Analysis of the rotational spectrum of the ground and first torsional excited states of monodeuterated ethane, CH3CH2D

Journal of Molecular Spectroscopy 307 (2015) 27–32

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Analysis of the rotational spectrum of the ground and first torsional excited states of monodeuterated ethane, CH3CH2D Adam M. Daly a,⇑, Brian J. Drouin a, Peter Groner b, Shanshan Yu a, John C. Pearson a a b

Science Division, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Department of Chemistry, University of Missouri – Kansas City, 5100 Rockhill Rd., Kansas City, MO 64110, USA

a r t i c l e

i n f o

Article history: Received 12 September 2014 In revised form 7 November 2014 Available online 22 November 2014 Keywords: Submillimeter Deuteroethane Potential barrier

a b s t r a c t The pure rotational spectrum of mono-deuterated ethane, CH3CH2D, has been measured up to 1600 GHz and spectroscopic constants have been fit to 984 transitions in the ground state and 422 transitions in the first torsional excited state (m18). Analyses of the ground state data were performed with the programs SPFIT, ERHAM and XIAM and of the first torsional state with SPFIT and ERHAM to extract molecular and spectroscopic constants. A combined fit of both states using ERHAM was used to determine q = 0.4344026(68), which in the symmetric limit is the ratio Ia/Iz and a measure of the periodicity of the internal rotation energy with K and the energy differences between the A and E torsional substates, DE(E–A), of 74.167(18) and 3382.23(34) MHz for the ground and excited states, respectively. Using these energy differences and the overtone transitions Dv = 2 from Raman measurements in the literature, the coefficients V3 and V6 of the potential function of the internal rotation in CH3CH2D were determined as V3 = 1004.56(4) cm1 and V6 = 7.09(12) cm1. This analysis lays the ground work for the assignment of the IR spectrum of CH3CH2D between (680–880 cm1) which will help quantify isotopic ratios by remote sensing missions. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The continuing improvement of remote sensing detection has significantly improved our understanding of the chemical processes in the atmosphere of earth, exoplanets and in space. Organic molecules are the basis of life and their spectroscopic signatures have been the focus of over a century of scientific investigation. The simplest hydrocarbons: methane, ethane and propane have been studied on earth due to their fundamental importance in the carbon cycle on earth. Isotopic fractionation of carbon and hydrogen measured through the isotopic ratios of

xð13 CÞ xð12 CÞ

and

xð2 HÞ xð1 HÞ

provides details of processes in oceans, crust and atmosphere [1]. These isotopic ratios are studied in the interstellar medium [2] using vibrational and rotational spectroscopy. Accurate spectroscopic frequencies of hydrocarbons also provide essential information that allows remote detections to inform chemical models of the planetary atmosphere. The Cassini mission has been expanding our knowledge of hydrocarbons’ role in the atmosphere of Saturn and its moon Titan where liquid ethane has been proposed to persist on the surface [3]. Detection and quantification of deuterated ethane in these systems will further constrain models, particularly with respect to origin and reactivity. ⇑ Corresponding author. http://dx.doi.org/10.1016/j.jms.2014.11.002 0022-2852/Ó 2014 Elsevier Inc. All rights reserved.

Generally, ro-vibrational analyses begin with the ground state and then proceed up through the fundamentals into the overtone and combination bands. Unfortunately, spectral analysis of hydrocarbons is made more difficult by the internal rotation of methyl groups and the small or non-existent permanent dipole moments. Since the first thermodynamic studies of ethane made by Pitzer [4], significant efforts in the theoretical development of hindered internal rotation [5–7] and the spectroscopic impacts [8–11] have been expended. The staggered ground state geometry belonging to the point group D3d was determined in the first high resolution infrared study by Smith [8]. It was later confirmed with the isotopic substitution structure of Duncan et al. [11]. Van Riet [12] reported the first measurements of the torsional band m18 for all deuterated isotopologues of ethane. Using these data and the gas phase structure, Lide [5] provided the first potential barrier (V3) determinations for the deuterated ethanes and found values to be in the range 2.5–3.5 kcal/mol; the V3 torsional barrier of CH3CH2D was determined to be 3.31 kcal/mol. This particular isotopologue has been studied with high resolution infrared [13] and microwave spectroscopy [14] owing to the small dipole moment induced by the charge separation between CH3 and CH2D which produces a weak rotational spectrum. The rotational spectrum in the ground state of CH3CH2D was recorded up to 160 GHz and 12 pairs of a- and 15 pairs of b-dipole transitions that were split into two components (A and E) due to internal rotation were

