Infrared diode laser spectroscopic investigation of four C–H stretching vibrational modes of propylene oxide

Chemical Physics Letters 494 (2010) 14–20

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Infrared diode laser spectroscopic investigation of four C–H stretching vibrational modes of propylene oxide Fumie X. Sunahori, Zheng Su, Cheolhwa Kang, Yunjie Xu * Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2

a r t i c l e

i n f o

Article history: Received 13 February 2010 In final form 22 May 2010 Available online 27 May 2010

a b s t r a c t The high resolution ro-vibrational spectra of propylene oxide have been recorded for the first time in the C–H stretching region using a rapid scan infrared laser spectrometer equipped with an astigmatic multipass cell. Detailed analyses of the three C–H bands centered at 2942 and 2975 cm1 reveal that there are significant perturbations in the methyl C–H symmetric and the two near-degenerate asymmetric fundamental bands. Low resolution Fourier transform infrared spectra of propylene oxide have also been measured with a static gas sample and under supersonic jet conditions. The MP2/6-311++G(d,p) harmonic and anharmonic frequency calculations have been performed to aid the C–H stretching band assignment. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction High resolution infrared (IR) spectroscopy of mid-sized organic molecules, particularly of chiral organic molecules, is an area of considerable current interest. Jet-cooled IR spectra of small organic molecules such as benzene [1], formyl fluoride [2], and dimethyl ether [3] had been investigated using diode laser spectroscopy. Quack and co-workers described the first high resolution IR study of a chiral molecule CHBrClF using a Fourier transform (FT) IR spectrometer [4]. They also determined the rotational and centrifugal distortion constants of the ground and several first excited vibrational states of a few other relatively simple chiral molecules such as fluorooxirane [5] and thiirane-1-oxide [6,7] in the related studies. There are a number of noticeable challenges in studying midsized organic molecules using high resolution IR spectroscopy. First, rotationally resolved IR spectra of organic molecules are often very difficult to obtain since the number of ro-vibrational levels populated is quite large even under jet expansion conditions. Thus, there are stringent requirements on the experimental sensitivity and resolution for such studies. Second, the spectral assignments are highly challenging because the ro-vibrational spectra observed are often severely perturbed by ro-vibrational coupling, Fermi resonance, and/or intramolecular vibrational redistribution (IVR). For example, ro-vibrational transitions of the acetylenic C–H stretch and the asymmetric methyl C–H stretch of 1-butyne were observed to be split into multiplets due to IVR [8,9]. Quack and coworkers included a Fermi resonance between the C–H bending and C–H stretching bands in order to interpret the perturbed C–H stretching band spectra in CF3H [10] and in (CF3)3CH [11]. * Corresponding author. Fax: +1 780 492 8231. E-mail address: [email protected] (Y. Xu). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.05.072

These and other publications [12–15] showed that the low-lying internal rotational states play an important role in the IVR processes. Because of these difficulties, only a very small number of organic molecules have been studied so far by high resolution IR spectroscopy, and indeed, a quick search with SciFinder found only about 40 such organic molecules reported. Propylene oxide (PO), C3H6O, one of the smallest chiral molecules, is the focus of both low and high resolution IR investigations described in this report. It is both rigid and stable, and has one stereogenic center, namely the center carbon atom bonded with the methyl group. PO has been a valuable prototype molecule for theoretical and rotational spectroscopic studies of chiral recognition effects [16,17] and chiroptical activities [18–21]. A series of rotational spectroscopic studies of PO in its ground vibrational and excited internal rotational states were published [22–25]. More recently, the rotational spectra of the PO-rare gas complexes were reported by the Caminati and Xu groups [26–29]. The room temperature (RT) gas phase low resolution FTIR spectrum of the C–H stretching bands of PO was reported by Winther and Hummel [30] in 1969. Together with the information obtained from the torsional transitions [31] and torsional combination bands, the authors tentatively assigned the C–H stretching fundamentals based on an empirical frequency sequence. They also determined the types of bands based on their appearance in the measured spectrum and the electric dipole moment of PO and its structure in the ground vibrational state [22]. The FTIR spectra of PO recorded at 15 K in a nitrogen matrix and in solution were reported by Polavarapu et al. [18] in 1985. Their solution spectrum shows four prominent bands in the region where the six C–H stretching bands are expected, while the matrix isolation spectrum presents many additional splittings, which were attributed to the matrix effects. A few years later, Lowe et al. [19] also measured the

