FTIR Spectroscopy of Three Fundamental Bands of H2F+ - The

Article pubs.acs.org/JPCA

FTIR Spectroscopy of Three Fundamental Bands of H2F+ R. Fujimori,†,§ Y. Hirata,† I. Morino,‡ and K. Kawaguchi*,† †

Department of Chemistry, Faculty of Sciences, Okayama University, Tsushima-naka 3-1-1, Okayama, 700 8530, Japan National Institute for Environmental Studies, Onogawa 16-2, Tsukuba, Ibaraki 305-8506, Japan

‡

S Supporting Information *

ABSTRACT: The ν1, ν2, and ν3 bands of H2F+ were observed with a Fourier transform absorption spectroscopic technique in the 3 and 7 μm regions. The ion was produced with a hollow cathode discharge in a F2, He, and H2 gas mixture. A simultaneous analysis of FT data combined with laser spectroscopic data was carried out using the Watson’s A-reduced Hamiltonian to determine molecular constants in vibrationally excited states. The effect of the vibration−rotation interaction between the ν1 and ν3 states was found to be small compared with the case of H2O. The vibration− rotation transitions of the ν2 band were first identified and analyzed to obtain molecular constants in the ν2 state, and the band origin was determined to be 1370.5236 (7) cm−1 with one standard deviation in parentheses. Determined molecular constants can be used to derive the re structure of H2F+ as re(H− F) = 0.9608(6) Å, ∠e(H−F−H) = 112.2(2)° with the error corresponding to the uncertainty of the assumed vibration rotation constant γ2a and the range of the values derived from three pairs of rotational constants.

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of H3+ and HF, H2F+ may be a direct proxy for H3+ in diffuse clouds. Many ab initio calculations have been carried out to obtain the potential energy surface, the vibrational frequencies, the infrared intensities, and the rotational energies of H2F+. In 1983, Botschwina published results of calculations of anharmonic vibrational frequencies for H2F+ isotopomers, making use of vibrational configuration interaction (VCI) in conjunction with an analytical potential energy function obtained by the Coupled Electron Pair Approximation (CEPA).9 In 1990, Bunker et al.10 employed the Morse Oscillator Rigid Bender Internal Dynamics Hamiltonian (MORBID) to calculate the vibration−rotation energies for several low-lying vibrational states by using the potential surface obtained by Petsalakis et al.11 The MORBID result was helpful for rotational assignments of the ν2 band, as described later. Recently, Gutlé and Coudert12 reported a potential energy surface obtained through ab initio calculations for H2F+, where high-resolution experimental data were incorporated to adjust the potential energy surface. It is noted that the adjusted potential energy surface reproduce the high-resolution experimental data with a root-mean-square deviation of 0.014 cm−1 up to J = 4.

INTRODUCTION H2F is isoelectronic to H2O, and the gas-phase ν1 and ν3 fundamental bands of the ion were first detected by Schäfer and Saykally1,2 using the velocity modulation laser absorption spectroscopic technique. A total of 109 lines for ν1 and 217 lines for ν 3 were measured with absolute frequency uncertainties of ±0.005 cm−1. We applied Fourier transform (FT) infrared absorption spectroscopy to observe the ν1, ν3, and ν2 bands. From the transition frequencies of the ν1 and ν3 bands, we obtained the ground-state combination differences to derive the molecular constants in the ground state, which were used for prediction of the pure rotational transition frequencies.3 In 2011, we observed 5 rotational lines of H2F+ in the ground state by using a backward-wave oscillator (BWO) based submillimeter-wave spectrometer.4 Because the BWO measurement was limited in the frequency region below 775 GHz, higher frequency transitions were covered by a tunable far-infrared spectrometer, and 7 lines were detected in the 1305−1851 GHz region.5 These pure rotational transitions were analyzed to obtain the improved ground-state molecular constants, where combination differences determined from the ν1 and ν3 bands were incorporated. H2F+ has attracted much interest of astrochemistry after the detections of HF6,7 and H2+Cl8 in space. In 2013, astronomical searches for H2F+ were carried out using pure rotational transitions with the heterodyne instrument for the far-infrared (HIFI) on board the Herschel Space Observatory, and the result will be published in a later paper. The proton affinity of HF (484 kJ/mol) is larger than that of H2 (422 kJ/mol), but smaller than that of CO (594 kJ/mol) and N2 (494 kJ/mol). Because the H2F+ is thought to be produced through a reaction +