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reported and fit to obtain a V3 barrier of 2.8838(43) kcal/mol or 1010.23(13) cm1 . We report an analysis of the pure rotational spectrum of the ground and first excited torsional state (m18) of CH3CH2D, with measurements made up to 1.6 THz for the ground state and 1.1 THz for the m18 state to provide accurate frequencies for atmospheric, exoplanet and interstellar detection as well as improved potential constants and predictions of the torsional sub-band positions. Infrared analyses of the simplest alkanes, e.g. methane and ethane, are non-trivial due to high symmetry as well as the interactions between energy levels. For remote sensing of CH3CH2D, a promising pair of fundamental bands near 800 cm1 has yet to be assigned due to (1) insufficient knowledge of the ground state and (2) a suspected interaction with the 3rd overtone of m18. This work extends knowledge of the ground state and m18 states to support the eventual assignment of the 680–850 cm1 region.

2. Methods All data reported here were recorded in the High Resolution Molecular Spectroscopy Laboratory at the Jet Propulsion Laboratory with the frequency multiplied submillimeter spectrometer [15,16]. CH3CH2D was purchased from ICON (98% D) in a 1 L lecture bottle and used without purification. For measurements below 1.1 THz, 200 mTorr of CH3CH2D was placed in a 3 m long 5-cm-diameter cell [17]. Above 1.1 THz a single pass 1 m cell with z-cut quartz windows was used [18] due to the more favorable transmission. When power levels allowed, specifically at frequencies below 1240 GHz, the radiation was double passed through incorporation of a rooftop reflector and a polarizing grid. The frequency source is an Agilent E8379 1–20 GHz synthesizer that is locked to a rubidium standard stabilized to one part in 1012. Synthesizer output is passed to a commercial Millitech 3mW output sextupler (AMC-10). With this source we utilized a variety of amplifiers and multipliers to achieve the frequencies reported here (260–320 GHz, 520–600 GHz, 680–810 GHz, 940–1240 GHz and 1400–1600 GHz). For data taken from 260–320 GHz, we utilized a Schottky detector. This signal was detected at 2f using a lock-in amplifier referenced from the FM applied at 2 kHz rate and 35 kHz depth (applied at synthesizer) demodulated and recorded by a software program. With this source we measured only a small subset of the strongest transitions of the ground state. A low temperature Si bolometer (1.8 K) was used up to 1.1 THz in the double pass configuration using the 3 m cell that made the effective path length 6 m. We also used a bolometer (at 4 K) for the frequencies near 1.1 THz and 1.5 THz. For all measurements made with the bolometer, tone burst modulation was utilized, (20 kHz tone and 500 Hz burst) to aid in the detection of the weak pure rotational spectrum of both the ground state and first torsional state. In this configuration, the signal is detected at the burst rate provided by the sync output of the function generator, the amplitude of the tone was adjusted to 30–40 kHz depth at the synthesizer. Spectra were too weak for effective broadband scanning (see e.g. [19]), however hundreds of transitions were measureable with modest integration times (t < 30 min). To maximize data return we used a software ‘macro’ to measure specific windows near predicted transition frequencies. Care was taken to observe enough baseline to estimate distortion of the line shape due to the presence of baseline and biases that may result from baseline removal techniques. Some survey spectra of the higher K components of a R-branches are shown with and without baseline removal in Fig. 1 to demonstrate the effect. The freely available SMAP program [spec.jpl.nasa.gov] developed at JPL offers many options to minimize the effect of the background: polynomial subtraction, Fourier filtering and numerical second derivative, which can be used in

