Laboratory spectroscopy of 1,2-propanediol at millimeter and submillimeter wavelengths
J.-B. Bossa, M. H. Ordu, H. S. P. Müller, F. Lewen, S. Schlemmer
AAstronomy & Astrophysics manuscript no. PD˙fin c (cid:13)
ESO 2018September 5, 2018
Laboratory spectroscopy of 1,2-propanediol at millimeter andsubmillimeter wavelengths (cid:63)
J.-B. Bossa , M. H. Ordu , H. S. P. M¨uller , F. Lewen , and S. Schlemmer Sackler Laboratory for Astrophysics, Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands. I. Physikalisches Institut, Universit¨at zu K¨oln, Z¨ulpicher Str. 77, 50937 K¨oln, Germanye-mail: [email protected]
Received 1 June 2014 / Accepted 14 August 2014
ABSTRACT
Context.
Ethanediol is one of the largest complex organic molecules detected in space thus far. It has been found in di ff erent typesof molecular clouds. The two propanediol isomers are the next larger diols. Hence, they are viable candidates to be searched for inspace. Aims.
We wish to provide su ffi ciently large and accurate sets of spectroscopic parameters of 1,2-propanediol to facilitate searches forthis molecule at millimeter and longer submillimeter wavelengths. Methods.
We recorded rotational spectra of 1,2-propanediol in three wide frequency windows between 38 and 400 GHz.
Results.
We made extensive assignments for the three lowest energy conformers to yield spectroscopic parameters up to eighth orderof angular momentum.
Conclusions.
Our present data will be helpful for identifying 1,2-propanediol at moderate submillimeter or longer wavelengths withradio telescope arrays such as ALMA, NOEMA, or EVLA. In particular, its detection with ALMA in sources, in which ethanediolwas detected, appears to be promising.
Key words. molecular data; methods: laboratory: molecular; techniques: spectroscopic; ISM: molecules
1. Introduction
The presence of molecular complexity in space has attractedconsiderable interest in the field of astrochemistry because ofthe question of the origin and evolution of life in the Universe.Laboratory spectroscopic data in the millimeter and submil-limeter domains for the unique identification of large complexmolecules are needed to interpret the ongoing spectral surveysof star-forming regions and young stellar objects.Ethanediol, (CH OH) , also known as ethylene glycol, isone of the largest complex organic molecules detected in spaceto date, see, for example, the Cologne Database for MolecularSpectroscopy (CDMS) (M¨uller et al. 2001; M¨uller et al. 2005). Ethanediol was detected first in the massive and luminousGalactic center source Sagittarius B2(N), Large MoleculeHeimat (Sgr B2(N-LMH) for short) (Hollis et al. 2002). There isalso strong evidence of ethanediol in three less-evolved molec-ular clouds in the Galactic center (Requena-Torres et al. 2008).Very recently, it was also detected in the hot cori-nos associated with the class 0 protostars NGC 1333-IRAS2A (Maury et al. 2014) and, tentatively, IRAS 16293-2422B (Jørgensen et al. 2012). Finally, ethanediol was alsofound to be abundant in the outflows of comet Hale-Bopp(Crovisier 2004).Even though ethanediol may exist in several dis-tinct conformations, only two of them have been (cid:63)
Full Table 4 and Tables 5 − aG’g.txt and text files gG’a.txt and g’G’g.txt are only available in elec-tronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or via http: // cdsweb.u-strasbg.fr / cgi-bin / qcat?J / A + A / Internet address: http: // / cdms / molecules identified in the laboratory by using rotational spec-troscopy (Christen et al. 1995; Christen et al. 2001;Christen & M¨uller 2003; M¨uller & Christen 2004), withthe higher energy conformer estimated to be 2.5 kJ mol − ( ∼
300 K) above the lowest one. Therefore, astronomicaldetections of ethanediol reported in the literature thus faronly refer to the lowest energy conformer. The rotationalspectra of both conformers display strong rotation-tunnelinginteraction caused by two equivalent minima on the po-tential energy surfaces. Molecular beam Fourier transformmicrowave spectroscopy (MB-FTMW) and microwave-microwave double resonance were required to achieve ini-tial assignments (Christen et al. 1995; Christen et al. 2001),which paved the way for later experimental investi-gations at millimeter and submillimeter wavelengths(Christen & M¨uller 2003; M¨uller & Christen 2004).Investigating propanediol constitutes the next step towardunderstanding the molecular complexity in space since it is astructural analog of ethanediol by replacing a hydrogen atomthat is bound to a carbon atom with a methyl group. Moreover,comparing the relative abundance of ethanediol and its deriva-tives (e.g., propanediol) can provide insights into the formationroutes of theses molecules and the chemical evolution of ob-jects in which they are detected. However, care is needed sincecolumn densities of molecules tend to decrease with increasingcomplexity.Two stable isomers of propanediol are known to date, 1,2-propanediol (CH CHOHCH OH) with the OH groups at two ad-jacent carbon atoms, and 1,3-propanediol (CH OHCH CH OH)with the OH groups at the outer carbon atoms. The con-formational landscape of both isomers has been thoroughly a r X i v : . [ phy s i c s . a t m - c l u s ] A ug .