The Limits of Rovibrational Analysis: The Severely Entangled Î½1

Article pubs.acs.org/JPCA

The Limits of Rovibrational Analysis: The Severely Entangled ν1 Polyad Vibration of Dichlorodifluoromethane in the Greenhouse IR Window Evan G. Robertson,†,* Chris Medcraft,‡,∥ Don McNaughton,‡ and Dominique Appadoo§ †

Department of Chemistry and La Trobe Institute of Molecular Sciences, La Trobe University, Melbourne, Victoria 3086, Australia School of Chemistry, Monash University, Melbourne, Victoria 3800 Australia § Australian Synchrotron, 800 Blackburn Rd, Clayton, Victoria 3168, Australia ‡

S Supporting Information *

ABSTRACT: Five intense bands of dichlorodifluoromethane (CFC-12, or R12) in the infrared atmospheric window help make it a major greenhouse contributor. These include the ν1 fundamental at 1101.4 cm−1 and the ν2 + ν3 combination at 1128.6 cm−1. Highresolution spectra measured using the Australian Synchrotron Far-Infrared beamline were analyzed, and transitions of C35Cl2F2 were assigned to ν1, ν2 + ν3, and the ν3 + 2ν5 combination at 1099.7 cm−1. The (v3 = 1; v5 = 2) state couples indirectly to v1 = 1 via Fermi resonances linking both states with v2 = v3 = 1. The v1 = 1 rotational levels are further riddled with perturbations and avoided crossings due to Coriolis resonance with the upper vibrational states of ν2 + ν9 at 1102.4 cm−1 and (indirectly) ν2 + ν7 at 1105.8 cm−1. A global treatment of all these states fits the observed line positions and satisfactorily accounts for the significant intensity of ν2 + ν3. Spectral simulations elucidate resonance perturbations that affect the distribution of IR absorption in the CF stretch region, and consequently the global warming potential of R12. Combination levels derived from rovibrational analysis lead to reassessment of the gas phase wavenumber values for the ν3 (458.6 cm−1), ν7 (437.7 cm−1) and ν9 (436.9 cm−1) fundamentals of C35Cl2F2, consistent with a cold, vapor phase far IR spectrum and previously published solid state spectra. B3LYP and MP2 anharmonic frequency calculations provide further support. At the MP2/aug-cc-pVTZ level, the root mean square (r.m.s.) error for unscaled anharmonic fundamentals is 6.2 cm−1, decreased to 1.7 cm−1 if only considering the seven lowest wavenumber modes, and integrated band intensities according with experimental literature values. Smaller basis sets produce band strengths that are too high. Low-resolution band assignments are reported for C35Cl37ClF2, C37Cl2F2, and 13C35Cl2F2. almost half the 0.36 Wm−2 from all halocarbons.5 R12 has a very large 100 year Global Warming Potential of 10 200,5 due in large part to its high radiative efficiency. It has five intensely absorbing IR bands, all of which lie within the atmospheric IR window of transparency (800−1400 cm−1) that allows some radiation to pass directly from Earth’s surface to space. The antisymmetric CCl2 stretch (ν6) and CF2 stretch (ν1, ν8) fundamentals and the ν2 + ν3 and ν3 + ν7 combinations owe their intensity to the large bond dipoles associated with multiple halogen substitution.6 It is worth noting that the coincidence of the ν1 and ν6 spectral regions with available CO2 laser lines has led to multiphoton dissociation schemes employing IR radiation for 13C isotopic enrichment from CCl2F2.7−11 Apart from the fundamental interest in these greenhouse related absorptions, IR spectroscopy is relevant for atmospheric monitoring by ground, airborne, or satellite based spectrometer

1. INTRODUCTION Dichlorodifluoromethane is also known as CFC-12 or R12, alluding to its widespread use as a refrigerant in the 20th century. Unfortunately, the chemical stability that made it so appealing for industrial application turned out to be something of a curse in the context of environmental impact. R12 has an atmospheric lifetime of ≈ 100 years,1 and recent analysis of Advanced Global Atmospheric Gases Experiment (AGAGE) observations even suggests a slightly longer value of 111 years.2 With the discovery of the role of CFCs in stratospheric ozone depletion, R12 was banned under the Montreal Protocol, and emissions fell throughout the 1990s. Tropospheric abundance peaked at 544 ppt during 2001−2004, falling slowly to just below 525 ppt in 2013.3 Even at these seemingly low concentrations, R12 is a significant greenhouse gas, ranking fourth after carbon dioxide (CO2), methane (CH4), and very recently nitrous oxide (N2O) in radiative forcing. Differences in the spectrum of outgoing longwave radiation between 1970 and 1997 provided evidence of increased IR absorption due to R12.4 Its contribution of 0.17 Wm−2 represents 6.0% of the total of 2.83 Wm−2 from well mixed greenhouse gases and is © 2014 American Chemical Society

Received: August 30, 2014 Revised: October 22, 2014 Published: October 22, 2014 10944

dx.doi.org/10.1021/jp5087784 | J. Phys. Chem. A 2014, 118, 10944−10954

The Journal of Physical Chemistry A

Article

Table 1. Experimental Conditions for Measurement of High-Resolution (0.00096 cm−1) Spectra sample temperature

sample pressure

path length

region

IR source

no. scans

figure

153−159 K 142−153 K

150 Pa 2.0 Pa 2.8 Pa 6.0 Pa 4.4 Pa ″

2.5 m 2.5 m ″ ″ 6.6 m ″

400 - 760 cm−1 950−1840 cm−1 ″ ″ 700−1360 cm−1 ″

synchrotron synchrotron ″ ″ synchrotron globar

508 136 18 12 272 236

Figure 5 Figures 1b, 4, and 6

298 K a

Figure 1ca Figure 1ca

These two sets of scans were combined following calibration and postzero filling to a total factor of 16.

