in correspondence with the measured blended-line frequency. A more detailed description of the RAM36 code can be found in Ilyushin et al. (2010, 2013).

4. Assignment and analysis of the spectra

We started our analysis of recorded spectra from the dataset of Kilb et al. (1957), which was combined with the low order torsion parameters of the main acetaldehyde isotopolog (Smirnov et al. 2014). In the initial stage the torsional parameters of the RAM Hamiltonian models were kept fixed at the values of the main isotopolog, and rotational parameters plus ρ parameters were varied to fit available transitions of 13CH3CHO and CH313CHO. Obtained in this way sets of RAM Hamiltonian parameters were used to produce the initial predictions of millimeter and submillimeter wave spectra for both 13C isotopologs. Analysis of the recorded spectra was done in the usual iterative manner by adding new assigned lines to the fit, refining of Hamiltonian model, and producing new predictions.

Table 2

Statistics of the data set for the global fit to vt = 0, 1, 2 torsional states of 13CH3CHO and CH313CHO isotopologs of acetaldehyde molecule.

thumbnail Fig. 1

Predicted (in blue) and observed (in red) rotational spectrum of 13CH3CHO between 891.3 and 893.2 GHz dominated by Q-type series of transitions with Ka = 10 ← 9. A slight inconsistency between predicted and observed spectrum, which may be visible for some strong lines, is due to source power and detector sensitivity variations.

Open with DEXTER

thumbnail Fig. 2

Predicted (in blue) and observed (in red) rotational spectrum of CH313CHO between 869.3 and 871.0 GHz dominated by Q-type series of transitions with Ka = 10 ← 9. A slight inconsistency between predicted and observed spectrum, which may be visible for some strong lines, is due to source power and detector sensitivity variations.

Open with DEXTER

Table 3

Assignments, measured transition frequencies, and residuals from the global fit of the microwave, millimeter-wave, and submillimeter-wave vt = 0,1,2 data for 13CH3CHO acetaldehyde.

Table 4

Assignments, measured transition frequencies, and residuals from the global fit of the microwave, millimeter-wave, and submillimeter-wave vt = 0,1,2 data for CH313CHO acetaldehyde.

Although from the point of view of future radio astronomy observations, we were mainly interested in the rotational transitions belonging to the ground torsional states of 13C acetaldehydes, several transitions belonging to the first and second excited torsional states have also been assigned. The band origins of the excited torsional states are νA = 143.7836 cm-1, νE = 142.0401 cm-1 (vt = 1), νA = 255.3495 cm-1, and νE = 269.2086 cm-1 (vt = 2) for 13CH3CHO, and νA = 143.1719 cm-1, νE = 141.4820 cm-1 (vt = 1) νA = 254.6352 cm-1, and νE = 268.1986 cm-1 (vt = 2) for CH313CHO. First of all the excited torsional states were added to the analysis to stabilize the fit and reduce the correlation between torsion parameters of the RAM Hamiltonian models. In addition several high-Ka series of the ground torsional state transitions were perturbed by interactions with the first and second excited torsional states, so it was necessary to get more precise information about the positions of energy levels of these states.

