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Rotational Spectroscopy of Isotopologues of Silicon Monoxide, SiO, and Spectroscopic Parameters from a Combined Fit of Rotational and Rovibrational Data Holger S. P. Müller,*,† Silvia Spezzano,‡,§,# Luca Bizzocchi,∥ Carl A. Gottlieb,‡,§ Claudio Degli Esposti,⊥ and Michael C. McCarthy‡,§ †

I. Physikalisches Institut, Universität zu Köln, Zülpicher Straβe 77, 50937 Köln, Germany, Harvard−Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, United States § School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, United States ∥ Centro de Astronomia e Astrofísica, Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal ⊥ Dipartimento di Chimica ‘G. Ciamician’ Università di Bologna, Via F. Selmi 2, 40126 Bologna, Italy ‡

S Supporting Information *

ABSTRACT: Pure rotational transitions of silicon monoxide, involving the main (28Si16O) as well as several rare isotopic species, were observed in their ground vibrational states by employing long-path absorption spectroscopy between 86 and 825 GHz (1 ≤ J″ ≤ 18). Fourier transform microwave spectroscopy was used to study the J″ = 0 transition frequencies in the ground and several vibrationally excited states. The vibrational excitation of the newly studied isotopologues extend to between υ = 9 and 29 for 28Si17O and 30Si16O, respectively. Data were extended for some previously investigated species up to υ = 51 for the main isotopologue. The high spectral resolution allowed us to resolve the hyperfine structure in 28Si17O caused by the nuclear electric quadrupole and magnetic dipole moments of 17O for the first time, and to resolve the much smaller nuclear spin-rotation splitting for isotopic species containing 29Si. These data were combined with previous rotational and rovibrational (infrared) data to determine an improved set of spectroscopic parameters of SiO in one global fit which takes the breakdown of the Born−Oppenheimer approximation into account. Highly accurate rotational transition frequencies for this important astronomical molecule can now be predicted well into the terahertz region with this parameter set. In addition, a more complete comparison among physical properties of group 14/16 diatomics is possible.

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SiO residing in the stellar atmosphere.3 These late-type stars eject large quantities of gas and dust, creating circumstellar envelopes (CSEs). In the case of VY Canis Majoris (VY CMa for short), the dust obscures the photosphere of the star even in large portions of the IR. Thus, the appearance of SiO fundamental transitions in a P Cygni (an apparent combination of absorption and emission) profile and the low rotational temperature of about 525 K indicate that the observed SiO is in the CSE of VY CMa.4 The authors also identified weaker features of 29SiO, of 30SiO, and of the υ = 2−1 hot band of the main isotopologue. Here, and in the following, unlabeled atoms refer to 28Si and 16 O. Even though the isotopic composition may differ greatly in space, either isotope is by far the dominant one. On Earth, the

INTRODUCTION The physical and chemical properties of SiO are of fundamental interest, in particular in comparison to the valence isoelectronic molecules CO, SiS, CS, etc. Extensive accurate rotational and rovibrational data of SiO are needed because of its important role in space. The first evidence for SiO in space was obtained almost 50 years ago by low and moderate resolution mid-infrared (MIR) observations of atmospheres of red M-type supergiants. An absorption feature near 8 μm was noticed but remained unassigned initially.1 In a subsequent observation, this absorption band was assigned to the fundamental mode of the SiO molecule.2 The band contour was found to be compatible with rotational temperatures similar to those of the stellar atmospheres.2 The carrier of the absorption was confirmed by the observation of the Δυ = 2 absorption band heads with υ = 2−0 to 5−3 near 4 μm in the MIR spectrum of α Orionis recorded with somewhat higher resolution. The relative intensities of the bands were again compatible with the © 2013 American Chemical Society

Special Issue: Terry A. Miller Festschrift Received: August 21, 2013 Revised: September 25, 2013 Published: September 26, 2013 13843

dx.doi.org/10.1021/jp408391f | J. Phys. Chem. A 2013, 117, 13843−13854

The Journal of Physical Chemistry A

Article

abundances of 28Si, 29Si, and 30Si are 0.922, 0.047 and 0.031, respectively, those of 16O, 17O, and 18O are 0.9976, 0.00038, and 0.0020, respectively.5 Rovibrational transitions of SiO have also been observed in sunspot spectra.6 The first interstellar detection and the first radio astronomical observation of SiO was made at millimeter wavelength in the early 1970s toward the giant molecular cloud Sagittarius B2 (Sgr B2 for short) in the Galactic Center, a birth place of many stars with very high masses,7,8 and toward the near-by Orion A molecular cloud.8 SiO was also observed, e.g., in photondominated regions,9 in low-mass star-forming regions,10 and even in external galaxies,11 but not in cold, quiescent molecular clouds.12 Therefore, this largely thermal SiO emission is usually viewed as a shock-indicator.13 Rather different, and sometimes very spectacular is the maser activity in SiO, often seen in very specific rotational transitions of vibrationally excited states. The first observations were made in the midseventies in υ = 1 toward the Orion molecular cloud.14,15 Soon thereafter, maser activity was observed even in the υ = 2 (and 1) ground state transitions toward Orion and several O-rich late-type stars.16 Explanation of these SiO masers is an important subject for astrophysics, but also for molecular physics. One proposed way to create a population inversion involves accidental overlap of a rovibrational transition of SiO involving one of the rotational levels, between which maser activity occurs, and a different rovibrational transition of SiO or possibly a different molecule, such as H2O or CO.17 An alternative model was also considered involving emission and reabsorption of photons, but pointed out that there are many ways to quench such maser activity.17 Another pumping mechanism involves photons which excite υ > 1 vibrational levels of SiO, which get radiatively trapped by cascading down via Δυ = 1 transitions.18 The pumping mechanism via IR overlap was revisited, e.g., in the course of recording the high-resolution IR spectrum of SiO.19 More recently, it was shown that the observation of maser activity in specific rotational levels in a given vibrational state, e.g., υ = 4, J = 5−4 of SiO20 and υ = 3, J = 8−7 of 29SiO,21 can only be explained well if mutual IR overlap among the SiO isotopologues is taken into account.22 Maser and thermal emission in Si18O J = 1−0 and 2−1 from Orion KL was also detected.23 Most of the radio astronomical observations were made at millimeter wavelengths; recent observations of CSEs of latetype stars with the high-resolution instrument HIFI on board the Herschel satellite revealed SiO emissions at submillimeter wavelengths.24−26 There has been even a report of SiO features in the CSE of CW Leonis, also known as IRC +10216, recorded with the low-resolution instrument PACS at frequencies beyond 1.9 THz (∼64 cm−1),27 i.e., beyond the frequencies of HIFI. The ground state fundamental rotational transition of SiO, 29 SiO, and 30SiO and three vibrationally excited state transitions of SiO near 43 GHz were recorded in the laboratory almost 50 years ago by Törring.28 Manson et al.29 extended the J range for the main isotopic species up to 7−6 near 304 GHz. Mollaaghababa et al.30 enlarged the data set of the main isotopologue considerably, mainly by observing vibrationally excited transitions up to υ = 40 and by reaching J = 9−8. Cho and Saito31 reported ground state rotational transitions of Si18O up to J = 11−10 near 444 GHz. Finally, Sanz et al.32 studied the vibrational excitation of molecules generated by an electric