© 2013 American Chemical Society

Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: December 31, 2012 Revised: February 20, 2013 Published: February 22, 2013 9882

dx.doi.org/10.1021/jp312863e | J. Phys. Chem. A 2013, 117, 9882−9888

The Journal of Physical Chemistry A

Article

measurement, presumably due to lower sensitivity of FT spectroscopy compared with laser spectroscopy. Measurement error was estimated to be 0.001 cm−1, which was smaller than that of the laser study. In the ν2 region, we employed the same discharge condition as the ν1 and ν3 band measurement. In this frequency region, many ν2 band spectral lines of H2O have been strongly observed, where the lines are thought to be originated from the inner surface of glass cell and/or leakage. When we applied the H2 discharge without F2, these H2O lines were also observed, so we could discriminate those lines from the H2F+ lines. An example of the observed spectral lines is shown in Figure 2, where a spectrum obtained with a diode laser velocity modulation technique is also shown for comparison. The experimental setup for velocity modulation was the same as ref 15, and the spectrum was observed with a discharge in a NF3 (45 mTorr, 6.0 Pa), H2 (50 mTorr, 6.7 Pa), and He (4 Torr, 532 Pa) mixture by using a 1.2 m long cell with a 20 mm inner diameter. The cell was cooled by a water jacket, and the discharge current was 200 mA peak-to-peak. Although the velocity modulated spectral line was thought to be due to H2F+ with the same phase as known positive ions, wide frequency coverage of the ν2 band region was not possible because of many mode gaps of diode lasers. The wide coverage was realized by FT measurements, and some velocity modulated lines were reproduced in the FT measurements as shown in Figure 2, where the observed line position in the FT measurement agreed with that of velocity modulation spectrum within 0.001 cm−1. The line of Figure 2 was found to be one of the strong lines in the FT measurement and finally assigned to the 505−414 transition. The observed spectral lines in the ν2 region are shown in Figure 3, which also includes the calculated spectral pattern by Bunker et al.10 We noticed the observed spectral pattern was nicely reproduced by the MORBID calculation, if the band origin frequency is shifted to the lower side by 18 cm−1. Although some lines were not explained by MORBID, we concluded from the above coincidence and property under velocity modulation that most of the observed strong lines are due to the H2F+ ν2 band.

The present paper reports the observations and analysis of three fundamental bands of H2F+ measured with by a high resolution FT spectrometer, including the first gas-phase observation of the ν2 band. Determined rotational constants of three vibrational states and the ground state made it possible to derive the equilibrium structure of H2F+. The observed relative intensities of three bands were compared with ab initio results.

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EXPERIMENTAL AND OBSERVED SPECTRA The infrared absorption spectra of H2F+ were recorded with a FT spectrometer (Bruker IFS 120 HR) at Okayama University. The H2F+ ion was produced with a dc hollow cathode discharge in a 5% F2/He and H2 gas mixture with partial pressure of 100 (13.3) and 1000 (133) mTorr (Pa), respectively. The same absorption measurement system as a previous NO3 study13 was used to attain 48 m effective path length with a multipath cell arrangement. The glass part of the cell was newly designed with an inner diameter of 94 mm and a length of 1 m for the hollow cathode discharge, which was connected to two 144 mm inner diameter glass tubes with 250 mm length in both sides, keeping a mirror interval of 150 cm. The discharge part was cooled at moderate temperature −80 to −100 °C using a liquid nitrogen jacket. The ν1 and ν3 band regions were observed with an InSb detector using a low pass filter below 3940 and a 0.016 cm−1 resolution, and the ν2 band region was observed with a HgCdTe detector using a band-pass filter covering 900−1540 and a 0.008 cm−1 resolution. Figure 1 shows an example of the

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RESULTS 1. ν1 and ν3 Bands. In the analysis, the rotational energies were calculated by using the Watson’s A-reduced Hamiltonian for the ground and vibrational states,16 H = (B̃ + C̃)/2J 2 + {Ã − (B̃ + C̃)/2)}Ja 2 + (B̃ − C̃)/4(J+2 + J−2 ) − ΔJ J 4 − ΔJK J2 Ja 2 − ΔK Ja 4

Figure 1. Example of the observed spectrum of the H2F+ ν3 band with a FT spectrometer. The ion was produced in a hollow cathod discharge in a F2/H2/He mixture.