Table 2. Experimentally Determined Gas Phase Fundamental Band Positions for C35Cl2F2, and Isotopic Shifts for 37Cl- and 13CSubstituted Species (in cm−1) mode 1 2 3 4 5 6 7 8 9

symmetrya A1 (b-type) A1 A1 A1 A2 B1 (a-type) B1 B2 (c-type) B2

description CF2 s-str. CCl2 s-str. CF2 sciss. CCl2 sciss. CF2 twist CCl2 a-str. CF2 wag CF2 a-str. CF2 rock

δ35Cl37Cl

C35Cl2F2

δ 37Cl2

b

1101.3756 668.4456 458.6c 261.6 320.7 923.2396b 437.7d 1161.0851 436.9e

δ 13C

reference

−27.6

this work 23 this work 27 27 16, 18, 19, 8 this work 23, 21, 35 this work

−1.238 −2.9b −2.5 −1.2 −1.420

−5.0 −2.3 −3.345

−47

−0.120

−0.238

−31.1

a Note that the designation of B1 and B2, and therefore mode number labels for ν6-ν9 differ in some of the earlier low-resolution studies. bObserved band centers. The Fermi resonance deperturbed values are 915.7 cm−1 for ν620 and 1104.44 cm−1 for ν1. cC35Cl2F2: from 1384.9 {ν3 + ν6, 310610} − 926.3 {ν3 + ν6 − ν3, 311610} = 458.6 cm−1. C35Cl37ClF2: 1380.5 cm−1 − 924.8 = 455.7 cm−1. Further evidence supporting these values for ν3 are given in the text. d1105.78 {ν2 + ν7} − 668.45 {ν2} − (−0.38) {x2,7 MP2/aug-cc-PVTZ} = 437.71 cm−1. Alternative x2,7 values are of very similar magnitude: −0.4 cm−1 {CCSD(T)/cc-pVTZ36}, −0.51 cm−1 {B3LYP/aug-cc-pVTZ}. e1102.43 {ν2 + ν9} − 668.45 {ν2} − (−2.89) {x2,9 MP2/augcc-PVTZ} = 436.88 cm−1.

R12, the ν2 + ν3 combination that has not been studied at all, perhaps overlooked through being somewhat obscured in room temperature spectra and sandwiched between the ν1 and ν8 fundamentals. Another matter to be settled is the uncertainty that remains concerning some of the lower wavenumber fundamentals, despite vibrational studies spanning 80 years. The liquid phase Raman spectrum was reported as early as 1932,26 when the technique was known as “Smekal−Raman” (in recognition of Adolf Smekal’s prediction of the effect in 1923 and its experimental confirmation by C. V. Raman in 1928). The R12 Raman experiment was a heroic effort requiring liquid NH3 as a coolant, mercury arc lamps as source, and plate exposures of 10 or 20 h. Vapor phase IR27 and Raman28 measurements have been supplemented by low-temperature solid phase measurements.29 However, unambiguous assignment of the ν3, ν7, and ν9 fundamentals in the 430−470 cm−1 region, particularly in the gas phase, has been hindered by weak IR absorption and overlapping bands, including hotbands and those from the different CCl2F2 isotopologues present in the sample in natural abundance. In this work, the assignment of combination levels through high-resolution analysis, the measurement of a cold, vapor phase far IR spectrum, and comparison with high level anharmonic vibrational frequency calculations help to resolve the issue.

systems. Quantification relies on comparison with library spectra collected at a discrete set of pressures and temperatures, or better still from simulations based on precisely known molecular constants that are more universally applicable to any set of conditions. A number of investigations have focused on the quantitative aspects, measuring integrated band strengths of R12 within the atmospheric window (e.g., refs 12−15). High-resolution investigations have been conducted for the ν6 band of C35Cl2F2,16,17 C35Cl37ClF2,17,18 and C37Cl2F2.19 D’Amico et al.20 subsequently studied the ν3 + ν7 combination at ≈ 888 cm−1, the fourth strongest band in the IR atmospheric window, with its considerable intensity stolen from ν6 via a Fermi resonance. A Fourier transform infrared (FTIR) spectrum of R12 cooled to a rotational temperature of 40 K in a jet expansion was analyzed in the ν821 and ν122 regions. Our recent study based on 150 K and ambient temperature spectra provided a more extensive set of assigned transitions and improved molecular constants for ν8, along with the first analysis of the ν2 symmetric CCl2 stretch band centered around 668 cm−1.23 The ν1 band that is further scrutinized in this work was first examined via a diode laser spectrum of R12 cooled to 200 K.24 In the face of evident Coriolis perturbations, series of transitions with restricted quantum number range were assigned and an effective (one state) fit obtained. The jetcooled FTIR spectroscopy work yielded an entirely different set of transitions with lower J but higher Ka and provided a second set of effective constants.22 However, it was recognized that, without treating the resonance perturbation(s), the two sets of ν1 constants cannot be reconciled: predictions from either one do not accord with observed transitions from the other.25 A more satisfactory treatment of ν1 is one of the aims of the present study. We also examine the fifth most intense band of

2. EXPERIMENTAL SECTION The spectra analyzed in this work were measured using a Bruker IFS125HR spectrometer on the Far-Infrared beamline of the Australian Synchrotron, as described previously.23 Briefly, an external SiB detector was employed for the far IR region, and a mercury−cadmium−telluride detector was used for mid10945