discharge of a pulsed molecular beam consisting of suitable precursor molecules heavily diluted with He or, mostly, Ne. The rotational transitions were probed by Fourier transform microwave (FTMW) spectroscopy. In the case of SiO, the main isotopologue, 29SiO, and Si18O were studied up to υ = 45, 26, and 43, respectively; O2 highly enriched in 18O was employed for the latter isotopic species. The high resolution available with FTMW permitted the small nuclear magnetic spin-rotation splitting of 29SiO to be resolved (I(29Si) = 1/2). Important for the present investigation are also determinations of the dipole moments33 and the magnetic properties34 of the SiO molecule in the first four and three vibrational states, respectively, by molecular beam electric resonance spectroscopy, in the latter case combined with an external magnetic field. Laboratory studies of the high-resolution gas phase IR spectrum of SiO appear to be limited to two studies. Lovas et al.19 obtained in a fairly early tunable diode laser study a somewhat limited number of precisely determined transition frequencies up to J″ = 60 and υ = 5−4 for SiO and, much more limited, to υ = 2−1 for 29SiO and 30SiO. More recently, Campbell et al.35 obtained a considerable number of fairly precise transition frequencies for the main isotopologue, which they combined with a less precise, but very extensive list of sunspot data, which extend for the main species up to J = 141 and υ = 13−12 as well as a considerable amount of 29SiO and 30 SiO data. The present investigation extends previous FTMW measurements considerably. Using O2 as one of the precursors for SiO, which was highly enriched in 18O (97%), but apparently also somewhat in 17O, we have obtained for the first time data for Si17O up to υ = 9 yielding, in particular, hyperfine structure (HFS) parameters caused by the I = 5/2 nucleus 17O. The parameters comprise the leading nuclear electric quadrupole coupling parameter, its first vibrational correction, and the nuclear magnetic spin-rotation coupling parameter. Extensive transition frequencies were determined for 29Si18O and 30Si18O, and those for Si18O were slightly extended in υ. Rotational transitions of 30SiO in excited vibrational states were recorded for the first time and up to υ = 29. The extent of vibrational excitation was also extended for SiO and for 29SiO. Conventional absorption spectroscopy at millimeter and submillimeter wavelengths was employed to extend the degree of rotational excitation. In the case of 29SiO and 30SiO, we reached J = 13−12; previously published data were constrained to J = 1−0. The range was more than doubled to J = 19−18 for the main isotopic species, and one line was remeasured for Si18O. The transition frequencies from the present study were combined with previously reported rotational and rovibrational data to determine a greatly improved set of spectroscopic parameters from which, in turn, rotational and rovibrational transitions can be predicted. These predictions should be particularly important for radio astronomical observations above 500 GHz. The derived physical properties of SiO are compared with those of CO,36 CS,37 SiS,38 SiSe,39 SiTe,39 and SnO.40

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EXPERIMENTAL DETAILS AND OBSERVED SPECTRA Long-path absorption spectroscopy of silicon monoxide isotopologues at millimeter and submillimeter wavelengths was carried out in Bologna, Cambridge, and in Cologne. These 13844



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Table 1. Rotational Transitionsa (MHz) of Isotopologues (iso) of SiOb, Uncertainties (unc.; kHz), Residualsc (o−c; kHz), and Sourced of the Measurement

data were obtained for the ground vibrational state only. The measurements at Università di Bologna employed a source modulation submillimeter-wave spectrometer41 equipped with a negative glow discharge cell.42 The SiO molecule was produced in the absorption cell by a DC glow discharge in a mixture of silicon tetrachloride (SiCl4), oxygen (O2), and argon. Optimal conditions were attained using partial pressures of 0.15 Pa of SiCl4, 0.15 Pa of O2, and 3 Pa of Ar, and using a discharge current of about 30 mA. Phase locked Gunn oscillators working in the frequency region 80−115 GHz were used as primary radiation sources and the submillimeterwave power was obtained using harmonic multiplication. Source frequency modulation at 16.7 kHz was applied, and the signal was demodulated at 2f by a lock-in amplifier, thus obtaining the second derivative of the actual spectrum profile. A liquid helium-cooled InSb hot electron bolometer was used as detector. Measurement accuracies of the line positions lie in the range 5−15 kHz, depending on the signal-to-noise ratio. Transition frequencies of SiO were obtained between 390 and 738 GHz, those of 29SiO and 30SiO between 338 and 558 GHz. The measurements at Harvard University were very similar to those described earlier,30 with modifications to improve the accuracy of the measurements as described in the investigation of CS and C34S.43 The main isotopologue was investigated between 86 and 825 GHz. The measurement conditions at Universität zu Köln were similar to the SO investigations in Cologne.44,45 A phase-locked backward-wave oscillator OB 30 was used as source, and a liquid He-cooled InSb hot-electron bolometer served as detector. SiO was generated by a DC glow discharge (∼190 mA) of about 1.5 Pa SiCl4, 1.5 Pa O2, and 5 Pa He inside the absorption cell. Only two transitions each of SiO and 30SiO as well as one of Si18O were recorded between 296 and 364 GHz. The absorption measurements used in the final fit are summarized in Table 1. The complete list of transition frequencies with assignments, uncertainties, and residuals between observed frequencies, and those calculated from the final set of spectroscopic parameters is available as Supporting Information as well as in the Spectroscopy Data section (http://www.astro.uni-koeln.de/site/vorhersagen/daten/SiO/) of the Cologne Database for Molecular Spectoscopy, CDMS.37,46 The J″ = 0 transitions were recorded for several isotopic species not studied in ref 32 using the same pulsed molecular beam FTMW spectrometer and discharge nozzle.47 As before, mixtures of 2% SiH4 in Ar and 1.5% O2 in Ne were further diluted with Ne to 0.15% and 0.4%, respectively, and mixed in the gas input line just before the discharge nozzle because SiH4 is spontaneously flammable in air. Subsequently, this gas mixture was subjected to a 1.1 kV discharge. O2 in natural isotopic composition was replaced with O2 containing 97% 18O (Cambridge Isotope Laboratories, Inc.) for investigations of isotopologues containing 18O and of 28Si17O, as it was suspected that a considerable part of the remaining oxygen was 17O. The data obtained for 30SiO, Si17O, 29Si18O, and 30Si18O reach υ = 29, 9, 23, and 24, respectively. In addition, measurements of SiO, 29SiO, and Si18O were extended from υ = 45, 26, and 43, respectively, to υ = 51, 29, and 45, respectively. Attempts were made to reach even higher vibrational states for the main isotopic species; however, no lines were found for vibrational states υ > 51. It is possible that the predictions for these high vibrational states were too unreliable or that the excitation mechanism, discussed in ref 32,

28

iso

J″

frequency

unc.

o−c

source

16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 7 8 9 10 11 12 6 7 8 9 10 11 12 8

86846.985 130268.683 173688.238 217104.919 260518.009 303926.812 347330.581 390728.631 434120.218 477504.635 520881.187 564249.098 607607.719 650956.290 694294.114 737620.462 780934.648 824235.900 342980.847 385835.631 428684.129 471525.620 514359.441 557184.861 296575.730 338930.058 381278.900 423621.621 465957.509 508285.880 550606.057 363100.652