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absorption spectra in an N2 matrix at 19 K with a higher resolution and confirmed the band frequencies reported by Polavarapu et al. Based mainly on their solution data and the ab initio harmonic frequency calculations, Polavarapu et al. [18] and Lowe et al. [19] made tentative C–H band assignments. In the following, we present the high resolution ro-vibrational spectra of four C–H stretching bands of PO and the corresponding low resolution RT and jet-cooled FTIR spectra, as well as the MP2/6-311++G(d,p) harmonic and anharmonic frequency calculations performed in order to achieve the C–H stretching band assignments. 2. Experimental The high resolution ro-vibrational spectrum of jet-cooled PO was recorded using a rapid scan mid-IR lead salt diode laser spectrometer coupled with an astigmatic multipass sample cell with a design similar to the one previously reported [32]. For this work, a powerful new pumping system which consists of a diffusion pump (Leybold, DIP8000) backed by a combination of a roots blower (Leybold, Ruvac WAU251) and a rotary pump (Leybold, Trivac D65B) was implemented. With a high pumping speed, it was possible to use two slit nozzles simultaneously to introduce the sample. One nozzle is located at the centre of the multipass cell, while the second nozzle, originally implemented for the cavity ring down and cavity enhanced absorption experiments [33,34], is situated along the optical axis and 12 cm away from the first nozzle. Each pulsed slit nozzle consists of a pinhole nozzle (General Valve Series 9) fitted with two homemade slit plates to form a 2 cm  60 lm slit. The signal intensity increased 2 times in comparison with that obtained with the central nozzle only. In order to further improve the signal-to-noise ratio, a pair of 2.500 diameter astigmatic mirrors (AMAC-100, Aerodyne Research Inc.) mounted on a homemade mirror assembly and separated by 55 cm was installed. A 3.3 lm single-mode lead salt diode laser beam was coupled into the multipass cell and made 182 passes through the jet expansion zone. The laser frequency was scanned at a rate of 1–2 cm1/ms, and the sample, etalon, and reference channels were recorded simultaneously. The etalon peaks were fitted to a polynomial function, and the reference lines were used to establish the free spectral range and the absolute frequencies. The accuracy of the calibrated line positions is estimated to be 0.0010 cm1 for most lines, although frequency differences as large as 0.002 cm1 were noticed for a few transitions situated at the edges of a scan when two different scans were compared. The optimal gas concentrations were 0.5% PO (P99.0%, Aldrich) in 2.5 bar of Ne (Praxair) or 0.25% PO in 1.3 bar of Ne, for the slit or pinhole nozzles, respectively. For a well resolved absorption line, the full line width at half maximum (FWHM) is about 300 MHz with the pinhole nozzles and about 120 MHz with the slit nozzles.

The best line width achieved here is mainly limited by the laser line width of the particular diode since a narrower line width of 90 MHz has been obtained with the same instrument but different diodes. The jet-cooled broadband low resolution spectrum of PO in the C–H stretching region was recorded in Suhm’s laboratory using an FTIR spectrometer coupled with a filet–jet where the slit has a dimension of 0.2 mm  600 mm [35,36]. 3. Ab initio calculations To facilitate the spectral search and assignment, ab initio harmonic frequency calculations have been carried out using the GAUSSIAN03 software packages [37]. Second-order Møller-Plesset perturbation theory (MP2) [38] with the basis set 6-311++G(d,p) [39] was chosen because of its proven performance in predicting geometries of organic molecules [40] and their IR spectra [21]. For comparison with the experimental data, the harmonic frequencies have been uniformly scaled with a factor of 0.94. In addition, anharmonic frequencies have been computed using a second-order perturbative theory based on cubic, and semi-diagonal quartic force constants [41,42]. The calculated rotational and centrifugal distortion constants of the ground state along with the rotational constants of the first vibrationally excited state of the C–H stretching modes are summarized in Table 1. The excellent agreement between the predicted quartic centrifugal distortion constants and the experimentally determined values demonstrates the good quality of the calculated harmonic force field. The differences between the predicted rotational constants at equilibrium geometry and the experimentally determined ground state rotational constants [25] are less than 0.05%, confirming the reliability of our calculations. There are six C–H stretching modes among the 24 vibrational fundamentals of PO. Since PO has –CH3, –CH2, and –CH groups, we label the corresponding C–H stretching vibrations as ma/s(CH3), ma/s(CH2), and m(CH) where subscripts a and s distinguish antisymmetric and symmetric stretch, respectively. The predicted anharmonic (not scaled) and harmonic frequencies (scaled), the band intensities, and the band shapes of these C–H stretching modes are listed in Table 2. 4. Results and discussions 4.1. Low resolution FTIR studies of the C–H stretching modes of PO In the present study, the RT static gas and jet-cooled broadband low resolution FTIR spectra of PO were measured in the 600– 3500 cm1 and the 2700–3250 cm1 region, respectively. For the C–H stretching region, the RT FTIR spectrum (Fig. 1) shows the same features as reported in Ref. [30] in the 2800–3150 cm1.