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Table 3. Unscaled vibrational wavenumber values computed at the MP2/aug-cc-PVTZ level for C35Cl2F2, and isotopic shifts for 37 Cl and 13C substituted species harmonic mode

symmetry

1 A1 2 A1 3 A1 4 A1 5 A2 6 B1 7 B1 8 B2 9 B2 rms deviation/cm−1c

anharmonic

C35Cl2F2

IR int.a

Raman act.a

C35Cl2F2

δ35Cl37Cl

δ37Cl2

δ 13C

IR int.a

1115.4 675.1 464.5 266.7 324.8 925.8 444.1 1171.6 442.1 1.3

281 10.1 0.056 0.11 0.00 371 0.028 195 0.073

2.60 9.80 6.95 1.44 0.86 2.86 2.40 1.62 0.77

1090.2 667.2 459.3 264.3 321.5 920.9 439.6 1146.8 438.6 6.2

+0.5b −1.3 −3.0 −2.6 −1.0 −1.3b −3.8 −0.10 −1.0

−1.5b −2.6 −6.9 −5.2 −2.0 −3.2b −6.7 −0.26 −2.0

−26.8 −4.5 0.1 −0.1 0.1 −46.9b 0.1 −30.4 −2.8

278 9.7 0.069 0.12 0.00 374 0.012 190 0.059

Units km mol−1 for IR intensity and Å4 amu−1 for Raman activity. bThe 37Cl isotopic shifts for ν1 and ν6 in particular are sensitive to the positions of nearby Fermi interacting levels. Hence these shifts are computed using the MP2/aug-cc-PVTZ anharmonic force field, but with the harmonic frequencies in the Gaussian09 input files adjusted by the amount required to produce in C35Cl2F2 the observed (anharmonic) fundamental. The uncorrected anharmonic MP2/aug-cc-PVTZ isotopic shifts are −0.7 cm−1 and +0.3 cm−1 for ν1 and −1.4 cm−1, −3.8 cm−1, and −46.4 cm−1 for ν6. c To calculate r.m.s. deviations, unscaled anharmonic wavenumber values are compared to observed band centers in Table 2, while harmonic wavenumbers are scaled by 0.990 and deperturbed experimental values used for ν1 and for ν6. a

for the ν5 CF stretch mode of C2F4.33,34 This is particularly evident for ν6, in Fermi resonance with ν3 + ν7. In the 12C species, ν6 is elevated by the resonance as ν3 + ν7 lies lower in energy,20 but in the 13C species, the lower wavenumber band at 876 cm−1 is more intense and so is assigned to ν6 rather than its accompanying (ν3 + ν7) band at ≈905 cm−1.8 As a result, the 13 C−12C shift is −47 cm−1, rather than −32.5 cm−1 as computed at the harmonic level. Given the superior performance of the MP2/aug-cc-pVTZ calculations, this level was chosen to provide Fermi parameters, anharmonic xij constants, rovibrational α values, and IR band intensities for comparison with experiment in the analyses that follows. Results from other levels of theory are summarized in Supporting Information Table S1. 3.2. The ν1 Band System of C35Cl2F2. High-resolution spectra of R12 in the region of the b-type ν1 and ν2 + ν3 bands are compared in Figure 1. The top traces show the jet cooled (40 K) spectrum at low resolution (0.25 cm−1) and at 0.0034 cm−1 resolution, which yielded a set of around 400 lines with Jmax = 27, Ka max = 19, Kc max = 13 in earlier work on ν1.22 The enhanced resolution of the present measurements produces a spectrum with well-resolved lines at the higher temperature of 150 K (middle trace) that was analyzed to obtain most of the assigned transitions. Assignments were made using Loomis− Wood plotting software37 to pick out pP and rR series with constant Ka, and confirmed using ground state combination differences. The room temperature spectrum in the lower trace was also examined to assign some transitions in the wings, and so extend the quantum number range from Jmax 73 to 96. Fits to the data were performed using Pickett’s SPFIT software.38 The assigned transitions show clear signs of resonance-induced perturbations that were noted but not treated in earlier studies. The residual plots from an effective one state fit to ν1 in Figure 2a show two regions of avoided crossings. From the patterns it is clear that both arise from vibrational states at higher energy, arbitrarily designated “p” and “q”. The first lot of avoided crossings in rotational levels around J′ = 20 has selection rule Ψ1Kc ↔ ΨpKc + 1 and the second set around J′ 40−50 has selection rule Ψ1Kc ↔ ΨqKc + 2. In the earlier studies, transitions of the jet-cooled (40 K) spectrum were assigned only to quantum numbers below the first

IR spectra. High-resolution room-temperature spectra were obtained using R12 (Sigma-Aldrich, >99% purity) in a standard White cell with path length set to 6.6 m. A cooling cell30 fitted with KBr or CaF2 windows and with optical path set to 2.5 m was used to measure low-temperature spectra. The sets of highresolution measurements are summarized in Table 1. Spectra were calibrated by N2O lines in the mid-IR region and residual CO2 in the far IR region, through comparison with the HITRAN database.31

3. RESULTS 3.1. Ab Initio Calculations. Experimental gas phase values for the fundamentals of R12 are summarized in Table 2. This includes revised values for ν3, ν7, and ν9 derived from this work that are discussed in detail later on. For the purpose of assigning symmetry and hence mode number labels, the IIl representation (a,b,c = x,z,y) is used here so that CF2 lies in the yz plane and CCl2 in the xz plane. This is consistent with all the previous high-resolution studies, and was explained by D’Amico et al.20 To avoid confusion, it should be noted that several (though not all) of the earlier low resolution studies instead employed the IIr representation (a,b,c = y,z,x), which swaps the designation of B1 and B2, and therefore affects the mode number labels for ν6−ν9. To facilitate the interpretation of the vibrational spectra of R12, anharmonic vibrational frequency calculations at the B3LYP/6-311+G(d,p), B3LYP/aug-ccpVTZ, MP2/6-311+G(d,p), and MP2/aug-cc-pVTZ levels were performed using Gaussian09.32 The MP2/aug-cc-pVTZ results summarized in Table 3 provided the best agreement with experiment. The r.m.s. error for the anharmonic fundamentals is 6.2 cm−1, and just 1.7 cm−1 excluding CF stretching modes ν1 and ν8. The harmonic frequencies, when scaled by 0.990 and compared to the Fermi resonance deperturbed experimental values, have an r.m.s error of 1.3 cm−1. The 37Cl and 13C isotopic shifts are also very well reproduced by the anharmonic calculations. In the case of ν1, ν6 and ν8, the shifts are affected by anharmonic contributions and a harmonic force field alone is not sufficient. This is generally an indicator of Fermi resonance, and the largest effects occur when isotopic substitution causes interacting levels to switch their energy ordering, as was recently observed and elaborated 10946