-B. Bossa et al.: Millimeter-wave spectroscopy of 1,2-propanediol investigated quite recently by using both FTMW spectro-scopy and quantum chemical calculations (Lovas et al. 2009;Plusquellic et al. 2009). Only two conformers were found ex-perimentally for 1,3-propanediol, which both displayed tunnel-ing caused by two equivalent minima on the potential energysurfaces (Plusquellic et al. 2009). Other conformers were calcu-lated to be at least 600 K higher in energy, except for one thatwas calculated to be about 400 K higher in energy, but witha rather small dipole moment. The lowest energy conformerwas studied before by using free-jet absorption microwave spec-troscopy (Caminati et al. 1995). Very recently, Smirnov et al.(2013) performed extensive millimeter measurements, analyzedthe rotation-tunneling interaction in the spectra of both con-formers, and provided the spectroscopic basis to search for 1,3-propanediol in space by radio astronomy.For 1,2-propanediol, seven conformers were identified us-ing FTMW spectroscopy, three of which are relatively low andclose in energy (Lovas et al. 2009). Lovas et al. (2009) also car-ried out quantum-chemical calculations on a variety of conform-ers, which included determining the relative energies, quarticcentrifugal distortion parameters, and dipole moment compo-nents; experimental dipole values were determined for three con-formers. The lowest energy conformer as well as two slightlyhigher energy forms had been studied to some extent before(Lockley et al. 2002; Caminati 1981). None of the conformersdisplayed rotation-tunneling splitting. Interestingly, rotationaltransitions of the lowest energy conformer were used very re-cently to demonstrate that FTMW spectroscopy can be used todetermine the enantiomeric composition of a chiral molecule(Patterson et al. 2013). Three-wave mixing was employed tocreate phase di ff erences between the two enantiomers that weredetected by FTMW.We investigated the rotational spectra of the three lowest en-ergy conformers of 1,2-propanediol at millimeter and submil-limeter wavelengths to permit searching for them in space byradio astronomical means.
2. Experimental details
The present experimental conditions are quite similar tothose employed for the lower frequency measurements (upto 230 GHz) of n -butyl cyanide (Ordu et al. 2012). Spectrawere recorded in three frequency bands (38 −
70, 200 − −
400 GHz). The fundamental frequency sources werecomputer-controlled sweep synthesizers that were referencedto a rubidium atomic clock. An Agilent E8257D sweeper wasused as a direct frequency source to record lines up to 70 GHz.The RF output from a microwave generator (Rohde & SchwarzSMF 100A; maximum frequency 43 GHz) was multiplied up tothe desired frequency with cascaded multipliers from VirginiaDiodes, Inc. (VDI). Factors of 16 and 21 were employed for thebands starting at 200 and 297 GHz. Both synthesizers enablequasi-continuous tuning in freely adjustable frequency incre-ments of typically some kilohertz. DC-biased room-temperatureSchottky diodes were used as detectors. The detector signalwas coupled to a lock-in amplifier for phase-sensitive detection.Frequency modulation was used to reduce baseline e ff ects; de-modulation was carried out at 2 f , resulting in a line shape ap-proximating the second derivative of a Gaussian.The millimeter or submillimeter beam was formed by a stan-dard gain horn antenna in combination with an HDPE lens forlow-loss coupling of the beam to the 7 m long Pyrex absorp-tion cell with 100 mm inner diameter. The cell windows weremade of PTFE and tilted by 10 degrees to reduce baseline ef- fects even more. A double-pass absorption scheme was used,which extended the absorption path length to 14 m.The vapor pressure of 1,2-propanediol is rather low at roomtemperature, ∼
19 Pa (Verevkin et al. 2009). To achieve a su ffi -cient and reasonably stable vapor pressure, measurements werecarried out under slow flow conditions. In addition, the sam-ple container, the needle valve, with which the flow of 1,2-propanediol was controlled at the inlet side, and the absorptioncell were heated to about 55 o C (328 K). The sample pressurewas between 1.0 and 1.5 Pa.After the integration time was optimized, which depends onthe desired signal-to-noise level, step size (20, 32, and 90 kHzat lower, medium, and higher frequencies) and scan widths, ourspectrometer setup allowed for full-band sweeps with a typicalspeed of about 1 to 4 weeks per 100 GHz because the lines weregenerally weak, even more so at lower frequencies.