Table 1 Rotational and centrifugal distortion constants of the ground and vibrational excited states of the six stretching modes of PO obtained with MP2/6-311++G(d,p) calculations, together with the values of the ground state from microwave experimental work.a Parameter

A (MHz) B (MHz) C (MHz) DJ (kHz) DJK (kHz) DK (kHz) dJ (kHz) dK (kHz) a

Ref. [25].

Experimenta

MP2/6-311++G(d,p) calculations

v=0

v=0

18 023.874 6682.139 5951.389 2.896 3.300 19.820 0.186 2.926

18 027.640 6680.119 5948.566 2.846 3.328 20.377 0.200 3.490

v=1

ma(CH2)

m(CH)

ms(CH2)

m1a(CH3)

m2a(CH3)

ms(CH3)

17 862.624 6611.983 5889.693

17 846.585 6617.259 5891.282

17 855.069 6613.182 5890.652

17 846.315 6616.539 5890.502

17 845.326 6616.160 5888.973

17 839.510 6618.398 5891.461

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Table 2 Anharmonic frequencies of the six C–H stretching modes of PO obtained with MP2/6-311++G(d,p) calculations and the experimental values from the RT FTIR measurements. Stretching mode

ma(CH2) m(CH) ms(CH2) m1a(CH3) m2a(CH3) ms(CH3) a b c d e f g

MP2/6-311++G(d,p)

Present assignment

Previous assignments Band centre (cm1)

Band shape

Band centera (cm1)

Intensityb (km/mol)

Bandshapec

Band centre (cm1)

o–cd (cm1)

RT gas phasee

N2 matrix at 15 Kf

N2 matrix at 19 Kg

A/C C B/A B/C C/B A

3101 3045 3035 3031 3027 3020

21.1 28.7 19.7 4.8 19.4 15.4

A C B B(B) B(B) A(A)

3050.5 3001.3 2995.0 2974.3 2974.3 2942.0

50.5 43.7 40.0 56.7 52.7 78.0

3050.5 3001.0 2995.8 2983.6 2974 2941.7

3053 3002 3002 2971 2971 2935

3047 2995 2995 2970 2970 2928

(3053) (2990) (2957) (2971) (2972) (2890)

(3047) (2995) (2995) (2970) (2928) (2900 or 2868)

Unscaled anharmonic frequencies. Values in parentheses are results from the scaled harmonic frequencies. Calculated for the harmonic frequencies. Estimated from the observed band features in the FTIR spectra. Letters in parenthesis are determined from the high resolution spectra obtained in this report. Observed minus calculated anharmonic frequency. Ref [30]. Ref [18]. Ref [19]. These authors proposed two tentative assignments and the numbers in parentheses are the second assignment.

Fig. 1. Broadband low resolution FTIR spectra of PO in the C–H stretching region; measured in a filet jet expansion with 1% PO in He (top) at 25 K; with 2 Torr static gas at RT in a 10 cm cell (middle); and in a nitrogen matrix at 19 K [19] (bottom). The frequency regions provided by the lead salt diode laser used are highlighted with rectangular boxes.