Fig. 1. The black central trace is the unprocessed result of 16 sweeps (8 scans in both directions) of 200 mTorr CH3CH2D in 6 m of absorption path. Below is a numerical second derivative(16 points differential) which reveals the regular pattern shown above for the K = 6–10 components of the J = 28–27 aR branch. Also observable in this scan are one K = 3 ground state component from the same aR branch as well as the corresponding torsional doublet of this transition for the first torsional state. Two trace impurities are also labeled in the lower trace.

combination with the smoothing routine that helps increase the signal to noise when the data are oversampled. Such algorithms are essential when the signal peaks are small compared to the baseline pattern(s). Using the same numerical second derivative technique, we were able to record a Q-branch assigned to the ground state (Fig. 2) which may have increased uncertainty due to the baseline removal and density of transitions. Uncertainties were assigned to the ground state: 100 kHz (520–600 GHz), 200 kHz (250–300 GHz, 680–1180 GHz) and 300 kHz (1400–1580 GHz), and v18: 200 kHz (520–600 GHz) and 300 kHz (680–1180 GHz).

Fig. 2. b-dipole Q-branch transitions of ground state Ka = 12 ? 11 are weak and exhibit more A–E splitting. Surveys near band origins were required to obtain comprehensive coverage. Strong signals observed are b-dipole R-branch transitions 118,4 ? 107,3.

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A.M. Daly et al. / Journal of Molecular Spectroscopy 307 (2015) 27–32

3. Analysis and results 3.1. Ground state A fit of the Hirota et al. microwave data [14] was made with the effective rotational Hamiltonian implemented in the program ERHAM [20][21] and used to make predictions up to 1 THz by fitting rotational constants, quartic distortion constants and tunneling parameters for the energy difference between A and E states and the rotational constants. Signals were readily detected at frequencies between 980 and 1035 GHz within a few MHz of the predictions. The addition of the new a- and b-dipole transitions to the fit significantly improved the reliability of predictions at other frequencies. Eventually, over 900 new transitions between 250 and 1600 GHz were measured and assigned with J up to 37 and Ka up to 15. Table 1 gives the final parameters fitted to 984 ground state transitions (including 54 from Hirota et al. [14]) between 0.1 and 1.6 THz. The quality of the fit was independent of the choice of the reduced Hamiltonian. The results reported in the tables are for the symmetric reduction for consistency with the torsional state analysis. In an effort to validate and vet the ERHAM analysis we also employed a reduced internal axis method implemented in SPFIT [22] that was successful in fitting the submillimeter spectrum of propane [16] where the ground state and two excited vibrational states were fit using SPFIT [23]. The flexible operator definitions in SPFIT enable several different methods for analyses of internal rotation including (1) a fully coupled approach in which the pre-calculated results of Mathieu equation are used to directly determine the barrier height [24–26]; (2) a phenomenological Hamiltonian much like that in ERHAM is applied [16]; and (3) separate fitting of internal rotor states [27]. In practice these methods are applied to (1) low barrier (2)

intermediate barrier and (3) high barrier problems, with the formulation and computational efforts roughly one order of magnitude worse for each step toward a fully coupled solution. Since ethane is an intermediate barrier, and we were interested in inter-comparisons with ERHAM, we chose the phenomenological approach. In this approach ad hoc Fourier terms are introduced for both the A and E states with fixed ratios determined by the internal rotation symmetry. The A and E states are coded in triples, with the E states being defined as l-doubled pairs each with half the spin weight of the non-degenerate A state. The l-doubling basis allows for the anti-symmetric Fourier operators that arise in the torsional Hamiltonian. The coefficients are

!