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Figure 1. Experimental spectra of R12 in the ν1 region. At each temperature, the upper trace is at 0.5 cm−1 resolution, and the lower trace at high resolution: 0.0034 cm−1 for the jet expansion measurements from ref 22 (a), or 0.00096 cm−1 (b,c). Arrows mark features in the low-resolution jet spectrum at 1105.8 cm−1 assigned to the Q-branch of ν2 + ν7 (for C35Cl2F2), and in the ν2 + ν3 region, the centers of b-type band profiles at 1128.61 cm−1 (C35Cl2F2), 1124.77 cm−1 (C35Cl37ClF2), and 1120.51 cm−1 (C37Cl2F2). The ν1 band center for 13C35Cl2F2/13C35Cl37ClF2 at 1073.7 cm−1 is also indicated. Figure 2. Avoided crossings in ν1. (a) Obs.-calc. residuals from an effective one-state fit (points) and from the resonance treated fit of Table 4 (hollow circles) showing avoided crossings with v2 = v9 = 1 occurring around J′ = 20 and with v2 = v7 = 1 at higher J′. (b) Reduced energy for Kc = 0 rotational levels: ν̃′ = E(JKa=J, Kc=0) − 1/2(B1 + C1). J − A1·J2, where the rotational constants are from Table 4. The plotted lines show deperturbed values computed from the parameters of Table 4 but with the Fermi term, W23,355, set to zero.

crossing,22 while transitions from the 200 K diode laser spectrum were limited to the second region between the two crossings.24 Neither study included the high J transitions above the second crossing. A series of preliminary fits trialling different resonance interaction parameters indicated that these perturbations could be best treated by including vibrational states “p” (≈1102.5 cm−1) linked via a first-order a-axis Coriolis term Ga1,p, and “q” (≈1106.0 cm−1) linked via a second order c-axis Coriolis term Fab 1,q (see Table 4 footnote for definitions of Coriolis G and F parameters). The positions and symmetries of the two states strongly suggest their assignment to v2 = v9 = 1 and v2 = v7 = 1, respectively. Their fitted rotational constants B29 = 2591 MHz and B27 = 2710 MHz diverged from the ground state value of B0 = 2639 MHz in such a way as to indicate first-order b-axis b Coriolis coupling between them. Inclusion of this G29,27 interaction significantly improved the fit and eliminated the need for the Fab 1,27 term: the second set of crossings from Figure 2a was found to result from indirect coupling as shown in Figure 3. The fitted Gb29,27 parameter of ≈2270 MHz is consistent with the similar value of Gb349,347 = 2180 MHz found between the upper states of ν3 + ν4 + ν7 and ν3 + ν4 + ν9.23 This is expected since in both instances the relevant vibrational quantum numbers are (v9 = 0; v7 = 1; ...) ↔ (v9 = 1; v7 = 0; ...) and hence Gb27,29 ≈ Gb347,349 ≈ Gb7,9 = ςb7,9Be(ω7 + ω9)(ω7ω9)−1/2, where ςb7,9 is the dimensionless Coriolis parameter. The weak peak observed in the low-resolution jet-cooled spectrum of Figure 1a at 1105.8 cm−1 can be attributed to Q-branch

transitions of ν2 + ν7 with intensity enhanced by its resonance interactions. Figure 2b shows another major perturbation resulting from Fermi resonances. Two sets of transitions were evident and assignable in the spectrum, one at slightly higher wavenumber with Ka′ series from 0 to 25, and another at lower wavenumber with Ka′ series ranging from 18 to 68 that was not recognized at all in the earlier studies.22,24 Both upper and lower sets of transitions could be fitted by introduction of another vibrational state originating at 1099.8 cm−1, linked to v1 = 1 by an anharmonic resonance of magnitude 15.3 GHz (0.51 cm−1). The only state of appropriate A1 symmetry in this region is (v3 = 1;v5 = 2). The associated ν3+2ν5 band is expected to have vanishingly small zero-order intensity. However, in the region of the crossing (around Ka′ 23) transitions notionally assigned as ν3+2ν5 gain intensity as the Ψ355 wave functions are considerably mixed with Ψ1. There is also heavy mixing between Ψ1 and Ψ29, to an extent that diagonalization of the Hamiltonian results in severe scrambling of the Ka and vibrational state identities within the Wang sub-blocks. This 10947



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Table 4. Spectroscopic Constants for the ν1 Band System of C35Cl2F2, Using Watson’s a-Reduced Hamiltonian in the Ir Representation parameter

ground statea

v1 = 1

v2 = v9 = 1

−1

v2 = v7 = 1

1104.4363(683)b 1102.4346(2) 1105.7809(13) ν0 /cm A /MHz 4118.87378 4085.4180(655) 4113.790(717) 4111.453(46) B /MHz 2638.674317 2633.2803(33) 2641.710(48) 2630.957(56) C /MHz 2233.691145 2233.8899(104) 2233.2020(106) 2230.7510(203) ΔJ /kHz 0.448801 0.45271(104) 0.448801c 0.448801c ΔJK /kHz −0.444257 −0.6567(141) −0.444257c −0.444257c ΔK /kHz 1.5875 1.3337(159) 1.6989(71) 1.3409(97) δJ /kHz 0.109591 0.11081(52) 0.109591c 0.109591c c δK /kHz 0.133538 0.0420(52) 0.133538 0.133538c no. of lines: 3835 max J, Ka, Kc 96, 68, 96 RMS error/cm−1 0.00015 Fermi resonancesd /MHz: W23,355 = 4.306(48) × 104; W1,23 = 2.640(24) × 105 a a b Coriolis resonancesd /MHz: Ga1,29 = −940(37); Fbc 1,29 = −0.4663(52); G29,355 = −343.2(20); G29,23 = 5123(49); G29,27

v3 = 1; v5 = 2

v2 = v3 = 1

1099.8888(17) 4151.071(31) 2635.5997(128) 2227.0051(172) 0.448801c −0.444257c 4.1590(355) 0.109591c 0.133538c 206 38, 25, 15 0.00015