Although not shown in Fig. 1, the bands between 3150 and 3250 cm1 in Fig. 1 of Ref. [30] are also present in our spectrum with very weak intensity. Comparison (see Fig. 1) of the nitrogen matrix absorption spectrum [19] with our RT FTIR spectrum reveals significant differences in the band positions and intensities. This is not surprising since the vibrational frequencies are often shifted and band intensities varied in a solid matrix due to the interference of surrounding environments. Furthermore, the rovibrational temperature is quite different in the two spectra. The low resolution jet-cooled FTIR spectrum, on the other hand, has little contribution from the excited torsional states and is free of any interference effects caused by a matrix. While it is difficult to completely rule out contributions from PO clusters in the jet expansion, the high resolution work in the same region suggests that such effects are negligible (vide infra). Three peaks at 3050, 3001, and 2942 cm1 are clearly visible in both the RT and jet-cooled spectra, and the frequencies and the relative intensities of these peaks are in good agreements with each other. PO belongs to the C1 point group and thus has no symmetry elements except C3 local symmetry of the methyl group. Because of its low symmetry, any vibrational level could be perturbed by its

neighbouring levels through Fermi resonance, anharmonic, Coriolis, and/or centrifugal coupling effects as long as the interacting states are close in energy. One can therefore expect spectral complications as the location of excited vibrational states and density of states become higher. Using the predicted frequencies and intensities of the fundamental bands, we could easily assign all of the observed bands as the fundamental bands in the 600– 1600 cm1 region. In contrast, assignment of the C–H stretching bands was difficult since the number of observed bands in the 2800–3150 cm1 region is more than the expected six fundamental bands. The weak bands between 2800 and 2930 cm1 are most likely combination bands or overtones, but not m(CH)–m(CH3 torsion) difference bands, since none of them are red shifted by the same amount of energy from the strong bands. The band positions and intensities of these weak bands are likely to be affected by Fermi resonance and/or anharmonic effects, since the band centres of the majority of these weak bands appear to be blue shifted in frequency. To assign the C–H stretching bands, we have simulated both the RT and jet-cooled FTIR spectra using PGOPHER [43]. The simulations were created initially with the ab initio rotational constants and band intensities, and the experimental band centers obtained from the RT FTIR spectrum. In the final simulations (Figs. S1 and S2, supporting information), the available high resolution band origins and rotational constants obtained (see Section 4.2) were used as they are, while the low resolution band origins were adjusted by up to ±1.2 cm1 and the ab initio rotational constants by up to ±1% to reproduce the observed features. Such adjustments are acceptable based on the uncertainties in the low resolution RT FTIR spectrum and the ab initio calculations [44]. As can be seen in Figs. S1 and S2, almost all of the spectral features observed under both experimental conditions are well reproduced. The C–H stretching band assignment in our experiments is summarized in Table 2, together with the previous assignments from Refs. [18,19,30]. Our assignments are in qualitative agreement with those of Refs. [18,19] in which assignments were made based on the comparison with harmonic frequencies predicted by lower level ab initio calculations. It is interesting to note that the anharmonic frequency calculation produces the same C–H stretching frequency ordering as the current assignment and as what had been reported for other related molecules such as propene [45], while the harmonic frequency calculation gives a somewhat different ordering. The deviations of the theoretical anharmonic frequencies from the experimental frequencies are all less than 2.7%, which are comparable to the deviations (2%) found for propene [45].

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is strong but the spectrum is highly congested (Fig. 2c). No attempt has been made to obtain detailed assignments for the spectra in these two regions. In the following sections, ro-vibrational analyses of the bands observed at 2942 and 2974 cm1 will be discussed. 4.3. The ms(CH3) band at 2942 cm1

Fig. 2. High resolution IR absorption spectra of PO taken with two slit nozzles in the: (a) 2940.5–2944.5 cm1; (b) 2972.2–2976.2 cm1; and (c) 3002–3007 cm1 regions. The rotational temperature is estimated to be 3 K.

4.2. High resolution IR studies of the C–H stretching modes The search for the spectra of PO was performed in the available frequency ranges of our rapid scan mid-IR diode laser in single mode: 2936.2–2945.6, 2970.4–2975.1, 2979.7–2989.8, and 3000.7–3009.2 cm1 (Fig. 1). Several hundred of spectral lines have been observed, and most of the transitions have been reproducible by using neon, argon, and helium as carrier gases, suggesting that lines due to the PO–rare gas complexes are not significant in these spectra. Based on the recent high resolution rotational spectroscopic study of the PO dimer [17], the formation of the PO dimer or larger clusters is also deemed insignificant under the experimental conditions used in our experiments. In Fig. 2, the central portions of the experimental spectra in the vicinity of their respective band origins in the 2940.5–2944.5, 2972.2–2976.2, and 3002–3007 cm1 region are shown. Measurements have also been carried out in the 2979.7–2989.8 cm1 region where the absorption is much weaker compared to the other regions. Although A-type band features can still be recognized in this region and there are hints of B-type transitions, the exact identity of this band has not been identified. In the 3000 cm1 frequency region, the absorption

