Rotational rest frequencies of the low lying vibrational states of npropyl cyanide from extensive laboratory measurements up to 506 GHz^{⋆}
^{1}
IRAP, Université de Toulouse, CNRS, CNES, UPS, 9 Av. Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
email: delong.liu@irap.omp.eu
^{2}
I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
email: hspm@ph1.unikoeln.de
Received:
12
September
2018
Accepted:
9
December
2018
Context. The spectra of four lowlying vibrational states of both anti and gauche conformers of normalpropyl cyanide were previously measured and analyzed in two spectral windows between 36 and 127 GHz. All states were then identified in a spectral line survey called Exploring Molecular Complexity with ALMA (EMoCA) toward Sagittarius B2(N) between 84.1 and 114.4 GHz with the Atacama Large Millimeter/submillimeter Array (ALMA) in its Cycles 0 and 1.
Aims. We wanted to extend the measurements and analysis up to 506 GHz to provide accurate predictions over a much wider range of frequencies, quantum numbers and energies.
Methods. We carried out measurements in two additional frequency windows up to 506 GHz.
Results. For the gauche conformer, a large number of both a and btype transitions were identified. For the anti conformer, transitions were predominantly, but not exclusively, atype. We hence improved molecular parameters for the ground states of both anti and gauchenpropyl cyanide and for excited vibrational states of the gauche conformer (v_{30} = 1, v_{29} = 1, v_{30} = 2, v_{28} = 1) and anti conformer (v_{30} = 1, v_{18} = 1, v_{30} = 2, v_{29} = 1) with high order coupling parameters determined between v_{18} = 1 and v_{30} = 2. Parameters are published for the first time for v_{18} = v_{30} = 1 of the anti conformer and for v_{29} = v_{30} = 1 of the gauche conformer.
Conclusions. In total 15385 lines have been incorporated in the fits and should allow good predictions for unperturbed lines over the whole operating range of radiotelescopes. Evidence is found for vibrational coupling for some levels above 380 GHz. The coupling between v_{18} = 1 and v_{30} = 2 of the anti conformer has been well characterized. An additional list of 740 lines showing potential but as yet unidentified coupling has been provided for astrophysical identification.
Key words: molecular data / line: identification / astrochemistry / methods: laboratory: molecular / ISM: molecules / submillimeter: ISM
Line lists (Tables 10–25) are only available at the CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/622/A82
© ESO 2019
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
Molecules in vibrationally excited states are generally found in hot dense and possibly shocked regions of space and can be used as probes of the gas close to deeply embedded luminous infrared sources. For example, relatively simple molecules and linear carbonchain molecules are found in the circumstellar envelopes of asymptotic giant branch stars. The following vibrationally excited molecules have been identified in IRC+10216, a masslosing carbon star that is embedded in a thick dust envelope: HCN (Ziurys & Turner 1986; Avery et al. 1994), H^{13}CN (Groesbeck et al. 1994), SiS (Turner 1987a), CS (Turner 1987b), C_{4}H (Guélin et al. 1987; Yamamoto et al. 1987). High lying vibrational states can be observed close to the photosphere, for example up to 10 700 K for HCN (Cernicharo et al. 2011). A maser source of HCN originating in the doubly excited bending state was reported by Guilloteau et al. (1987) in CIT6 around 89 GHz (J = 1 − 0), and then IRC+10216 (177 GHz, J = 2 − 1) by Lucas & Cernicharo (1989). Schilke et al. (1999) reported a maser line originating in the quadruply excited bending state (805 GHz, J = 9 − 8) in IRC+10216. A stronger line around 891 GHz (J = 10 − 9) in IRC+10216, CIT6 and Y CVn was later reported by Schilke & Menten (2003). CIT6 and Y CVn are also masslosing carbon stars. Simpler molecules may also be observed in protoplanetary nebula, for example HCN in CRL 618 (Thorwirth et al. 2003).
Vibrationally excited molecules including complex organic molecules, can also be found in star forming regions. The lowest energy vibrations are the easiest to detect and often include torsions. The first molecule detected in the ISM in a vibrationally excited state was cyanoacetylene (linear HCCCN) in the Orion molecular cloud (Clark et al. 1976). HCN was detected in its bending vibration in Orion KL (Ziurys & Turner 1986). Vibrationally excited ammonia (NH_{3}) was also detected toward Orion KL (Mauersberger et al. 1988; Schilke et al. 1992). Torsionally excited Obearing organic molecules identified include methanol (CH_{3}OH) in Orion A (Lovas et al. 1982; Hollis et al. 1983), acetone [(CH_{3})_{2}CO] in Orion KL (Friedel et al. 2005), methyl formate [HC(O)OCH_{3}] in Orion KL (Kobayashi et al. 2007) and W51 e2 (Demyk et al. 2008). Nbearing organic molecules detected in a vibrationally excited state include formamide (HCONH_{2}) in Orion KL (Motiyenko et al. 2012), and alkyl cyanides that will be discussed later. The emission from complex organic molecules usually arises in compact regions, called hot cores, which are typically less than about 0.2 pc in diameter (for example Mehringer et al. 2004). Hence the development of interferometers and in particular ALMA is creating a need for the spectra of the vibrational states (and isotopologues) of these molecules because of the increased sensitivity, and column density due to the decreased beam size.
The study of vibrationally excited states of known molecules in space has several astrophysical interests. Firstly, the frequencies of these lines need to be known so as to make a complete spectroscopic model of an object, identify all lines due to known molecules and hence be able to focus on remaining lines as candidates for new unidentified species (see for example, Mehringer et al. 2004; Daly et al. 2013). Secondly, work on the vibrational states can be used to take the latter into account in the partition function and hence to better estimate the column density of the molecule observed (for example Müller et al. 2016). Thirdly, lines of molecules in vibrationally excited states can be used to focus on hotter, or shocked regions of an object such as hot cores in starforming regions and to model the physical and chemical properties of these regions (for example Goldsmith et al. 1983; Ziurys & Turner 1986; Mehringer et al. 2004). Applications include determining vibrational temperatures to check whether they are in equilibrium (for example Motiyenko et al. 2012) exploring infrared pumping (for example Schilke & Menten 2003; Belloche et al. 2013) and determining the temperature of dust in the cores (Schilke et al. 1992).
Methyl cyanide, the simplest alkyl cyanide, is among the molecules detected early by radio astronomy (Solomon et al. 1971) and an unknown line at 92.3527 GHz observed in Orion and toward the Sagittarius B2 molecular cloud complex (denoted Sgr B2) was suggested to be due to this molecule in its lowest v_{8} = 1 vibrational state as early as 1976 (Clark et al. 1976). Then Goldsmith et al. (1983), using the Five College Radio Astronomical Observatory, modeled 12 components of the J = 6 − 5 transition around 111 GHz to confirm the detection of vibrationally excited CH_{3}CN in its lowest v_{8} = 1 state, a degenerative bending mode at around 525 K equivalent energy, toward the central region of Orion. Using early science verification data from the Atacama Large Millimeter/submillimeter Array (ALMA), the higher state of v_{8} = 2 at around 1030 K was also detected in the hot core of Orion KL (Fortman et al. 2012). Belloche et al. (2013) published a complete IRAM 30 m line survey of Sgr B2(N) and (M), through which, they detected both v_{8} = 1 and 2 states of methyl cyanide in the two sources; as well as that, of a higher state v_{4} = 1 at around 1320 K and for the first time transitions of v_{8} = 1 ^{13}C substituted methyl cyanide in Sgr B2(N).
