Infrared Spectroscopy of Disilicon-Carbide, Si2C: The Î½3 Fundamental

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Infrared Spectroscopy of Disilicon-Carbide, SiC: The # Fundamental Band Daniel Witsch, Volker Lutter, Alexander Breier, Koichi M. T. Yamada, Guido W. Fuchs, Jürgen Gauss, and Thomas F. Giesen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01605 • Publication Date (Web): 22 Apr 2019 Downloaded from http://pubs.acs.org on April 22, 2019

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The Journal of Physical Chemistry

Infrared Spectroscopy of Disilicon-Carbide, Si2 C: The ∗,†

Daniel Witsch,

†

Volker Lutter,

Guido W. Fuchs,

†University

†

Fundamental Band

Alexander A. Breier,

¶

Jürgen Gauss,

†

Koichi M. T. Yamada,

and Thomas F. Giesen

‡

∗,†

of Kassel, Institute of Physics, Heinrich-Plett Str. 40, 34132 Kassel, Germany

‡AIST, ¶Institut

ν3

Tsukuba-West, Onogawa 16-1, Tsukuba 305-8569, Japan

für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany

E-mail: [email protected]; [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The ν3 antisymmetric stretching mode of disilicon-carbide, Si2 C, was studied using a narrow line width infrared quantum cascade laser spectrometer operating at 8.3 µm. The Si2 C molecules were produced in a Nd:YAG laser ablation source from a pure silicon sample with the addition of a few percent methane diluted in a helium buer gas. Subsequent adiabatic expansion was used to cool the gas down to rotational temperatures of a few tens of Kelvin. A total of 183 infrared transitions recorded in the spectral range between 1200 and 1220 cm−1 were assigned to the fundamental ν3 mode of Si2 C. In addition, pure rotational transitions of Ka = 1 and 2 between

278 and 375 GHz were recorded using a supersonic jet spectrometer for sub-millimeter wavelengths. Molecular parameters for the (ν1 ν2 ν3 ) = (001) vibrationally excited state were derived and improved molecular parameters for the vibrational ground-state (000) were obtained from a global t data analysis which includes our new laboratory data as well as millimeter wavelength data from the literature. We found the rotational levels Ka = 0 and Ka = 2 in the vibrationally excited (001) state being perturbed by a Coriolis-type interaction with energetically close lying levels of the symmetric stretching and triple excited bending mode (130). The data analysis was supported by quantum chemical calculations performed at the coupled-cluster level of theory. All experimental results were found to be in excellent agreement with theory.

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Introduction Carbon and silicon are major constituents of interstellar dust grains which to a large extent are formed in the winds of late-type stars. 14 Several small carbon and silicon containing molecules which are related to dust formation were found in the shells around carbon stars. In the prototypical carbon star IRC+10216 silicon-carbides containing only one single silicon atom, e.g., SiC, 5 SiC2 , 6 SiC3 , 7 and SiC4 , 8 were observed by means of their rotational spectra in the millimeter wavelength region, whereas the pure carbon chains C3 9,10 and C5 11 were identied by their ro-vibrational spectra in the mid-infrared region. In 2015 Cernicharo al.

12

et

reported the detection of disilicon carbide, Si2 C, in IRC+10216 after previous labora-

tory investigations by McCarthy and co-workers. 13 In 2018 Cernicharo

et al.

published 30

additional transitions of Si2 C observed with the IRAM 30m telescope towards IRC+10216. Based on these astrophysical detections, the molecular ground-state parameters for Si2 C were rened. 14 In the inner region around carbon-rich late-type stars where the temperatures exceed a few hundreds of Kelvin vibrationally excited molecules, including SiC2 , 15,16 are present. It thus is very likely that the signature of hot Si2 C will be found in the spectra of late-type stars once precise laboratory data are available. Besides its relevance with regard to astrophysics, Si2 C is a classical case study of a bent molecule possessing large amplitude motions with a low barrier to linearity. Only recently its ground-state structure was derived from microwave spectroscopic investigations by McCarthy

et al.

13

and the large experimentally derived inertial defect gave evidence for a shal-

low bending potential surface. McCarthy

et al.

concluded that the molecule is near-prolate

asymmetric top (κ = −0.9902). Spectroscopic studies on Si2 C date back to the 1960s when Weltner

et al.

17

reported optical

spectra of vaporized silicon carbides trapped in rare gas matrices of argon and neon. Later, Kafa

et al.

18

(1983) and Presilla-Márquez

et al.

19

(1991) recorded matrix isolated infrared

spectra of Si2 C and assigned, based on isotopic shift measurements supported by quantum3



Page 4 of 40

chemical calculations, two features at 1188.4 cm−1 and 839.5 cm−1 to the ν3 (b2 ) antisymmetric and ν1 (a1 ) symmetric stretching mode of Si2 C, respectively. The ν2 (a1 ) bending vibration could not be observed directly in these experiments. Nevertheless, using the combination band (ν2 + ν3 ) the low-lying bending vibration was estimated to be at 166.4 cm−1 . 19 In 2015 Steglich

et al.

20

reported the rst gas-phase spectra of Si2 C at UV- and optical wavelength

with Si2C being produced among other silicon-carbon molecules in a laser ablation source and spectroscopically studied by means of resonant two-color two-photon ionization (R2C2PI) spectroscopy between 250 and 710 nm. In the same year Reilly

et al.