Fig. 2(a) shows the high resolution IR spectrum of PO recorded with the slit nozzles in the vicinity of 2942 cm1. The spectrum is predominated by a-type transitions which obey DKa = 0 selection rule with clumps of transitions separated by roughly B + C. However, each clump contains more lines than expected for a regular a-type transition pattern. These splittings are likely due to vibrational state mixing (vide infra). Considering the band shape and band origin, it has been assigned as the methyl group symmetric stretching vibration, ms(CH3). Assignments of the observed transitions have been made with the help of the ground state combination differences calculated from the ground state spectroscopic constants [25]. Fits, predictions, and simulations of the ro-vibrational transitions have been performed with the Watson’s A-reduction Hamiltonian in the Ir representation using Pickett’s SPFIT/SPCAT programs [46] and Kisiel’s spectrum simulation program ASCP [47]. Once the spectra were assigned, the data were fitted to determine the vibrationally excited state molecular constants while the ground vibrational state constants were fixed at the values reported by Creswell and Schwendeman [25]. Since the observed spectrum is fairly congested, initially, only the lines confirmed by the ground state combination differences have been included in the fit. In the final analysis, a total of 35 lines with J 6 5 and Ka 6 2 have been fitted to an overall standard deviation of 0.0032 cm1. The resulting spectroscopic constants of the analysis are summarized in Table 3 and the set of transitions used for the fit is listed in Table S1 (supporting information). Fig. 3 shows the agreement between the experimental and simulated spectrum. The band origin determined from this ro-vibrational analysis is 2942.6 cm1, in very good agreement with that from the FTIR measurements (Table 2). The excited vibrational state rotational constants B and C are in reasonable agreement with the ab initio values listed in Table 1, while A0 = 18 030 MHz is slightly larger than that of the ground state A0 = 18 023.874 MHz, whereas a slightly smaller A0 compared to A00 was predicted with the ab initio calculation. Perry and co-workers [8] had observed a similar clumping phenomenon in the study of the accetylenic C–H stretch of 1-butyne. They found that while the K 0a ¼ 1 lines for J0 = 0, 1, 2 are well-behaved, the K 0a ¼ 0 levels are split as a result of the vibrational state mixing caused by anharmonic coupling [8]. Although in our case we could still use one of the strongest lines of the K 0a ¼ 0 multiplets to the spectral fit, the large overall standard deviation of

Table 3 Molecular parameters of the vs(CH3) = 1 and the two methyl asymmetric stretches v1a(CH3) = 1 and v2a(CH3) = 1 excited vibrational states of PO derived with the semi-rigid rotor Hamiltonian. v = 0a

vs(CH3) = 1 b

A (MHz) B (MHz) C (MHz) Band origin (cm1) rms (cm1) a b c d

18 023.874 6682.139 5951.389 0

v1a(CH3) = 1

v2a(CH3) = 1

c

Assignment I

Assignment II

18 030 (15)d 6639.7 (41) 5963.7 (34) 2942.5847 (10)

18 064 (10) 6635.3 (28) 5959.4 (23) 2942.5839 (7)

17 004 (37) 6979 (15) 5687 (11) 2 974.8352 (13)

19 901 (41) 6690.1 (71) 6024.9 (86) 2 974.7273 (13)

0.0032

0.0022

0.0022

0.0027

Ref. [25]. Only rotational constants are included for comparison. See Table 1 for the complete set of spectroscopic constants. For each set of the K 0a ¼ 0 multiplets, only the strongest component was used in the fit. See text for details. For each set of the K 0a ¼ 0 multiplets, the averaged frequency based on the relative intensity of the multiplets was used in the fit. See text for details. Numbers in parentheses are standard errors of 1r.

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Fig. 3. Comparison of the central portion of the high resolution IR spectrum of PO around 2942 cm1 taken with two slit nozzles with the calculated spectrum based on the constants in Table 3. A FWHM of 0.004 cm1 and a rotational temperature of 3 K were used in the simulation.

Fig. 4. Comparison of the central portion of the high resolution IR spectrum of PO around 2974 cm1 taken with two pinhole nozzles with the simulated spectrum based on the constants in Table 3. The orange and blue stick plots represent the m1a(CH3) and m2a(CH3) fundamental band transitions, respectively. A FWHM of 0.01 cm1 and a rotational temperature of 1.2 K were used in the simulation.