The first publication of an observation of vibrationally excited ethyl cyanide was by Gibb et al. (2000). Transitions of its two lowestlying states (v_{13} = 1 inplane bending mode and v_{21} = 1 methyl torsional mode both around 300 K) were observed toward the organicrich hot core G327.3−0.6 using the SwedishESO Submillimetre Telescope. A paper devoted to the detection of vibrationally excited ethyl cyanide in the Sgr B2 Large Molecule Heimat source (Sgr B2(NLMH)) was published by Mehringer et al. (2004). By using the Caltech Submillimeter Observatory, in the range 215−270 GHz, the BerkeleyIllinoisMaryland Association Array and the Caltech Millimeter Array in the 107−114 GHz range, the authors detected several lines from these two vibrationally excited states that lie about 302 K above the ground state. Higher excited states of ethyl cyanide, v_{20} = 1 at around 530 K and v_{12} = 1, CCC bending state at around 760 K, were first detected toward three hot cores of Orion KL by Daly et al. (2013), along with the two other lower states. Ethyl cyanide in all these four states was also detected in Sgr B2(N) and its lowest states (v_{13} = 1 and v_{21} = 1) in Sgr B2(M) by Belloche et al. (2013).
There are two isomers of propyl cyanide (also known as cyanopropane or butyronitrile), the straightchain normal, npropyl cyanide (here nPrCN for short), and the branched iso, ipropyl cyanide (here iPrCN for short). Early laboratory work on the ground state of iPrCN (Herberich 1967; Durig & Li 1974) was extended to frequencies needed for radioastronomy by Müller et al. (2011). This isomer became the first molecule found in the interstellar medium with a branched carbon backbone (Belloche et al. 2014). Recently, very comprehensive work on the laboratory measurements and analysis of vibrationally excited states of iPrCN was reported (Kolesniková et al. 2017). There are two conformers of npropyl cyanide as schematically depicted in Fig. 1: anti (here anPrCN for short) with a planar heavy atom frame (i.e., a dihedral CCCC angle of 180°); and gauche (here gnPrCN for short) in which the CH_{3} group, or equivalently the CN group, is rotated by ∼120° to form a dihedral CCCC angle of about ±60°.
Fig. 1. Schematic depiction of the anti (left) and the gauche (right) conformers of nPrCN. The C and N atoms are represented by gray and violet “spheres” respectively, and the H atoms by small, light gray ones. 

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Belloche et al. (2009) identified anPrCN (in its ground vibrational state) for the first time toward Sgr B2(N) a site of highmass star formation, in a line survey using the IRAM 30 m telescope. Lines of the gauche conformer could be included correctly in their model but were too blended for a conclusive identification. Transitions of gnPrCN were later detected unambiguously along with the detection of iPrCN. These identifications were made in a spectral line survey called Exploring Molecular Complexity with ALMA (EMoCA; Belloche et al. 2016). This survey, between 84.1 and 114.4 GHz was taken with ALMA toward Sgr B2(N). Müller et al. (2016), using the same survey, reported the identification of four vibrationally excited states for both anti and gauchenPrCN following new spectroscopic work summarized in the last paragraph.
Laboratory measurements of nPrCN in the vibrational ground states have been sufficient to detect this molecule in space for some time, however, it is only recently that predictions of some of the vibrational states have been good enough to envisage their detection. The ground state rotational constants of nPrCN were first reported by Hirota (1962) following measurements up to 32 GHz. Demaison & Dreizler (1982) and Vormann & Dreizler (1988) used Fourier transform microwave spectroscopy to study the ^{14}N quadrupole structure up to 26 GHz. The latter authors also studied the methyl internal rotation. Wlodarczak et al. (1988) extended the measurements up to 300 GHz and measured the dipole moment components. The energy difference between the two conformers is small leading to some confusion as to that of lower energy. The previous authors determined from intensity measurements that the anti conformer is lower in energy than the gauche by 1.1 ± 0.3 kJ mol^{−1}. Durig et al. (2001) used infrared spectroscopy of nPrCN dissolved in liquid Xenon to determine that the gauche conformer is lower than the anti by 0.48 ± 0.04 kJ mol^{−1} (or 58 ± 4 K) and Müller et al. (2016) found this value to be fully consistent with their model of the ALMA spectra.
Hirota (1962) also determined the rotational constants of the three lowest fundamental vibrational states of the anti and gauche conformers. The information of these excited states for both conformers is summarized in Table 1. Since no gas phase measurements are available the vibrational frequencies given are scaled abinito values from Durig et al. (2001). The nomenclature of the states differs from that in the aforementioned publication since although the gauche conformer has C_{1} symmetry, with all vibrations belong to the symmetry class a; the anti conformer has C_{S} symmetry with 18 fundamental vibrations belonging to the symmetry class a′ and 12 to the symmetry class a″ (Crowder 1987). The equivalent energy for the anPrCN includes the energy of this conformer above that of the gauche. As can be seen from the equivalent temperatures in Table 1, these vibrational states are predicted to be substantially populated in hot core regions of starformation where temperatures can rise to around 100−300 K. For comparison the lowest vibrational states are around 525 K for methyl cyanide, 302 K for ethyl cyanide, as detailed above, and 266 K for iPrCN. Recently, the laboratory spectroscopic study up to 127 GHz of these vibrationally excited states (Müller et al. 2016) led to their detection in space as explained above. Following this identification we decided to carry out a more extensive analysis up to 506 GHz of these vibrational states with the aim of providing reliable predictions over the whole operating band of ALMA. The present data should be useful to search for vibrationally excited states of nPrCN in Orion KL where transitions of the ground vibrational states of both conformers were detected recently with ALMA (Pagani et al. 2017). During our work we also extended the spectral analysis of the ground state, and carried out new work on the combination states of v_{18} = v_{30} = 1 for the anti conformer and v_{29} = v_{30} = 1 for the gauche conformer. Transitions of these and other higherlying vibrational states may be observable in the new EMoCA data obtained in ALMA Cycle 4.
Lowest fundamental vibrational states of nPrCN.