In total the new datasets for the rotational spectra of 13CH3CHO and CH313CHO isotopologs include 6894 and 6465 measured line frequencies, respectively, with an upper value of J = 60. As already mentioned, both datasets include transitions belonging to the ground, first, and second excited torsional states of the 13C acetaldehyde isotopologs. These sets of rotational transitions were fitted to the RAM theoretical model described above. The fits adopted in the present study as the best achieved the root mean square (rms) deviations of 0.032 MHz for 13CH3CHO and 0.034 MHz for CH313CHO. The weighted rms deviations for the fits were 0.88 and 0.95, respectively. The RAM Hamiltonian models include 91 parameters for 13CH3CHO and 87 for CH313CHO. The values of the molecular parameters obtained from the final fits are presented in Table 1, where they are compared with the parameters of the main isotopolog Smirnov et al. (2014; owing to its significant size, the complete version of Table 1 is presented in Table 7), here only the parameters up to fourth order are given. It is seen from the comparison that up to the fourth order the RAM Hamiltonian models for the 13C isotopologs are very close to the corresponding model of the main isotopolog. Starting from the sixth order, some discrepancies in the sets of parameters begin to appear. In our opinion these discrepancies are caused by the differences in the datasets. For example, the far-infrared data on the fundamental torsional band is only available for the main acetaldehyde isotopolog. The Ka = 9 ← 8Q series of lines presented at Fig. 1 of Smirnov et al. (2014) may serve as one more example of such differences in the datasets: this series of transitions is present in the datasets of 12CH312CHO and 13CH312CHO, but is out of range of the Lille spectrometer for 12CH313CHO.

Table 2 summarizes the fitting results for different groups of the data. It is seen that the two main groups of data with 0.030 MHz and 0.050 MHz uncertainties are fit within the experimental error. The separate rms deviations for the A and E symmetry species are close to each other and do not differ much between torsional excited states. Figures 1 and 2, in which observed and predicted spectra are compared, give additional illustrations of our current understanding of the 13C acetaldehydes spectra. The regions of the Q series of Ka = 10 ← 9 transitions are presented in these figures. It is seen that the majority of strong lines are assigned and predicted by our current model, although a number of rather strong unassigned lines presumably belonging to the higher excited states may still be found in the experimental spectra.

The lists of measured rotational transitions of the 13CH3CHO and CH313CHO isotopologs are presented in Tables 3 and 4. They include the transition frequencies obtained in this study, as well as those available from the previous study (Kilb et al. 1957). In the first ten columns of Tables 3 and 4, the labeling for each spectral line is given: symmetry, vt, J, Ka, and Kc. In the following columns we provide the observed transition frequencies, measurement uncertainties, residuals from the fit, and the reference in the case of Kilb et al. (1957) data (column Source). The last column Comment provides differences between the intensity-weighted average of calculated (but experimentally unresolved) transition frequencies and the observed position of the cluster of blended lines (indicated by “b” in this column). The transitions in Tables 3 and 4 are grouped in series where transitions with the same symmetry, vt, and Ka quantum numbers are sorted in ascending order by J quantum number. Owing to their large sizes, the complete versions of Tables (S3 and S4) are presented at the CDS. Here only parts of these tables are given for illustration purposes.

Table 5

List of calculated positions and assignments of A–A and E–E transitions in the vt = 0,1 torsional states of 13CH3CHO acetaldehyde up to J = 65 in the 1–1000 GHz frequency range.

Table 6

List of calculated positions and assignments of A–A and E–E transitions in the vt = 0,1 torsional states of CH313CHO acetaldehyde up to J = 65 in the 1–1000 GHz frequency range.

Table 7

Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.

Table 8

Torsion-rotation part Qrt(T) of the total internal partition function Q(T) = Qv(T) ∗ Qrt(T), calculated from first principles using the parameter set of Table 7.

