Journal of Molecular Spectroscopy 257 (2009) 24–28

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Journal of Molecular Spectroscopy

journal homepage: www.elsevier .com/locate / jms

Submillimeter-wave spectrum of anti–anti and anti–gauche diethyl ether

Adam Walters a,*, Holger S.P. Müller b, Frank Lewen b, Stephan Schlemmer b

a CESR, Centre d’Etude Spatiale des Rayonnements, Université de Toulouse [UPS], CNRS [UMR 5187], BP 44346, 9 av. du Colonel Roche, F-31028 Toulouse Cedex 4, Franceb I. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany

a r t i c l e i n f o

Article history:Received 12 February 2009In revised form 6 May 2009Available online 7 June 2009

Keywords:Diethyl etherRotational spectroscopySubmillimeter spectroscopyALMAConformersRadio-astronomy

0022-2852/$ - see front matter � 2009 Elsevier Inc. Adoi:10.1016/j.jms.2009.06.002

* Corresponding author. Fax: +33 561 556 701.E-mail address: adam.walters@cesr.fr (A. Walters)

a b s t r a c t

Measurements of the rotational spectrum of diethyl ether have been extended up to 903 GHz for the aa-conformer and up to 638 GHz for the ag-conformer. These measurements supplement previous ones upto 366 GHz and improve predictions into the THz region to be used in particular for astronomicalsearches for this species using the next-generation of radio-astronomy instruments such as the AtacamaLarge Millimeter Array.

� 2009 Elsevier Inc. All rights reserved.

1. Introduction

Diethyl ether (DEE) is of potential interstellar relevance since ofthe two smaller members of this series, dimethyl ether (DME) isubiquitous in regions of massive star formation and ethyl methylether (EME) has been tentatively identified. DME has been foundto possess high abundances in hot-core type sources within denseinterstellar clouds [1–6] and has also been detected recently in thehot corino of the low-mass binary system IRAS 16293-2422 [7] andin the low-mass protostar NGC 1333 IRAS 2A [8]. A small numberof 3r transitions of EME as well as some less significant transitionshave been observed toward W51e2 [9]. The derived column den-sity was compatible with values for related molecules and the rota-tional temperature (70 K) slightly lower. The spectrum synthesizedfrom these values was compatible with all observed lines. Since thenumber of significant lines is still small the detection should beviewed with some caution. However, as stated by the authors‘‘there are lines at EME transition frequencies which until nowcan best be explained by the existence of EME in W51e2”. Interfer-ometric observations, e.g. with the Atacama Large MillimeterArray, are likely to confirm the tentative detection of EME andmay provide the means for the detection of the next heavierdiethyl ether.

The trans–trans conformer of DEE (CH3CH2OCH2CH3) more cor-rectly known by its IUPAC designation as anti–anti (aa) is the moststable and should hence be the easiest to detect. The most recentgeometry has been deduced from the combined results of

ll rights reserved.

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rotational spectroscopy and electron diffraction [10]. The carbonatoms lie in a zig-zag structure in which they are most stronglyseparated; all of the heavy atoms and two hydrogen atoms lie ina plane, while the remaining pairs of hydrogen atoms are symmet-rically disposed about this plane. The rotational spectrum ofaa-diethyl ether was first measured in the 15–30 GHz range[11,12]. Recently a comprehensive study of the rotational spectrumof aa-DEE was carried out up to 350 GHz with transitions assignedup to a rotational quantum number J of 90 [13]. These measure-ments form the basis of predictions presently available in theCDMS database (tag 74503; no entry in JPL). The electric dipolemoment of aa-DEE was determined in that work as 1.0976 (9) D.Subsequently, a new millimeter-wave spectrum was recorded,with an improved frequency calibration over the range 108–366 GHz and used to increase the total data set to over 2000 lines[14]. In the same work, rotational spectra in the first excitedvibrational states, v20, v39, and v12 = 1 were assigned. Similarly,an analysis of the rotational spectrum of anti–gauche diethyl ether(less correctly also termed as trans–gauche) was reported [15] witha total of 1090 absorption line frequencies measured and analyzedin the range 108–366 GHz.