2. Laboratory spectroscopic details
All measurements were carried out at Universität zu Köln. A schematic diagram of the experimental arrangement is shown in Fig. 2. The experimental arrangement for measurements between 36−70 GHz and between 89.25−126.75 GHz have been described previously (Müller et al. 2016). In the two new higher frequency ranges (171−251 and 310−506 GHz) we used a 5.1 m long double path (10.2 m total) absorption cell with inner diameter of 100 mm and equipped with Teflon windows. A commercial sample of nPrCN was flowed slowly through the cell at pressures of around 1 Pa. The cell was at room temperature but the inlet system was heated to about 50°C to achieve a stable pressure in the cell and prevent condensation blocking the needle valve used for flow adjustment. Measurements between 171−251 GHz and between 310−506 GHz used a Virginia Diodes WR9.0 THz starter kit with cascaded multipliers and respectively 3 mW and 0.18 mW middle range output power. Toward the edges the power is around a factor of 15 smaller. This chain was driven by a Rohde & Schwarz SMF 100A synthesizer. From 171−251 GHz eighteen times multiplication and 63 kHz point spacing was used, from 310−506 GHz thirty six times and 144 kHz. We carried out large spectral scans of around 6−7 GHz taking typically several hours to acquire. Up and down scans were coadded. Schottky diode detectors were used to detect output power. We used frequency modulation (FM) throughout with demodulation at 2f, which causes an isolated line to appear approximately as a second derivative of a Gaussian. Optimally the FM deviation was set to half the linewidth, hence typically 250 kHz around 300 GHz. The sensitivity of the spectrometer systems varied with frequency showing both a diminution on the edges of the frequency bands and fluctuations throughout (source power, coupling, reflections, absorption by the optics) in spite of periodic optimization. Nevertheless, relative intensities could be used as guidance for assignments by comparing lines relatively close in frequency.
Fig. 2. Setup diagram for the molecular absorption spectra measurements. The arrow and dot between the wiregrid polarizer and tilted window express the polarizations of the incident and outgoing radiation. 

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3. Spectroscopic results and discussion
3.1. Ground vibrational state
The frequency of previous fits of the ground states was limited to 300 GHz. Our latest fits of the vibrationally excited states were based on deviations from the groundstate parameters and were made up to 506 GHz. Hence we found it useful to also include new higher frequency measurements and make an updated fit of the ground state. The extension of the fit, and the increasing precision of predictions allowed us to also include 1002 additional transitions for the anti conformer and 1545 for the gauche in the range below 300 GHz, including btype and hyperfine split transitions. The assigned uncertainties were 0.01−0.1 MHz, depending on the quality of lines. Usually uncertainties of 0.05−0.1 MHz were assigned above 310 GHz because of the very crowed spectrum which is caused for example by the increase of lines for a given J and the increase in line width (to more than 1 MHz). The difference in the components of the dipole moment for the anti and gauche conformers has an implication on the type of transitions that can be measured and on the parameters that can be determined as will be elaborated below. We took the following dipole moment components for our predictions: for anPrCN, μ_{a} = 4.0 D, μ_{b} = 0.98 D, μ_{c} = 0 (by symmetry); for gnPrCN, μ_{a} = 3.27 D, μ_{b} = 2.14 D, μ_{c} = 0.45 D. Most of the values are those determined by Wlodarczak et al. (1988), however, μ_{a} for anPrCN, and μ_{c} for gnPrCN were taken from quantumchemical calculations made by H.S.P Müller using the method described in Müller et al. (2011). The value of μ_{a} for anPrCN, some 10% larger than that quoted by Wlodarczak et al. (1988) is also consistent with astrophysical observations (Belloche et al. 2014).
In total we added 1992 new measured transitions (1284 lines because of transitions close or at the same frequency) for the anti conformer in the frequency bands of 36−70, 89−127, 171−251 and 310−506 GHz with K_{a} up to 29 and J up to 115 for the lower state (denoted K″_{a} and J″). The fitted lines for the anti conformer are shown in Table 10 (available at the CDS, contains the following information: rotational transition represented by quantum numbers of upper and lower levels, assigned frequency, calculated frequency, residual (assigned−predicted), uncertainty assigned; and for nonresolved transitions: weighted average predicted frequency and difference from assigned frequency). In these newly assigned lines, there were 154 hyperfine split transitions and all of them could be fitted with the hyperfine structure parameters from Vormann & Dreizler (1988). The hyperfine split lines were all below 100 GHz, because of the increasing overlap and broadening of lines at higher frequencies. Besides mainly atype transitions, 20 btype lines were assigned and fitted. All transitions were Rbranch because of their stronger intensities in anPrCN. The assigned btype Rbranch lines with (ΔJ, ΔK_{a}, ΔK_{c})=(1, ±1, 1) were in the frequency below 251 GHz and have a K″_{a} up to 2 and J″ up to 55. Using the larger set of fitted lines, we were able to refine the molecular parameters which are listed in Table 2 together with the parameters determined in Belloche et al. (2009). By comparison we can see that uncertainties on the parameters are smaller. However, the WRMS of our fits is somewhat higher as it is close to or slightly less than 1, which indicates experimental uncertainties are comparable to residuals. We were also able to add some octic centrifugal distortion parameters (L_{KKJ}, L_{JJK} and L_{J}). We constrained the value of H_{K} to the same value as its estimation in Belloche et al. (2009) since it could not be correctly fit because of the persistent lack of btype transitions with higher values of K_{a}.
Molecular parameters for the ground vibrational states of nPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Belloche et al. (2009).
We give some additional information to quantify the reliability of predictions. For Rbranch atype transitions the limit of good predictions is J″ = 123 at K″_{a} = 32. This limit is specified for uncertainties on the predictions less than 0.1 MHz and a similar criterion will be used for the following sections. For lower K_{a} the limit in J increases slowly and for higher K_{a} it decreases rapidly as is the case for the examples that will be cited for the other conformer and other vibrational states.
For the gauche conformer, because of its more asymmetrical geometry and larger bcomponent of the dipole moment, more different types of transition (compared to the anti) were intense enough to be identified and assigned. Totally 3290 more transitions (1861 new lines) were fitted and shown in Table 11 (available at the CDS); they are 1318 Rbranch atype transitions, 143 Qbranch atype transitions, 1255 Rbranch btype transitions, 448 Qbranch btype transitions and 126 Pbranch btype transitions. All of the newly assigned Q and P branch lines are below 320 GHz. 442 hyperfine split transitions were included and fitted with parameters from Vormann & Dreizler (1988). Both anPrCN and gnPrCN showed prolate pairing. Again due to the more asymmetrical geometry of gnPrCN only K″_{a} = 0 and 1 lines could be found oblate paired for the anti conformer whereas for the gauche conformer oblate pairing could be observed up to between K″_{a} = 7 and 8. The newly fitted lines of gnPrCN also allowed us to refine the parameter list as shown in Table 2, with all parameters showing uncertainties at least ten times lower than those quoted in Belloche et al. (2009). Additionally, higher order centrifugal distortion parameters: L_{JJK}, L_{J}, l_{1} and P_{KKKJ} could be determined. As regards good predictions (see the anti conformer) the limit of Rbranch atype transitions is for example J″ = 99 at K″_{a} = 50. Considering oblate pairing at high frequencies, transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, 1) were used to make confident predictions. Finally, all btype transitions at frequencies below 950 GHz were well predicted with K″_{a} up to 34.