4 3 3 2 12 5 7 3 3 4 10 10 10 10 10 10 4 4 10 10 10 10 10 10 20 5 10 10 10 10 10 20

0.53 −1.44 4.31 3.69 −3.41 3.91 −4.46 3.37 0.28 −3.86 12.83 −8.80 −0.90 −6.62 −6.13 −11.61 7.75 −3.25 −6.88 −4.52 3.00 −6.32 3.52 0.50 −16.70 −0.97 −10.65 1.81 6.98 3.38 −3.44 10.62

C C C C C Ke Cf,e Cg Cg Cg B B B B B B C C B B B B B B K Kg B B B B B Kh

Si O Si16O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 28 16 Si O 29 16 Si O 29 16 Si O 29 16 Si O 29 16 Si O 29 16 Si O 29 16 Si O 30 16 Si O 30 16 Si O 30 16 Si O 30 16 Si O 30 16 Si O 30 16 Si O 30 16 Si O 28 18 Si O 28

J′ − J″. bPresent long-path absorption measurements. cObserved frequency minus frequency calculated from the final set of spectroscopic parameters. dB: Bologna, C: Cambridge, K: Köln. e Also measured in ref 30 with greater uncertainty. fAlso measured in Köln with greater uncertainty. gAlso measured in Bologna with greater uncertainty. hAlso measured in ref 31 with greater uncertainty. a

was much less effective at very high υ than estimated. The transition frequencies of SiO and 29SiO were redetermined for υ ≤ 5 and υ ≤ 1, respectively, as some of the data exhibited rather large residuals in the fits. With the exception of SiO υ = 0, the new data were used in the final fit. Transition frequencies recorded with good signal-to-noise ratio and good line shape were assigned 1 kHz as uncertainties, all others 2 kHz. The investigation of Si17O permitted the determination of 17O hyperfine parameters, nuclear electric quadrupole, and nuclear magnetic spin-rotation coupling parameters of SiO for the first time. In addition, the much smaller 29Si nuclear magnetic spinrotation splitting was resolved for all transitions involving 29SiO and 29Si18O. Table 2 lists the transition frequencies obtained for Si17O as a demonstration of the centimeter-wave data set. Figure 1 displays the good signal-to-noise ratio achieved for the ground state vibrational transition of Si17O. 13845



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Table 2. J = 1−0 Rotational Transitions Frequenciesa (MHz) of 28Si17O Hyperfine Components and Residualsb o−c (kHz) F = 3/2−5/2

F = 7/2−5/2

F = 5/2−5/2

υ

frequency

o−c

frequency

o−c

frequency

o−c

0 1 2 3 4 5 6 7 8 9

41794.1002 41509.1821

−1.39 −1.08

−1.04 −0.31

0.36 −0.14 0.73

40657.1738

−0.78

39805.0977

0.23

0.18 0.11 0.85 0.08 −1.40 −0.51 −0.70 −1.37 0.94 −0.06

41795.3660 41510.4206

40940.1495 40656.0199 40372.1408

41794.4002 41509.4734 41224.8172 40940.4227 40656.2838 40372.3964 40088.7496 39805.3363 39522.152* 39239.1822

40089.6005 39806.1694

−0.37 0.57

a

Uncertainties are 1 kHz throughout, except for line marked with asterisk, for which it is 2 kHz. bObserved frequency minus frequency calculated from the final set of spectroscopic parameters.

⎛ meΔijA meΔijB ⎞ −(i + 2j)/2 ⎟μ Yi , j = Ui , j⎜⎜1 + + MA MB ⎟⎠ ⎝

where Ui,j is isotope invariant, me is the mass of the electron, μ is the reduced mass of AB, MA is the mass of atom A, and ΔAij is a Born−Oppenheimer breakdown (BOB) term.49 The abbreviation δAij is sometimes used for Uijμ−(i+2j)/2 ΔAij me/MA. Moreover, it is noteworthy that both ΔAij and δAij are defined negatively in some papers. Obviously, ΔBij and δBij are defined equivalently. Initially, fits were carried by determining all Yij (or Uij) independently, even though they can, in fact, be constrained in a way that only the Yij (or Uij) with j = 0 and 1 are independent.50 Such constraints were used e.g., in a previous fit of SiO data35 or in a very recent fit of CO data.36 Nevertheless, one finds still quite commonly that none or almost none of the Dunham parameters are constrained.51−55 The Dunham approach, with or without constraints, is suitable for fitting spectra of diatomics in excited vibrational states, as long as these are not so close to dissociation; it will become difficult eventually to represent a molecular potential by a polynomial. Both Si and O only have one isotope with a nonzero nuclear spin, 29Si (I = 1/2) and 17O (I = 5/2), which gives rise to hyperfine structure in SiO from electric quadrupole coupling eQqij (17O), or magnetic spin-rotation coupling Cij (17O, 29Si), that is readily resolved at high spectral resolution. All hyperfine parameters follow standard definitions.56 Their vibrational and rotational dependences can be expressed analogously to the Dunham parameters, and the parameter with i = j = 0 is the parameter lowest in order. The HFS would be slightly more complicated for 29Si17O, because of scalar (normally denoted by the parameter J) and tensorial nuclear spin-nuclear spin coupling (S). For fairly light nuclei with small magnetic moments, the scalar contribution is typically negligible, and the tensorial contribution is dominated by a term that can be derived from the structure.57 This term amounts to −0.940 kHz for SiO and has been included for 29Si17O predictions. The quadrupole coupling parameters eQqij scale with μ−(i+2j)/2, as do Sij and Jij while the spin-rotation parameters Cij scale with μ−(i+2j+2)/2. The atomic masses were initially taken from the 2003 Atomic Mass Evaluation.58 However, in an ongoing analysis of the CO molecule, see, e.g., ref 59, it was found that the 18O mass must be in serious error. This was confirmed shortly thereafter.60 In addition, improved masses have been published recently for

Figure 1. A portion of the rotational spectrum of silicon monoxide in the region of the J = 1→0, υ = 0 transition of 28Si17O, recorded using a dilute mixture of silane (0.1%) and 18-oxygen (0.1%) in neon. The spectrum is a concatenation of 22 individual spectra, each 200 kHz wide; the total integration time was approximately 25 min. Owing to the I = 5/2 moment of the 17O nucleus, the transition is split into several strong hyperfine lines in this frequency range. Because the supersonic molecular beam travels parallel to the propagation of the microwave radiation, each hyperfine line is further split into two components owing to the Doppler effect; the rest frequency for each line is simply the arithmetic average of the two Doppler components. The relative intensities are only approximately correct even under the most favorable conditions.