3. Conformational landscape and spectroscopicproperties of 1,2-propanediol
The molecule 1,2-propanediol may exist in up to 27 di ff erentconformers; chirality is ignored. It is usually assumed that dif-ferent enantiomers (conformations that behave as mirror im-ages) have the same spectroscopic parameters. The assumptionmay be not entirely correct, but to date there is no experimentalevidence for distinguishable spectroscopic parameters of enan-tiomers. Quantum chemical calculations suggest that any suchdi ff erences would require very heavy atoms in a molecule. Theconformers of 1,2-propanediol can be distiguished by the tor-sional angles of the HOCC atoms involving the outer OH groupof the OCCO atoms, and of the CCOH atoms with the OH groupat the central C atom. The OCCO torsional angle also determinesthe position of the methyl group with respect to the rest of themolecule. This angle can be about 180 o , + o , or − o , desig-nated by A , G , and G (cid:48) , respectively, with A for anti (or trans ),and G for gauche . T instead of A was used in Lovas et al. (2009).The two torsional angles involving the OH groups are designatedanalogously by lower case characters.Lovas et al. (2009) used MP2 quantum chemical calcula-tions with basis sets of triple zeta quality to investigate struc-tures and energetics of the 12 1,2-propanediol conformers foundto be lowest in energy in earlier calculations with smaller ba-sis sets (V´azquez et al. 1989). The first nine conformers fromV´azquez et al. (1989) were also stable in the more recent calcu-lations, whereas the two conformers next in energy were trans-formed into other conformers in the structure optimization pro-cess. Dipole moment components as well as quartic centrifu-gal distortion parameters were determined for the ten remainingconformers (Lovas et al. 2009). Lovas et al. (2009) recorded ro-tational spectra of 1,2-propanediol between 6.4 and 26.0 GHzusing two types of FTMW spectrometers and were able to as-sign transition frequencies to seven di ff erent conformers basedon calculated and observed spectroscopic parameters and on therelative magnitudes of the dipole moment components. The con-former assignments are quite secure, in particular for the fiveconformers lowest in energy. The calculated energy ordering ofthese conformers appears to agree with experimental intensitieswhen collisional cooling is considered, especially for the threelowest energy conformers.The predicted structures and relative energies for the threelowest energy conformers are depicted in Fig. 1. The low-est energy conformer is aG (cid:48) g , in agreement with an earlierFTMW study (Lockley et al. 2002). Two other conformers, gG (cid:48) a Fig. 1.
Predicted structures and relative energies for the three lowest energy conformers of 1,2-propanediol. The C and O atoms areindicated by gray and red spheres. The H atoms are indicated by smaller light-gray spheres. Atom labels and structural parametersare taken from Lovas et al. (2009). Upper panel: skewed view from the side of the carbon chain; lower panel: view from above theO atoms.
Table 1.