3.2. v_{30} = 1 and 2 of gnPrCN
v_{30} = 1 is the lowestlying vibrationally excited state of gnPrCN which corresponds to a C_{2}H_{5} torsion around the central C atom (Crowder 1987; Müller et al. 2016). In this work, measurements at 171−251 and 310−506 GHz were added to refine the parameters; the frequency of transitions was limited to 127 GHz in Müller et al. (2016). We assigned new lines in the sequence of increasing J for each K_{a} first in the lower frequency range and then for the higher one, so as to carefully check the coherence of the evolution of molecular parameters. When new lines could not be fit within experimental uncertainties, and especially when trends were observed, new additional parameters were tried sequentially. The final derived parameters with their uncertainties are listed in Table 3 and those determined in Müller et al. (2016) are listed simultaneously as comparison. Lines of v_{30} = 1 and v_{30} = 2 were fit together. We followed the method for coding the parameters of vibrationally excited states used in previous papers, that is ΔX represents X_{v = 1} − X_{v = 0}, and ΔΔX = X_{v = 2} − X_{v = 0} − 2ΔX. Using this method, we took advantage of the relation between vibrational states to reduce the number of parameters needed to be determined. Furthermore, ΔX should be significantly smaller than X_{v = 0}, and ΔΔX significantly smaller than ΔX, giving a useful check on parameters with abnormal values. The decrease in intensities of lines of higher excited states made their fitting more difficult, especially at high frequency. Finally we could fit 2632 more transitions (1524 new lines) for v_{30} = 1. All of the newly fitted 1457 atype transitions were Rbranch with ΔK_{a} = 0; we tried to find Qbranch atype lines but they were much weaker (for example for two lines compared around 178.9 GHz the Qbranch atype transition was about 50 times weaker than a nearby Rbranch atype transition). The highest J″ of atype lines we could fit in our available frequency was around 90 near 500 GHz, with somewhat higher values for low K_{a} and somewhat lower values for high K_{a}. We fitted atype transitions with K″_{a} up to 20 over all ranges, and an additional 32 transitions with K″_{a} between 21 and 25 between 171−251 GHz. Like in the ground state, atype high J low K_{a} transitions were usually oblate paired with btype transitions in the same branch. Totally 1175 btype transitions in both R and Qbranches were added to the fit. Most btype transitions assigned were Rbranch and more occurred in the high frequency range as the energy between neighboring K_{a} levels gets larger quickly with increasing K_{a}. Among the newly fitted Rbranch btype transitions about half had (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, 1) with K″_{a} covering 0 to 19, while the transitions with (1, −1, 1) all had K″_{a} up to 12 and the transitions with (1, 1, −1) had K″_{a} not less than 6. Among the Qbranch, previously fitted transitions have K″_{a} less than 12 between 37.30−125.54 GHz, and 204 newly fitted transitions were all btype with K″_{a} ≤ 12 between 171−251 GHz. The refined parameters enable good predictions (see Sect. 3.1) of Rbranch atype transitions up to J″ = 91 at K″_{a} = 30, and btype transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, 1) up to J″ = 95 at K″_{a} = 20.
Changes of molecular parameters for the v_{30} = 1 and 2 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Fitted transitions of v_{30} = 2 above 171 GHz were similar in type to those of v_{30} = 1: 1045 Rbranch atype transitions, 778 Rbranch btype transitions, and 214 Qbranch btype transitions; with no new hyperfine split transitions. Table 12 (available at the CDS) gives all lines of v_{30} = 1 and v_{30} = 2 used in the final fit. We found it was difficult to fit atype transitions with J″ larger than 89 for K″_{a} = 0 and 1, as all these transitions showed residuals (assigned−predicted) with a trend of increasing negative values. New parameters could not be determined to remove this trend. Therefore we put all these identified transitions in a separate list (Table 13, at the CDS). As a precaution, all sametype transitions with J″ larger than 89 for higher K″_{a} were put into this supplementary list even if the lines appeared to fit correctly. An obvious trend of residuals also took place with J″ larger than 59 for K″_{a} = 20. The limit of safe atype lines climbs to K″_{a} = 22 with J″ up to 58. Rbranch btype transitions in our newly assigned frequency ranges could be classified in 3 groups as was the case for v_{30} = 1: transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, 1),(1, −1, 1) and (1, 1, −1). All 3 groups of transitions are in the frequency ranges of 171−251 and 310−506 GHz, with the coverage of K_{a} and J similar to those of v_{30} = 1. The Qbranch btype transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(0, 1, −1) are all in the range 171−251 GHz with K″_{a} from 12−17, J″ from 19−65 and not sequential with frequency. The two subbranches of the Qbranch btype transitions (J = K_{a} + K_{c} and J = K_{a} + K_{c} − 1) show prolate pairing and hence have doubled intensities facilitating the assignments. Taking into account that vibrational coupling may cause some transitions to shift in frequency by up to the order of 1 MHz, safe predictions can be made up to J″ = 88 at K″_{a} ≤ 19 and J″ = 59 for 20 ≤ K″_{a} ≤ 25 for atype transitions, and up to K″_{a} = 14 for btype transitions.
3.3. v_{29} = 1 of gnPrCN
v_{29} = 1 is a vibrational state lying in energy between v_{30} = 1 and v_{30} = 2. We started from the fit of Müller et al. (2016) and first added lines up to 251 GHz. When we got to K″_{a} = 8 for new lines we started to have problems with a calculated WRMS larger than 1.40. We noticed that Qbranch btype lines with high J numbers in Müller et al. (2016) all had residuals more than three times the attributed uncertainties (3σ) with the same sign for a particular K″_{a}. We decided to remove these problem lines from the fit, and concentrate on Qbranch btype transitions at higher frequency which have stronger intensities (176 transitions with K″_{a} between 12−17 at 176−242 GHz). The newly determined parameters allowed us to make more precise predictions and identify clearly that the problem lines show internal rotation splitting, that was previously difficult to differentiate from line crowding and quadrupole hyperfine splitting. The split lines show two components separated by around 0.5 MHz with similar intensity and center on the updated predictions. The center frequencies (all calculated by averaging the positions of the two components) were hence assigned with a higher uncertainty (0.05 MHz). All lines included in our new fit up to 506 GHz are listed in Table 14 (at the CDS). No hyperfine splitting was resolved above 171 GHz, while all lowerfrequency hyperfine split lines from Müller et al. (2016) were fitted with the groundstate hyperfine structure parameters from Vormann & Dreizler (1988). If not indicated specifically, it is the same for other states. Rbranch btype transitions were in the same three groups as v_{30} = 1 and 2, with the largest K″_{a} = 19 and largest J″ = 91 near 500 GHz. The btype transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, ±1) are prolate paired (or close) with low J″ and high K″_{a}; while (1, ±1, 1) transitions are more oblate paired with high J″ and low K″_{a}, therefore nearly half of the newly assigned, 715 Rbranch btype transitions had (ΔJ, ΔK_{a}, ΔK_{c})=(1, 1, 1). All newly assigned Rbranch atype transitions with K″_{a} up to 20 and 32 were successfully fit at frequencies up to respectively 506 and 251 GHz. atype transitions with K″_{a} = 11 were badly fit above J″ = 77 for the subbranch J = K_{a} + K_{c} and J″ = 82 for J = K_{a} + K_{c} − 1 with obvious trends. We put all these lines, with lines of larger J″ and K″_{a} (even if some had reasonable residuals), into a separate list (Table 15, available at the CDS) as we did in v_{30} = 2 and they were excluded from our final fit. Finally we derived the parameter list as shown in Table 4 additionally determining ΔH_{K} and Δh_{1}. ΔH_{JK} was decreased by 60% compared with Müller et al. (2016), because of the correction of the assignment of lines with internal rotation splitting. These corrected transition frequencies as well as the newly assigned transitions allowed us to determine Δh_{1} and this, in turn, changed the values of Δh_{2} and Δh_{3} significantly. The value of ΔH_{J} was also better determined. The refined parameters allow confident predictions above 310 GHz for atype transitions with J″ up to 121 at K″_{a} = 10, but less than 77 at K″_{a} between 11 and 35. For btype transitions, the largest K″_{a} is 14.