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DETERMINATION OF SPECTROSCOPIC PARAMETERS Dunham48 showed that the rovibrational energy levels of a diatomic molecule AB in a Σ electronic state can be represented by E (v , J ) =

∑ Yij(v + 1/2)i J j (J + 1) j i,j

(2)

(1)

where the Yij are called the Dunham parameters. Watson showed that several isotopic species of AB can be fit jointly by constraining the Yij to 13846



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O,61 28Si,62 and 29Si.62,63 These mass determinations have been incorporated into the AME2012 Atomic Mass Evaluation;64 the values from that mass evaluation, differing slightly (within uncertainties) from the ones originally reported, have been used in the present work and are listed in Table 3. 17

uncertainties, as is usually the case. The adequacy of the assigned uncertainties was tested by checking how well various subsets of the data could be reproduced. Such tests are very important for an extensive and rather diverse data set as in the present case. The choice of spectroscopic parameters was rather straightforward from the previous IR35 and FTMW studies.32 It is also necessary to point out that in most cases, parameters to be varied were only kept in the fit if they were determined with significance, i.e., the value was at least three times the uncertainty, and the variation of the parameter reduced the rms error of the fit by an appreciable amount. This criterion is necessarily vague, as the type of parameter and the nature of the data set determine whether an amount is appreciable or not. It can also be helpful to try to estimate if the approximate magnitude or the sign of a parameter is correct, though this may be difficult rather frequently. The parameters Y71, Y81, and Y42 were determined here for the first time. The value of Y50 was not determined with significance; therefore, Y50 was omitted from the final fit even though it was reasonably well constrained. Campbell et al.35 also considered in their fits very high-υ vibrational spacings from ref 69. Three of these spacings, υ = 24−23, 25−24, and 27−26, were reproduced within the quoted digits of 0.01 cm−1 by the final set of parameters, but three others, υ = 23−0, 26− 25, and 28−27 showed larger residuals of 0.09, −0.16, and −0.10 cm−1, which do not change much if these spacings are included in the fit. Hence, appropriate uncertainties can only be of order of 0.10 cm−1. At this level of uncertainty, Y50 = 1.05 ± 0.76 kHz was obtained even with these data. These data were subsequently omitted from the final line list because the predicted uncertainties were much smaller when these data were omitted from the fit than the experimental ones, and the amount of data was too small to compensate these differences by statistics. The parameter Y91 was not determined reliably, and was also omitted from the final fit. No attempt was made to determine Y52 because already for Y42 it was uncertain how reliable its value is. However, Y42 was determined with significance, and its introduction into the fit improved the rms error of the fit sufficiently to retain it in the fit. In a later stage of the fitting process, it was noted that the spectroscopic parameters determined in the present investigation were in many instances rather close to those from the previous IR work.35 Therefore, we studied the effect of higher order parameter values from that work, which were not used in the present fit, on those already included in our fit. While none of these added, constrained parameters affected the rms error of the fit by more than one percent, much larger effects occurred for the parameter values. The largest effect was caused by Y23, which increased the magnitude of Y32 by slightly more than its value and concomitantly reduced the magnitude of Y42 by slightly less than half its value. A much smaller effect on Y03 and Y13 was caused by Y04. Additional constrained parameters from ref 35 were added to our parameter set until all parameter changes were within the calculated uncertainties. These parameters were Y33, Y14, and Y24. Y05 was the lowest order parameter not to be included in our fit. Besides the negligible effect on the lower order parameters, these parameters were also omitted from the fit because their values affected the predicted transition frequencies within the uncertainties and because their uncertainties were not given. The Si BOB terms for U10 and U11 have been determined for the first time in the present analysis. The term for U11 was just

Table 3. Atomic Masses (amu) Used in the Present Study massa

isotope 28

Si Si 30 Si 16 O 17 O 18 O 29

27.976 28.976 29.973 15.994 16.999 17.999

926 494 770 914 131 159

534 664 136 619 756 612

6 (4) 9 (5) (23) 57 (17) 5 (7) 9 (8)

a

Numbers in parentheses are one standard deviation in units of the least significant figures.

The experimental line list consists of the rotational data from Mollaaghababa et al.30 employing the reported uncertainties; however, the υ = 0 transitions have been remeasured here, and the υ = 1, J = 8−7 transition was omitted because of large residuals in the fits. The data from Sanz et al.32 were also used with the reported uncertainties, except for the υ = 1 to 5 transitions of SiO and the υ = 0 and 1 transitions of 29SiO for which present remeasurements were taken. The standard deviations of the frequency determinations of the Si18O transitions stated by Cho and Saito31 are overall not compatible with the often much larger residuals even in the published fit. An extreme case is the J = 4−3 transition frequency, for which 2 kHz were stated as standard deviations of the frequency determination, but their calculated frequency is 27 kHz lower. We assigned uniform uncertainties of 30 kHz in order to obtain a partial root-mean-square (rms) error slightly smaller than the ideal 1.0. The early rotational data28,29 were not used in the present fits because of their larger uncertainties and because all28 and some29 data, respectively, have been remeasured much more accurately in the present or in earlier studies.30,32 The tunable diode laser IR data were used in the fit with their reported uncertainties.19 The neglect of a possible calibration error appears to be justified because a comparison of the N2O calibration data used in that study65 with the most recent N2O data from HITRAN (2004 version)66 suggests that the differences between the strongest and most accurate calibration lines differ by less than the reported uncertainties. According to ref 67, the agreement is meaningful. The very extensive SiO laboratory emission and sunspot absorption data35 were employed as provided by one of its authors (P. F. Bernath). According to eq 2, one isotopic substitution for each atom should, in theory, be sufficient to determine the required BOB terms; additional substitutions simply add redundant information, except for those, such as Si17O, which also provide 17O hyperfine parameters. In practice, however, multiple substitutions of each atom are desirable to reduce correlations between the parameters and their BOB terms, reducing in effect the calculated uncertainties. In addition, multiple substitution provides a consistency check on the data. This check was important in our SiS study38 to correct the previous analysis of the 29SiS HFS pattern,32 or in the ongoing analysis of CO data, which revealed a significant error in the mass of 18O.60 All fits and predictions were carried out with Pickett’s SPFIT and SPCAT programmes.68 The input data were weighted inversely proportional to the square of the measurement 13847



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Table 4. Spectroscopic Parametersa (MHz) of 28Si16O Determined from the Global Fit in Comparison to Selected Previous Data parameter −1/2

−6

× 10 U10μ U10μ−1/2ΔSi10me/MS Y10 × 10−6 ΔSi10 Y20 × 10−3 Y30 Y40 × 103 U01μ−1 U01μ−1/2ΔSi01me/MSi U01μ−1/2ΔSi01me/MO Y01 ΔSi01 ΔO01 Be U11μ−3/2 U11μ−3/2ΔSi01me/MS U11μ−3/2ΔO01me/MO Y11 ΔSi11 ΔO11 Y21 × 103 Y31 × 106 Y41 × 106 Y51 × 109 Y61 × 109 Y71 × 1012 Y81 × 1012 Y02 × 103 Y12 × 106 Y22 × 109 Y32 × 109 Y42 × 1012 Y03 × 109 Y13 × 1012 Y23 × 1012 Y33 × 1015 Y04 × 1015 Y14 × 1018 Y24 × 1018 Y05 × 1018 eQq00(17O) eQq10(17O) × 103 C00(29Si) × 103 C00(17O) × 103 S00 × 103

this wrkb 37.220 137 1 (274) 413.7 (273) 37.220 550 81 (185)e 0.567 (37)e,f −179.109 64 (69) 182.826 (88) −340.3 (36) 21 789.572 21 (211) −0.554 39 (189) −1.532 53 (121) 21 787.485 29 (14)e −1.2976 (44)e,f −2.0507 (16)e,f 21 787.496 933 (139)e,g −151.046 828 (278) 0.000 500 (153) 0.008 401 (74) −151.037 927 (196)e −0.169 (52)e,f −1.622 (14)e,f 75.323 (69) −540.4 (102) −8.92 (78) 184. (34) −6.23 (81) 126.0 (102) −1.131 (52) −29.864 75 (20) −12.530 (64) −571.2 (75) −5.80 (59) −71.9 (114) 1.142 (69) −229.2 (45) −3.70 −41.6 −31.4 −953. −23.9

ref 32c

37.220 549 0 (13) −179.107 1 (5) 182.58 (6) −332.9 (25) −0.553 −1.545 21 787.478 −1.294 −2.068