  2pqr ¼ cos cos C q ¼ cos n n !   2pqr pqðK þ KÞq sin þ sin n n

pqð2r  ðK þ KÞqÞ

Tunneling terms 2⁄e10 (MHz) 2⁄e20 (MHz) a

q

ba (deg) h i (kHz) A  ðBþCÞ 2 q¼1 h i ðBþCÞ (kHz) 2 q¼1 h i ðBCÞ (kHz) 4

N F V3 a b c

n ð1Þ

which can be expanded into cosine and sine terms whose coeffiqffiffi 3 in the case of a threefold rotor for 2

A cosine term: E cosine: E sine term. SPFIT maintains the ratio if coded sequentially with a negative sign appearing before the parameter definitions of the second and third terms. We have included our fit in the Supplementary Information. Higher order terms may be coded by substituting values of q (up to 3), n (only 3) and r (0 for A and 1 for E) into the expanded formula. The results from this SPFIT analysis are also included in Table 1, as well as those obtained from the XIAM code [28] in order to compare capabilities and effectiveness of the different methods. This is the preferable method if a full period of 2pqK will be fit in SPFIT.

ERHAMb

XIAM

SPFIT

69653.3909(24) 18859.08109(89) 18214.15883(88) 26.8802(17) 66.3855(65) 245.154(41) 1.01116(29) 0.08252(19) 0.0026(10) 0.2021(47) 0.021(30) 4.68(17)

69653.40371(560) 18863.36431(162) 18209.87139(167) 26.874969(889) 66.380719(129) 245.472(90) 1.023951(712) 0.087814(493) – 0.194(10) 0.080(0.058) 6.329(0.386)

69653.39174(229) 18859.082000(933) 18214.159640(933) 26.88264(192) 66.38600(583) 245.1560(408) 1.011226(282) 0.082538(186) 0.00419(117) 0.20090(476) – 4.663(175)

49.4754(138) 0.0306(84) 0.4344026(68) 0.905(62) 9.11(24)

– – 0.4348069(447) 3.129643(338) –

49.4695(135) 0.02560(806) [0.434361174]c

1.07(16)

–

0.2110(408)

15.950(369)

0.748(90)

–

2.6660(826)

– 0.252 984 9.4348(30) –

– 0.320 984 9.44095 cm1 1012.25(16) cm1

0.917 0.212 984 – –

q¼1

rRMS r (MHz)

!

cients are related by 1 :  12 :

Table 1 Summary of parameters for the ground vibrational state of C2H5D using Watson’s symmetric reduction.a

Pure rotation A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) HJ (Hz) HJK (Hz) HKJ (Hz) HK (Hz)

pqðK þ KÞq

Brackets indicate fixed value. Combined fit in which q and b were fit with g.s. and m18 simultaneously. SPFIT fixed to ground state optimized value (produced lowest RMS) from ERHAM.

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A.M. Daly et al. / Journal of Molecular Spectroscopy 307 (2015) 27–32