The purpose of this present work is to increase the frequencyrange of laboratory measurements for both aa-DEE and ag-DEE inprevision of near future astrophysical instruments with both ex-tended frequency coverage and sensitivity. Multi-dish ground-based instruments such as the IRAM Plateau de Bure interferome-ter (PdBI), the Sub-Millimeter Array (SMA) on Hawaii, and in par-ticular the upcoming international interferometer ALMA with itsfrequency coverage up to 720 GHz and later maybe up to900 GHz will allow the search of new potential interstellar species

A. Walters et al. / Journal of Molecular Spectroscopy 257 (2009) 24–28 25

both because of increased photon collecting area and the ability topinpoint chemically interesting regions. The importance of observ-ing a sufficient number of spectroscopic features whose rest fre-quencies are known with sufficient accuracy has been pointedout, e.g., in the context of the purported detection of the simplestamino acid glycine and its subsequent contestation [16]. On theother hand, the recent detection of aminoacetonitrile [17], a possi-ble precursor of glycine, indicates not only that the quest forincreasingly complex molecules may well be successful, but alsohow it may benefit from observations with radio-telescope arrays.

2. Experimental

The spectrum of DEE was recorded with the Cologne TerahertzSpectrometer (CTS) that is described in detail elsewhere [18]. Twophase-locked backward wave oscillators provided submillimeter-wave power (one for each frequency range). A magnetically tuned,liquid-He-cooled InSb hot electron bolometer was used as detector.All measurements were carried out in a 3-m-long glass cell at roomtemperature in static mode.

For aa-DEE, most measurements were taken in the range 875–903 GHz with cell pressures of 10–20 Pa. The pressure was chosenas a compromise between minimizing line-width for precisionwhile having sufficient intensity to measure the weaker lines. Sincelines of the ag-species are weaker they were measured in the range618–638 using a lower frequency BWO operating at higher power.Some transitions of aa-DEE were subsequently measured in thisrange to check the reliability of the new predictions.

892290 892300 892310Frequency / MHz

(a)

(b)

(c)

55, 29 − 55, 2856, 29 − 56, 28

57, 21 − 56, 20

Fig. 1. Part of the spectrum of aa-DEE before any software treatment. The quantumnumbers are given in the format: upper state (J0 K0a) lower state (J00 Ka

00). SinceKa + Kc = J or J + 1, the Kc quantum numbers have been omitted for these prolatepaired transitions. (a) Somewhat convoluted line given lower weight in fit, (b) clearline, (c) highly convoluted line not used in fit.

3. Analysis and discussion

DEE is an asymmetric top rotor close to the prolate symmetriclimit with j = �0.982 for the aa-conformer and �0.972 for ag. Thedipole moment of aa-DEE lies along the b principal axis, so thatrotational transitions obey b-type selection rules. According toab initio calculations discussed in Ref. [15] ag-DEE has threenon-zero dipole moment components which are la = 0.409,lb = 0.792, and lc = 0.872 D. The same theoretical calculationspredict the ag-DEE conformer to be higher in energy than theaa-conformer by about 5.40 kJ mol�1 or about 450 cm�1. More-over, unlike dimethyl ether [19] and ethyl methyl ether [20],diethyl ether shows no signs of splitting due to internal rotationof the methyl groups, so the rotational spectrum can be analyzedby standard quasi-rigid rotor techniques involving centrifugal dis-tortion. Analysis was made with Pickett’s SPFIT, SPCAT suite [21].First, predictions were made for aa-DEE around 0.9 THz using thedata of Medvedev et al. [13] allowing the strongest new high-fre-quency lines to be easily identified. These new lines were then in-cluded in the fit allowing other transitions to be identified veryclose to the new predictions. Both Q (Ka = 29 28) and R branchtransitions were measured. P branches and transitions withDKa = 3 were too weak to observe in our experiments. In later lim-ited measurements around 0.62 THz all lines were found withinthe calculated experimental error. This was as expected sincehigher quantum number lines at higher frequencies had alreadybeen included in the fit. An attempt was also made to search forlower intensity lines in this region where the radiation sourcehad considerably more power. This attempt was unsuccessfulsince lower intensity lines were inevitably convoluted with stron-ger or similar intensity lines making measurements of line centerstoo imprecise to improve the fit. Ninety-two new independentfrequencies were measured corresponding to 179 transitions sincefor all but the lowest Ka transitions the two Kc components werenot resolved. Maximum values of J and Ka measured were, respec-tively, 126 and 29.

Since good predictions were available continuous scanning wasnot necessary in this work and most lines were measured indepen-dently in small frequency intervals (typically 4–6 MHz). Somewhatlarger scans (up to around 30 MHz) were taken when other stronglines were close, either to measure these lines simultaneously and/or to be sure of the lineshape and baseline in case of convolution.Fig. 1 shows one such larger scan before processing such assmoothing, baseline reduction etc. that was used selectively beforemeasurement of centre frequencies. It indicates the different casesin analysis. As shown in the caption the centre line (b) is clearlyvisible. It should be noted, however, that this is a ‘‘typical” not a‘‘best” recording and that a fair number of the stronger single linesmeasured had better signal to noise and perfectly symmetric andnon-deformed line shapes. The line to low frequency (a) is some-what convoluted and given lower weight in the fit. The line to highfrequency (c) is unusually broad and distorted, most likely becauseof convolution with another unknown line of similar amplitude;lines of this type were omitted from the fit. Several other linescan be observed on the figure that have not been identified andmay correspond to vibrational states not considered in this work.Lines of this intensity were present all over the measured spectrumand limited measurements of the weakest transitions as indicatedabove.