Experimental and theoretical (in bold text) dipole mo-ments (in Debye) for the three lowest energy conformers a of 1,2-propanediol (Lovas et al. 2009). Conformer µ a µ b µ c aG’g gG’a g’G’g a Conformers aG’g and gG’a were designated as tG’g and gG’t inLovas et al. (2009). and g (cid:48) Ga , found in an even earlier millimeter wave study(Caminati 1981), are the second and, probably, the fourth low-est energy conformers, calculated to be 74 and 212 cm − higher.The third lowest conformer is g (cid:48) G (cid:48) g , 115 cm − higher in energythan the lowest one.Lovas et al. (2009) also determined dipole moment compo-nents experimentally for the aG (cid:48) g , gG (cid:48) a , and g (cid:48) Ga conformers.We present in Table 1 the values of the two lowest energy con-formers and the calculated components for g (cid:48) G (cid:48) g .The three lowest energy conformers of 1,2-propanediol arefairly asymmetric top molecules with a Ray’s asymmetry param-eter κ = (2 B − A − C ) / ( A − C ) not close to the prolate sym-metric top limit of − κ values for aG (cid:48) g , gG (cid:48) a , and g (cid:48) G (cid:48) g conformers are − − −
4. Results
With 13 atoms, 1,2-propanediol is a comparatively heavymolecule with relatively small rotational constants, which, in turn, lead to a dense rotational spectrum even at low energies.The fairly large number of conformers as well as the largernumber of usually lower lying vibrational states compared withlighter molecules increase the line density even more.Lovas et al. (2009) identified more than 140 transitions be-tween 6.4 and 26.0 GHz for the three lowest 1,2-propanediolconformers. Transitions obeying all three types of selection ruleswere recorded for each of the conformer. Internal rotation split-ting of the outer methyl group was not resolved with eitherFTMW spectrometer. Therefore, we did not expect to resolveit either because of the larger line widths in our experiments.We used Pickett’s SPFIT and SPCAT programs(Pickett 1991) for fitting and predicting spectra of the 1,2-propanediol conformers. Watson’s S reduction of the rotationalHamiltonian (Watson 1977) was used here. Predictions basedon the previous works (Lockley et al. 2002; Lovas et al. 2009)allowed us to easily assign stronger R -branch transitionswith similar or slightly higher J and K a quantum numbersin the 38 −
70 GHz region. Using these transitions to improvethe predictions, other assignments could be made until thesignal-to-noise ratio was too low to determine the transitionfrequency with reasonable uncertainty. We were only ableto assign transitions pertaining to the strong dipole momentcomponents ( ≥ J up to 42 and K a up to 13 were assigned in this region for the lowest energy aG (cid:48) g conformer. Similar quantum numbers were reached forthe third lowest conformer g (cid:48) G (cid:48) g . For both conformers, b -type R - and Q -branch transitions were observed. In addition, a -type R -branch transitions were observed for the aG’g conformer and c -type R - and Q -branch transitions for the g’G’g conformer. Table 2.
Total number of transitions and other statistical infor-mation of our 1,2-propanediol data sets. aG’g gG’a g’G’g no. of transitions 2013 1401 11986 −
26 GHz 82 a , b a a −
70 GHz 256 115 211200 −
230 GHz 553 280 177297 −
400 GHz 1122 965 769no. of R -branch trans. 1436 1338 950no. of Q -branch trans. 577 63 248no. of a -types 756 1372 6 a no. of b -types 1261 14 a c -types 16 a , b a ff erent lines 1176 723 718rms error of the fit 0.975 1.022 0.985standard deviation c (kHz) 20.8 20.9 23.6uncertainty range (kHz) 10 −
90 10 −
50 10 − J max
69 71 69 K a , max
38 45 33 a From Lovas et al. (2009). b From Lockley et al. (2002). c Given for completeness; see Sect. 4.
Fewer assignments, all pertaining to a -type selection rules,were made for the gG (cid:48) a conformer because of the small b - and c -dipole moment components. On the other hand, we were ableto assign several weaker Q -branch transitions with ∆ K a = R -branch transitions because of therelatively large a -dipole moment component.Line overlap or proximity of two lines occurred quite rarelyat these frequencies, therefore the uncertainties were estimatedbased on the base line quality and the signal-to-noise ratio.Assigned uncertainties at these low frequencies ranged mostlyfrom 10 to 25 kHz, with some weak lines having uncertaintiesup to 50 kHz. The assigned uncertainties increased at higher fre-quencies up to 90 kHz. After each round of assignments, theneed for more spectroscopic parameters was tested. We searchedfor the parameter that reduced the rms error of the fit mostamong the parameters that were useful based on the previouslyemployed parameters. An additional parameter whose inclusionlead to a substantial reduction of the rms error was generallydetermined with great significance, meaning that its uncertaintywas lower than one fifth of its magnitude. The search for addi-tional parameters was continued as long as substantial reductionof the rms error was obtained.Subsequently, analyses of spectra in the 200 −
230 GHz re-gion and then in the 297 −
400 GHz region were made in a simi-lar way. Line overlap or proximity of lines was more widespreadat higher frequencies and restricted the assignments somewhatin the 200 −
230 GHz and severely in the 297 −
400 GHz regions,in particular for weaker lines. Figure 2 shows a section of thespectrum near 334 GHz. Overlapping lines were not used in thefit except for unresolved asymmetry splitting. This refers to two a -, b -, or c -type transitions with the same J quantum numbers inthe upper and the lower state, the same K a (prolate pairing) or K c (oblate pairing), and K c or K a di ff ering by one (note: K a + K c = J or J + aG’g conformer with a - and b -dipole moment components ofsimilar magnitude, oblate pairing may involve four transitions Fig. 2.