1125.3193(666) 4117.510(740) 2633.0533(42) 2230.5300(115) 0.46430(265) −0.2784(147) 1.5128(168) 0.11670(133) 0.2850(111) 1540 70, 43, 70 0.00029

= 2269.13(52)

Ground state constants taken from ref 39. Sextic centrifugal distortion constants for all states constrained to ground state values of ref 39: ΦJ = 1.17 × 10−4 Hz; ΦJK = −5.487 × 10−4 Hz; ΦK = 2.17 × 10−3 Hz; ϕJ = 3.935 × 10−5 Hz; ϕJK = 8.18 × 10−5 Hz; ϕK = −2.231 × 10−3 Hz. bNumbers in parentheses represent one standard deviation of the fitted value. cFixed to ground state value. dFermi resonance terms, W, are the direct off-diagonal matrix element. The Coriolis terms G (equivalent to ξ) and F (equivalent to η) are defined, for the a-axis in this example, as ⟨v1|ψfirst order|v2+9⟩ = iGa1,29Pa for the first-order, and ⟨v1|ψsecond order|v29⟩ = Fbc 1,29 (PbPc + PcPb) for the second-order interaction. a

around Ka′ = 38. An effective, one upper state fit was obtained by assigning zero weight to around 700 of the more heavily perturbed ν2 + ν3 transitions in the vicinity of these crossings. The results, summarized in Supporting Information Table S2, include a band origin of 1128.60 cm−1. The pattern of residuals points to perturbing states at higher energy than this. In particular, a series of trial fits suggested the avoided crossings around Ka′=38 can be treated by introduction of a perturbing state “r” originating at ≈1135.6 ± 0.6 cm−1 and connected by a first order b-axis Coriolis term Gb23,r ≈ 75 ± 5 MHz. The only nearby vibrational state with the required A2 symmetry is v4 = v7 = v9 = 1, predicted to occur at 1135.9 cm−1. It will be strongly coupled to (v4 = 1; v7 = 2) (predicted at 1136.4 cm−1) and to (v4 = 1; v9 = 2) (predicted at 1135.1 cm−1) via the same ςb7,9 term discussed earlier, except that the interaction terms will be even larger: Gb477,479 ≈ Gb479,499 ≈ √2Gb7,9 due to the vibrational quantum number dependence. The close proximity and strong coupling of these three states precluded further progress with the analysis of the remaining avoided crossings. However, even without accounting for those local resonances, the effective one upper state treatment of ν2 + ν3 was sufficient to proceed with analysis of the Fermi resonance with ν1. Next, the transitions assigned to ν1, ν3+2ν5 and ν2+ν3 were fitted together in a combined treatment that involved five upper states, and their interactions are outlined in Figure 3. Beginning with the effective one state parameters for v2 = v3 = 1 and the linked four upper state parameters for ν1, a Fermi interaction term W1,23, introduced with initial value of zero, converged to a well-determined value, with magnitude around 9 cm−1. The aaxis Coriolis term Ga29,23 was also fitted. The influence of a further Fermi term linking v2 = v3 = 1 and (v3 = 1; v5 = 2) was suspected due to theoretical prediction of a ν2/2ν5 interaction (MP2/aug-cc-PVTZ value, W2,55 = 2.3 cm−1), and the corresponding appearance of a weak band assignable to 2ν5 in the far IR spectrum (see Figure 5). It was found that the Fermi term W23,355, together with W1,23 could account for the avoided crossing between v1 = 1 and (v3 = 1;v5 = 2). The “effective” W1,355 term, invoked in the initial, preliminary fits was eliminated. Accounting for these additional interactions

Figure 3. Resonance interactions of nearby vibrational levels affecting ν1. The wavenumber values are the observed band centers, as distinct from the fitted origins of Table 4.

scrambling led to difficulties in fitting these four linked states v1 = 1, v2 = v7 = 1, v2 = v9 = 1, (v3 = 1; v5 = 2) and in the subsequent treatment, including v2 = v3 = 1. Progression toward convergence was only possible by making multiple quantum number assignments to observed peaks while specifying a threshold for (obs. − calc.) residuals to ensure that only the one with the correct eigenvalue is retained in the fit. The strategy is outlined in Supporting Information Note 1. 3.3. The ν2 + ν3 band of C35Cl2F2. Adding further complication, the spectra in Figure 1 reveal evidence for yet another Fermi resonance affecting ν1. The ν2+ν3 combination band around 1128 cm−1 has intensity one-seventh of ν1, which is much stronger than can be explained by zero-order transition strength alone. Through analysis of the 150 K spectrum, it was possible to assign 2238 b-type transitions of ν2 + ν3 up to J′max = 70 and Ka′ max= 43 for C35Cl2F2, and confirm their assignment through ground state combination differences. The upper state is once again affected by perturbations, and three sets of avoided crossings were detected: one in rotational levels around Kc′ = 40, one around Ka′ = 29, and another 10948