Changes of molecular parameters for the v_{29} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
3.4. v_{28} = 1 of gnPrCN
Most transitions fitted in Müller et al. (2016) were Rbranch atype with J″ less than 22 and K″_{a} less than 19. The v_{28} vibrational mode involves mainly methyl group torsion (Crowder 1987; Durig et al. 2001) leading to a considerable internal rotation character in the microwave spectra; some evidence was observed in Müller et al. (2016) when assigning transitions with K″_{a} ≥ 3. Owing to this, our confident assignments for the highKRbranch atype transitions could not climb as high in J″ as the lowerenergy states of gnPrCN: J″ = 40 between K″_{a} = 10 − 20 at about 245 GHz. Since the internal rotation causes broadening, shoulders or splits which are more prominent in high J transitions, we followed a similar procedure to Müller et al. (2016). For symmetric broadening, or splits with similar intensities of the two components with the separation around 0.6 MHz, we assigned the prediction to the center and gave an uncertainty of 0.05 MHz. For splits with an intensity ratio of 1:2 or 2:1, we assigned the prediction to the weighted average frequency and gave an uncertainty of 0.10 MHz. This is indicated in the line lists available at the CDS. The broadening and line density above 310 GHz made secure assignments for internalrotation affected lines impossible; finally atype transitions could be fit with K″_{a} up to 9 between 310−506 GHz. The small number of btype transitions fitted in Müller et al. (2016) made it difficult to determine the pure K parameters, D_{K} and H_{K}. For Rbranch btype transitions, the assignments with higher K″_{a} were difficult because they were close to each other. This was already the case at lower frequency as described in Müller et al. (2016). However, 309 Rbranch btype transitions with (ΔJ, ΔK_{a}, ΔK_{c})=(1, ±1, 1) whose K″_{a} up to 9 and J″ up to 89 could be added to the fit up to 506 GHz. Because of the difficulty in assigning highK transitions, it was not possible to add new (1, 1, −1) transitions at higher frequency. Additionally, 12 new Qbranch btype transitions could be assigned and fit; all of these lines have K″_{a} between 12−17 from 174.93−245.03 GHz. These newly assigned btype transitions proved useful to determine the molecular parameters especially ΔD_{K}, whose value was freed and determined consistent to the estimation in Müller et al. (2016; as Table 5). All fitted lines of v_{28} = 1 can be found in Table 16 (available at the CDS) and additional lines were put in Table 17 (available at the CDS) as we did for other states of the gauche conformer. The limit of good predictions above 310 GHz is J″ = 89 at K″_{a} up to 5 and J″ = 78 at larger K″_{a} (≤9) for both a and btype transitions, owing to the difficulty in assigning highK transitions.
Changes of molecular parameters for the v_{28} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
3.5. v_{29} = v_{30} = 1 of gnPrCN
Hirota (1962) refers to seeing combination states in his measurements but gives no further details or analysis. We used the empirical method of estimating the parameters by addition of the changes of each individual vibrational state: X_{v29 = v30 = 1} = X_{v = 0} + ΔX_{v30 = 1} + ΔX_{v29 = 1} + ΔΔX. First predictions were made with ΔΔX = 0. Lines could then be easily assigned to transitions with low quantum numbers, and subsequently the correction ΔΔX was liberated for certain parameters to fit successively more transitions. The exploratory assignments began with intense Rbranch atype transitions and then btype transitions. After all Rbranch transitions were assigned and fitted, Qbranch btype transitions were measured with particular care because of the already identified internal rotation of v_{29} = 1 involved in the movement of this combination vibrational state and the higher energy giving weaker lines. For Rbranch atype transitions, we could successfully fit all transtions with K″_{a} up to 20 (excluding lines of K″_{a} = 18, which showed a clear trend in residuals between 197.48 and 221.45 GHz) for frequencies below 251 GHz. But in the range 310–506 GHz, the assignments appeared difficult in spite of larger intensities. As for other vibrational states of gnPrCN, the oblate pairing consisting of atype and btype transitions facilitated the assignments. However, the increasing separation of paired transitions with increase in quantum numbers made assignments more difficult combined with the blending and broadening in the high frequency range and the possible splits caused by internal rotations. Therefore very secure assignments with K″_{a} up to 4 or 5 (for each subbranch) were first made. Even after the improvement of the parameters several lines at each K″_{a} could not be correctly fitted showing systematic residuals. All these lines are in the ranges of J″ from 68 to 73 and from 89 to 93. We attributed this as due coupling with other vibrational states. Finally 935 Rbranch atype transitions were identified in all four frequency ranges. The assignment of btype transitions was not easy due to low intensities at low frequencies and blending and broadening at high frequencies. The confidently assigned btype transitions at high frequency were all oblate paired with intense atype transitions with K″_{a} less than 6. Totally, 487 btype transitions were fitted. Qbranch btype transitions were useful to correctly determine the parameter D_{K}. We identified internal rotation causing splits (with the components separated by around 0.6 MHz) at frequencies between 89.25–126.75 GHz, in transitions with large J″. In this range, Qbranch btype transitions have K″_{a} less than 11 and those that could be securely assigned have J″ less than 45. For Qbranch btype transitions with K″_{a} between 13 and 18 in the range 171–251 GHz, only prolate pairs were assigned. These transitions have low J″ and hence are not affected by internal rotation. Finally 466 Qbranch btype transitions were correctly fitted. Moreover, 110 hyperfine split transitions were fitted with fixed hyperfine parameters from v_{30} = 1. These are Rbranch atype transitions with J″ approaching K″_{a} (less than 11), btype transitions (both Rbranch and Qbranch) with K″_{a} less than 4 at frequencies below 70 GHz. The derived parameters are shown in Table 6. The fitted transitions are in Table 18 (available at the CDS), and those confidently assigned but not correctly fitted with systematic residuals are separated in Table 19 (available at the CDS). Using the newly derived molecular parameters, confident predictions of atype transitions can be made up to J″ = 68 for K″_{a} ≤ 5 below 380 GHz, and J″ = 41 for K″_{a} ≤ 41 below 251 GHz (excluding lines of K″_{a} = 18 that show residuals that cannot be fitted). For btype transitions, all Rbranch predictions with K″_{a} ≤ 11 below 251 GHz are reliable, and J″ ≤ 41 for K″_{a} ≤ 17 for the Qbranch also below 251 GHz. For frequencies above 310 GHz, the limit of btype transitions has the same limit as the atype because of oblate pairing.
Changes of molecular parameters for the v_{29} = v_{30} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction.