− δJ J2 (J+2 + J−2 ) − δK [Ja 2 , (J+2 + J−2 )]+ /2 + ΦJ J6 + ΦJK J 4 Ja 2 + ΦKJ J2 Ja 4 + ΦK Ja 6 + ϕJ J 4 (J+2 + J−2 )

observed spectrum in the ν3 band, where the number of accumulation was 100. We also observed a spectrum of discharge in pure H2 and confirmed that the spectral lines were not produced in the pure H2 discharge. Wavenumber calibration was carried out by using the HITRAN database of H2O,14 present during the measurements as an impurity. The observed frequencies in our discharge agreed with the H2F+ line frequencies reported by the velocity modulation laser absorption technique2 within measurement error of ±0.005 cm−1. Therefore, we concluded that the observed spectral lines are due to H2F+, where some lines observed by the velocity modulation technique were not detected in the present

+ ϕJK J2 [Ja 2 , (J+2 + J−2 )]+ /2 + ϕK [Ja 4 , (J+2 + J−2 )]+ /2 + LJ J8 + LJJK J6 Ja 2 + LJK J 4 Ja 4 + LKKJ J2 Ja 6 + LK Ja 8

(1)

where J±= Jb ± iJc and [A, B]+ is an anticommutator defined as AB + BA. Higher-order centrifugal distortion constants are needed to fully characterize the spectra of H2F+ with the Watson Hamiltonian, because it is a light asymmetric-top molecule and also the potential barrier to the linearity is relatively low, 6732 cm−1 10 and 6290 cm−1,12 almost half that 9883



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Figure 2. (a) Observed FT spectrum of the H2F+ ν2 band. (b) The same spectral line as (a) was observed with velocity modulated diode laser spectroscopy. The ion was produced in a positive column discahrge in a NF3/H2/He mixture. The phase of the first derivative line shape was consistent with that of the positive ion. The lower part of (b) shows fringe pattern of a vacuum spaced Ge etalon with a free spectral range of 0.00993(1) cm−1.

of H2O.17 In such a case, a Euler series was proposed to fit high J, K transitions, and in the case of H2O, Pickett et al.18 could fit transitions involving levels up to J = 22 and K = 22 to the Euler series with experimental accuracy. Deviation of sixth-order power series and sixth-order Euler series was recognized in rotational energy levels with J = K > 10 from Figure 1 of their paper. In the present H2F+ study, because we treated the rotational levels up to J = 11 and K = 6, so the fitting using the Euler series was not carried out. First, we derived the combination differences for the ground state from the measured frequencies of the ν1 and ν3 fundamental bands. A simultaneous least-squares analysis of the ground-state combination differences and 12 pure rotational transition frequencies was carried out to determine the ground-state constants which have been reported in ref 5 and are also listed in Table 1.

Figure 3. (a) Calculated spectrum of the H2F+ ν2 band by MORBID. (b) Observed spectrum of the ν2 band as stick diagram.

Table 1. Molecular Constants of the H2F+ Iona constant ν0 Ã B̃ C̃ ΔJ ΔJK ΔK δJ × 103 δK × 102 ΦJ × 106 ΦJK × 106 ΦKJ × 104 ΦK × 103 ϕJ × 106 ϕJK × 106 ϕK × 104 LJK × 107 LKKJ × 106 LK × 105 a

v1 = 1

v3 = 1

v2 = 1

ground stateb

3378.7284(12) 33.8947(17) 12.60441(18) 8.88493(18) 0.0010494(35) −0.007151(68) 0.08726(59) 0.3988(14) 0.3448(61) [0.3901]c [0.1768]c −1.11(12) 1.004(65) [0.1809]c [-0.4837]c 0.923(91) [0.5467]c 2.14(73) −1.28(22)