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Results from the MP2/aug-cc-pVTZ anharmonic force field provide confirmation that the fitted parameters are physically meaningful and that the interpretation of interacting levels is correct. Both Fermi resonance terms W1,23 and W23,355, and the two largest Coriolis resonance terms Ga29,23 and Gb29,27 (arising from ςa3,9 and ςb7,9, respectively) may be predicted from theory and have similar magnitudes to the fitted parameters (see Table 5). In this table, experimental and MP2/aug-cc-PVTZ vibration−rotation constants, α, are also compared. For v1 = 1 and the four combination levels fitted in this work, most of the constants agree to within 0.5 MHz. The large, Coriolisinduced magnitude of αA found experimentally for two of these states, v1 = 1 and (v3 = 1; v5 = 2), is in accord with the predictions. The largest (exp. − calc.) deviations are for the αB constants of v2 = v7 = 1 and v2 = v9 = 1: +5.2 and −6.8 MHz, respectively. The similar magnitude but opposing sign of these deviations is not surprising given the close proximity of v2 = v7 = 1 and v2 = v9 = 1 (3.3 cm−1), the strong b-axis Coriolis coupling between them, and the fact that their constants are derived indirectly via their effect on ν1 rather than from directly assigned transitions. Table 5 also includes constants from previous studies: for ν4 and ν5, correspondence to within 0.2 MHz confirms the ν6 hot-band assignments of Taubman and Jones.19 Comparison of experimental and MP2/aug-cc-PVTZ rotational (R0) and centrifugal distortion constants for C35Cl2F2 (in Supporting Information Table S3) further supports the reliability of the computed force field. 3.4. Reassessment of ν3, ν7, and ν9. The high-resolution analysis outlined above strongly supports revising the positions

improved the r.m.s. residuals of ν1 and ν3 + 2ν5 only slightly (by 7 × 10−6 cm−1), but those of ν2 + ν3 more markedly, from 0.00035 to 0.00029 cm−1. The molecular constants from this 5state fit are summarized in Table 4. The constants were used for the simulation shown along with the expanded experimental spectrum in Figure 4.

Figure 4. (a) A portion of the 150 K high-resolution IR spectrum of ν2 of R12. (b) A simulation for the ν1 spectrum of C35Cl2F2 at T = 150 K, using the molecular parameters of Table 4. Line positions and intensities were generated with Pickett’s SPCAT program30 and convolved using a Gaussian line shape with FWHM linewidth 0.0012 cm−1. (c) The difference spectrum between the two, revealing additional features associated with C35Cl37ClF2, C37Cl2F2, or hotbands.

Table 5. MP2/aug-cc-pVTZ Vibration-Rotation Constants in Megahertz for C35Cl2F2, Where αB (νi) = B0 − Bi, etc., and Other Molecular Parameters expa

MP2 ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν2+ν9 ν2+ν7 ν3+2ν5 ν2+ν3 ν3+ν7 Other Parameters W1,23 W2,55 Ga9,3 Gb9,7 W6,37

αA

αB

αC

33.25 1.66 −39.93 −5.29 5.16 7.41 4.31 −10.44 41.88 1.89b 5.97 −29.61 3.37b −35.62

5.79 3.31 1.79 3.35 0.67 10.55 −0.87a −0.08 0.34a 3.65a 2.45a 3.13 5.10 22.84c

−0.32 2.29 0.45 4.87 2.91 10.58 −0.08 1.26 −1.62 0.67 2.21 6.26 2.74 0.37

αA

αC

notes this work ref 23

33.46 1.81

5.39 3.27

−0.20 2.37

−5.39 5.35 3.35

3.34 0.60 7.75

4.90 2.90 7.93

ref 19 ref 19 ref 19

−9.20

0.46

1.44

ref 23

−3.04 7.72 3.07 5.62 22.71

0.49 2.94 6.69 3.16 1.65

this work this work this work this work ref 20

5.08 7.42 −32.20 1.36 −44.55

9.14 cm−1 2.28 cm−1 5296 MHz 2067 MHz 13.4 cm−1

αB

8.81 ± 0.08 cm−1 1.44 ± 0.02 cm−1 (W23,355) 5123 ± 49 MHz (Ga29,23) 2269 ± 1 MHz (Gb29,27) 15 ± 2 cm−1

this work this work this work this work ref 20

MP2 αB value excludes contribution from Coriolis ςb7,9 due to a threshold in the Gaussian software. As a result, the computed αB values for ν2 + ν7 and ν2 + ν9 values are directly comparable with those from the fit where the ςb7,9 term is explicitly treated. bMP2 value for αA in ν2 + ν3 and ν2 + ν9 corrected to remove the computed MP2 contribution of 41.64 MHz from Coriolis ςa3,9 = 0.6429, in order to enable direct comparison with the experimental, fitted αA values from Table 4. cMP2 value of αB for ν3 + ν7 corrected to include contribution from Coriolis ςb7,9, to facilitate direct comparison with the experimental value from an effective, one-state fit. The magnitude of the Coriolis correction, ΔαB ≈ (Gb7,9)2/ΔE, where Gb7,9 = ςb7,9Be(ω7 + ω9)(ω7ω9)−1/2, ςb7,9 (MP2) = −0.3917, and the spacing between the interacting vibrational levels, ΔE, is computed using the fitted value 888.497 cm−1 for ν3 + ν720 and the best predicted position for ν3 + ν9 = 458.6 + 436.9−0.5 {MP2 x3,9} = 895.0 cm−1. a

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of the fundamentals found in the 430−470 cm−1 region, as proposed in Table 2: for C35Cl2F2, ν3 (458.6 cm−1), ν7 (437.7 cm−1), and ν9 (436.9 cm−1). Previous gas phase values for ν3 (468.5 cm−1), ν7 (437.0 cm−1), and ν9 (461.8 cm−1) were based on a far-infrared spectrum measured at room temperature.27 However, the overlapping contours of these close lying, Coriolis-coupled fundamentals and their associated hot-bands for multiple isotopic species makes interpretation of this spectrum difficult. In such cases, cooling of a gaseous sample can help to clarify assignments by reducing hotbands and narrowing contours without causing matrix-induced shifts.40 Figure 5 shows a 155 K far IR spectrum of R12 in which the