(5) 6 (24) 6 (4) (12)e,f 2 (32)e,f

0.008 69 (10) −151.030 63 (22) −1.678 (19)e,f 73.28 (4) −316. (4) −19.71 (15) 360.8 (30) −3.445 (22)

−179.110 92 (58) 183.005 (74) −347.3 (30)

21 787.484 4 (11)

21 787.468 8 (8)

−151.038 00 (28)

−151.040 13 (9)

75.380 (56) −565.7 (34) −5.725 (60)

76.669 (7) −681.3 (2) −1.876 (7) −44.2 (1)

−29.86178 −12.387 −556.8 −7.62

−4.20 (31)

1.072 −237.9 −3.70 −41.6 −31.4 −953. −23.9 −0.0677

−434. (23)

ref 30

37.220 550 8 (16)

−29.845 8 (15) −14.64 (4) −504.3 (31) −9.42 (11)

−6.0 (5) 4.3918 (36) −92.42 (75) −21.331 (162) −15.468 (87) −0.940

ref 35d

−29.675 (7) −43.1 (4)

−21.40 (34)

Numbers in parentheses are one standard deviation in units of the least significant figures. Empty fields indicate that the parameter was not used in the fit or constrained to zero. bNumbers without uncertainties were kept fixed to the quoted value; Yij with j ≥ 3 were kept fixed to values taken from ref 35, S00 was calculated from the structure; see also remarks on the hyperfine parameters at the beginning of the section “Determination of Spectroscopic Parameters”. cRounded 1σ uncertainties derived from quoted 3σ uncertainties. dThe Uij and Yij, respectively, with j ≥ 2 were constrained to values derived from the parameters with j ≤ 1. No uncertainties were determined for these derived parameters. In addition to the values in the table, values for U0j with j = 6 − 9, U1j with j = 5−7, and U25 were given as well as the derived Yij. No Born−Oppenheimer breakdown terms were determined significantly. Original units were cm−1. eDerived value. fUnitless. gSee structure evaluation in the Discussion. a

barely determined with significance. It was retained in the fit because its magnitude was deemed reasonable. BOB terms for U02 were not used because their values were not significant. The leading 17O nuclear electric quadrupole coupling term and its first vibrational correction were determined here for the first time. The second vibrational correction appeared to be reasonably well constrained, but was far from being determined

with significance and was consequently omitted from the final fit. The 17O nuclear magnetic spin-rotation coupling term was also determined for the first time. Vibrational corrections to either spin-rotation term were insignificant. As mentioned earlier, the 29Si17O nuclear spin-nuclear spin coupling term S was calculated to describe the HFS of this isotopologue as appropriately as possible. 13848



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Table 5. Comparison of Born−Oppenheimer Breakdown Termsa Δ10, Δ01, and Δ11 for Molecules AB with A = C, Si, and B = O, S ΔA10 ΔB10 ΔA01 ΔB01 ΔA11 ΔB11 a

COb

CSc

SiOd

SiSe

0.69547 (69) −0.16886 (71) −2.05603 (24) −2.09934 (24) −1.841 (10) −1.859 (12)

0.7606 (115) −0.6598 (346) −2.5434 (49) −2.3945 (34) −2.697 (130) −0.985 (118)

0.567 (37) − −1.2976 (44) −2.0507 (16) −0.169 (52) −1.622 (14)

0.893 (43) −0.174 (54) −1.3935 (42) −1.8728 (55) −0.146 (132) −1.306 (144)

Numbers in parentheses are one standard deviation in units of the least significant figures. bReference 36. cReference 37. dThis work. eReference 38.

The final set of spectroscopic parameter for 28Si16O is presented in Table 4. The rms error is 0.791 for the global fit consisting of 2460 transition frequencies, indicating that the input data are generally well reproduced to within the experimental uncertainties; some of the uncertainties may be slightly conservative. The υ = 1, J = 8−7 transition frequency of Mollaaghababa et al.,30 which was omitted from the fit, is calculated 85 kHz higher than the reported frequency, not compatible with an assigned uncertainty of 10 kHz. The rms error is 0.803 for 62 lines retained from that data set, meaning that the data are reproduced here within experimental uncertainties for the first time. The rms errors for the previous 134 FTMW lines32 is 0.783, for the 146 present FTMW data, it is 0.831. The rms errors for 11, 17, and 4 mm or submillimeter transition frequencies from Harvard, Bologna, and Cologne are 1.079, 0.676, and 0.638, respectively. The 8 remaining Si18O lines reported by Cho and Saito31 yield an rms error of 0.841, suggesting that the assigned uncertainty of 30 kHz for each line is appropriate. Finally, the rms errors are 0.971, 0.639, and 0.813 for 42 IR transitions from Lovas et al.,19 for 375 lines from the laboratory,35 and for 1661 lines from sunspot spectra,35 respectively.

The comparison of our parameters with those of the previous FTMW study32 is quite complex. The purely vibrational parameters agree well to very well. The agreement is still good for the Yi1 for lower values of i, but less so for i ≥ 3. Truncation of the Hamiltonian is probably not an explanation because a better agreement is seen for Y31 and Y41 from the IR study.35 A possible explanation is the use of Y04 and Y05 in the fit, which appear to be determined with significance, but their magnitudes are about a factor of more than 10 and almost 100 larger than those derived in ref 35. We suspect that the use of these parameters in their fit improved its rms error only slightly. Furthermore, inclusion of these higher order parameters as fitted parameters leads to severe deviation between predicted and measured frequencies at higher quantum numbers. The agreement among the BOB terms is good, and the same applies to the 29Si nuclear magnetic spin-rotation coupling parameter. The BOB parameters of SiO are compared with the corresponding values of CO, CS, and SiS in Table 5. The ΔSi10 value agrees well with corresponding values of these three molecules; interestingly, the differences between SiO and SiS are slightly larger than the respective C values in CO and CS. Unfortunately, no high-resolution IR data are available for 18OO could not be containing isotopologues of SiO, so Δ10 determined for SiO. Its value is of some importance for locating exactly the rovibrational energies of the 18O-containing SiO isotopologues, but it is also difficult to estimate its value from the related molecules because the value in CO is rather small in magnitude, as is the corresponding S value in SiS, but the S value in CS is not. The ΔSi11 value in SiO is very small in magnitude, similar to that in SiS, though the real value in the latter may be more different because its uncertainty is not much smaller than its magnitude. The respective C values of CO and CS are also negative, but much larger in magnitude. Among the Born−Oppenheimer breakdown terms, the ones for Y01 ≈ Be are usually the ones determined best, while others often were obtained with, at best, little significance. It is therefore not surprising that, in the Dunham formalism, only these terms have been discussed in detail. Watson showed how three contributions to these terms can be derived.49 These are (i) a higher-order semiclassical term that originates in the Dunham formalism and is usually very small, (ii) a diabatic (or nonadiabatic) term that is proportional to the dipole moment μ and the molecular g-value gJ, and finally, (iii) an adiabatic term that is derived by subtracting the two former contributions from the experimental value. Tiemann et al.70 discussed Born− Oppenheimer breakdown terms for two groups of molecules with 10 valence electrons consisting of C to Pb and O to Te as one group and of Ga to In and F to I as the other. They found that the adiabatic contribution is more a property that depends on the respective atom than on the particular molecule. Moreover, its value is negative and usually small in magnitude