3334.68783(79) 33.22460(52) 12.66997(12) 8.899761(93) 0.0011042(11) −0.007449(17) 0.081234(77) 0.4154(10) 0.3269(17) [0.3901]c [0.1768]c −0.496(23) 0.6824(34) 0.2049(59) [−0.4837]c 0.870(13) [0.5467]c −0.276(72) 0.1568(70)

1370.52356(67) 42.41864(82) 12.89581(15) 8.89639(11) 0.0012840(16) −0.012573(13) 0.26718(26) 0.47878(78) 1.1649(37) [0.3901]c [0.1768]c [-0.7485]c 5.670(20) [0.1809]c [−0.4837]c [0.9240]c [0.5467]c [0.6314]c

34.535552 12.8935908 9.0731570 0.0010852 −0.00740886 0.087808 0.40778 0.34030 0.3901 0.1768 −0.7485 0.7863 0.1809 −0.4837 0.9240 0.5467 0.6314

cm−1 unit. Numbers in parentheses denote one standard deviation and apply to the last digits. bReference 5. cFixed to the ground-state value. 9884



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Table 2. Observed ν2 Band of H2F+ (cm−1) J′ 3 3 3 2 3 2 6 5 4 5 1 1 3 6 4 4 3 4 2 3 2 3 5 1 7 4 5 4 0 7 2 a

Ka′ 3 3 2 2 1 1 1 0 0 1 1 1 0 2 1 1 2 2 0 1 1 1 0 0 1 1 1 0 0 1 1

Kc′ 1 0 1 1 2 2 6 5 4 5 1 0 3 5 4 4 1 2 2 3 2 3 5 1 6 3 4 4 0 6 2

J″ 4 4 4 3 4 3 7 6 5 6 2 2 4 6 5 4 3 4 3 3 2 4 5 2 7 4 5 4 1 7 3

Ka″ 4 4 3 3 2 2 0 1 1 0 2 2 1 3 0 2 3 3 1 2 2 0 1 1 2 2 2 1 1 2 0

Kc″ 0 1 2 0 3 1 7 6 5 6 0 1 4 4 5 3 0 1 3 2 1 4 4 2 5 2 3 3 1 5 3

obs b

1189.5709 1189.5965b 1198.7040 1220.2067 1231.7590 1234.1930 1240.9280 1246.1621 1261.3573 1262.1099 1262.2751 1266.6829 1276.3800 1276.5378 1284.3181 1286.7126 1287.5640 1288.8750 1291.9189 1295.6600 1302.3902 1307.6646 1307.9258 1308.6377 1311.8056 1319.3095 1319.6635 1322.2822 1326.9849 1311.8056 1331.8747

δa

J′

Ka′

Kc′

J″

Ka″

Kc″

obs

δa

3 −4 17 42 −14 17 36 7 16 −16 4 21 21 −4 −15 −9 −11 20 3 −17 10 5 6 −13 4 2 14 −7 −16 4 −3

3 2 1 1 2 3 3 1 4 4 2 5 5 5 6 3 4 5 4 2 6 5 6 7 6 2 7 2 2 8

0 0 0 1 1 1 0 1 1 0 1 1 1 2 2 1 2 0 1 2 0 1 1 0 2 2 1 2 2 1

3 2 1 0 1 2 3 1 3 4 2 4 4 3 4 3 2 5 4 1 6 5 6 7 5 1 7 0 0 8

3 2 1 1 2 3 2 0 4 3 1 5 4 5 6 2 4 4 3 2 5 4 5 6 6 1 6 1 1 7

1 1 1 0 0 0 1 0 0 1 0 0 2 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0

2 1 0 1 2 3 2 0 4 3 1 5 3 4 5 2 3 4 3 2 5 4 5 6 6 0 6 1 1 7

1333.0189 1340.4161 1344.9678 1403.6064 1407.7017 1414.6547 1415.5983 1421.6227 1425.1787 1439.1124 1439.3157 1439.6657 1442.0611 1453.7514 1454.7683 1455.1003 1455.7025 1461.7874 1469.6109 1474.6538 1483.2083 1483.6749 1497.9844 1503.2989 1509.2502 1510.9820 1512.8398 1515.1602 1515.1603 1528.2040