0.0032 cm1, compared to the measurement accuracy of 0.001– 0.002 cm1, is likely the result of the vibrational state mixing. Guided by Perry’s finding, we have inspected the P and R branches closely and found while the other lines seem to be well-behaved, the K 0a ¼ 0 lines are indeed split into a couple of lines. Expanded plots of several transitions, showing the same splitting pattern for a pair of the P and R transitions such as R(0) and P(2) which have the same 101 upper level, are depicted in Fig. S3, available as supporting information. By using the averaged frequency based on the relative intensity of the multiplets for these K 0a ¼ 0 transitions, the overall standard deviation of the fit was improved to be 0.0022 cm1 with A0 = 18 064 MHz and almost the same B0 and C0 as found in the previous fit. The resulting constants are summarized in Table 3 as Assignment II, while the transitions included in this fit are given in Table S2 (supporting information) together with the differences between the observed and calculated frequencies. In addition to these splittings, the density of the clump at the

P(1) line in Fig. 3 seems to suggest the possibility of another band with its Q-branch nearby. Several attempts have been made to assign these lines without much success since no satisfying ground state combination differences could be found. This is partially caused by the limited resolution provided by the particular diode laser used and the high density of lines. 4.4. The m1a(CH3) and m2a(CH3) bands at 2974 cm1 Figs. 2(b) and 4 show the high resolution PO spectrum recorded between 2970 and 2976 cm1 using the slit and pinhole nozzles, respectively. The analysis has been carried out with the pinhole nozzle spectrum since it is much simpler because of the lower rotational temperature of 1.2 K achieved. The spectrum shows a typical B-type band characteristic without a strong central Q-branch. Close inspection of the spectrum reveals that two bands with very similar overall features and an intensity ratio of about 1:0.6

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co-exist. We have assigned these two bands to the fundamentals of m1a(CH3) and m2a(CH3) based on the band shape and the frequency ordering predicted by the anharmonic calculation and the scaled harmonic frequencies (Table 2), as well as our analyses of the available low resolution spectra (Section 4.1). The ro-vibrational analysis began with simulations of the stronger m2a(CH3) band using the ground state molecular constants from Ref. [25]nd the ab initio excited state rotational constants with the b-type selection rules. Even in the early stage of our analysis, it was clear that the excited state rotational constant A0 must be increased by 2 GHz from the ground state A00 in order to reproduce the Ka experimentally observed ‘gap’ between the pQ1 and r Q 0 ðD DJ Ka00 Þ branches. Based on the ground state combination differences, we have assigned nineteen lines of the m2a(CH3) band and fitted them using the PGOPHER program [43] by varying the band origin, A0 , B0 and C0 , to an overall standard deviation of 0.0027 cm1, which is slightly larger than the experimental accuracy. The weaker m1a(CH3) band was analyzed in a similar way, and fifteen transitions were fitted with an overall standard deviation of 0.0022 cm1. Interestingly, with this initial assignment, the excited state rotational constant A0 for this band was found to be about 1 GHz smaller than that of the ground state. The band origin of the m2a(CH3) band was only slightly red shifted by 0.1 cm1 to that of the m1a(CH3) band. The resulting molecular spectroscopic constants of the two excited states are also summarized in Table 3, and the transitions used in the fits are given in Tables S3 and S4. The simulated spectrum with these molecular constants is compared with the observed one in Fig. 4. It had been reported previously that Coriolis coupling can adequately explain why the effective B rotational constants of the two closely spaced excited vibrational states could have a value half or double that of the ground vibrational state [48]. We therefore suspected that an a-type Coriolis coupling between the two closely located excited vibrational states v1a(CH3) = 1 and v2a(CH3) = 1 to be the cause of the similar abnormality in A’s. The effective Hamiltonian incorporating the a-axis Coriolis interaction term is ð1Þ ð1;2Þ H ¼ Hrot þ Hð2Þ rot þ Hcor;a þ E1 þ E2

ð1Þ

ðiÞ Hrot

where is the rotational Hamiltonian of the via(CH3) = 1 (i = 1 or ð1;2Þ 2) vibrational state, Hcor;a is the a-axis Coriolis term [49] which connects v1a(CH3) = 1 and v2a(CH3) = 1 states, and Ei (i = 1 or 2) is the energy difference between the excited state via(CH3) = 1 (i = 1 or 2) and the ground state. Neglecting higher order constants, the Corið1;2Þ olis term Hcor;a in (1) is described by ð1;2Þ Hcor;a ¼ iGa Pa þ F bc ðPb Pc þ Pc Pb Þ