3.2. Excited torsional state (m18) The ground state energy splitting of the A and the E states, DE(E–A), was combined with the estimated value of F from an ab initio structure (MP2/6–31G(d) using Gaussian09 [29]) to produce approximate values of the barrier to internal rotation of the methyl group (V3 = 1015 cm1), the energy of the first torsional excited state m18, (271 cm1 above the ground state) and the DE(m18)(E–A). This energy difference was used with rotational and quartic centrifugal distortion constants transferred from the ground state together with vibration–rotation constants from the ab initio quadratic and cubic force fields to predict the rotational spectrum within m18. The torsional vibrational energy level is expected to be significantly populated at room temperature. Since only few broadband scans were performed in the assignment of the ground state, only very few, if any, transitions in the spectrum of the ground state were left unassigned. Initial integrations revealed no transitions within a 100 MHz (±50 MHz) of the prediction described above, so larger 1 GHz scans were made near the aR-branch at 990 GHz for the ground state, J = 27 26 (see Fig. 1). This branch is at the peak power of the 1 THz source and presented the best signal to noise ratio of the ground state data set. A weak set of signals were observed approximately 2 GHz lower in frequency, about 250 MHz away from the predicted frequency. Similar scans were made in the other two aR branches that are within the bandwidth of that source and transitions consistent with a weak near prolate aR-branch were observed in each range. Initially, transitions with K > 4 were fit using the program ERHAM, but difficulty in extending the analysis to the lowest K values revealed the necessity of utilizing a Watson S-reduction for analysis of the torsional state. Unlike the ground state, the fit for the m18 state did not converge with DK, but both the ground and m18 states readily converged with the d2 term in the ERHAM formulation. Due to the larger A–E splittings and higher thermal energy, transitions within the m18 state had generally intensities of about 15% compared to the ground state, with most of them requiring 10–30 min integration time. After properly assigning the quantum numbers to these weak signals, a fit was obtained that predicted all of the measured a- and b-dipole transitions within the measurement uncertainty. Of the more than 400 observed transitions, 248 and 173 belong to the A- and E-states, respectively, with J up to 32 and K up to 12 for A and 11 for E. They were fit successfully with both ERHAM and SPFIT while no stable and satisfactory fit could be obtained with XIAM. The spectroscopic parameters from ERHAM and SPFIT are listed in Table 2. The ERHAM results for both the ground and the torsional excited state were obtained from a combined fit in which the q-vector (length q and angle b between the vector and the principal axis a) is identical to both states. 3.3. Barrier determination Hirota et al. [14] determined the potential barrier to internal rotation (V3 = 1010.23(13) cm1). An improved potential function including a V6 term was derived from the microwave results reported here and the Raman data reported by Fernández-Sánchez and Montero [30]. To assign the peaks in Raman spectrum of CH3CH2D, the rotationally unresolved spectrum was simulated by predicting the rotational spectrum of each torsional transition (Dv = 2) with SPFIT and convoluting it with a broad line shape while adjusting the ratio of the tunneling coefficients e1/e2 for the individual torsional states. The ‘‘best’’ simulation reproduced the 430– 470 cm1 feature even better than the simulation in [30]. This procedure led to the assignments of the peaks reported in [30] as shown in Table 3. The Raman frequencies from [30] were used in the program ASTOR [31] with DE(E–A) for both the ground and

Table 2 Fitted Spectroscopic and molecular parameters for the first torsional state, m18, using Watson’s symmetric reduction.

Pure rotation A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz) HJ (Hz) HJK (Hz) HKJ (Hz) HK (Hz) DbcK2c Tunneling terms 2e10 (MHz) 2e20 (MHz) a

q

ba (deg) h i (kHz) A  ðBþCÞ 2 q¼1 h i ðBþCÞ (kHz) 2 q¼1 h i ðBCÞ (kHz) 4

ERHAMa

SPFITb

69633.200(14) 18774.4230(22) 18164.4840(21) 26.6142(21) 68.555(40) 241.90(18) 0.92182(74) 0.12200(48) 0.0026(10) 0.166(25) 1.45(21) 2.54(75) –

69633.1671(109) 18774.42052(184) 18164.48792(176) 26.618150(800) 68.4596(129) 241.373(166) 0.920500(790) 0.128580(820) [0.00419] [0.20090] – –3.660(710) 0.01908(267)

2253.82(22) 0.980(38) 0.4344026(68) 0.905(62) 409(10)

2253.351(160) 1.0550(320) [0.434361174] – 651.9(87)

43.8(75)

24.650(380)

31.9(36)

113.230(380)

[d2]q=1 (kHz) [d1]q=1 (kHz) [DK]q=1 (kHz) [DJ]q=1 (kHz) [Djk]q=1 (kHz) [Dab]q=1 (kHz)

0.002411(541) 0.002883(220) 0.775(105) 0.001069(418) 0.0336(70) 1583.736(0.254)