3.6. v_{30} = 1 of anPrCN
v_{30} = 1 of anPrCN was fit together with v_{30} = 2 and v_{18} = 1, in order to take into account Coriolistype and Fermi coupling effects between the latter two states. All lines of v_{30} = 1, 2 and v_{18} = 1 included in the final fit are given in Table 20 (available at the CDS). All confident assignments showing large residuals and a trend that could not be corrected with additional parameters were put in a separate list (Table 21, available at the CDS) as was done for the gauche conformer. Finally we obtained changes of the molecular parameters for all three vibrational states shown in Table 7. We discuss v_{30} = 1 first. Most transitions fitted were atype (516 out of 540 in Müller et al. (2016); 1134 new transitions out of 1259 in this work) because of the low value of μ_{b}. New assignments between 171−251 GHz could be smoothly fit for all atype transitions with K″_{a} up to 19, by adding ΔH_{JK}. For K″_{a} = 20, transitions with J″ between 38−48 between 173−217 GHz could not be correctly assigned because of the poor line shape; assignments could be made with larger J″, but the residuals were already over our acceptable value (3σ). For assignments between 310−506 GHz, we were only able to fit up to K″_{a} = 3 with the previous parameter list. First we tried to add Δh_{1} and Δh_{2}, as h_{1} and h_{2} could be determined for the ground vibrational state but these parameters did not allow us to fit higher K″_{a} lines correctly. In order to do this we had to add Δh_{3}, but in this case Δh_{1} could not be determined any more. Finally the best fit was obtained using Δh_{2} and Δh_{3}. For lines above 310 GHz, we could not successfully fit above J″ larger than 84 for K″_{a} = 14 with all problem lines showing negatively trended residuals. Similarly K″_{a} = 15 showed positive trended residuals and 16 positive trended but smaller residuals. The addition of high order parameters did not allow an adequate fit of these lines, and the value of parameters varied largely and became dependent on the data set used. We hence omitted them from the final fit. Although K″_{a} = 17, 18 and 19 could then be fitted with all determined parameters, by precaution we put all lines with J″ > 84 and K″_{a} > 13 into our separate list in Table 21. Extensive fitting of btype lines proved difficult. We did, however succeed in measuring 125 btype transitions, up to 251 GHz. Most of these btype transitions are Qbranch with K″_{a} up to 3 because of their higher intensities. For Rbranch btype transitions we could get to J″ = 55 and K″_{a} = 2. btype lines were very useful for determining ΔA and ΔD_{K}, whose uncertainties were decreased to one tenth of their previous values (as Table 7). The value of H_{K} in the groundstate of anPrCN could not be correctly determined, and no differences (ΔH_{K}) were hence determined for the vibrationally excited states. Using the new parameters, predictions should be relatively confident with J″ up to 119 for K″_{a} ≤ 28, but predictions for K″_{a} = 14, 15 and 16 with J″ ≥ 84 may not all be reliably precise because of the vibrational coupling. Hence the measured frequency should be used when available.
Changes of molecular parameters for the v_{30} = 1, 2 and v_{18} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
3.7. v_{30} = 2 and v_{18} = 1 of anPrCN
The fitting for v_{30} = 2 was started after the parameters of v_{30} = 1 were obtained. We first fitted the transitions from 171−251 GHz with increasing K″_{a}. For K″_{a} = 9, transitions with J″ between 43−55 could not be correctly fit, neither could the transitions with K″_{a} = 10 and 11. Our new assignments with higher values of K″_{a} in the final line list enabled us to determine ΔΔH_{KJ} which took a larger than estimated value of about three times ΔH_{KJ}. This then allowed lines with K″_{a} up to 11 to be successfully fit. We then started to assign lines of v_{18} = 1 at 171−251 GHz, since no major coupling had been observed previously up to this K″_{a} value. Lines with K″_{a} up to 12 could be fit for v_{18} = 1. However, lines with higher K″_{a} were calculated with residuals beyond our expectance. After including the new data, previously assigned v_{30} = 2 lines with K″_{a} = 12 and 13 had positive residuals above 3σ whereas residuals with negative values could be found for previous assignments of v_{18} = 1 with K″_{a} = 13 and 14. For K″_{a} = 14 of v_{30} = 2, residuals were between −0.22 to −0.30 MHz for previous assignments. These deviations are likely caused by deficiencies in describing the Coriolistype interaction between v_{18} = 1 and v_{30} = 2. In contrast, the residuals for K″_{a} = 15 of v_{18} = 1 were positive with almost same absolute values as v_{30} = 2. Restraining ΔΔH_{KJ} as Müller et al. (2016), did not help. We attributed the problem to insufficient coupling parameters, and determined that G_{cJ} and F_{K} were necessary for fitting these lines. The effect of adding these two parameters is shown in Fig. 3. We could then fit lines of v_{30} = 2 with K″_{a} up to 19. Lines with K″_{a} = 19 above J″ = 51 showed asymmetrical shapes and even splits. For v_{18} = 1 we could safely assign and fit lines with K″_{a} up to 20. We then moved on to the higher frequency range above 310 GHz. Fitting was successful for K″_{a} = 8 for v_{30} = 2 up to 506 GHz, but at K″_{a} = 9 we were hindered by separation of transitions from their prolate pairs at J″ = 95, which lead to a broadening of the line shape or even unresolved splits. Fitting with higher K″_{a} proved difficult, and at higher energy, coupling with other vibrational states is possible. We noticed obvious trends in the residuals of lines with K″_{a} ≥ 10. For example, positivetrend residuals (0.12 to 0.31 MHz) for J″ between 83−111 at K″_{a} = 10, negativetrend residuals (−0.08 to −1.46 MHz) for J″ between 84−109 at K″_{a} = 11. Lines showing identified trends in the residuals with K″_{a} up to 17 are listed in Table 21; higher K″_{a} lines could not be followed and assigned confidently. For v_{18} = 1, the separation of subbranches of Rbranch atype transitions also stopped us fitting transitions with J″ larger than 85 at K″_{a} = 9. Up to K″_{a} = 16, assignments could be correctly fit up to J″ = 76 at around 336 GHz; the fits for higher J″ transitions with trended residuals are included in Table 21. We could successfully fit another 25 btype transitions with K″_{a} = 0 and 1 for v_{30} = 2 that are included in Table 20 (available at the CDS), most of them Rbranch transitions between 171−251 GHz. For these two states, confident predictions should be possible up to J″ = 110 for K″_{a} ≤ 9; for higher K″_{a} ≤ 17 confident predictions are limited to J″ ≤ 82. Note that interstate transitions between v_{30} = 2 and v_{18} = 1 can be predicted but are too weak to be measured in laboratory and most certainly in space.
Fig. 3. Spectral extracts showing the effect of coupling parameters. The dot dash lines are predictions without coupling parameters; the dashed lines show predictions with coupling parameters from Müller et al. (2016) and the solid lines show predictions with additional coupling parameters determined in this work. Lines for other identified transitions are shown in the figures as well: • for ground state of anPrCN, for v_{30} = 1 of anPrCN, ° for v_{30} = 1 of gnPrCN, and × for v_{29} = 1 of gnPrCN. 