ð2Þ

where Ga and Fbc are the first and second order Coriolis constants, respectively. The first-order Coriolis coupling constant Ga is given by

Ga ¼ A0 fa1;2

rffiffiffiffiffiffiffi

x1 þ x2

rffiffiffiffiffiffiffi

x2 x1

ð3Þ

where A0 is the ground state rotational constant, fa1;2 is the Coriolis coupling coefficient, and x1 and x2 are harmonic frequencies of the normal modes m1a(CH3) and m2a(CH3), respectively. Using the ab initio value of jfa1;2 j ¼ 0:01106 derived from the harmonic force field and the predicted harmonic frequencies in Table 2, Ga was calculated to be 398.7 MHz or 0.0133 cm1. A simultaneous fit for both bands with the Hamiltonian shown in Eq. (1) resulted in a higher standard deviation of 0.004 cm1, while the two resulting A0 values became even more different than that of the ground state. Clearly, the Coriolis coupling between the two excited states alone cannot explain the abnormal excited state A0 values satisfactorily. In a further attempt to explain the observed spectrum with more physically reasonable constants, we have also tried to fit these two

19

bands using a Hamiltonian which incorporates the coupling effect of the overall rotation of the molecule with the internal rotation of the methyl group. In other words, we have considered the two bands as subbands A A and E E. Despite our effort, we could not obtain a more satisfactory fit with this Hamiltonian compared to the effective fits reported in Table 3. We also did a closer examination of the Coriolis fit we described above. Since PO is a near prolate top and the B0 and C0 constants of the two excited states appear to behave normally, with very similar values as their corresponding ground state values, the first few low J transitions of the pQ1 (Ka = 0 1) branch are therefore not or hardly affected by the abnormal A0 values and their assignment can be made with high confidence. This analysis provided us the solid evidence that the excited state with the much smaller effective A0 value should have a higher band origin than the other excited state with the much larger effective A0 . It is therefore not surprising that the inclusion of Coriolis coupling changed the A0 values further to the wrong directions. There are likely one or more dark states nearby, which interact with these two upper states through possibly Fermi-type resonance and/or some other mechanism which are so far not accounted for in our Hamiltonian. Further detailed analyses which incorporate other possible perturbations were not pursued because of the limited amount of data and spectral resolution. Our assignments based on the ground state combination differences offer the first solid step to unravel the very complicated perturbations associated with the m1a(CH3) and m2a(CH3) C–H stretching bands of PO. 5. Conclusion We have used the MP2/6-311++G(d,p) harmonic and anharmonic frequency calculations to re-assign the six C–H stretching bands observed in the RT and jet-cooled low resolution FTIR spectra of PO. The rotationally resolved IR spectra of four C–H stretching modes of PO in a free jet expansion have been recorded for the first time. Detailed analyses of the high resolution IR absorption spectra of the three methyl C–H stretching fundamental bands, ms(CH3), m1a(CH3), and m2a(CH3), reveal strong perturbations which are likely due to Coriolis coupling, and possibly Fermi-type resonances and/or other interactions with near-by dark states. Although the ro-vibrational spectra are quite complicated, many of the measured transitions could be assigned solidly based on the ground state combination differences and be explained semi-quantitatively using relatively simple Hamiltonians. It appears that the degree of perturbations in some of these ro-vibrational levels are not as severe as those found in t-ethanol [14] or 1-butyne [8,9]. To the best of our knowledge, this is the first high resolution spectroscopic study on the C–H stretching bands of a chiral molecule. Acknowledgements This research was funded by the University of Alberta, the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation, and Alberta Ingenuity. We thank Drs. N. Borho and M. Suhm for the jet-cooled broadband FTIR spectrum and W. Moffat for the RT gas phase FTIR spectrum. We also gratefully acknowledge access to the computing facilities provided by the Academic Information and Communication Technology group at the University of Alberta. F.X.S. acknowledges the support of a University of Alberta Izaak Walton Killam Memorial Postdoctoral Fellowship and Z.S. thanks Alberta Ingenuity for a Studentship. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2010.05.072.

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