21

reported gas-phase

optical spectra of Si2 C near 390 nm and revealed parts of the ro-vibrational structure of the 1

A1 electronic ground-state using uorescence spectroscopy and ab initio ro-vibrational ener-

gies determined from variational calculations. From their experiments the authors derived a barrier to linearity of 783(48) cm−1 and observed a pronounced quantum monodromy eect in the excited levels of the ν2 bending mode. Furthermore, the experimental band center frequencies of ν1 at 830(2) cm−1 and ν2 at 140(2) cm−1 were found in good agreement with quantum-chemically computed values. The ν3 fundamental band could not be observed in these experiments due to symmetry and the selection rules, but the authors concluded from their

ab initio

calculations that 1198 cm−1 should serve as a reliable starting point for high-

resolution infrared studies of the ν3 mode. Similar results were obtained by Changala al.

22

et

based on a curvilinear implementation of second-order vibrational Møller-Plesset per-

turbation theory. In 2017 Koput 23 used a new potential surface to predict ν1 = 832.8 cm−1 ,

ν2 = 140.1 cm−1 and ν3 = 1203.6 cm−1 as the fundamental modes of vibration. Despite all the experimental progress and the availability of results from high-level quantum-chemical calculations none of the fundamental modes of Si2 C have been studied directly by means of gas-phase infrared spectroscopy. Here, we present the rst rotational resolved laboratory spectra on the ν3 antisymmetric stretching mode of Si2 C in the range of 1200 to 1220 cm−1 and provide accurate molecular parameters for future astronomical observations. Our experimental study was guided and supported by high-level quantum-chemical calculations 4


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performed using coupled-cluster methods together with large basis sets.

Production of Disilicon Carbide Laser ablation is an appropriate technique to produce small molecules in the gas phase from samples of refractory elements such as carbon, silicon, or metals. In the past, we have used the laser ablation technique together with graphite samples to produce linear carbon chains, e.g., Cn , with n = 210, and 13, 2428 and silicon-carbide targets were used for gas-phase studies on SiC4 and Si2 C3 . 29,30 Mass spectroscopic investigations of silicon carbide vapor produced + by laser ablation revealed that several small silicon-carbide ions, e.g., SiC+ , SiC+ 2 , Si2 C , + 3133 Si2 C+ although the absolute yields strongly vary with 3 , and Si3 C were quite abundant,

the conditions of production and detection. Instead of using silicon carbide, in the present study a pure silicon sample was ablated and 2 − 5% of methane diluted in a helium buer gas was added to produce Si2 C. For the ablation we operated either a 30 Hz Nd:YAG laser at 1064 nm with output power of the order of 100 mJ or a frequency-tripled 20 Hz Nd:YAG laser at 355 nm and with 33.5 mJ output power. The Nd:YAG laser light was focused onto a solid silicon rod of 10 mm diameter and 5 cm length, which rotates and translates in the throat of the source to provide a pristine sample during the experiment. Fig. 1 shows an optical spectrum of the plasma plume between 400 to 700 nm, which was recorded by an optical spectrometer (HR2000+, Ocean Optics Inc.) of 0.1 nm resolution. We found sharp emission lines from ionized silicon atoms in the optical spectra. From a Planck curve t to the broad background prole we derived a plasma temperature of around 12,000 K, which is in good agreement with results published by Milan

, 34 who found temperatures of

et al.

around 8,000 K in a similar experimental setup. The ablated silicon together with methane diluted in the buer gas reacts in an 8 mm long reaction channel of 1 mm x 12 mm cross section to form molecules composed of silicon and

5



carbon atoms, including the Si2 C molecules. Both ablation lasers (mentioned above) produced comparable yields of Si2 C and the best absorption signals were obtained at backing pressures of 2 bar and 20 bar for submillimeter and infrared measurements, respectively. In both experiments, the background pressure in the vacuum chamber was 0.1 mbar.

Experiment Rotationally resolved infrared gas-phase spectra of Si2 C were recorded using a narrow line width mid-infrared Quantum Cascade Laser (QCL) spectrometer at 8.3 µm. In addition, we used a high-resolution Terahertz spectrometer to measure the purely rotational transitions of the Si2 C ground-state. The molecules, produced from a hot plasma of a pulsed laser ablation source, were subsequently cooled in the adiabatically expanding buer gas of a supersonic jet. The experimental setup of the infrared spectrometer is shown in Fig. 2. The spectral range between 1200 and 1220 cm−1 was covered by two narrow line width (100 kHz) continuouswave distributed feedback quantum cascade lasers (cw DFB-QCLs), with output powers well above 10 mW. The QCL beam intersected the supersonic jet perpendicularly in a Herriotttype multi-path optics adjusted to 38 passes, which was located few millimeters downstream of the exit of the laser ablation source. The laser beam was focussed on a fast liquid nitrogen cooled mercury cadmium tellurid detector (MCT) of 300 kHz response time to record absorption signals. A monochromator in front of the detector served as an infrared band pass lter of roughly 1 cm−1 bandwidth to reduce the noise from the thermal background. For absolute and relative frequency calibration of the recorded signal, parts of the QCL beam were used to simultaneously record a reference gas spectrum and equidistant etalon fringes from an internally coupled Farby-Pérot interferometer (icFPI). 35 We used SO2 and N2 O as reference gases