0.002580(710) 0.3420(340) 0.5250(360) – – 3310(460)

r (MHz) rRed

– 1.14 420

0.298 1.07 420

q¼1

N a b c

Combined fit in which q and b were fit with g.s. and m18 simultaneously. Values in brackets were fixed to ground state values. This parameter represents the anticommutator 1/2 {Pa2, PbPc + PcPb}, where Pa, Pb, Pc are the projections of the rotational operator onto the rho-axis system.

m18 states and assigned as described above to determine two coefficients of the potential function, the torsional energy levels and DE(E–A) for all torsional states up to m18 = 4. The internal rotation constant F, 9.43489 cm1, obtained from the output of ERHAM from q, b and the rotational constants of the torsional ground state was treated as a constant with no error. The results of this fit are shown in Table 3. 4. Discussion For the ground state, the extended spectral analysis adds precision and improves the predictability of the prior millimeter wavelength effort, for which the data are included in the present analyses. Of the three programs vetted for use with this dataset (SPFIT, ERHAM, XIAM), all three provide acceptable fits to the ground state data. The parameters listed in the SPFIT column of Table 1 will be used to provide a prediction to 2 THz for the JPL catalog [25]. For the first torsional state we were unable to obtain a satisfactory fit with the XIAM program, and the SPFIT and ERHAM programs gave very similar results. The smaller energy difference between the torsional vibrational state to the top of the potential well produces larger torsional perturbations in the effective Hamiltonians employed in the SPFIT and ERHAM programs, whose models are similar but not exactly identical. Specifically, ERHAM makes use of Wigner rotations for the torsional momenta from the top-axis to the principal axes via an angle denoted b. This essentially allows the q-vector to be parameterized in one, two or three

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A.M. Daly et al. / Journal of Molecular Spectroscopy 307 (2015) 27–32 Table 3 Energy level differences used to determine the coefficients of the torsional potential function for C2H5D.

DE a 2A–0A 2E–0E 3E–1E 3A–1A 4A–2A 4E–2E 0E–0A 1E–1A

a

mobs b

515.1 515.1b 440.1b 463.1b 336.5b 390.0b 74.167 3382.229

Uncertainty

mobs–mcalc

Weighted residual

1.0 1.0 1.0 1.0 1.0 1.0 0.018 0.342

2.129 0.047 -2.918 0.199 2.192 1.022 0.000 0.006

2.129 0.047 -2.918 0.199 2.192 1.022 0.008 0.018

Coefficient

This work

Ref. [14]

Ref. [30]

V3 (cm1) V6 (cm1) F (cm1) (constant)

1004.561(44) 7.09(12) 9.43489

1010.23(13)

1007 7.3 9.43303

9.43303

Torsional energy levels are labeled by the (harmonic) vibrational quantum number v and A or E for the torsional sublevel. The units of the columns mobs, Uncertainty, and

mobs–mcalc are cm1 except for the last two which are in MHz. b

Ref. [30], peak assignment for K = 0.