■

DISCUSSION The agreement between the present parameters and the smaller set determined in ref 30 is reasonable for those of lowest order, but the ones of higher order, Y41, Y51, and Y12 differ considerably. If this is not caused by numerical problems in the fitting employed for that study, then truncation of the Hamiltonian is the most likely explanation, because the stated rms of the fit is 60 kHz, much larger than the quoted uncertainties. Truncation of the Hamiltonian is probably the main reason for the poor reproduction of these rotational data30 in a subsequent IR study35 as the assigned uncertainties exceeded 100 kHz (see eq 4 and surrounding text in ref 35). We suspect that use of Y51 and Y61 would have reproduced these data much better. On the other hand, the lower order parameters agree with ours well to very well, and even the parameters highest in vibrational order agree for each rotational order reasonably well. In view of the effect of constrained higher order parameters taken from ref 35 in our fit, it appears useful to try to fit the data with independent parameters only. In addition, it is worthwhile to try to determine a potential function directly from the data. However, the determination of a modified Morse potential in ref 35 shows that this is not always straightforward without significant loss of accuracy: although the authors had already increased the uncertainties from ref 30 considerably, they omitted data with υ > 34 because of larger residuals in their potential function fit. 13849



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Table 7. SiO Equilibrium Bond Lengths re (pm)a in the Born−Oppenheimer Limit and Values for the Various Isotopic Species Taking into Account the Deviations from the Born−Oppenheimer Approximation

for light or fairly light atoms, but it may have a large one for heavier atoms such as Sn and In, and even more so for Pb and Tl because of the finite nuclear sizes.71,72 The evidence put forth70 was in some cases not so conclusive as in others. However, recent investigations have supported this view in many instances: e.g., the values previously derived by Sanz et al.32 for SiO and SiS agree well with that picture, with the exception of the Si contribution in SiS, which was barely determined and positive. However, this was caused by a misinterpretation of the 29Si HFS splitting, which was reconciled in our recent SiS study;38 a value ΔSi01 = −1.39 instead of −1.1 yields an adiabatic contribution to ΔSi01 of about −0.2, in line with the SiO value of −0.276 (39).32 Recent values for ΔSn 01 show a gradual decrease in magnitude from SnO to SnTe,40 possibly indicative of the onset of effects caused by the finite size of the Sn nucleus. The BOB parameter in Table 6 are quite similar and show a small and steady increase in magnitude at the Si nucleus,

species SiOBO 28 16 Si O 29 16 Si O 30 16 Si O 28 17 Si O 29 17 Si O 30 17 Si O 28 18 Si O 29 18 Si O 30 18 Si O

ΔSi01 ΔE01

c

SiO

SiS

−1.2976 (44) −2.0507 (16)

−1.3935 (42) −1.8728 (55)

SiSe

d

−1.431 (11) −1.915 (17)

467 697 631 569 383 317 255 106 039 978

8 (146) 47 (48) 21 (48) 51 (48) 80 (48) 54 (48) 84 (48) 22 (48) 96 (48) 26 (48)

a

Numbers in parentheses are one standard deviation in units of the least significant figures.

Table 6. Comparison of Born−Oppenheimer Breakdown Termsa Δ01 for Silicon Chalcogenides SiE b

value 150.966 150.973 150.973 150.973 150.973 150.973 150.973 150.973 150.973 150.972

and reflects the slightly poorer reproduction of the experimental data within that model compared to the Dunham model. We also note agreement well within their relatively large uncertainies with initial microwave studies.28,29 The eQq00(17O) values of CO and SiO in Table 8 are remarkably similar, even more so than the 33S values of CS and SiS. Moreover, the differences between the 17O values and the 33 S values approximately reflect the 2.65 times larger quadrupole moment of 33S compared with 17O.77 The quadrupole tensor is usually interpreted in terms of multiple and ionic bonding.78 As there is only one value for each molecule (eQq ≡ eQqaa = − 2eQqbb = − 2eQqcc), the two contributions cannot be disentangled. Nevertheless, it is probably safe to state that these diatomics all exhibit considerable double bond character, though the bond order in CO is usually viewed as being closer to 2.5.79 In fact, the SiO bond length in the SiO molecule, 150.97 pm, is very similar to 151.6 and 150.64 pm in silanone, H2SiO,80 and silicon oxysulfide, OSiS,81 respectively, but much shorter than ∼164.7 pm determined for hydroxysilylidyne, SiOH, also known as silicon monohydroxide.82 The latter value is possibly typical for a SiO single bond. Reference 81 discussed the considerable amount of double bonding in di- and triatomics containing one C or Si atom and one or two O or S atoms. The differences in bonding are more apparent when the 17O and 33S eQq values of these four molecules are compared to the corresponding values of SnO, 1.6372 (94) MHz,83 and SnS, 3.6556 (19) MHz,84 probably reflecting a larger degree of ionic bonding. The similarity of the eQqi0(33S) values of CS and SiS has been pointed out earlier,38 in particular if the differences in the reduced masses are taken into account. Hence, eQq10(17O) of CO can be estimated as being around −110 to −140 kHz in comparison to the corresponding SiO value. This would cause an increase in eQq00(17O) of CO by around 55 to 70 kHz and bring it even closer to the SiO value. The nuclear magnetic spin-rotation coupling parameter C is the sum of an electronic part Cel and a nuclear part Cnucl; the latter can be calculated directly from the structure, as described, e.g., in ref 57. Cel is proportional to the rotational constant Be, the magnetic g factor of the nucleus, and the paramagnetic shielding σp at the nucleus. As an excited state property, it is σp and thus also Cel that may be a challenge for ab initio calculations. The value of σp can be obtained as a sum in which

d

SiTe

−1.569 (14) −2.101 (49)

a

Numbers in parentheses are one standard deviation in units of the least significant figures. bThis work. cReference 38. dReference 39.