In the final fits our data was combined with the improved dataof follow-on work to Ref. [13] published two years later [14]. Table1 compares our fit using the A-reduction of the Ir representationwith that of Ref. [14]. The reduced standard deviation:

rw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXfðobs� calcÞ=rexpg2

=Nlines

h ir

is quoted in terms of the difference between observed and cal-culated frequencies, the supposed experimental uncertainty rexp

on each measurement and the number of experimentally mea-sured lines fitted. It can be rapidly verified that rw is equal toone if statistical errors are the same as supposed measured uncer-tainties. There are, however reasons why rw may differ from 1.First, a line list that is short with respect to the number of fittedspectroscopic parameters should lead to rw values smaller than 1if error estimates are realistic. An incomplete model, on the otherhand, can account for rw values larger than 1. Systematic errors

Table 1Present and previous molecular parametersa (MHz) of aa-DEE using Watson’sA-reduction, dimensionless rms error rw, numbers of lines N, maximum frequency(GHz), and maximum quantum numbers J and Ka used in the fit.

Parameter Present work Ref. [14]

A 17956.15739 (31) 17956.15695 (43)B 2244.225666 (63) 2244.225588 (77)C 2101.793580 (66) 2101.793481 (83)DJ � 106 274.042 (13) 274.008 (22)DJK � 103 �3.64876 (19) �3.64898 (23)DK � 103 85.92195 (72) 85.9198 (20)dJ � 106 32.9739 (42) 32.9764 (43)dK � 106 513.59 (27) 513.60 (28)UJ � 1012 86.80 (99) 84.0 (20)UJK � 109 �2.582 (23) �2.615 (29)UKJ � 109 �17.83 (20) �18.45 (31)UK � 109 146.84 (55) 144.2 (34)uJ � 1012 26.07 (43) 26.35 (44)LJK � 1015 �99. (18) –rw

b 0.742 0.735

N(measured)c 92N(new_fit)d 179N(total_fit)e 2525 2346Freq maxf 903 365.6J’ maxf 126 90K’a maxf 29 21

a Uncertainties in parentheses in units of the least significant figures have beenpropagated from experimental uncertainties for each line, see Section 3. Uncer-tainties from Ref. [14] have been converted from standard errors for directcomparison.

b Weighted deviation (or rms error) of the fit, see Section 3.c Number of new independent measured frequencies.d Number of new fitted transitions.e Total number of fitted transitions including previous data.f Highest values in fit.

Table 2Preferred molecular parametersa (MHz) of aa-DEE and ag-DEE using Watson’sS-reduction and the dimensionless rms error rw.

Parameter aa-DEE ag-DEE

A 17956.15735 (31) 13572.0932 (17)B 2244.224631 (62) 2495.41376 (22)C 2101.794595 (66) 2340.39339 (19)DJ � 106 272.883 (13) 759.689 (67)DJK � 103 �3.64187 (19) �6.2647 (17)DK � 103 85.91620 (70) 106.397 (13)d1 � 106 �32.9752 (42) �134.768 (27)d2 � 106 �0.57545 (30) �4.7638 (69)HJ � 1012 85.56 (99) 400.8 (81)HJK � 109 �2.567 (23) �31.53 (40)HKJ � 109 �17.94 (19) �820. (12)HK � 106 0.14699 (55) �1.504 (38)h1 � 1012 26.29 (43) �355.6 (44)h2 � 1012 – �194.2 (18)h3 � 1012 – 68.57 (75)LJJK � 1012 – 1.038 (32)LJK � 1012 �.093 (18) �26.7 (21)LKKJ � 1012 – �338. (32)LK � 1012 – �589. (30)PKJ � 1015 – �22.2 (40)PKKJ � 1015 – 125. (26)rw

b 0.741 0.782

a The quantities in parentheses are one standard deviation uncertainties in unitsof the least significant digit. These are calculated by SPFIT and depend on experi-mental uncertainties attributed to each measurement.

b Weighted deviation (or rms error) of the fit, see Section 3.