In room-temperature IR spectra of ν6, such as those available from NIST,41 a pair of hot-bands is observed to be shifted from the respective C35Cl2F2 and C35Cl37ClF2 fundamentals by +3.1 and +3.0 cm−1. Assignment to ν3 + ν6 − ν3 explains the atypical blue shift because the Fermi resonance term W36,337 between v3 = v6 = 1 and (v3 = 2; v7 = 1) is greater than W6,37 between v6 = 1 and v3 = v7 = 1 by a factor of √2. Subtraction from the corresponding ν3 + ν6 combination band positions, 1384.9/ 1380.5 cm−1 in the IR spectrum at 150 K, yields ν3 origins 458.6/455.7 cm−1. These IR bands are shown in Supporting Information Figure S2. The ν2 + ν7 (1105.78 cm−1) and ν2 + ν9 (1102.43 cm−1) combination bands, with symmetries unambiguously confirmed through the rovibrational analysis, lead to band centers of 437.7 cm−1 for ν7 and 436.9 cm−1 for ν9, very much consistent with the observed far-IR spectrum of Figure 5. The revised wavenumber values for ν3, ν7, and ν9 help to explain some aspects of the previous high-resolution study of ν3 + ν7.20 For the main C35Cl2F2 isotopologue, this combination band is observed at 888.5 cm−1, although the deperturbed origin, accounting for the strong Fermi resonance W6,37, was estimated at ≈896−898 cm−1. The B′ rotational constant for ν3 + ν7 is 22.7 MHz lower than the ground state value. According to the anharmonic MP2/aug-cc-pVTZ results, this large change is almost entirely due to the ςb7,9 Coriolis interaction with v3 = v9 = 1, with other factors contributing only 1.0 MHz (see Table 5). It may be inferred from the relationship ΔB ≈ (2Beςb7,9)/(Δν) that the separation between interacting levels, Δν̃, is 6.5 cm−1, and hence ν3 + ν9 is located at ≈895.0 cm−1. Table 6 compares the positions of several combination bands obtained from high-resolution analysis with those computed

Figure 5. Far IR spectrum of R12, transformed at 0.5 cm−1 resolution (150 Pa at temperature 155 K, path length 2.5 m). The b-type ν2 band is shown for comparison with ν3.

spectral feature at 468 cm−1 previously assigned to ν3 is no longer apparent; it may be assigned instead to the a-type ν6 − ν3 difference-bands, for which the deduced origins are 464.6 cm−1 (C35Cl2F2) and 466.1 cm−1 (C37Cl35ClF2). The twin dips at 458.6 and 455.2 cm−1 with a peak maximum in between are consistent with overlapping b-type ν3 bands of the two isotopic species separated by around 3 cm−1. The sharp Q-branch feature located around 437 cm−1 is now assigned to overlapping a-type ν7 and c-type ν9 bands for the reasons that follow. First, the revised assignments are consistent with the IR and Raman spectra of R12 solid at 20 K reported by Le Blanc and Anderson.29 Isotopic splitting patterns in the IR spectrum suggest that the C35Cl2F2 fundamentals are located at 459 cm−1 (ν3), 438 cm−1 (ν7), and 440 cm−1 (ν9) in the solid state, within a few wavenumbers of the new gas phase values. Second, an earlier Raman spectrum of R12 vapor at 7 atm and 35 °C from 60 years ago28 shows ν3 at 457.5 cm−1, with the A1 modes identifiable by their relatively sharp bands. This band position is very much in accord with expectation for a sample with natural isotopic abundance where the ν3 bands centered at 458.6/455.7 cm−1 for C35Cl2F2/C35Cl37ClF are merged and unresolved. Unfortunately, the gas phase Raman spectrum in the ν7/ν9 region contains only a poorly resolved shoulder peak at 433 cm−1. Third, high-level anharmonic vibrational calculations are in excellent agreement with the revised values for ν3, ν7, and ν9: for MP2/aug-cc-pVTZ (see Table 3) 459.3, 439.6, and 438.6 cm−1; for CCSD(T)/cc-pVTZ (from ref 36, see Supporting Information Table S1) 461, 441, and 439 cm−1. At the B3LYP/ 6-311+G** and B3LYP/aug-cc-pVTZ levels (Supporting Information Table S1), the absolute agreement is poorer but the trend is similar. Finally, the fundamental band centers may be derived from combination and hot-band assignments as specified in Table 2 footnotes and outlined here.

Table 6. Comparison of Combination Bands (cm−1) Observed in C35Cl2F2 with Those Estimated for C35Cl2F2, C35Cl37ClF2, and C37Cl2F2 observed band ν1 ν2 ν2 ν3 ν2 ν3 ν3 ν4 ν3 ν3

+ + + + + + + + +

ν9 ν7 2ν5 ν3 ν7 ν9 ν7 + ν9 ν4 + ν7 ν4 + ν9

C

35

Cl2F2b

1101.38 1102.43 1105.78 1099.67 1128.60 888.50 895.0d 1135.6 ± 0.6 1150.22 1155.92

adjusted MP2/aug-cc-pVTZ anharmonica C35Cl2F2

C35Cl37ClF2

C37Cl2F2

A1 1101.4 B2 1102.4 B1 1105.7 A1 1098.5 A1 1128.7 B1 888.9 B2 895.1 A2 1135.9 B1 1149.8 B2 1155.9

A′ 1101.8 A″ 1100.2 A′ 1099.4 A′ 1093.5 A′ 1124.9c A′ 883.5c A″ 891.1

A1 1099.9 B2 1098.0 B1 1096.3 A1 1089.2 A1 1120.5c B1 876.9 B2 886.2

a

Calculated energy levels and isotopic shifts based on the MP2/augcc-pVTZ anharmonic force field, but with the harmonic frequencies in the Gaussian09 input files adjusted by the amount required to produce in C35Cl2F2 the experimental (anharmonic) fundamentals from Table 2. bObserved (not Fermi deperturbed) band positions for C35Cl2F2, from this work and from ref 23. cExperimental data on 37Cl-substituted variants is available for these bands: ν2 + ν3 (1124.77 and 1120.51 cm−1) and ν3 + ν7 (883.20 cm−1, ref 20) dInferred from the Coriolis perturbed B rotational constant of ν3 + ν7, as outlined in text.