6


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where the absolute line positions are known to an accuracy of better than 10−4 cm−1 . 3638 The icFPI had a base length of 100 cm corresponding to a free spectral range of FSR = 0.01 cm−1 and a nesse of better than 10. The full width half maximum (FWHM) line widths of the recorded Si2 C transitions were around 2 × 10−3 cm−1 (60 MHz) and the measured line center positions were accurate to better than 10−3 cm−1 . High-resolution absorption spectra of Si2 C were recorded while slowly scanning the QCL frequency at a rate of 10−4 cm−1 per second (3 MHz/s). When the QCL was in resonance with a molecular line an absorption signal of a few tens of microseconds duration was measured by a fast MCT detector. A fast digital oscilloscope with a sample rate of 10 MS/s recorded 100 µs long time resolved detector signals consisting of 1000 individual sample points. To reduce shot-to-shot uctuations 40 single time-resolved signals were averaged before storing the data. Finally two 10 µs long time frames (A and B) of a digital box-car integrator were set on (A) and o (B) resonance with respect to the maximum of the absorption signal to obtain a background substracted integrated signal (A minus B). The integrated signal intensity was then plotted versus the laser frequency to nally obtain the absorption spectrum as shown in Fig. 3. The trigger signals for laser ablation, buer gas, and data recording were controlled by a trigger pulsedelay generator (Quantum Composers 9300 series). In addition to the infrared spectra we recorded selected rotational transitions of the Si2 C ground-state at millimeter wavelengths using the S

SuJeSTA

instrument (Su personic

Je

t

pectrometer for T Hz Application). Briey, in this experimental setup microwave-radiation

was generated by a 2 18 GHz synthesizer (Virginia Diodes, Inc.) which was frequency up-converted to 260 - 380 GHz by an amplier-multiplier chain (AMC). This microwave radiation passed the supersonic jet twelve times in a Herriott-type multi-reection optics and subsequently the absorption signal was detected on a liquid helium cooled hot electron bolometer (QMC Instruments Ltd.). Further experimental details can be found in Breier et al.

24

The microwave experiment encompassing data recording and data processing was

similar to that used in our infrared experiment, except for absolute frequency calibration, 7



which was directly read out at the synthesizer, while the infrared experiment required the recording of a reference spectrum and etalon fringes.

Quantum-Chemical Calculations In support of the experiments, high-level quantum-chemical calculations at the coupledcluster (CC) level 39 were performed to determine the structure and spectroscopic properties of Si2 C. We used the CC singles and doubles (CCSD) approach augmented by a perturbative treatment of triple excitations (CCSD(T)) 40 together with the core polarized correlation consistent quadruple-zeta (cc-pCVQZ) basis set. 41,42 The equilibrium geometry was determined using analytic gradients, 43 the harmonic force-eld was evaluated using analytic second derivative techniques, 44 and anharmonic corrections were calculated using secondorder vibrational perturbation theory (VPT2) 45 based on quantum-chemically determined cubic and semi-diagonal quartic force elds. 46 These calculations provided the fundamental frequencies of Si2 C as well as hot band and combination band frequencies together with the corresponding transition intensities. Furthermore, vibration-rotation interaction constants

αiX , zero-point vibrational corrections to rotational constants, as well as Coriolis coupling X constants ζrq were obtained from these computations. For this work it was of particular

relevance that the computed vibration-rotation interaction constants provided theoretical estimates for the rotational constants in vibrationally excited states. To further improve the theoretical predictions, theoretical best estimates for the structure and the equilibrium rotational constants were determined via a composite approach 47,48 denoted as fc − CCSD(T)/cc − pV∞Z+ ∆T/ccpVTZ +∆Q/cc − pVDZ +∆core/cc− pCV5Z. It comprised a frozen-core CCSD(T) contribution extrapolated to the basis-set limit 49,50 augmented by corrections for a full CC singles, doubles, triples (CCSDT) treatment 51 (using the cc-pVTZ basis 52,53 ), as well as for the eect of quadruple excitations at the CC

8


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singles, doubles, triples, quadruples (CCSDTQ) level 54 (using the cc-pVDZ basis 52,53 ), and for core-correlation eects treated at the CCSD(T) level using the cc-pCV5Z basis. 41,42 A detailed description of the composite approach in connection to the computation of geometries can be found in Heckert

et al.

47,48

All calculations were performed with the CFOUR

quantum-chemical program package. 55 Equilibrium rotational constants, geometrical structure parameters and Coriolis coupling terms are given in Tab. 1, the calculated fundamental vibrational frequencies, band intensities, and vibration-rotation interaction constants are listed in Tab. 2.

Observed Spectra and Analysis In the present study, we have identied 183 a-type ro-vibrational transitions (∆Ka = 0) of the ν3 fundamental band in the specral range form 1200 and 1220 cm−1 and 14 b-type pure rotational transitions (∆Ka = ±1) in the frequency range from 278 to 375 GHz. Molecular parameters for the ground- and the ν3 excited state were derived from a global t data analysis, which includes our infrared and mm-wavelength data as well as ground-state data reported in the literature. 1214 The assignments of infrared transitions were guided by our high level quantum-chemical calculations. The measured line positions are listed in Tab. S1 of "Supporting Information". As shown in Fig. 3, the infrared spectrum measured in the present study covers strong R-branch transitions, two Q-branches, and a few P-branch transitions. The stick diagram in Fig. 3 of the ν3 (b2 ) band is based on molecular constants derived from a least-squares t data analysis. Comparisions of measured and tted spectra of Si2 C are shown as insets in Fig. 3. In the cold environment of the expanding jet only the lowest Ka levels are populated. Accordingly, we only observed transitions of Ka levels not higher than Ka0 = 4, but due to a less ecient cooling of the high J rotational levels we were able to measure transitions up to