26 A. Walters et al. / Journal of Molecular Spectroscopy 257 (2009) 24–28

such as uncertainties in the frequency calibration, quite commonin infrared spectroscopy, but also not negligible for the FASSST datae.g. from Refs [13–15] or for astronomically derived rest frequen-cies, may also justify rw values smaller than 1. Finally, adequateuncertainty estimates can be difficult to obtain in cases of weaklines, a dense spectrum, or large base line effects. As regards appli-cations of the data, such as in astrophysics, it is preferable to be tooconservative than too optimistic. Therefore, we prefer to quoteexperimentally estimated uncertainties if these are higher thanstatistical ones and seem realistic. As can be seen from Table 1,rw was significantly lower than unity for the entire fit. However,rw is 0.88 for the lines from the present investigation, suggestingapproximately adequate uncertainty estimates. The rw values are0.54, 0.68 and 0.74 for the three millimeter-wave data sets fromRef. [14], and 1.09 and 1.67 for the microwave transitions mea-sured by Fourier transform and conventional absorption spectros-copy and used in the previous data set [14]. Since the sources ofdata are different it would not seem appropriate to correct lineuncertainties by the overall average rw. In order to compare our re-sults directly with those of Ref. [14] we report the latter uncertain-ties divided by their rw value. It can be seen that all parameters aresomewhat improved and that DK, UJ and UK are significantly im-proved. Attempts were made to fit the missing higher order param-eters (u’s and L’s). In addition to uJ that always fitted well (as inRef. [14]) it was possible to fit all the missing parameters sepa-rately but only LJK made a significant improvement and was henceretained in the final choice. Fitting combinations of the missingparameters was not successful.

Usually for slightly asymmetric tops with j > 0.97 the S-reduc-tion is preferred for reason of the bad convergence of the A-reduc-tion [22]. We hence also carried out a fit using the S-reduction asshown in Table 2. The fit was of near identical quality to that madeusing the A-reduction and led to a similar choice of parameters.

An extract of the fit in the S-reduction showing the newly mea-sured data is given in Appendix A of the Supplementary material.

At the time of this work there was no entry for ag-DEE in eitherof the two public databases for submillimeter, millimeter, andmicrowave spectroscopy (JPL and CDMS) which can be attributedto the fact that this conformer is considerably higher in energythan the aa-conformer, which has not yet been detected in space.Predictions for ag-DEE were made using previous data [15] andthe same data was incorporated in the final overall fit. As for aa-DEE, line uncertainties were estimated taking into account thequality of the measured line (signal-to-noise, symmetry, baseline,convolution with a nearby line) and values between 20 and120 kHz were attributed. Thirty-seven new frequencies were mea-sured representing 148 transitions, all of them R-branch transi-tions of b- and c-type with unresolved asymmetry splitting. a-type transitions were too weak to be observed. Again the intensitylimit on measured lines was due to line confusion. The molecularconstants from the best fit using the S-reduction are given in Table2 and an extract showing new measured frequencies is given inAppendix B of the Supplementary material. PKJ and PKKJ have beendetermined for the first time. The constants l2 and l3 could be justdetermined but made no meaningful improvement, hence theywere not retained in the final fit; l1 and l4 were not determined(even without inclusion of the decadics).

Table 3 compares our best fit using the A-reduction with theprevious fit of Ref. [15]. In order to correctly fit our data it was nec-essary to include the PKJ and PKKJ parameters. lKJ could also bedetermined but the rms error of the fit did not decrease. It canbe difficult to find a unique set of spectroscopic parameters thatreproduces a large set of transition frequencies best. Since thepresent parameter set necessarily differs somewhat from the pre-vious one it should not be surprising that some parameter values,in particular those of higher order, differ considerably. Once againin order to compare uncertainties under the same conditions wedivided those from Ref. [15] by their rw value. The uncertaintiesare fairly similar for several parameters, in particular for the lowerorder terms; rather large differences for some higher order param-eters are expected because the choice of parameters differs. The rw

Table 3Present and previous molecular parametersa (MHz) of ag-DEE using Watson’s A-reduction, dimensionless rms error rw, numbers of lines N, maximum frequency(GHz), and maximum quantum numbers J and Ka used in the fit.