11 3 −13 25 −2 6 15 −7 −19 0 −6 −9 −12 22 −11 −23 −20 −3 −14 −10 −6 5 2 −31 −2 8 22 −24 −25 −3

(calc − obs) × 104 cm−1. bObserved with velocity modulated diode laser spectroscopy.

of inertia into normal coordinates. In the case of H2O, ξ13cJc in eq 2 was estimated theoretically to be very small,20 and the Z value was determined to be −0.31881(65) by fixing ξ13c = 0,21 where the energy difference between (001) and (100) ΔE is 104 cm−1. The Z value has been reported to be 0.442 cm−1 [ΔE = 46 cm−1] and −0.277 cm−1 [ΔE = 81 cm−1] for H2O+ 20 and NH2,22 respectively. In the case of NH2−,23 this effect was found to be small, and the Z parameter was not determined experimentally, although the anion has a small energy difference ΔE = 68 cm−1 between two interactive states. In the case of H2F+, Schäfer and Saykally2 referred to the presence of perturbations at J = 6 and higher for Ka = 5 and 6, but their analysis did not treat explicitly the ν1−ν3 vibration−rotation perturbation. In the present study we improved the accuracy of frequency measurements for strong intensity lines. On the other hand, less intense lines have not been detected by the FT measurements, so we used velocity modulation data for the weaker intensity lines. From a least-squares fitting in a condition of fixing the LKKJ constants of the ν1 and ν3 states to that of the ground state, 28 parameters including Z = 0.0137(28) cm−1 were determined. However, the Z value may be too small compared with those of H2O, H2O+, and NH2, and moreover the standard deviation 0.003 cm−1 of the fitting was worse compared with the fit described above. When two LKKJ in the ν1 and ν2 states were added to a group of variable parameters, the Z parameter could not be determined. This implies that the effect of perturbation between the ν1 and ν3

In the analysis of the vibration−rotation transition frequencies of the ν1 and ν3 bands, the ground-state molecular constants were fixed to the value of Table 1. For excited vibrational states, eq 1 was used for the energy level calculations in each vibrational state. Determined constants are listed in Table 1, where some constants were fixed to the values of the ground state. In the least-squares fitting, the statistical weights of the FT data and laser spectroscopic data were set to be 1 and 0.04, respectively, by considering the measurement errors. The assigned transitions and the difference between the calculated and observed frequencies are provided in A1 of the Supporting Information. The standard deviation of the fitting was 0.0023 cm−1, which is slightly larger than the measurement error of 0.001 cm−1. Although the observed transition frequencies of the ν1 and ν3 bands could be fitted to the standard Watson’s Hamiltonian, LKKJ and LK were determined with different signs between the ν1 and ν3 states, and LKKJ (2.14 × 10−6 cm−1) of ν1 was large compared with the value (0.32 × 10−6 cm−1)19 of the H2O ground state. It may be originated from perturbation from other states. In previous studies of H2O,20 H2O+,21 and NH2,22 the ctype vibration−rotation interaction between the ν1 and ν3 states was considered as follows, Hc = iξ13cJc + Z(Ja Jb + Jb Ja )

(2)

The first term in eq 2 presents the Coliolis interaction and the second term is originated from the expansion of the moments 9885



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Table 3. Rotational Constants and Inertial Defects of H2F+ A (cm−1) B (cm−1) C (cm−1) IA (amu Å2) IB (amu Å2) IC (amu Å2) Δ (amu Å2) αa (cm−1) αb (cm−1) αc (cm−1) a

ground

ν1

ν3

ν2

equilibrium

34.53772 12.88073 9.07554 0.488093 1.308748 1.857479 0.060638

33.89683 12.59166 8.88757 0.497322 1.338793 1.896764 0.060649 0.64089 0.28907 0.18797

33.22681 12.65736 8.90190 0.507350 1.331844 1.893713 0.054519 1.31091 0.22337 0.17365

42.42120 12.86155 8.91064 0.3973869 1.310700 1.891854 0.18376 −6.08348a 0.00212a 0.16654a

32.24688 13.14015 9.33941 0.522768 1.282910 1.804999 −0.00068

Higher order vibration rotation constants γ2a = 0.9 cm−1, γ2b = −0.0085 cm−1, γ2c = 0.00082 cm−1 were assumed.