J 0 = 48. The population of rotational levels in a Boltzmann plot clearly shows a non-thermal

9



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distribution with temperatures of 20 K for low J levels and temperatures well above 120 K for high J levels as shown in Fig. 4. Furthermore, we nd the transitions with Ka0 = 0 near

J 0 = 27 and Ka0 = 2 near J 0 = 12 strongly perturbed by a Coriolis-type interaction with the close lying (130) vibrational state. In addition to the infrared spectra we recorded ground-state rotational transitions of Si2 C around 300 GHz using the SuJeSTA instrument. We measured two transitions with Ka0 = 2 and 12 lines with Ka0 = 3 to further improve the molecular ground-state constants. A stick spectrum of the rotational ground-state transitions of Si2 C is shown in Fig. 5. Lines in yellow indicate the transitions of the r Q0 and r Q1 branches reported by McCarthy et al., 13 while red lines of r Q1 and r Q2 were measured in this work (see Tab. A2 of "Supplemental Material"). Finally, the blue colored lines are from astronomical observations reported by Cernicharo al.

12,14

et

In order to check the dierent data sets for consistency and to calibrate these data

to absolute frequencies given from laboratory data we measured three of the astronomically detected transitions with high accuracy in our laboratory.

The infrared and millimeter wavelength data were tted to a Watson-type Hamiltonian in S-reduction using the PGOPHER program by C. Western. 56 The global t of the groundand vibrationally excited state parameters encompasses the 14 here presented millimeterwavelength transitions and the 149 rotational lines reported by Cernicharo include the 22 lines measured in the laboratory by McCarthy

, 14 which

et al.

. In addition to these

et al.

163 rotational lines of microwave accuracy (≤ 100 kHz for laboratory data and ≤ 1 MHz for astronomical observations) we added 183 weighted infrared ro-vibrational transitions with uncertainties better then 30 MHz (10−3 cm−1 ) to derive molecular parameters for the groundand vibrationally excited ν3 state (see Tab. 3). The weighted standard deviation of the t is 0.972σ (the obs-calc standard deviation is better than 17 MHz). A Coriolis-type interaction (c-type) is introduced in the analysis of the vibrationally excited state by adding o-diagonal terms to the Hamiltonian, thereby coupling the energy levels of 10


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the (001) and (130) state. The perturbation is expressed by (1)

H 0 = ξJc ,

where ξ is the eective interaction constants. The corresponding transitions involving the (130) vibrationally excited state are too weak to be observed in our spectra. The analysis is backed up by quantum-chemical calculations of the (130) level (see Tab. 4) performed by Koput according to Reference. 23

Results The experimentally derived molecular parameters of the vibrational ground and ν3 excited state are listed in Tab. 3. We nd the band center at 1202.208286(98) cm−1 to be in very good agreement with our best value of 1206.6 cm−1 obtained from quantum-chemical calculations. The only other experimental values to compare with are those from rare gas matrix measurements. A strong infrared peak at 1188.4 cm−1 found in the IR spectrum of argon matrix isolated silicon carbide vapor was reported by Presilla-Márquez

, 19 and

et al.

a vibrational mode at 1205 cm−1 derived from the optical spectra of neon matrix isolated silicon-carbide vapor by Weltner

et al.

was tentatively assigned to Si2 C. 17 The rotational

ground-state constant A0 agrees within 1 % with our calculated value and B0 , and C0 within 3 %. Higher-order centrifugal distortion parameters up to sextic terms could be determined from the available experimental data. Quartic centrifugal distortion parameters agree within a factor of 1 21 with the corresponding values from our quantum-chemical calculations. Furthermore, we nd our results for the ground-state constants in to be excellent agreement with the values reported by McCarthy et al. (2015) 13 and Cernicharo et al. (2018), 14 respectively. For the v3 = 1 vibrationally excited state all constants up to the quartic centrifugal distortion constants as well as HK , HJK , HJ and h2 were determined. Our quantum-chemically computed rotational constants as well as recently calculated values reported by Changala 22 11



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and Koput 23 are found to be in good agreement with experimental values. From the analysis of the Coriolis-type interaction between the states (001) and (130) we obtain values for the band center ν130 = 1166.892(11) cm−1 and for the average of the two rotational constants B and C in the vibrational excited state state (130): B = (B + C)/2 =

3923.31(78) MHz. Both values agree with theory within 0.5 % and 2 % respectively. The interaction strength is found to be ξ = 0.01289(12) cm−1 . Due to the limited dataset A and

δ = B − C could not be determined and were xed to the corresponding theoretical values. As shown in Fig. 6, the energy levels with Ka = 3 in the (130) state cross energy the levels of the singly excited (001) state with Ka = 0 near J = 27 and those with Ka = 2 near J = 12. Tab. 2 reports the calculated frequencies and band intensities of the three fundamental modes as obtained at the CCSD(T)/cc-pCVQZ level of theory. We nd the ν3 antisymmetric stretching mode to be strongest, which is in agreement with experimental and computational results reported in the literature. The experimental band centers for the ν1 and ν2 symmetric stretching and bending mode reported by Reilly et al. 21 are in agreement with our calculations. Furthermore, Tab. 2 gives the calculated and experimental rotation-vibration shifts ∆Xi = Xi0 − Xi1 , where Xi0 and Xi1 are the rotational constants (X = A, B, C) of the vibrational ground-state and the rst vibrationally excited states vi = 0, 1 for each vibrational mode i = 1, 2, 3. While the ∆X3 values derived from our experiments agree with our calculated values within 10 %, ∆X1 and ∆X2 deviate somewhat from experimental values calculated from rotational constants reported by McCarthy

et al.