(via a 2nd rotation not used here) dimensions. In SPFIT there is no equivalent operation, and the chosen parameterization contains a single projection of the q-vector, which is chosen as the qa component in this molecule. For high-barrier molecules, and those with alignment between the q-axis and a principal axis (or both), this assumption is typically a minor issue and the small contributions from minor projections are swept into effective constants. However, as the energy difference between torsional level and the barrier decreases these small contributions manifest a need for additional torsional operators and additional centrifugal distortion (or both). An additional non-Watson reduced parameter, DbcK2, is introduced to phenomenologically account for small perturbations associated with the torsional angular momenta along the b and c axes that are not part of the periodic parameterization in the SPFIT q-axis method. The two models fit the data equivalently. The program XIAM [28] directly solves the Mathieu equation and provides a fitted value for V3 of 1012.25(16) cm1 that is consistent with the results of the post analysis with ASTOR which achieves a V3 value of 1004.7 cm1 when only the m18(A)–m18(E) value is fitted. The ASTOR value using only ground state data is very close to value reported by Hirota et al. [11] 1010.23(13) cm1. Finally, the calculated V3, V6 values of Fernandez et al. [30] obtained from their analysis of the Raman spectra, V3 = 1007(2) cm1 and V6 = 7.3(2) cm1 are also in close agreement with the results from the ASTOR analysis of only Raman data. Using all the microwave and Raman data listed in [30], V3 = 1004.561(44) cm1 and V6 = 7.091(117) cm1 were determined. With such small absorptions, it is unlikely that deuteroethane and the ethane D/H ratio will be determined through measurements of pure rotational spectra. To extend the assignment of the spectrum of CH3CH2D up to the stronger absorbing bending modes (m17 and m11) between 700 and 850 cm1 we have provided (1) extended analysis of the ground state rotational spectrum, up through and beyond the a-dipole Boltzmann peak; (2) characterized the first excited state of the torsional mode. This enables a subsequent effort to assign the bending modes with an essentially fixed ground state Hamiltonian. The m18 mode at 271 cm1 is thermally populated, and hot-bands arising from this state will contribute up to 25% of the intensity at room temperature. Therefore an experimental spectrum has been recorded at 130 K where m18 will contribute only 4% to the band intensity. The direct knowledge of the energy levels of the ground and v18 states will enable discrimination between lower states of paired infrared transitions via combination differences. A full analysis of the m17 (711 cm1) and m11 (805 cm1) bands is underway, and will be presented in a subsequent report. An initial inspection of the high-resolution spectra in the 680–850 cm1 region has revealed that many transitions within sub-bands appear

as pairs with variable splittings, implying that the modes have significant torsional character. This is a priori unexpected since the ground state torsional splittings are <3.3  103 cm1 and the instrument line width is 2.8  103 cm1, such that only small, unresolved A/E doubling might be expected. However, the bending modes lie close to the 3rd (714–733 cm1) and 4th (850–905 cm1) overtones of the torsion and these overtones have components with the correct symmetries to interact with the bending modes via Fermi and Coriolis resonances. Due to the proximity of the bending modes, we infer that 3m18 is interacting with m17. The nature of the perturbations to the m18 band are qualitatively different, suggesting a simple Fermi resonance with 3m18, however we have not ruled out a Coriolis resonance with 4m18 or m17 or all of the above. This precludes a straightforward analysis of the bending mode spectra as perpendicular transitions between semi-rigid rotor asymmetric tops. Since the infrared activities of the second and third overtones are very small, there are no obvious transitions assignable in the infrared spectrum, and thus the potential interactions just discussed will likely be dealt with as couplings with dark states. The refinement in the torsional sub-band positions will greatly facilitate a fully coupled analysis by providing a more accurate set of energy levels of the dark states. Toward this purpose we have improved the torsional potential as much as possible with extensive ground and m18 state characterizations. Acknowledgments This paper presents research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration Ó 2011 California Institute of Technology. Government sponsorship acknowledged. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jms.2014.11.002. References [1] B. Sherwood Lollar, T.D. Westgate, J.A. Ward, G.F. Slater, G. LacrampeCouloume, Nature 416 (2002) 522–524, http://dx.doi.org/10.1038/416522a. [2] E. Herbst, Chem. Soc. Rev. 30 (2001) 168–176, http://dx.doi.org/10.1039/ A909040A. [3] R.H. Brown, L.A. Soderblom, J.M. Soderblom, R.N. Clark, R. Jaumann, J.W. Barnes, et al., Nature. 454 (2008) 607–610, http://dx.doi.org/10.1038/nature 07100. [4] K.S. Pitzer, J. Chem. Phys. 5 (1937) 469–472, http://dx.doi.org/10.1063/ 1.1750058. [5] D.R. Lide Jr., J. Chem. Phys. 29 (1958) 1426–1427, http://dx.doi.org/10.1063/ 1.1744745.