Parameter Present work Ref. [15]

A 13572.0922 (17) 13572.0904 (15)B 2495.41965 (22) 2495.41982 (23)C 2340.38808 (19) 2340.38842 (20)DJ � 106 769.358 (68) 769.546 (75)DJK � 103 �6.3186 (17) �6.3236 (13)DK � 103 106.414 (13) 106.416 (14)dJ � 106 134.615 (27) 134.543 (32)dK � 103 2.8469 (44) 2.8683 (52)UJ � 1012 31.6 (90) 63.4 (102)UJK � 109 136.3 (19) 158.9 (33)UKJ � 106 �1.373 (13) �1.510 (11)UK � 106 �1.277 (38) �1.038 (61)uJ � 1012 �291.1 (44) �306.8 (53)uJK � 109 �127.2 (11) �121.4 (13)uK � 106 15.64 (17) 17.92 (30)LJJK � 1012 0.157 (34) �6.33 (61)LJK � 1012 �43.7 (21) �6.7 (15)LKKJ � 1012 �224. (32) �80. (11)LK � 109 �0.370 (31) –1.07 (11)lKJ � 1012 – �622. (59)PKJ � 1015 53.2 (44) –PKKJ � 1015 –157. (26) –rw

b 0.755 0.736

N(measured)c 37 1090N(new_fit)d 148N(total_fit)e 2278 2130Freq. max.f 637.8 365.6J’ maxf 79 79K’a maxf 24 24

a Uncertainties in parentheses in units of the least significant figures have beenpropagated from experimental uncertainties for each line, see Section 3. Uncer-tainties from Ref. [15] have been converted from standard errors for directcomparison.

b Weighted deviation (or rms error) of the fit, see Section 3.c Number of new independent measured frequencies.d Number of new fitted transitions.e Total number of fitted transitions including previous data.f Highest values in fit.

A. Walters et al. / Journal of Molecular Spectroscopy 257 (2009) 24–28 27

values for the newly measured lines are 0.88 and 0.86 for the fitsemploying the S and A reduction, respectively, again suggestingthat the uncertainties of these lines have been estimated ratherappropriately overall.

Direct comparison of the spectroscopic parameters for bothconformers shows that the one at higher energies (ag) displays amuch slower converging Hamiltonian. This has already been notedpreviously [15] and was attributed to ag-DEE being much closer tothe barrier of inter-conversion than the lower energy aa-con-former. Similarly, slower converging Hamiltonians were obtainede.g. for the higher lying gauche-conformers of ethyl formate [23]and n-propyl cyanide [24] compared with their anti-conformers.

4. Conclusions

Previous extensive datasets have been measured and analyzedfor both aa-DEE and ag-DEE but did not exceed 370 GHz. Alsoag-DEE has not yet been included in a molecular spectroscopydatabase facilitating astrophysical prediction and modeling of itsspectra by programs such as CASSIS1. The objective of this workwas to make measurements at higher frequency in order to increasethe precision and reliability of measurements into the THz range.

It was found for aa-DEE that the previous dataset [14] predictedthe newly measured frequencies well, with shifts not exceeding a

1 cassis.cesr.fr/. 2

few 100 kHz. While this is to be expected from the quality andquantity of the previous data it is always interesting to confirmby measurements, predictions that have been extrapolated to high-er frequency. Also the uncertainties on further extrapolations arereduced. The measured lines of ag-DEE deviated much more signif-icantly from predictions made using the previous dataset. Theseshifts exceeded 5 MHz for the higher Ka transitions at 600 GHzand are consequently greater when extrapolating into the THz re-gion. Predictions of the rotational spectrum of ag-DEE based on thepresent dataset should be reliable at least up to 720 GHz, the cur-rently foreseen upper frequency limit of ALMA. Extrapolation to900 GHz should be viewed with caution because of the slowly con-verging Hamiltonian. Predictions of aa-DEE (more important inastrophysics because of the lower energy of formation) should bereliable up to at least 1.5 THz because of the higher frequency mea-surements and the more rigid nature of this conformer. At this fre-quency, the line intensity is well below the Boltzmann peak evensupposing relatively warm astrophysical conditions of 200 K orso. Catalogue files for both conformers, resulting from our pre-ferred fits, as well as complete line lists, parameter and fit files willshortly be made available on the Cologne Database for MolecularSpectroscopy2 [25,26].

Acknowledgments

H.S.P.M. is grateful for support by the Bundesministerium fürBildung und Forschung (BMBF), administered through DeutschesZentrum für Luft- und Raumfahrt (DLR; the German space agency).AW thanks the CNRS (INSU) and Toulouse University (UPS) for sup-port and the Observatoire Midi-Pyrénées and the EU FP6 RTNMolecular Universe network for funding travel expenses.

Appendix A. Supplementary data

Supplementary data for this article are available on ScienceDi-rect (www.sciencedirect.com) and as part of the Ohio State Univer-sity Molecular Spectroscopy Archives (http://library.osu.edu/sites/msa/jmsa_hp.htm).

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