The high-resolution infrared spectrum of the m 3 þ m 5 combination band of jet-cooled propyne

We present the ﬁrst detection of the high-resolution ro-vibrational spectrum of the m 3 þ m 5 combination band of propyne around 3070 cm (cid:2) 1 . The fully resolved spectrum is recorded for supersonically jet-cooled propyne using continuous wave cavity ring-down spectroscopy (cw-CRDS). The assignments are sup- ported with the help of accurate ab initio vibration-rotation interaction constants ( a i ) and anharmonic frequencies. A detailed analysis of the rotationally cold spectrum is given. (cid:1)


Introduction
Propyne, also known as methylacetylene (H 3 CAC"CH), is a small unsaturated hydrocarbon of astrophysical importance. It is believed to play a role in the chemistry of a number of hydrocarbon-rich astronomical objects, including the atmosphere of Titan [1], the dark cloud TMC-1 [2], the circumstellar shell of the AGB star IRC+10216 [3], and two protoplanetary nebulae CRL 618 [4] and SMP LMC 11 [5], where it has been observed in the infrared (IR) through the m 9 (HAC"C bending) mode, and by radio astronomy through pure rotational transitions. In addition, the close spacing of the rotational transitions of different K 0 subbands, and the relatively low dipole moment (l = 0.78 D) [6] make propyne an ideal probe of the interstellar medium's kinetic temperature; since the excitation temperature increases as K 0 increases [7][8][9].
From a pure spectroscopic point of view this molecule is also interesting. As a prolate symmetric top the aliphatic (CH 3 ) and acetylenic (CH) stretches are suitably decoupled from each other that the strong acetylenic CH stretch mode (m 1 ) is not strongly per-turbed [10]. Studies of spectra that are perturbed through weak near-resonant couplings to background vibrational states, as seen in other transitions of propyne, make it of interest for studying intramolecular vibrational relaxation (IVR) [11][12][13]10,[14][15][16][17]. Moreover, comparison between high-resolution measurements as presented here for propyne and ab initio methods offers a good test of the accuracy of the Hamiltonians used to describe the involved molecular energy levels.
Propyne has been extensively studied in the electronic ground state (X 1 A 1 ) through a number of microwave and IR experimental studies and ab initio calculations (Ref. [18], and references therein). In fact, all of the fundamental bands and a substantial number of combination bands involving either m 3 (C"C stretch) or m 5 (CAC stretch) excitations have been studied at high-resolution [19-23, 10,14,16,24,9,18,25,26]. The spectroscopic identification of the m 3 þ m 5 combination band has not yet been reported. Based on the published band origins for m 3 [20] and m 5 [25], the m 3 þ m 5 combination band is expected at $ 3068 cm À1 .
The results of a survey around this wavelength are presented here. The experimental and theoretical details are given in Section 2. The spectroscopic analysis and discussion are presented in Section 3. Line positions are available from the supplementary material.
used to create a high pressure jet expansion, increasing the local number density of propyne molecules at the nozzle slit.
The absorption spectrum is recorded using cw-CRDS, with the IR laser path intersecting the expansion roughly 1 cm downstream from the nozzle body. The optical cavity is comprised of two highly reflective plano-concave mirrors (R $ 99.98%, centered at 3300 cm À1 ). Typical empty cavity ring-down times (s 0 ) are about 9 ls. The hardware (boxcar integrator) based multi-trigger and timing scheme described in detail in Ref. [27] is used to coincide the laser light and gas pulse. This guarantees that the trigger scheme compensates for the low duty cycle when combining a cw laser with a pulsed gas expansion. For this experiment the optical cavity length is modulated at $ 26 Hz, using a piezo crystal mounted on the back of one of the cavity mirrors.
The resulting spectrum is recorded in a series of $1.2 cm À1 parts that partially overlap to guarantee that spectra can be directly compared. While the spectrum is recorded, the laser fre-quency is simultaneously measured using a wavelength meter (Bristol Instruments, 621A-IR). The frequency accuracy is independently calibrated by measuring known transitions of ethylene (C 2 H 4 ) [29]. The resulting maximum frequency uncertainty of AE0.002 cm À1 is dictated by the wavemeter.