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[6] R.M. Pitzer, Acc. Chem. Res. 16 (1983) 207–210, http://dx.doi.org/10.1021/ ar00090a004. [7] D. Herschbach, J. Chem. Phys (1959). [8] L.G. Smith, J. Chem. Phys. 17 (1949) 139–167, http://dx.doi.org/10.1063/ 1.1747206. [9] G.E. Hansen, D.M. Dennison, J. Chem. Phys. 20 (1952) 313–326, http:// dx.doi.org/10.1063/1.1700400. [10] N. Moazzen-Ahmadi, H.P. Gush, M. Halpern, H. Jagannath, A. Leung, I. Ozier, J. Chem. Phys. 88 (1988) 563–577, http://dx.doi.org/10.1063/1.454183. [11] J.L. Duncan, D.C. McKean, A.J. Bruce, J. Mol. Spectrosc. 74 (1979) 361–374, http://dx.doi.org/10.1016/0022-2852(79)90160-7. [12] R. Van Riet, Ann. Soc. Sci. Brux. 71 (1957) 102. [13] L.R. Posey Jr., E.F. Barker, J. Chem. Phys. 17 (1949) 182–187, http://dx.doi.org/ 10.1063/1.1747209. [14] E. Hirota, Y. Endo, S. Saito, J.L. Duncan, J. Mol. Spectrosc. 89 (1981) 285–295, http://dx.doi.org/10.1016/0022-2852(81)90024-2. [15] B.J. Drouin, F.W. Maiwald, J.C. Pearson, Rev. Sci. Instrum. 76 (2005) 093113, http://dx.doi.org/10.1063/1.2042687. [16] B.J. Drouin, J.C. Pearson, A. Walters, V. Lattanzi, J. Mol. Spectrosc. 240 (2006) 227–237, http://dx.doi.org/10.1016/j.jms.2006.10.007. [17] B.J. Drouin, V. Payne, F. Oyafuso, K. Sung, E. Mlawer, J. Quant. Spectrosc. Radiat. Transf. 133 (2014) 190–198. . [18] B.J. Drouin, S. Yu, J.C. Pearson, H.S.P. Müller, J. Quant. Spectrosc. Radiat. Transf. 110 (2009) 2077–2081, http://dx.doi.org/10.1016/j.jqsrt.2009.05.014. [19] J.C. Pearson, S. Yu, B.J. Drouin, J. Mol. Spectrosc. 280 (2012) 119–133, http:// dx.doi.org/10.1016/j.jms.2012.06.012. [20] P. Groner, J. Chem. Phys. 107 (1997) 4483–4498, http://dx.doi.org/10.1063/ 1.474810. [21] P. Groner, J. Mol. Spectrosc. 278 (2012) 52–67.

[22] H.M. Pickett, J. Chem. Phys. 107 (1997) 6732–6735, http://dx.doi.org/10.1063/ 1.474916. [23] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377, http://dx.doi.org/10.1016/ 0022-2852(91)90393-O. [24] See molecule reference 60003. . [25] H.M. Pickett, R.L. Poynter, E.A. Cohen, M.L. Delitsky, J.C. Pearson, H.S.P. Muller, J. Quant. Spectrosc. Rad. Transfer 60 (1998) 883–890. [26] M. Carvajal, F. Willaert, J. Demaison, I. Kleiner, J. Mol. Spectrosc. 246 (2007) 158–166. [27] G.S. Grubbs, P. Groner, S.E. Novick, S.A. Cooke, J. Mol. Spec. 280 (2012) 21–35. [28] H. Hartwig, H. Dreizler, Z. Naturforsch. A 51 (1996) 923–932. [29] Gaussian 09, Revision A.02, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian Inc, Wallingford CT, 2009]. [30] J.M. Fernández-Sánchez, S. Montero, J. Chem. Phys. 94 (1991) 7788–7800, http://dx.doi.org/10.1063/1.460165. [31] P. Groner, R.D. Johnson, J.R. Durig, J. Mol. Struct. 142 (1986) 363–366.