Open with DEXTER 
The difficulty of the fits for v_{30} = 1, 2 and v_{18} = 1 of anPrCN is increased by a nonresonant Coriolis interaction between v_{30} = 1 and v_{18} = 1. This interaction is apparent in the relatively large vibrational corrections of many spectroscopic parameters of v_{18} = 1 and v_{30} = 2 which are often of similar magnitude, but of opposite sign (see Table 7). Fitting of the entire present data set may thus require more changes in spectroscopic parameters than can safely be determined. Because of the multiple interactions possible between several vibrational states the determination of these parameters most likely requires substantial further measurements and analysis that are outside the scope of this work for predicting lines strong enough to be clearly seen in an astrophysical survey. However, this may be done in future.
3.8. v_{29} = 1 of anPrCN
v_{29} = 1 of the anti conformer is a vibrational state with energy between v_{30} = 2 and v_{18} = v_{30} = 1. The assignments for transitions in higher states were difficult since their intensities get weaker and because the possibility of coupling with other states increases. As explained previously the identification of btype transitions was even harder. Since only atype transitions with ΔK_{a} = 0 were identified it was not possible to determine ΔD_{K}. ΔA was not so well determined. We could identify internal rotation splitting caused by the methyl group torsion with K″_{a} = 1 and 2 (only for the subbranch, J = K_{a} + K_{c}). All of the split lines showing similarintensity components separated by around 0.5 MHz, are between 171−251 GHz, with J″ between 39−57 (for K″_{a} = 1) and between 46−55 (for K″_{a} = 2). At higher frequencies internal rotation splitting and accidental line overlap could not be discriminated and hence assignments were not made if a single symmetric line was not identified. Finally, transitions with K″_{a} up to 17 could be fit between 171−251 GHz with J″ between 39 and 58. Above 171 GHz transitions with K″_{a} = 11 could not be correctly fit, with residuals from 0.43 to 1.53 MHz showing a trend with increasing J″. This is probably due to coupling with another vibrational state, as other K″_{a} transitions (above and below) in the frequency range could be well fitted. For assignments from 310−506 GHz, we could fit transitions with K″_{a} up to 8. For weaker noneprolate paired transitions with K″_{a} less than 8, overlaps stopped us fitting more transitions, especially those with K″_{a} from 4 to 7. Higher K″_{a} transitions were assigned but all with trends in the residuals, and were removed to the supplementary list given in Table 23 (available at the CDS) with all assigned K″_{a} = 11 transitions not included in the fit. Explorative fits including transitions with K″_{a} = 9 and 10 at 310−506 GHz changed determined parameters significantly and required illogical higher order parameters. Also the fits became dataset dependent since the newly determined parameters fit transitions with even higher K″_{a}, worse than the previous. Therefore all assignments of transitions with K″_{a} ≥ 9 were moved to Table 23 leaving transitions included in the fit in Table 22 (available at the CDS). Finally the changes of parameters are shown in Table 8. Confident predictions can be made with K″_{a} ≤ 8 with good results (see section 3.1) for J″ up to 90. Higher K″_{a} predictions can be made with relative confidence especially at lower frequencies except for K″_{a} = 11 because of the unidentified vibrational coupling.
Changes of molecular parameters for the v_{29} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
3.9. v_{18} = v_{30} = 1 of anPrCN
We present in Table 9 the first published molecular parameters for v_{18} = v_{30} = 1 of anPrCN. Hirota (1962) refers to seeing combination states in his measurements but gives no further details or analysis. The assignments were quite difficult as this state has the highest energy in our present study. Moreover, just as v_{18} = 1 and v_{30} = 2 interact resonantly, v_{18} = v_{30} = 1 and v_{30} = 3 are expected to interact resonantly, and v_{18} = v_{30} = 1 is expected to interact at least nonresonantly with v_{30} = 2 and with v_{18} = 2. Finally 613 transitions (492 lines) were assigned and fitted below 506 GHz (Table 24, available at the CDS). All transitions assigned are atype Rbranch because of their strong intensities. At the beginning, only parameters of v_{30} = 1 and v_{18} = 1 were used to make predictions, that can be seen from the table to give relatively correct estimates of B, C and D_{J}. These estimates were sufficiently correct, along with the other approximate parameters, to identify lines with K″_{a} between 0 and 5 below 70 GHz. Then more lines could be identified with iterative fitting and refinement of the parameters. Lines were assigned sequentially through all four available frequency ranges: 36−70, 89−126, 171−251, and 310−506 GHz as increasing J″ and K″_{a}. We could safely assign transitions with the highest K″_{a} = 8 in all available frequency ranges. Below 70 GHz we were able to assign some additional lines (J″ between 10 and 14 for K″_{a} = 9; J″ between 11 and 13 for K″_{a} = 10). Assignments for higher K″_{a} transitions need high order centrifugal distortion parameters, which are also better determined by fitted transitions with high quantum numbers. Lower intensities of higher K″_{a} transitions and possible coupling with v_{29} = 1 presented ambiguities for their assignments. Conversely lack of lines with high K″_{a} make it difficult to characterize any coupling with v_{29} = 1. Exploratory fits for transitions with K″_{a} = 9 and 10 between 89−126 GHz resulted in negative residuals of about −0.2 MHz (20 ≤ J″ ≤ 22) and −0.36 – −0.45 MHz (20 ≤ J″ ≤ 24) respectively, however without any clear trends; all these tentative assignments are listed in Table 25 (available at the CDS). Other assignments fitted with significant residuals (showing that more parameters are needed), include lines with 51 ≤ J″ ≤ 55 of K″_{a} = 8 at 230.61−248.34 GHz (residuals between 0.09−0.34 MHz) and 90 ≤ J″ ≤ 111 of K″_{a} = 1 at 396.84−486.70 GHz (residuals between −0.16 – −0.36 MHz). The WRMS we derived was somewhat larger than other states because high frequency lines were somewhat less well predicted with the current parameter list. We note that including ΔΔH_{KJ} in the fit gave a determined value of −547(43)×10^{−9}, however, since this value was unreasonably large we did not use it in the final fit. When J approaches K_{a}, broadening and splitting caused by quadrupole hyperfine splitting were identified. 58 hyperfine split transitions below 70 GHz were added to the list with K″_{a} between four and ten. Hyperfine structure parameters from Vormann & Dreizler (1988) for the ground state are sufficient to fit them. Confident predictions are possible up to K″_{a} = 7, for J″ ≤ 89. For K″_{a} = 8, up to J″ = 50 and for K″_{a} = 9 and 10, only predictions below 70 GHz can be treated with full confidence.
Changes of molecular parameters for the v_{18} = v_{30} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction.