whereas the chalcogen values show a more negative value for SiO than for SiS; from SiS to SiTe, a similar trend is seen as at the Si nucleus. As no experimental dipole moments μ and no molecular g-value gJ are available for SiSe and SiTe, we refrain from redetermining the contributions for the remaining Si chalcogenides SiO and SiS. The SiO equilibrium bond lengths re have been calculated for the various isotopic species according to r2e × Be × μ = ℏ2/2. Here Be is the equilibrium rotational constant derived from Y01, μ is the reduced mass as above, and ℏ2/2 = 505379.00956 ± 0.00036 amu MHz Å2 with 1 Å = 100 pm. The value of ℏ2/2 has been reevaluated recently from the speed of light and updated values for the Compton wavelength of the proton and the mass of the proton.73 It should be noted that Be is slightly different from Y01.74 In the case of 28Si16O, Be is 11.645 ± 0.017 kHz larger than the Y01 value. The fictitious, nonphysical bond distance in the Born−Oppenheimer approximation is evaluated from U01 as above. The corresponding values for the various isotopologues are summarized in Table 7. It should be pointed out that the uncertainties of the atomic masses have negligible effects in the present study. The main uncertainties in the calculated bond lengths originated from the uncertainties in Be. The improvement in the accuracy of the value of ℏ2/2 in units of amu MHz Å2 by almost a factor of 10 relative to the value used in our SiS study38 makes the effect of its uncertainty essentially negligible. The bond lengths from the previous FTMW study32 agree well with the present, much more accurate values, the deviations are only slightly larger than one standard deviation of the previous uncertainties. Campbell et al. 35 did not derive bond lengths from their mass-dependent Dunham fit. However, their implied value would agree with ours within their uncertainties as this level of agreement also holds for Y01. Their bond length from the modified Morse potential agrees within twice their uncertainties with our 28Si16O bond length 13850



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Table 8. Comparison of the 17O Quadrupole Coupling Parameters eQqij (MHz)a of CO and SiO with 33S Values of CS and SiS eQq00 eQq10 × 103 eQq20 × 103

COb

SiOc

CSd

SiSe

4.3192 (17) − −

4.3918 (36) −92.42 (75) −

13.0265 (68) −400.7 (39) 2.50 (48)

11.07684 (148) −249.84 (62) 1.125 (43)

Numbers in parentheses are one standard deviation in units of the least significant figures. bReferences 75 and 76. cThis work. dReference 37. Reference 38.

a e

each summand is proportional to ⟨r−3⟩, which is the expectation value over electron coordinates on valence orbitals of the respective atom, an occupation or weighting number and inversely proportional to the energy of excited singlet states in the case of a singlet molecule; see, e.g., in ref 57. Values were derived already for CS and SiS.38 Using updated values of the nuclear magnetic moments,85 our present spinrotation parameters for SiO, and corresponding values for CO,75,76,86 we evaluated the paramagnetic shielding values σp at the corresponding nuclei of these two molecules and summarize the σp values of these four molecules with data for heavier group 14/16 (group IVa/VIa) molecules in Table 9.

range was more than doubled for the main isotopic species. The HFS parameters as well as the BOB parameters derived here are consistent with those of related molecules. The improved spectroscopic parameters permit reliable predictions of rotational transitions well into the terahertz region. The predicted uncertainties of the ground state rotational transitions of 28 16 Si O reach uncertainties of ∼6, 26 and 80 kHz near 1.0, 1.5 and 2.0 THz, respectively, which corresponds to J″ of 22, 34, and 45. These uncertainties are almost irrespective of the isotopic species or vibrational state considered. This is a considerable improvement with respect to the data previously available in the CDMS,37,46 because the ground state rotational transitions of all isotopologues had uncertainties exceeding 3 MHz at 2 THz; the currently predicted frequencies are only about twice the larger uncertainties higher than the earlier values. The initial 29SiO and 30SiO predictions benefitted already from the Cologne data published here. However, small, but not always negligible deviations of several kilohertz occur at frequencies lower than about 200 GHz because the initial predictions are from 2000 and did not include any FTMW data. We estimate that below 2 THz, possibly even higher, actual transitions are found not farther away from the predicted frequencies than 3−10 times the predicted uncertainties. Reducing the accuracy requirements somewhat, it should be possible to extend the predictions to even higher J quantum numbers and to much higher υ, at least to υ = 30. At υ much higher than ∼40, problems may arise not only because of the lack of experimental vibrational data, but probably also increasingly because of the deficiencies of the Dunham model. Predictions of the rotational spectra of various SiO isotopic species, including those for excited vibrational states as well as rovibrational transitions for the more abundant ones, will be available in the catalog section of the CDMS (http://www. astro.uni-koeln.de/cdms/catalog, http://www.astro.uni-koeln. de/cdms/entries),37 together with documentation files which include partition function values at selected temperatures. Emphasis is put on serving the radio astronomical community, in particular for observations with ALMA, and to provide accuarate predictions. The permanent dipole moments in the four lowest vibrational states were determined experimentally with great accuracy.33 Vibrational intensity information is available from quantum chemical calculations.88,89 Very recently, the generation of line lists of the rovibrational spectrum of SiO has been published, which, judging from their Figure 2, also includes the pure rotational spectrum.89 The line lists were constructed to model stellar atmospheres, and they are thus complementary to our predictions. They were constructed from the sun-spot data published by Campbell et al.,35 and the data from the previous FTMW study32 by determining an extended Morse oscillator potential function without taking into account the breakdown of the Born− Oppenheimer approximation. The line lists extend to very high J, υ, and Δυ of up to 423, 98, and 98, respectively. The authors mention that the experimental data have been reproduced to

Table 9. Comparison of Paramagnetic Shielding Values σpa (ppm) for Diatomic Group 14/16 Molecules AB at the Corresponding Nucleus molecule COb SiOc CSd SiSe SiSef SiTef SnOg SnSh

nucleus A −313.8 −589.6 −576.8 −952.8 −1160.0 −1442.0 −3510.0 −4470.0

(13) (41) (105) (13) (102) (25) (27) (70)

nucleus B −491.1 −660.8 −1079.4 −1165.2 −2573.0 −4394.0 −1203.0 −1579.0

(12) (32) (145) (136) (26) (30) (40) (89)

a

Numbers in parentheses are one standard deviation in units of the least significant figures. bDerived from refs 75, 76, and 86. cThis work. d Reference 37. eReference 38. fReference 39. gReferences 40, 83. h Reference 87, derived from ref 84.

The paramagnetic shielding increases for all group 14 or group 16 sequences of molecules from lighter to heavier ones, as one expects. The group 14 value almost doubles from CO to SiO, but it is about a factor of 6, to reach the SnO value. The values double almost also from CS to SiS, and to SnS it is a factor of 5. In the sequence of silicon chalcogenides, however, the value almost doubles from SiO to SiS, similar to the change from CO to CS, but increase much less to SiSe and SiTe, similar to the change from SnO to SnS. The group 16 value roughly doubles in the series of silicon chalcogenides, similar to the change from CO to CS, and again a much smaller change from SnO to SnS. The increases are also quite small in the series of group 14 oxides or sulfides.