Theoretical
Equilibrium geometry and second-order vibrational perturbation theory (VPT2) calculations are carried out at the CCSD(T) level of theory. The core-valence correlation-consistent quadruple-f basis set (cc-pCVQZ) [30] is used to determine the equilibrium geometry and rotational constants, since it has been shown to give highly accurate geometries for acetylenic molecules [31,32]. The atomic natural orbital (ANO) basis set with the truncation [4s3p2d1f] for non-hydrogen atoms and [4s2p1d] for hydrogen (hereafter known as ANO1) [33] is used to determine the anharmonic vibrational frequencies and electronic ground state spectroscopic constants of propyne. It has been shown to reproduce experimental frequencies better than the correlation-consistent basis sets [34,32]. All calculations are performed with the development version of the CFOUR program [35].

Results and discussion
An overview of the experimental spectrum is shown in the upper trace of Fig. 1(a). It shows a regular pattern with excellent signal-to-noise spreading over 15 cm À1 . A parallel band consistent with a C 3v symmetric top molecule A 1 -A 1 transition is clearly seen with a Q-branch at $3070.1 cm À1 , very close to the predicted v 3 + v 5 frequency of 3068 cm À1 . The experimental spectrum is analyzed using the PGOPHER software [36], assuming a rotational temperature of 18 K and a Gaussian linewidth of 0.004 cm À1 . The latter is determined by minimal residual Doppler broadening in the slit nozzle expansion. A first fit of the strongest transitions gives lower state rotational constants in good agreement with those already known for propyne. For a more accurate rotational analysis the lower state constants are fixed to the ground state parameters reported by Pracna et al. [25]. The rotational constants for the upper state are calculated by the standard relation for a prolate symmetric top molecule: where D J , D JK , and D K are the centrifugal distortion constants, f is the coriolis coupling constant (in this case f = 0), l is the quantum number related to the projection of the total vibrational angular momentum on the symmetry axis, and A and B are the rotational constants, which can be given as: where a i is the vibration-rotation interaction constant.
The rotational analysis starts from a least-squares fit, which gives excited state parameters that reproduce the overall pattern with reasonable accuracy. However, many of the K 0 = 1 and 2 transitions show large deviations between the observed and calculated frequencies, suggestive of perturbations. As such, the K 0 subbands were fit separately, based on the method described by Zhao et al. [26]; this is shown in Fig. 1b. The resulting effective spectroscopic parameters, and the parameters of the m 3 [20] and m 5 [25] states are summarized in Table 1. From a least-squares fit of the K 0 = 0 subband the band origin is determined to be 3070.1411(4) cm À1 (which we fix for the K 0 > 0 subbands), and B 0 = 0.282428(8) cm À1 . In addition to transitions to the main state, transitions to three perturbing states are identified in the experimental spectrum, and the spectroscopic parameters of those bands are summarized in Table 2. The o-c (obs.-calc.) values of all the assigned transitions are listed in the Supplementary Material. The summed spectrum of all the individual simulated subbands, including transitions to perturbing states, is given in the lower trace of (a) in Fig. 1, and a zoom-in of the Q-branch is given in Fig. 2. This shows that the measured and simulated spectra are in excellent agreement. As in the jet-cooled propyne study described previously by Zhao et al. [26], only one rotational temperature of 18 ± 2 K, and a 1:1 E: (A 1 , A 2 ) statistical weights is needed to reproduce the overall observed intensity pattern.