Section of the rotational spectrum of 1,2-propanediol near333.8 GHz. Transitions assignable to the three lowest energyconformers are marked. The 53 − transition of the aG (cid:48) g conformer occurs at 333812.0 MHz, but it is overlapped by astronger, unidentified line. All other unmarked lines belong tohigher energy conformers or to excited states of the three low-energy conformers. The transitions appear as approximate sec-ond derivatives of a Gaussian line shape because of the 2 f -modulation.with similar intensities, two a - and two b -types. Analogously,prolate pairing of transitions of the g’G’g conformer may in-volve four ( b - and c -type) transitions with similar intensities.As the average frequency is in this special case identical to theintensity-weighted average, we omitted the intensity-weighting(specified in the line file after the uncertainties in SPFIT). Themaximum J quantum numbers of transitions used in the fits are69, 71, and 69 for the aG’g , gG’a , and g’G’g , respectively; thecorresponding K a values are 38, 45, and 33.Previous data from Lovas et al. (2009) were used in the fi-nal fits with the reported uncertainties with the exception of twolines of the aG’g conformer and of three lines of the g’G’g con-former, for which the uncertainties were increased from 2 to5 kHz (four lines) and from 5 to 10 kHz (one line) because ofhigh residuals in the final fits. In addition, three lines of the g’G’g conformer were omitted for the same reason. Uncertainties of4 kHz were assigned to the aG’g data from Lockley et al. (2002).The gG’a data from Caminati (1981) were not used in Lovas etal. (2009), and we did not use them either. Ultimately, a full setof up to sextic centrifugal distortion parameters plus one octicterm were determined for the lowest energy conformer; two pa-rameters less each were used in the final fits of the two higherenergy conformers. The rms error of each fit, overall as well asrestricted to one of the three frequency windows or to the previ-ous data sets, was close to 1.0 throughout, in most cases slightlylower. Table 2 presents the unitless rms error as well as the stan-dard deviation of each fit along with additional statistical infor-mation. The standard deviation is only given for completeness. Itcannot be used as a measure for the quality of the fit because weused more than one uncertainty to reflect the changing quality of Table 3.
Spectroscopic parameters a (MHz) of the three lowest energy conformers of 1,2-propanediol. Parameter aG’g gG’a g’G’gA B C D K × D JK × D J × d × − − − d × − − − H K × H KJ × − − − H JK × − − − H J × h × − h × − − − h × L JK × − − a Watson’s S -reduction was used in the representation I r . Numbers in parentheses are one standard deviation in units of the least significant digits. the experimental lines. The final parameters of the three lowestenergy conformers of 1,2-propanediol are given in Table 3.The newly recorded transitions with their assignments, un-certainties, and residuals between observed frequency and thosecalculated from the final set of spectroscopic parameters areavailable in the supplementary material, as outlined in the ap-pendix. The entire line, parameter, and fit files along with ad-ditional auxiliary files will be available in the spectroscopysection of the CDMS (M¨uller et al. 2001; M¨uller et al. 2005).Updated predictions for all three lower energy conformers of1,2-propanediol will be available in the catalog section of theCDMS.
5. Discussion and conclusion
The rotational constants of all three 1,2-propanediol conformersare very similar, as one can see in Table 3. Therefore, it is not sur-prising that the centrifugal distortion parameters are mostly verysimilar as well. A rotational temperature of 50 K was recentlyreported for the lighter homologue ethanediol in Sgr B2(N)(Belloche et al. 2013). Assuming that the rotational temperatureof propanediol in this source will be similar, the quantum num-ber range covered for 1,2-propanediol in the present work is suf-ficient for astronomical observations, see Fig. 3. Some extrapo-lation to higher quantum numbers is possible in case of muchhigher rotational temperatures. We expect the actual transitionfrequency to be close to the prediction, that is, within three tofive times the predicted uncertainty, as long as the predicted un-certainty does not exceed 300 kHz.According to Belloche et al. (2013), it is advantageous tosearch for the weak spectroscopic features of a rather complexmolecule at frequencies below the Boltzmann peak at an ex-pected rotational temperature. At centimeter wavelengths, how-ever, local thermodynamic equilibrium (LTE) with one rotationaltemperature may be a poor assumption even for a prolific hot-core source such as Sgr B2(N), at least in case of the lowest en-ergy transitions. These transitions sample in particular the outer,less dense, and often colder envelope that surrounds the hot core. Internet address: http: // / cdms / daten Fig. 3.