By inclusion of the γ2a term, the rotational constant A in the vibrational state is expressed as follows,

states is not large in the observed J, K levels. Other interactions, such as the Fermi interaction between the 2ν2 and ν1 states and higher order Coriolis interactions, are expected as in the case of H2O and NH2. The determination of the Z parameter for the vibration−rotation interaction of H2F+ needs more data for the ν1 and 2ν2 bands, although the 2ν2 band has not been detected so far. 2. ν2 Band. As described in the previous section, the MORBID result was helpful for the rotational assignments of the observed spectrum. The assignments were also confirmed by the ground-state combination differences obtained from the analysis of the ν1 and ν3 bands. Eight lines observed with the diode laser velocity modulation technique were also detected in the FT measurement, and we adopted line positions of the 331− 440 and 330−441 transitions from the velocity modulation data, because of the high signal-to-noise ratio. Because the lower states 440 and 441 of these transitions have the rotational energy ∼579 cm−1, the populations on the levels are very low at −80 °C in the FT measurement. On the other hand, the velocity modulation experiment employing room temperature and a high current density was suitable for detection of such transitions starting from high-energy rotational levels. A total of 61 lines with Ka = 0, 1, 2, and 3 in the ν2 band were identified and are listed in Table 2. In the least-squares fitting, some parameters were fixed to the ground-state values, and determined molecular constants in the ν2 state are listed in Table 1. The standard deviation of the fitting was 0.0017 cm−1, which is comparable with the measurement error of 0.001 cm−1. The ν2 band origin frequency of 1370.52356(67) cm−1 was in good agreement with the value of 1373 cm−1 predicted by Botschwina9 who pointed out that the anharmonic contribution to the ν2 frequency is unusually large (ω2/ν2 = 1.063), where ω2 is the harmonic frequency (1460 cm−1).

A v = Ae − α2 a(v2 + 1/2) + γ2 a(v2 + 1/2)2

(3)

Similar formulas are assumed for Bv and Cv by changing A in eq 3 to B and C. Such vibrational quantum number dependence must be considered for the ν1 and ν3 vibrational modes, but analyses of the 2ν1 and 2ν3 bands have not been reported in the Watson’s A reduced Hamiltonian. The changes in rotational constants upon ν1 and ν3 excitations are not large as the case of the ν2 excitation, so we only consider the effect of γ in the ν2 vibrational mode. Because the Watson’s A-reduced rotational constants of H2O have been reported in the v2 = 1 and v2 = 2 states, we derived the γ values for H2O as follows, γ2 a = 0.6036 cm−1

γ2 b = − 0.008528 cm−1

γ2 c = 0.00082 cm−1

by using the data of Matsushima et al.19 for v = 0, Matsushima et al.24 for v2 = 1, and Flaud and Camy-Peyret21 for the v2 = 2 state. When these γ values were assumed for the H2F+ ν2 state, the inertial defect in the equilibrium structure was determined to be −0.005 amu·Å2, which is small compared with the value of −0.01 amu·Å2 in the case of γ2a = 0, but it is still large for the equilibrium structure. The inertial defect at equilibrium should contain only electronic contribution, and in the case of H2S it is expected to be 0.0001 amu·Å2.25,26 The change in the rotational constant A between v2 = 0 and v2 = 1 is 7.78 cm−1 for H2F+, which is much larger than 3.25 cm−1 for H2O, so the γa value may be larger than that of H2O. By considering these facts, we assumed γa = 0.7−0.12 cm−1 and obtained the equilibrium structure. Table 3 lists the case of γa = 0.9 cm−1, giving the inertial defect of −0.00068 amu·Å2. The equilibrium structure is obtained as follows,

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DISCUSSION The present study reports the first measurement of the ν2 vibration−rotation transitions of H2F+. We could determine the rotational constants in the three fundamental vibrational states using the Watson’s A-reduced Hamiltonian. From the fitted constants in each vibrational state, the rotational constants, A, B, C were derived after correcting the centrifugal distortion contributions.16 Table 3 lists the corrected rotational constants and the vibration−rotation constant α values. Some molecular constants in the ν2 state are largely changed from those of the ground state. If we use only the ν1, ν2, ν3, and ground-state data, higher-order vibration−rotation constants γia, γib, γic (i: vibrational mode) could not be determined, although they may contribute some degree of the equilibrium values of Ae, Be, Ce.