4. Conclusion and outlook
We have added 11453 new lines to fits for both conformers of nPrCN, mainly in the frequency ranges 171−251 and 310−506 GHz. We have hence improved molecular parameters for the ground states of both anti and gauchenpropyl cyanide and for excited vibrational states of the gauche conformer (v_{30} = 1, v_{29} = 1, v_{30} = 2, v_{28} = 1) and anti conformer (v_{30} = 1, v_{18} = 1, v_{30} = 2, v_{29} = 1). The inclusion of these newly assigned lines gives a more precise and extended list of molecular parameters to improve the predictions over the entire operating range of ALMA. The present data should be useful to search for vibrationally excited states of nPrCN in Orion KL with ALMA. For Coriolis and Fermi coupling between v_{30} = 2 (K″_{a} ≥ 13) and v_{18} = 1 (K″_{a} ≥ 14), two more coupling parameters F_{K} and G_{CJ} were derived from fitting. During the analysis, we not only continued assigning internal rotation split transitions in v_{28} = 1 of gnPrCN between 171−251 GHz but also identified additional internal rotation splitting of the Qbranch btype transitions occuring in v_{29} = 1 (for both the fundamental and combination states) of the gauche conformer at frequencies below 125 GHz and also in the Rbranch atype transitions in v_{29} = 1 of the anti conformer with K″_{a} = 1 and 2, at 171−251 GHz. This splitting is not expected to be resolved in astrophysical spectra. We gave the first published measurements and derived parameters for the combination state v_{18} = v_{30} = 1 for anPrCN and for the combination state v_{29} = v_{30} = 1 for gnPrCN, both found by using our parameters for the individual vibrational states. Transitions of these and other higher lying vibrational states may be observable in the new EMoCA data obtained in ALMA Cycle 4. After each state and conformer, the reliability of predictions is discussed in particular as regards vibrational coupling, and limits of quantum numbers and frequencies are given. No problems have been found with the ground states. For the vibrational states above the limits given, it is best to use the measured frequencies given in the CDS when available. Measurements are presently not available in the ranges: 70−89, 127−171, and 251−310 GHz. As most of the perturbations observed are above about 350 GHz, confident predictions are available in these gaps. However, there are some particular cases. For v_{29} = 1 of the anti conformer, lines of K″_{a} = 11 are perturbed above 176 GHz hence no confident frequencies are available in the highest frequency gap. Similarly for the combination state v_{29} = v_{30} = 1 of the gauche conformer, for K″_{a} = 18 there are no confident frequencies available in the highest frequency gap. For the combination state v_{18} = v_{30} = 1 of the anti conformer, confident data is not available if not measured above K″_{a} = 8 for frequencies above 70 GHz, and for K″_{a} = 8 for frequencies above 221 GHz.
Lines assigned but not fitted correctly with our updated parameters are given as separate lists for astrophysical identification and will require future work to identify other vibrational couplings. These lines either have a shift more than three times the estimated experimental uncertainty or show clear trends in deviation, or both. Also lines that fit correctly but above K_{a} and J ranges already showing deviations have been included in the supplementary list and not in the fit by precaution. There is most likely in anPrCN, a nonresonant interaction between v_{30} = 1 and v_{18} = 1 as indicated by large but opposite variations in the determined ΔA rotational constant. v_{30} = 2 is also probably affected by coupling with nearby states. Hence full treatment of the perturbed lines most likely requires the measurement at higher sensitivity of several additional higher vibrational states such as v_{30} = 3 and v_{18} = 2 by combined analysis. Tentative attempts to identify transitions of v_{30} = 3 in both conformers by extrapolation of the parameters from v_{30} = 0, 1 and v_{30} = 2 have not as yet been successful and require further work. Measurements of gasphase rovibrational spectra in the far infrared may also provide useful data for a more extensive analysis. Evidence for coupling in the gauche conformer is also seen but affects less the fitting. In general fitting of the gauche conformer is easier because the higher asymmetry allows more parameters to be determined independently.
Acknowledgments
The work in Cologne was supported by the Deutsche Forschungsgemeinschaft (DFG) through the collaborative research grant SFB 956 project B3 and through the Gerätezentrum “Cologne Center for Terahertz Spectroscopy”. D.L. and A.W. thank PCMI for funding visits to Cologne for measurements and discussion with collaborators. PCMI is the French program “Physique et Chimie du Milieu Interstellaire” funded by the Conseil National de la Recherche Scientifique (CNRS) and Centre National d’Etudes Spatiales (CNES). They also thank the DFG via SFB 956 project B3 for funding additionalvisits to Cologne. D.L. thanks the Chinese Scholarship Council (CSC) for funding his PhD study in France.
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Appendix A: Line lists at the CDS
Line lists availabe at the CDS include: fitted transitions at 36−70, 89.25−126.75, 171−251 and 310−506 GHz for anPrCN in the ground state (Table 10), v_{30} = 1, v_{30} = 2 and v_{18} = 1 (Table 20), v_{29} = 1 (Table 22) and v_{18} = v_{30} = 1 (Table 24); for gnPrCN in the ground state (Table 11), v_{30} = 1, v_{30} = 2 (Table 12), v_{29} = 1 (Table 14), v_{28} = 1 (Table 16) and v_{29} = v_{30} = 1 (Table 18). Additionally, a smaller number of lines confidently assigned but not fitted correctly and showing systematic residuals indicating as yet uncharacterized vibrational coupling are given in separate lists. The lines that could be correctly fitted but are above quantum number limits first showing systematic residuals are also placed in these separate lists and not used in the final fits by precaution. The separate lists include for gnPrCN, v_{30} = 2 (Table 13), v_{29} = 1 (Table 15), v_{28} = 1 (Table 17) and v_{29} = v_{30} = 1 (Table 19); and for anPrCN, v_{30} = 1, v_{30} = 2 and v_{18} = 1 (Table 21), v_{29} = 1 (Table 23) and v_{18} = v_{30} = 1 (Table 25).
All Tables
Molecular parameters for the ground vibrational states of nPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Belloche et al. (2009).
Changes of molecular parameters for the v_{30} = 1 and 2 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Changes of molecular parameters for the v_{29} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Changes of molecular parameters for the v_{28} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Changes of molecular parameters for the v_{29} = v_{30} = 1 vibrational states of gnPrCN obtained from our latest fit using Watson’s S reduction.
Changes of molecular parameters for the v_{30} = 1, 2 and v_{18} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Changes of molecular parameters for the v_{29} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction compared to the fit of Müller et al. (2016).
Changes of molecular parameters for the v_{18} = v_{30} = 1 vibrational states of anPrCN obtained from our latest fit using Watson’s S reduction.
All Figures
Fig. 1. Schematic depiction of the anti (left) and the gauche (right) conformers of nPrCN. The C and N atoms are represented by gray and violet “spheres” respectively, and the H atoms by small, light gray ones. 

Open with DEXTER  
In the text 
Fig. 2. Setup diagram for the molecular absorption spectra measurements. The arrow and dot between the wiregrid polarizer and tilted window express the polarizations of the incident and outgoing radiation. 

Open with DEXTER  
In the text 
Fig. 3. Spectral extracts showing the effect of coupling parameters. The dot dash lines are predictions without coupling parameters; the dashed lines show predictions with coupling parameters from Müller et al. (2016) and the solid lines show predictions with additional coupling parameters determined in this work. Lines for other identified transitions are shown in the figures as well: • for ground state of anPrCN, for v_{30} = 1 of anPrCN, ° for v_{30} = 1 of gnPrCN, and × for v_{29} = 1 of gnPrCN. 

Open with DEXTER  
In the text 