57

Particularly, the ∆A1

and ∆A2 values are o by more than 50 % and 40 %, respectively, and thus, further accurate experimental values are in demand. In a simple approximation without considering the oppy nature of the molecule, semiexperimental equilibrium rotational constants are calculated using the ∆X3 from the analysis of our experimental data and the ∆Xi with i = 1, 2 from our theoretical result. Based on these constants, the equilibrium structure is determined using the STRFIT program 58 by Kisiel. As given in Tab. 1, we obtain an equilibrium bond length re of 1.6917(8) Å, which 12


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agrees very with our theoretical value of 1.69248 Å and with results from the literature 13 of

1.69272(2) Å. The apex angle of θ = 115.03(10)◦ is slightly higher than the corresponding values from our calculations and the literature 13 (114.709 ◦ and 114.8741(3) ◦ , respectively). For more accurate results, experimental data for ∆Xi with i = 1, 2 are in need.

Discussion The vibrational energy levels G(v1 v2 v3 ) of a three-atomic non-linear molecule are approximately given by:

X 1 1 1 + χij vi + , vj + G(v1 v2 v3 ) = ωi vi + 2 2 2 i=1,2,3 i≥j {z } | | {z } X

harmonic contribution

(2)

=AC, anharmonic contribution

with vi as the quantum numbers of the normal vibrational modes, ωi the harmonic frequencies, and χij the anharmonic coupling terms of the vibrational modes (e.g., see Bernath 59 ). The three harmonic frequencies and six anharmonic coupling terms can be derived from a set of nine vbrational energy levels. In our analysis we use eight of the energy levels derived from LIF/REMPI spectra published by Reilly et

al.

21

with experimental uncertainties of ±2 cm−1

and the very accurate value for the antisymmetric stretching mode (v1 v2 v3 ) = (001) from our measurements. To minimize anharmonic frequency shifts, which are present in excited levels, we choose the nine lowest available energy levels: G(v1 v2 v3 ) = (100), (010), (001), (200), (020), (002), (110), (012), (112). The values given by Reilly

et al.

refer to energy

levels with Ka = 1. For consistency reasons we choose the Ka = 1 level of the (001) level at 1204.358(3) cm−1 from our measurements and solve the nine coupled energy equations of Eq. 2. The three harmonic frequencies ωi and six anharmonic coupling constants χij derived for Ka = 1 are listed in Tab. 5. The harmonic frequencies ωi for Ka = 0 are calculated from the experimental frequencies νi via ωi = νi − ACi , where ACi are the experimentally derived anharmonic correction terms for the ith vibrational mode. Note that the ACi values 13



Page 14 of 40

are derived for Ka = 1 levels, but in good approximation we assume those for Ka = 0 to be the same. Measured band center frequencies for ν1 and ν2 and Ka = 0 are taken from Reilly et al.

and the value for ν3 are from the present study (see Tab. 6).

The derived harmonic and anharmonic parameters, ωi and ACi from Eq. 2 reproduce the observed values from Reilly et

al.

21

within the error limits (±2 cm−1 ). For the antisymmetric

ν3 stretching mode we obtain the harmonic band center frequency of 1222.7(17) cm−1 and an anharmonic correction of -20.5(17) cm−1 . Both values agree very well with our calculated values of ω3 = 1222.5 cm−1 and AC3 = −15.9 cm−1 . However, the anharmonic AC3 term is slightly underestimated by theory in comparison to what we obtain in our analyis of the experimental data. In addition, we derive the harmonic frequencies ω1 = 850.8(59) cm−1 and ω2 = 150.0(64) cm−1 from Eq. 2 in accordance with the calculations. The anharmonic corrections AC1 and AC2 for ν1 and ν2 are found to be in good agreement with theory as well, although the error bars of the experimentally derived AC values are large. Furthermore, we obtain an experimental value for the zero-point energy of Si2 C of 1105.0(44) cm−1 using Eq. 2. Finally, the total and vibrational inertial defects of ground and excited (001) state were derived. From the Av , Bv , Cv rotational constants we obtain the ground-state and vibrationally 2

2

excited total inertial defect ∆0 = Ic0 −Ib0 −Ia0 = 0.335774(21) uÅ and ∆1 = 0.26150(84) uÅ . The inertial defect has contributions from vibrational and electronic motions, and centrifugal distortion ( ∆ = ∆vib + ∆elec + ∆cent ). Neglecting the electronic and centrifugal contributions which are usually small, the inertial defect for a planar XY2 molecule of C2v symmetry in vibrational state n can be written as (e.g., see 60 )

∆nvib

2 −ωj2 1 X h X vi + ζijc = 2 2 2 π c i 2 j6=i ωi (ωi − ωj )

(3)

c where ωi , ωj are the harmonic frequencies coupled by the Coriolis constants ζijc = −ζji to

14


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the out-of-plane axis c. For symmetry reasons the rotation along the c(b2 ) axis couples c the symmetric modes ν1 (a1 ) and ν2 (a1 ) to the antisymmetric ν3 (b2 ) stretching mode via ζ13 c , whereas the coupling of the two symmetric modes is symmetry forbidden and thus and ζ23 c c ζ12 = ζ21 = 0 (e.g., see Papousek & Aliev 60 ). We use the experimental harmonic frequencies c c given in Tab. 6 to derive values for ζ13 = 0.676892(12) and ζ23 = −0.736082(11) according

to Eq. 9 of Laurie and Herschbach, 61 thereby making use of the condition c 2 c 2 (ζ13 ) + (ζ23 ) = 1.