The predictions for the rotational spectra of the ground and first excited torsional states of the 13CH3CHO and CH313CHO isotopologs up to 1 THz are given in Tables 5 and 6. The spectra were calculated using the sets of RAM Hamiltonian parameters presented in Table 7. As in Tables 3 and 4, the first ten columns contain the labeling of transitions. The quantum numbers are followed by the columns with calculated transition frequencies and corresponding uncertainties. The next two columns contain the energy of the lower state in cm-1 and the product μ2S, where μ is the dipole moment of the molecule and S a transition linestrength. In our calculations of the 13CH3CHO and CH313CHO spectra, the values for the dipole moment components were taken to be equal to the corresponding values of the parent acetaldehyde isotopolog (Smirnov et al. 2014). In predictions we have adopted the limitations on rotational quantum numbers of J = 65,Ka = 20. In Tables 5 and 6, those transitions that match the frequency range requirement (from 1 GHz to 1 THz), whose predicted uncertainties are less than 0.1 MHz, and line strengths exceeding the limit of 0.01 are included. The complete versions of these tables will also be presented at the CDS: S5 and S6. We provide in Table 8 the rotational parts of the partition functions Qr(T) for 13CH3CHO and CH313CHO calculated from first principles, i.e., via direct summation over the rotational-torsional states. The maximum value of the J quantum number for the energy levels taken for calculating the partition function is 100. The vibrational part Qv(T) may be estimated in the harmonic approximation using the normal modes reported for the main isotopolog of acetaldehyde by Schimanouchi (1972). Simple formulas for calculating Qv(T) can be found elsewhere (see, for example, Gordy & Cook 1984).

5. Conclusion

A new study of the rotational spectra of the 13CH3CHO and CH313CHO isotopologs of the acetaldehyde molecule was carried out in a wide frequency range up to 945 GHz. The study represents more than a twenty-fold expansion in terms of frequency range coverage for the rotational spectra of mono-13C acetaldehydes. Using the RAM Hamiltonian models, we were able to fit the available data within experimental accuracy. The results of the present study allowed us to produce reliable predictions of rotational spectra in the ground and first excited torsional states of 13CH3CHO and CH313CHO isotopologs for astrophysical purposes in the frequency range up to 1 THz for 0 <J< 65 and 0 <Ka< 20.

Acknowledgments

This work was done with the support of the Ukrainian-French CNRS-PICS 6051 project. The Centre National d’Etudes Spatiales (CNES) and the Action sur Projets de l’INSU, “Physique et Chimie du Milieu Interstellaire” are acknowledged for financial support. This work was also done under the ANR-08-BLAN-0054.

References

All Tables

Table 1

Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.

Table 2

Statistics of the data set for the global fit to vt = 0, 1, 2 torsional states of 13CH3CHO and CH313CHO isotopologs of acetaldehyde molecule.

Table 3

Assignments, measured transition frequencies, and residuals from the global fit of the microwave, millimeter-wave, and submillimeter-wave vt = 0,1,2 data for 13CH3CHO acetaldehyde.

Table 4

Assignments, measured transition frequencies, and residuals from the global fit of the microwave, millimeter-wave, and submillimeter-wave vt = 0,1,2 data for CH313CHO acetaldehyde.

Table 5

List of calculated positions and assignments of A–A and E–E transitions in the vt = 0,1 torsional states of 13CH3CHO acetaldehyde up to J = 65 in the 1–1000 GHz frequency range.

Table 6

List of calculated positions and assignments of A–A and E–E transitions in the vt = 0,1 torsional states of CH313CHO acetaldehyde up to J = 65 in the 1–1000 GHz frequency range.

Table 7

Fitted parameters of the RAM Hamiltonian for 13C acetaldehyde isotopologs.

Table 8

Torsion-rotation part Qrt(T) of the total internal partition function Q(T) = Qv(T) ∗ Qrt(T), calculated from first principles using the parameter set of Table 7.

All Figures

thumbnail Fig. 1

Predicted (in blue) and observed (in red) rotational spectrum of 13CH3CHO between 891.3 and 893.2 GHz dominated by Q-type series of transitions with Ka = 10 ← 9. A slight inconsistency between predicted and observed spectrum, which may be visible for some strong lines, is due to source power and detector sensitivity variations.

Open with DEXTER
In the text
thumbnail Fig. 2

Predicted (in blue) and observed (in red) rotational spectrum of CH313CHO between 869.3 and 871.0 GHz dominated by Q-type series of transitions with Ka = 10 ← 9. A slight inconsistency between predicted and observed spectrum, which may be visible for some strong lines, is due to source power and detector sensitivity variations.

Open with DEXTER
In the text

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