re(H−F) = 0.9608(6) Å

and

∠e(H−F−H) = 112.2(2)°

where the uncertainty originates from the range of assumed γa value and the range of the values derived from three pairs of rotational constants in the case of a relatively large inertial defect. The values are compared with theoretically predicted values; Bunker et al.’s7 of 0.96023(17) Å, and 135.1(2)°, and Botschwina’s9 0.966 Å and 112.7° and recent Gutlé and Coudert’s12 of 0.960290(44) Å, and 112.49948(55)°. Gutlé and Coudert reported an ab initio potential energy surface and further improved it by fitting the high-resolution spectroscopic data, including five pure rotational transitions, the ν2 band 9886



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Table 4. Observed Intensities of Vibration−Rotation Transitions in the Three Bands of H2F+ and the Band Intensity Ratioa ν1 band

ν2 band

transition

Sb

calcc

obsd

transitiona

110−101

1.500

0.111

0.477

110−101 212−101

0.112 0.211

414−303

(I2/I1 = 1.64 212−303 414−303

523−514

1.402 2.786

4.299

0.041 0.073 (I2/I1 = 1.61 0.234

0.288

505−514 523−514

(I2/I1 = 2.40 330−221

2.442

0.681 (I2/I1 = 1.26

0.363

110−221

321−312 423−312 303−312

2.058 1.918 2.798

0.054 0.480 0.047 0.350 0.080 0.527 (I2/I1 = 2.09 I2/I1 = 1.80(45)

303−312

average ratio

ν3 band

Sb

calcc

(i) Transitions from 101 1.500 0.040 1.500 0.039 I3/I1 = 4.42) (ii) Transitions from 303 2.779 0.211 I3/I1 = 3.70) (iii) Transitions from 514 3.385 0.380 3.869 0.111 I3/I1 = 4.77) (iv) Transitions from 221 1.500 0.398 I3/I1 = 4.69) (v) Transitions from 312 2.798 0.296

obsd

transitiona

Sb

calcc

obsd

0.297 0.366

000−101 110−101

1.000 1.990

0.100 0.199

1.317 2.928

0.410

202−303 404−303

2.964 3.916

0.298 0.391

2.450 2.807

0.256 0.209

413−514

4.759

0.479

1.440

0.279

220−221

3.316

0.330

2.30

0.478

211−312 313−312 413−312

2.662 0.587 3.731

0.267 0.059 0.374

1.915 0.462 2.530

I3/I1 = 3.75) I3/I1 = 4.27(51)

I1, I2, and I3 are proportional to the square of the dipole moments for the ν1, ν2, and ν3 bands, respectively. Numbers in parentheses denote one standard deviation. bLine strength. cCalculated intensity by Gutlé and Coudert.12 dObserved integrated intensity with a unit of absorbance·cm−1 × 10−4. The uncertainty was estimated to be 0.31 × 10−5 and 0.90 × 10−5 absorbance·cm−1 for the ν2 and ν1/ν3 bands, respectively. a

origin frequency, and the ν1 and ν3 vibration−rotation transition frequencies. The potential energy surface was fitted using the analytical expression introduced by Partridge and Schwenke.27 The root-mean-square error was 0.014 cm−1 for high-resolution data with J < 5. Supplementary Table S2 in their paper lists the predicted ν2 transition frequencies with intensities, and they are found to be in good agreement with the observed frequencies in the present study within 0.038 cm−1 in the case of J < 5. Table 4 lists the observed integrated intensities for vibration−rotation transitions of the three bands, where we used transitions with a common lower rotational state in three fundamental bands, which makes a direct comparison possible without incorporating the Boltzmann factor. The observed integrated intensity from the same lower rotational state is proportional to νμ2S, where ν is the transition frequency, μ is the transition dipole moment, and S is the line strength. In the same band, most of the observed integrated intensities were proportional to the line strength (S) within experimental error, which is given in the footnote of Table 4. However, there was a discrepancy in the intensities of the 505−514 and 523−514 transitions of the ν2 band. The line strength S listed in Table 4 was calculated by using wave functions of an asymmetric rotor after diagonalization of the energy matrix. In the case of transitions with the common lower level in the same band, the intensities are proportional to the νS, so the intensity ratio of above two transitions is expected to be 1.27 by using S listed in Table 4. On the other hand, the observed ratio was 0.81, which is close to the ratio of 0.62 predicted by Gutlé and Coudert.12 This implies that the large amplitude motion may affect rotational intensities. From the observed intensities, we derived ratios of the square of the transition dipole moment to be I2/I1 = 1.80(45) and I3/I1 = 4.27(51), which are comparable with 1.04 and 3.56, respectively, predicted by MORBID. If the