(4)

Both values are in very good agreement with results from our quantum-chemical calcuc c = −0.756 (see Tab. 1). With the Coriolis terms derived from = 0.655 and ζ23 lations, ζ13

experiment we obtain for the vibrational inertial defects in the ground and ν3 rst excited 2

2

vibrational state ∆0vib = 0.294(11) uÅ and ∆1vib = 0.245(11) uÅ which are slightly smaller 2

2

than the inertial defects ∆0 = 0.335774(21) uÅ and ∆1 = 0.26150(84) uÅ derived from the measured rotational constants. Our results show that the inertial defect of the excited vibrational state is mainly caused by the harmonic vibrational motion and that dierences between ∆0 and ∆1 found for the ground-state values provide evidence for the oppiness of Si2 C.

Conclusion In this study we present the rst high-resolution infrared measurements of the ν3 antisymmetric stretching mode of Si2 C guided and supported by corresponding high-level quantumchemical calculations. Theory and experiment are in excellent agreement. In addition, selected pure rotational transitions have been measured. Based on a global t including results from the present work as well as data from the literature, 1214 molecular parameters for the vibrational ground- and excited state have been derived. This investigation is a 15



further step toward a comprehensive picture of the three-atomic silicon-carbide family. For better understanding, future laboratory investigations are in need, e.g., the frequency of the

ν1 symmetric mode of Si2 C is accessible by QCLs. Furthermore, a vibrational study of other related species such as, for example, Si3 might be warranted. The present study provides line positions of sucient accuracy in order to guide future astronomical observation of Si2 C, e.g., towards IRC+10216 where ground-state transitions of Si2 C have been already observed. 12,14 The EXES instrument 62 aboard SOFIA aircraft and the TEXES instrument 63 at the Gemini North observatory are well suited for this kind of investigations. At lower frequencies the IRAM 30m telescope might be used to search for rotational transitions within the vibrationally excited state of Si2 C. Furthermore, by using telescopes with high spatial resolution, e.g., ALMA, it might be possible to investigate the formation process of silicon carbides around IRC+10216.

Supporting Information Supplementary material containing linelists of our IR (table S1) and THz measurements (table S2). Tables include quantum numbers, lower level energies, observed and calculated frequencies for all transitions measured in this work.

Acknowledgement Prof. Jacek Koput from the Adam Mickiewicz University in Pozna« is acknowledged for sending unpublished results concerning the vibrationally excited states of Si2 C. The authors are grateful to Doris Herberth and Björn Waÿmuth from the University of Kassel for their assistance. Finally, the authors thank the DFG for funding via grants GI 319/5-1, GA 370/6-1, GA 370/6-2, and FU 715/2-1.

16


Page 16 of 40

Page 17 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: Semi-experimental and calculated equilibrium rotational constants, structure parameters and Coriolis coupling terms of Si2 C

Ae [MHz] Be [MHz] Ce [MHz] θ [◦ ] re [Å] 2 ∆e [ uÅ ] ζ13 ζ23 a

semi-experimental 62 119.6(11) 4435.743(11) 4137.9225(89) 115.03(10) 1.6917(8) 0.064 60(42) 0.676 892(12) −0.736 082(11)

Semi-experimental results from McCarthy

theory 61 361.1 4447.3 4146.7 114.709 1.692 48 0.0037 0.655 −0.756 et al.

17

13


other worka 61 627.30 4438.01 4139.70 114.871(3) 1.692 72(2) 0.0053


Page 18 of 40

Table 2: Si2 C fundamental frequencies, band intensities and the rotationvibration shifts ∆Xi = Xi0 − Xi1 (X = A, B, C and i = 1, 2, 3)

Vibrational mode νi ν1 (a1 ) (symmetric)

ν2 (a1 ) (bending)

Frequency [cm−1 ] 838.0a 830(2)d 839.5e

Intensity [km/mol] 17.7a

142.7a 140(2)d

ν3 (b2 ) 1206.6a (antisymmetric) 1202.208286(98)f 1205b 1188.4e

∆Ai [MHz] -2904.7a -4584.373(12)c

∆Bi [MHz] 87.4a 103.9353(13)c

∆Ci [MHz] 49.9a 79.308(3)c

1.0a

-5082.0a -7155.77(3)c

63.6a 72.221(4)c

67.3a 56.346(2)c

211.0a

3737.8a 4077.2(23)f 4082.19(5)c

-68.1a -70.517(23)f -70.505(7)c

-43.9a -45.575(18)f -45.768(8)c

Experimental uncertainties are given in parentheses. a CCSD(T)/cc-pCVQZ calculations (this work) b Vibrational frequencies from neon matrix isolated Si2 C by Weltner et al. 17 c Experimental values calculated from rotational constants reported by McCarthy et al. 57 (table 4 and table 7) d LIF/REMPI spectroscopy of Si2 C electronic ground-state published by Reilly et al. 21 e Vibrational frequencies from argon matrix isolated Si2 C by Presilla-Márquez et al. 19 f Experimental results (this work)

18


Page 19 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3: Ground-state and ν3 vibrationally excited state molecular parameters of Si2 C in S-reduction