■

CONCLUSIONS Very accurate rotational transition frequencies of most of the stable SiO isotopic species are now available in the microwave region. They extend to very high vibrational levels for the more abundant species. HFS parameters caused by the 17O nucleus were determined here for the first time, and the nuclear magnetic spin-rotation parameter for 29Si was improved. Rotational transition frequencies beyond the J = 1−0 transition were obtained for the first time for 29SiO and 30SiO, and the J 13851



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better than 0.01 cm−1, often much better, in particular for the pure rotational data. The sunspot spectra have thus been reproduced within about 1.5 times the uncertainties, which is satisfactory. The statement concerning the pure rotational transitions is not meaningful given that their uncertainties are 5 orders of magnitude better. Consideration of the breakdown of the Born−Oppenheimer approximation is indispensable for calculating the pure rotational spectrum accurately. Therefore, we expect our predictions of pure rotational transition frequencies to be much better, probably even at the highest J provided in our predictions, even more so as no pure rotational transitions with J″ > 0 were included in the treatment of ref 89. At J and υ values much higher than those intended for the CDMS catalog, the shortcoming of the Dunham approach will likely be more important than the shortcomings in the treatment of ref 89. Predictions of the rovibrational spectrum are probably of similar quality up to fairly high J and υ of at least 100 and around 30, respectively, as the predictions are dominated by the sunspot spectra.35 We suspect, however, that the use of additional rotational and rovibrational data in our fit should be advantageous at lower J and υ values. In fact, the υ = 24−23 to 28−27 vibrational spacings from ref 69 have been calculated slightly better from our parameters than from those of ref 89, though it is not clear how significant this comparison is. Eventually, the shortcomings of the Dunham approach will take over.

■

was supported by NASA Grants NNX13AE59G and NNX08AE05G.

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ASSOCIATED CONTENT

S Supporting Information *

A modification of the SiO fit file was prepared, which contains explanations, sources for the experimental lines, quantum numbers, frequencies, uncertainties, and residuals between observed frequencies and those calculated from the final set of spectroscopic parameters. This material is available free of charge via the Internet at http://pubs.acs.org/.

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REFERENCES

(1) Gillett, F. C.; Low, F. J.; Stein, W. A. Stellar Spectra from 2.8 to 14 Microns. Astrophys. J. 1968, 154, 677−687. (2) Knacke, R. F.; Gaustad, J. E.; Gillett, F. C.; Stein, W. A. A Possible Identification of Interstellar Silicate Absorption in the Infrared Spectrum of 119 Tauri. Astrophys. J. 1969, 155, L189−L192. (3) Cudaback, D. D.; Gaustad, J. E.; Knacke, R. F. Silicon Monoxide in the Infrared Spectrum of Alpha Orionis. Astrophys. J. 1971, 166, L49−L51. (4) Geballe, T. R.; Lacy, J. H.; Beck, S. C. The 8 Micron Band of Silicon Monoxide in the Expanding Cloud around VY Canis Majoris. Astrophys. J. 1979, 230, L47−L51. (5) Böhlke, J. K.; de Laeter, J. R.; De Bièvre, P.; Hidaka, H.; Peiser, H. S.; Rosman, K. J. R.; Taylor, P. D. P. Isotopic Composition of the Elements, 2001. J. Phys. Chem. Ref. Data 2005, 34, 57−67. (6) Glenar, D. A.; Deming, D.; Jennings, D. E.; Kostiuk, T.; Mumma, M. J. Diode Laser Heterodyne Observations of Silicon Monoxide in Sunspots − A Test of Three Sunspot Models. Astrophys. J. 1983, 269, 309−318. (7) Wilson, R. W.; Penzias, A. A.; Jefferts, K. B.; Kutner, M.; Thaddeus, P. Discovery of Interstellar Silicon Monoxide. Astrophys. J. 1972, 175, L43−L46. (8) Dickinson, D. F. Detection of Silicon Monoxide at 87 GHz. Astrophys. J. 1971, 167, L97−L100. (9) Schilke, P.; Pineau des Forêts, G.; Walmsley, C. M.; MartínPintado, J. Observations of SiO towards Photon Dominated Regions. Astron. Astrophys. 2001, 372, 291−301. (10) Yamamoto, S.; Mikami, H.; Saito, S.; Kaifu, N.; Ohishi, M.; Kawaguchi, K. SiO in Barnard 1. Publ. Astron. Soc. Jpn. 1992, 44, 459− 467. (11) Mauersberger, R.; Henkel, C. Dense gas in nearby galaxies. IV − The Detection of N2H+, SiO, H13CO+, H13CN, and HN13C. Astron. Astrophys. 1991, 245, 457−466. (12) Ziurys, L. M.; Friberg, P.; Irvine, W. M. Interstellar SiO as a Tracer of High-temperature Chemistry. Astrophys. J. 1989, 343, 201− 207. (13) Martín-Pintado, J.; Bachiller, R.; Fuente, A. SiO Emission as a Tracer of Shocked Gas in Molecular Outflows. Astron. Astrophys. 1992, 254, 315−326. (14) Snyder, L. E.; Buhl, D. Detection of Possible Maser Emission Near 3.48 Millimeters from an Unidentified Molecular Species in Orion. Astrophys. J. 1974, 189, L31−L33. (15) Davis, J. H.; Blair, G. N.; van Till, H.; Thaddeus, P. Vibrationally Excited Silicon Monoxide in the Orion Nebula. Astrophys. J. 1974, 190, L117−L119. (16) Buhl, D.; Snyder, L. E.; Lovas, F. J.; Johnson, D. R. Silicon Monoxide: Detection of Maser Emission from the Second Vibrationally Excited State. Astrophys. J. 1974, 192, L97−L100. (17) Geballe, T. R.; Townes, C. H. Infrared Pumping Processes for SiO Masers. Astrophys. J. 1974, 191, L37−L41. (18) Kwan, J.; Scoville, N. Radiative Trapping and Population Inversions of the SiO Masers. Astrophys. J. 1974, 194, L97−L101. (19) Lovas, F. J.; Maki, A. G.; Olson, W. B. The Infrared Spectrum of SiO near 1240 cm−1 and its Relation to the Circumstellar SiO Maser. J. Mol. Spectrosc. 1981, 87, 449−458. (20) Cernicharo, J.; Bujarrabal, V.; Santarén, J. L. High-excitation SiO Maser Emission in VY Canis Majoris − Detection of the υ = 4 J = 5−4 Transition. Astrophys. J. 1993, 407, L33−L36. (21) González-Alfonso, E.; Alcolea, J.; Cernicharo, J. Detection of 29 SiO υ = 3 J = 8→7 Maser Emission: a New IR SiO Overlap. Astron. Astrophys. 1996, 322, 938−942. (22) González-Alfonso, E.; Cernicharo, J. Explanation of 29SiO, 30SiO and High-υ 28SiO Maser Emission. Astron. Astrophys. 1997, 313, L13− L16.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Present Address #

I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Kö ln, Germany; and Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS H.S.P.M. thanks Peter Bernath for an electronic line list of the data from ref 35. In addition, he is grateful to the Bundesministerium für Bildung und Forschung (BMBF) for financial support through project FKZ 50OF0901 (ICC HIFI Herschel). S.S. thanks Alma Mater Studiorum, University of Bologna for the ‘Fondazione Toso-Montanari’ fellowship through which her stay at Harvard University was supported between February 2009 and January 2010. C.D.E. gratefully acknowledges financial support from MIUR (PRIN 2009 funds, project “Spettroscopia molecolare per la Ricerca Atmosferica e Astrochimica: Esperimento, Teoria ed Applicazioni”) and from the University of Bologna (RFO funds). L.B. thanks the Portuguese Science and Technology Foundation (FCT) for his Fellowships SFRH/BPD/62966/2009. The work in Cambridge 13852



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