Stick spectrum of the lowest energy aG’g conformer ofpropanediol at 50 K.In fact, it was shown recently that the low-energy transitions ofmethyl formate, observed with the 100 m Greenbank telescopeup to ∼
50 GHz, deviated significantly from LTE, and several ofthese transitions were masing weakly (Faure et al. 2014).An interesting aspect is the question whether we shouldexpect an even greater molecular complexity to occur in theISM. Bossa et al. (2009) reported on the thermal formation ofaminomethanol in laboratory experiments consisting of H O,NH , and H CO. The molecule was identified in the solid phaseby infrared spectroscopy. It is not known so far whether themolecule can be transferred into the gas phase without com-plete decomposition. Moreover, it is not known what its aver-age lifetime in the gas phase would be compared with relatedmolecules. Nevertheless, this intriguing result may indicate that methanediol, 1,1-ethanediol, 1,1-propanediol, 2,2-propanediol,etc. could also be formed in interstellar ice analogs. In thiscontext, it may be of interest that carbonic acid, OC(OH) , isfairly stable in water-poor environments, in particular at lowtemperatures, and that it can be transferred into the gas phasewithout complete decomposition (Bernard et al. 2013). The mi-crowave spectrum of carbonic acid was also recorded recently(Mori et al. 2011). And while OS(OH) is, to our knowledge,not stable in the gas phase, O S(OH) , sulfuric acid, is, andits rotational spectrum was studied extensively quite recently(Cohen & Drouin 2013). Apparently, the stability of a moleculecontaining two OH groups (or one OH group and one NH group) attached to one atom X depends critically on the atomX and on other atoms or molecule groups attached to X. Acknowledgements.
These investigations have been supported by the DeutscheForschungsgemeinschaft (DFG) in the framework of the collaborative researchgrant SFB 956, project B3. JBB is grateful for support from the Marie CurieIntra-European Fellowship (FP7-PEOPLE-2011-IEF-299258).
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The newly recorded experimental transition frequencies for the aG’g , gG’a , and g’G’g conformers of 1,2-propanediol are givenas Tables 4, 5 and 6, respectively, in the supplementary mate-rial as text files. Only the first and the last ten lines of Table 4appear in the paper edition. The tables give the rotational quan-tum numbers J , K a , and K c for the upper state followed by thosefor the lower state. The observed transition frequency is givenin megahertz units with its uncertainty and the residual betweenobserved frequency and that calculated from the final set of spec-troscopic parameters. In the case of unresolved asymmetry split-ting, frequencies and residuals refer to the unsplit line center.Additional text files aG’g.txt , gG’a.txt , and g’G’g.txt provide the internal coordinates of the three propanediol con-formers. A schematic representation is given in Table 7. Table 4.
Transitions of the aG’g conformer of 1,2-propanediol, observed transition frequencies (MHz), experimental uncertaintiesUnc. (MHz), and residuals o − c between observed frequency and that calculated from the final set of spectroscopic parameters. J (cid:48) K (cid:48) a K (cid:48) c J (cid:48)(cid:48) K (cid:48)(cid:48) a K (cid:48)(cid:48) c Frequency Unc. o − c1 0 1 0 0 0 6431.0705 0.004 0.000522 1 1 2 0 2 6730.6486 0.004 − − − − − − − − − − // cdsarc.ustrasbg.fr / cgi-bin / VizieR?-source = J / A + A / Vol / Num. A portion is shown here for guidance regarding its form and content.
Table 7.
Part of the schematic representation of the internal coordinates (in 100 pm and degrees) of the aG’g conformer of 1,2-propanediol given in aG’g.txt . atom atom ref. no. bond length label atom ref. no. bond angle label atom ref. no. dihedral angle labelHO 1 B1C 2 B2 1 A1C 3 B3 2 A2 1 D1label valueB1 0.96170000B2 1.43000000D9 178.50000000D10 59.30000000Notes. This text file as well as those of other conformers are available in their entirety in the electronic edition in the online journal:http: // cdsarc.ustrasbg.fr / cgi-bin / VizieR?-source = J / A + A / Vol //