transitions from the 514 level are not included in the calculation, the ratios become 1.65 and 4.14, which are within the error limit.

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SUMMARY The high-resolution FT spectrum of the ν2 band of H2F+ has been observed in the gas phase for the first time. The ν1 and ν3 bands were also observed, and the data were analyzed by the Watson’s Hamiltonian to derive molecular constants at equilibrium structure. By considering the higher-order vibration rotation interaction constants, the rotational constants in equilibrium structure were derived.

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ASSOCIATED CONTENT

S Supporting Information *

Tabulation of the assigned transitions of the ν1 and ν3 bands and their calculated minus observed values (A1). References 7, 8, and 14 include more than ten authors, so the references are given. This information is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address §

Solar Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank T. Amano for providing us with his computer program including the vibration−rotation interaction. We are 9887



Article

(19) Matsushima, F.; Odashima, H.; Iwasaki, T.; Tsunekawa, S.; Takagi, K. Frequency Measurement of Pure Rotational Transitions of H2O from 0.5 to 5 THz. J. Mol. Struct. 1995, 352/353, 371−378. (20) Dinelli, B. M.; Crofton, M. W.; Oka, T. Infrared Spectroscopy of the v3 Band of H2O+. J. Mol. Spectrosc. 1988, 127, 1−11. (21) Flaud, J. M.; Camy-Peyret, C. The Interacting States (020), (100), and (001) of H216O. J. Mol. Spectrosc. 1974, 51, 142−150. (22) McKellar, A. R. W.; Vervloet, M. A Combined Analysis of The v1, v3, and 2v2 Vibrational States of the NH2 Radical Using Fourier Transform Absorption and Emission data. J. Mol. Spectrosc. 1990, 142, 319−335. (23) Tack, L. M.; Rosenbaum, N. H.; Owrutsky, J. C.; Saykally, R. J. Velocity Modulation Infrared Laser Spectroscopy and Structure of the Amide Anion (NH2−). J. Chem. Phys. 1986, 85, 4222−4227. (24) Matsushima, F.; Tomatsu, N.; Nagai, T.; Moriwaki, Y.; Takagi, K. Frequency Measurement of Pure Rotational Transitions in the v2 = 1 State of H2O. J. Mol. Spectrosc. 2006, 235, 190−195. (25) Oka, T.; Morino, Y. Calculation of Inertia Defect: Part II. Nonlinear Symmetric XY2 Molecules. J. Mol. Spectrosc. 1961, 8, 9−21. (26) Burrus, C. A. Zeeman Effect in the 1- to 3-Millimeter Wave Region: Molecular g Factors of Several Light Molecules. J. Chem. Phys. 1959, 30, 976−983. (27) Partridge, H.; Schwenke, D. W. The Determination of an Accurate Isotope Dependent Potential Energy Surface for Water From Extensive ab initio Calculations and Experimental Data. J. Chem. Phys. 1997, 106, 4618−4639.

grateful K. Matsumura for collaboration of velocity modulated diode laser spectroscopy of the H2F+ ν2 band. K.K. thanks H. S. P. Müller for helpful suggestions about the analysis and astronomical observations. The present study was partly supported by the Grant-in-Aid (Grant No. 21104003) from the Ministry of Education, Culture, Sports, Science and Technology of Japan

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REFERENCES

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FTIR Spectroscopy of Three Fundamental Bands of H2F+ - The

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