ν3 [cm−1 ] A B C DK DJK · 10 DJ · 103 d1 · 103 d2 · 105 HK · 102 HKJ · 103 HJK · 105 HJ · 108 h1 · 109 h2 · 109 2 ∆[ uÅ ]a 2 ∆vib [ uÅ ]b

ground-state (000) experimental theory 64 074.3252(72) 63 485.6 4395.517 07(59) 4405.9 4102.129 48(96) 4110.0 23.5848(20) 15.93 −8.569 09(54) −6.86 9.6648(22) 9.04 −1.527 66(31) −1.43 −3.186(20) −2.33 4.891(17) −1.9235(45) 1.9692(39) −3.63(13) −4.00(20) −1.50(18) 0.335 774(21) 0.298 0.294(11) 0.295

excited state (001) experimental theory 1202.208 286(98) 1206.6 59 997.3(23) 59 747.8 4466.034(23) 4474.0 4147.706(18) 4153.9 16.84(37) −6.706(13) 9.174(12) −1.4912(75) −1.26(52) 5.0(15)

1.026(82) −4.44(39) −26.0(30) 0.261 50(84) 0.245(11)

0.246 0.246

Unless otherwise stated, all values are given in MHz. Values in parentheses are 1σ uncertainties from the data analysis. a ∆ = Ic − Ia − Ib b ∆vib derived from Eq. 3 using experimental Coriolis coupling constants from Tab. 1 Table 4: Molecular parameters of the (130) excited state of Si2 C in S-reduction

ν130 [cm−1 ] A∗ [MHz] b B [MHz] δ c,∗ [MHz] ξ d [cm−1 ]

excited state (130) experimental theorya 1166.892(11) 1172.4 ... 152 278.7 3923.31(78) 3849.4 ... 194.9 0.012 89(12)

Values in parentheses are 1σ uncertainties from the data analysis. ∗ A and δ in the (130) state can not be determined and have been xed to theoretical values. a calculated by Koput according to Reference 23 b B = (B + C)/2 c δ =B−C d dimensioned Coriolis parameter 19



Page 20 of 40

Table 5: Si2 C experimentally derived vibrational coupling constants χi,j and harmonic frequencies ωi for Ka = 1 energy levels

χi,j 1 2 3

1 -8.0(25)

2 -15.0(35) -3.0(25)

3 5.5(20) 7.0(18) -13.4(10)

ωiKa =1 852.8(74) 152.0(80) 1224.8(17)

All values are given in cm−1 . Energy levels (v1 v2 v3 ) = (100), (010), (200), (020), (002), (110), (012), (112) taken from 21 and (001)= 1204.358(3) cm−1 from our measurements.

Table 6: Measured fundamental frequencies νi , derived harmonic frequencies ωi (for Ka = 0), and derived anharmonic corrections ACi

i 1 2 3

νi exp. 830.0(20)c 140.0(20)c 1202.208286(98)

ωi

exp. 850.8(59) 150.0(64) 1222.7(17) a

theory 855.2 150.5 1222.5 b

ACi

exp. -20.8(55) -10.0(61) -20.5(17) a

theoryb -17.2 -7.8 -15.9

All values are given in cm−1 . a derived from χij in Tab. 5 and νi b CCSD(T)/cc-pCVQZ calculations (this work) c LIF/REMPI spectroscopy of Si2 C (Ka = 0) electronic ground-state published by Reilly al.

21

20


et

Page 21 of 40

WavelengthF[nm] Y::

A::

G::

4::

5::

6::

T≈YA:::FK

7::

8::

ObservedFSpect rum Background Planck)Fit Ft oFbackground

Si5II6

IntensityF[arbVuV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Si5III6

Si5IV6 Si5II6 Si5I6

Si5II6

cap Si5II6

plasma sample

Si5III6

Si5II6

rotation AG :Y m Nd 55n reactionF FG channel

translatio

n

Figure 1: Observed optical spectrum of a silicon plasma with sketch of the laser ablation source indicating the region of radiation. The plasma emission spectrum is calibrated between 400-700 nm. The underlying background spectrum is tted to a Planck curve corresponding to a temperature of around 12,000 K. The discrete emission lines indicate the presence of neutral (Si(I)) as well as ionized silicon atoms, such as Si(II) and Si(III).

Figure 2: The QCL based high-resolution mid-IR absorption spectrometer and supersonic jet laser ablation source.

21


Intensity [arb.u.]

1209.6

1209.7

R1(22)

1209.5

R1(23)

1209.4

R0(22)

R2(23)

R2(22)

Intensity [arb.u.]

Intensity [arb.u.]

1201.72

R3(23)

R4(27)

R3(24)

Q2(5)

1201.66

Q2(6)

1201.60

Page 22 of 40

Frequency [cm−1 ]

1209.8

Frequency [cm−1 ]

ν3 band origin

Simulated spectrum of Si2C at 30 K

1196

1201.54

Q2(2)

1201.48

Q2(4) Q2(3)

1201.0

Frequency [cm−1 ]

1194

P0(2)

1200.9

R5(8)

1200.8

*

P1(2)

1200.7

*

P1(4)

1200.6

R4(4)

P2(3)

P1(5)

1200.5

P2(4) P0(6)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Intensity [arb.u.]