The 3000 cm À1 region of the propyne spectrum is expected to have a high density of states, many of which originate from highorder combination states. As such, the assignment of the experimental data is supported by ab initio calculations. The CCSD(T)/ ANO1 VPT2 calculations of propyne are able to predict the Table 1 Spectroscopic parameters of the vibrational levels m3; m5, and m3 þ m5 state a (in cm À1 ).   Table 2 Effective spectroscopic parameters of the perturbing states a (in cm À1 ).  anharmonic frequencies and intensities of fundamental and combination states; this applies even to states with ten or more quanta of excitation. However, states involving three or less quanta of excitation are believed to be the most accurate, since many states at that level can be compared to experimentally determined band origins [18]. As shown in Table 3, our VPT2 calculations are able to reproduce the experimental frequencies of both fundamental and combination bands to within 10 cm À1 . This suggests that the predicted anharmonic frequencies for new transitions are equally accurate. Within $100 cm À1 of 3070 cm À1 the calculations predict only three states with appreciable IR intensity: m 6 at 2976.8 cm À1 , and m 3 þ m 8 at 3170.5 cm À1 , which are both E states, and m 3 þ m 5 at 3060.1 cm À1 , which is an A 1 state ( Table 3). The calculated anharmonic frequency for m 3 þ m 5 at 3060.1 cm À1 has an o-c difference of 10.04 cm À1 relative to our experimentally determined band origin, which is consistent with that expected for the accuracy of our calculations. In addition, both the calculated and experimental values agree well with the frequency predicted based on the experimental frequencies of the m 3 and m 5 fundamental bands (Table 1) (Table 4) are A = 5.2997 cm À1 and B = 0.28500 cm À1 , and based on the experimental a i (Table 1)  The perturbing states all have the same A 1 symmetry, and we assume that all of the perturbations are homogeneous perturbations that to our best approximation are independent of any quantum numbers. Two perturbing states are required to accurately reproduce the experimental line positions of the m 3 þ m 5 state K 0 = 1 subband. One (P1) with a perturbation coefficient of 0.007 (1) cm À1 has 8 observed transitions, including a noticeable Qbranch, and it affects the J 0 6 5 transitions. While the second (P2) only has 4 observed transitions, with no observed Q-branch transitions, but it has a larger perturbation coefficient of 0.011(1) cm À1 and strongly affects J 0 = 9. Finally, while only 2 transitions are observed to the P3 states, the interaction has a perturbation coefficient of 0.009(1) cm À1 , and significantly influences the J 0 6 7 transitions, particularly the Q-branch, of the m 3 þ m 5 K 0 = 2 subband.
Unfortunately, at this time we cannot conclusively identify the perturbing states. However, with the inclusion of the perturbing states Table 3 Harmonic and anharmonic (VPT2) frequencies of propyne a (in cm À1 ).  the least-square fit analysis gives an effective A = 5.293 07(40), 5.294 17 (12), and 5.294 91(10) cm À1 , for the three K 0 subbands respectively, which all differ by less than 0.1% from the predicted A 3+5 values. The present data set can be compared with the results presented by Zhao et al. [26]. The VPT2 calculations predict the intensity of the m 3 þ m 5 combination band to be about 3Â the intensity of the m 3 þ m 8 combination band. A comparison of the m 3 þ m 5 data presented here and the m 3 þ m 8 data published earlier by Zhao et al. [26] -all recorded for similar expansion conditions and corrected for small changes in the ring-down time -results in a factor 2.8Â difference in the intensity. This provides a further argument supporting the assignment made here.

Conclusion
The current high-resolution study of jet-cooled propyne using cw-CRDS has yielded the first fully resolved observation of the m 3 þ m 5 state. As also found in the recent work on m 3 þ m 8 , our analysis indicates that near-resonant or non-resonant perturbations are involved in the m 3 þ m 5 spectrum. The experimental data are fully consistent with high level ab initio calculations, presented here, for the anharmonic frequencies. These calculations also give ground state spectroscopic constants accurate enough to aid in the assignment of ro-vibrational spectra of propyne.