1198

1200

1202

Frequency [cm−1 ]

1204

1206

1208

1210

Figure 3: Stick spectrum of the ν3 vibrational band of Si2 C. Line positions are calculated from parameters given in Tab. 3. The spectrum is simulated for a typical jet temperature of 30 K. Lines in red are all measured, lines in black are outside the accessible range of the used QCL or weakly populated and are only calculated. The band origin is found at 1202.20868(9) cm−1 . The insets show examples of recorded P -, Q- and R-branch spectra (upper trace) as well as simulated spectra based on derived molecular parameters (lower trace). The measured spectra are scaled to arbitrary units and assigned transitions are labeled by quantum numbers ∆JKa00 (J 00 ). Transitions marked with an asterisk are not thermally populated in the supersonic cooled jet and thus were not observed.

22


Page 23 of 40

rel. Population Nlow N

10

Data Exponential Fit

-4

/

A e-Bx+C+Dx T=

10

127.9

K

-5

T= 20. 6K

0

50

100

150

200

250

300

Energy Elow k B [K] /

Figure 4: Boltzmann-Plot of the ro-vibrational transitions of the ν3 antisymmetric stretching mode. For the supersonic jet expansion no thermodynamical equilibrium temperature can be assumed. Instead an exponential t for the level population is plotted (solid line). For energetically low lying transitions an equivalent equilibrium temperature of 20.6 K can be assumed (dashed lines) and for high lying transitions an equilibrium temperature of 127.9 K is plotted (dotted lines).

Q2(7)

Simulated rotational spectrum of Si 2 C at 30 K transitions: observed in space observed by McCarthy et. al. (lab) observed in our lab

Intensity [arb.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

50

100

150

200

250

300

350

400

Frequency [GHz]

Figure 5: Stick spectrum of ground-state rotational lines of Si2 C for a typical jet temperature of 30 K. The spectrum is based on parameters from Tab. 3. Transitions measured previously in the lab 13 and from astrophysical observations 12,14 are colored in yellow and blue. Our new measurements are marked in red. The inlay displays the line prole of the ∆JKa00 (J 00 ) = Q2 (7) transition as one example of our measurements.

23



J even J odd

1214

1212 Energy E − BJ(J + 1) / cm −1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 40

State (001) State (130)

Ka=3

1210

Ka=2 1208

1206

1204

1202

Ka=0

1200 5

10

15 20 Quantumnumber J

25

30

Figure 6: Crossing of energy levels for the vibrational state (130) Ka = 3 in black and the vibrational state (001) Ka = 0, 2 in red. Energy levels with even (odd) J are marked by squares (circles). The term BJ(J + 1) has been substracted from the energies using B = (B001 + C001 )/2. Levels with Ka = 1 of the (001) vibrational state are not shown, since they are not aected by the pertubation due to symmetry reasons.

24


Page 25 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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32


Page 32 of 40

Page 33 of 40

Measured ν3 vibrational band

Intensity [arb.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


band origin

1202

1204

1206

Frequency [cm −1 ]

Figure 7: TOC Graphic

33


WavelengthF[nm ] The Journal of Physical Chemistry Y::

IntensityF[arbVuV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

A::

G::

4::

Page 34 of 40

5::

6::

ObservedFSpect rum Background Planck)Fit Ft oFbackground

Si5II6 T≈YA:::FK

7::

Si5III6

Si5IV6 Si5II6 Si5I6

Si5II6

cap Si5II6

plasma sample

rotation AG Y : m Nd 55n reactionF FG channel

translat

ion


Si5III6

Si5II6

8::

Page 35 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27



Intensity [arb.u.]

1209.6

Intensity [arb.u.]

Intensity [arb.u.]

Frequency [cm

1209.7 −1

R1(22)

]

1209.5

R1(23)

1209.4

R0(22)

R2(23)

R2(22)

1201.72

R3(23)

R4(27)

R3(24)

1201.66 −1

Q2(6)

1196

1201.60

Frequency [cm

]

1209.8

]

ν3 band origin

Simulated spectrum of Si2C at 30 K

1194

1201.54

Q2(5)

1201.48

Q2(4) Q2(3)

1201.0

Q2(2)

1200.9

P0(2)

Frequency [cm

−1

R5(8)

1200.8

Page 36 of 40

*

P1(2)

1200.7

*

P1(4)

1200.6

R4(4)

P2(3)

P1(5)

1200.5

P2(4) P0(6)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Intensity [arb.u.]


1198

1200


1202

Frequency [cm−1 ]

1204

1206

1208

1210

Page 37 of 40

/

rel. Population Nlow N

10

Data Exponential Fit

-4

A e-Bx+C+Dx T=

10

127.

9K

-5

T= 20. 6K

0

50

100

150


200

Energy Elow k B [K] /

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30


250

300


Simulated rotational spectrum of Si 2 C at 30 K transitions: observed in space observed by McCarthy et. al. (lab) observed in our lab

Intensity [arb.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Page 38 of 40

Q2(7)

0

50

100

150


200

250

Frequency [GHz]

300

350

400

Page 39 of 40

Energy E − BJ(J + 1) / cm −1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


J even J odd

1214

1212

State (001) State (130)

Ka=3

1210

Ka=2 1208

1206

1204

1202

Ka=0

1200 5

10

ACS Paragon 15 Plus Environment 20

Quantumnumber J

25

30

Intensity [arb.u.]

Measured ν3 vibrational band

The Journal of Physical Chemistry Page 40 of 40 band origin

1 2 3 4 5 6

ACS Paragon Plus Environment 1202

1204

Frequency [cm −1 ]

1206

Infrared Spectroscopy of Disilicon-Carbide, Si2C: The Î½3 Fundamental

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