using the MP2/aug-cc-PVTZ anharmonic force field, but with the harmonic frequencies in the Gaussian 09 input files adjusted by the amount required to produce in C35Cl2 F2 the experimental (anharmonic) fundamentals of Table 2. Supporting the above reassessment of the ν3 fundamental, the observed 10950



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ν2 + ν3 band positions are in excellent agreement (within 0.2 cm−1) with the predicted values for all three isotopologues. The generally close agreement found for all the other combination modes provides strong evidence to support the revised ν3, ν7, and ν9 origins. The only remaining modes not directly measured by high -resolution analysis are ν4 and the IR inactive (A2 symmetry) ν5, where the gas phase values of 261.6 and 320.7 cm−1 derived by Giorgianni et al.27 stand. 3.5. The ν1 Band System of C35Cl37ClF2. In the analysis of ν8,23 a method denoted as “spectral analysis by subtraction of simulated intensities (SASSI)”42,43 was successfully employed, whereby the C35Cl2F2 component was simulated at 150 K and subtracted from the corresponding cool spectrum to help reveal and assign the spectrum of the slightly less abundant C35Cl37ClF2 isotopologue. Applying the same approach to the ν1 region, additional spectral features are uncovered (see Figure 4). However, the underlying spectrum was found to be abnormally lacking in evident series of regularly spaced transitions that would provide the basis for rovibrational assignments. A likely explanation for the very complex, disorderly spectrum is afforded by considering the energy levels and interactions in C35Cl37ClF2. Single 37Cl substitution brings the a-axis and b-axis Coriolis-coupled v1 = 1, v2 = v9 = 1 and v2 = v7 = 1 levels (refer to Figure 3) even closer together; see Table 6. According to the MP2/aug-cc-pVTZ calculations, relaxation of symmetry from C2v in C35Cl2F2 to Cs in C35Cl37ClF2 slightly mixes the ν3 CF2 scissor and ν7 CF2 wagging motions and also allows additional Fermi resonances (e.g., W1,27 is possible, and has a computed value of 1.3 cm−1) and Coriolis interactions (e.g., ςa7,9 = −0.094, ςa7,9 = −0.067). As a consequence, the wave functions will be even more severely mixed than in C35Cl2F2. This dilutes the intensity of individual transitions and disrupts their regular spacing due to the quantum number dependence of the strong perturbations. Thus, the accidental near degeneracy of levels in C35Cl37ClF2 creates a perfect (Coriolis) storm! Application of the SASSI method to subtract the simulated C35Cl2F2 component at low spectral resolution yields a compound profile that appears to comprise two b-type bands just 2.5 cm−1 apart. Their positions are consistent with those predicted for ν1 and ν2 + ν7 in C35Cl37ClF2; see Supporting Information Figure S3. 3.6. Simulations and Resonance Intensity Effects. In Figure 6, the experimental spectrum is compared to spectral simulations performed for the C35Cl2F2 isotopologue. Simulation II is based on the molecular parameters for ν8 from ref 23 that incorporate the Coriolis-coupled v3 = v4 = v7 = 1 and v3 = v4 = v9 = 1 states, simulation III employs the constants for the ν1/ν2 + ν3 system from Table 4, while simulation I is derived from an integrated eight-state fit of the ν1, ν2 + ν3, and ν8 band systems that incorporates the Coriolis parameter Ga1,8 = 6342 MHz corresponding to the MP2/aug-cc-PVTZ value for ςa1,8 = 0.770. The simulations are necessarily limited by the absence of rovibrational parameters for the ν1 band system of C35Cl37ClF2 (and C37Cl2F2). However, they do illustrate several important aspects of the spectroscopy, when taken together with band intensity integrations summarized in Table 7. The band profile is simulated satisfactorily, despite heavy mixing of the Ψ1 wave functions and the identity scrambling with Ψ29 that is manifest in the least-squares fitting. Comparison of integrated P & R branch intensities of experimental and simulated spectra allowed determination of the transition dipole ratio, μ 08(c‑type)/ μ 01(b‑type) = 0.77 ± 0.02.

Figure 6. Top trace: Experimental (150 K) spectrum of R12. Lower Traces: Simulations for C35Cl2F2 at T = 150 K. Line positions and intensities were generated with Pickett’s SPCAT program30 and convolved using a Gaussian line shape with FWHM linewidth 0.0012 cm−1. Sim I: Constants from a global, integrated eight-state fit incorporating the ν1, ν23, and ν8 band systems. Sim II: ν8 constants from Table 4 of ref 23. Sim III: constants for ν1 system from Table 4. The μ 08(c‑type)/μ 01(b‑type) transition dipole ratio used was 0.77.

No direct transition dipole moment was necessary to simulate the ν2 + ν3 band. The Fermi term W1,23 = 8.8 cm−1, which was obtained from fitting line positions alone, is shown to be physically realistic in reproducing the required ν2 + ν3 band intensity. In the experimental spectrum at 150 K, ν2 + ν3 has integrated intensity 14.6% of that for ν1. The proportion is 13.0% in simulation I and 12.8% in simulation III. The slightly larger experimental intensity is explained by enhanced wave function mixing in C35Cl37ClF2 due to the decreased separation between ν1 and ν2 + ν3: the top trace of Figure 1 shows that C35Cl37ClF2 has its ν2 + ν3 band ≈ 4 cm−1 lower than in C35Cl2F2 and almost as strong despite having two-thirds the concentration. In the higher wavenumber region, the P-branch of the ν8 experimental spectrum is more intense than the R-branch. The integrated intensity ratio for P/R is 1.34 (or 1.25 ± 0.05 if the appearance of hot-band Q-branches appearing in the P region is accounted for). This stands in marked contrast to simulation II, where the ratio is 0.91. In the previous analysis, an empirically determined Herman−Wallis correction was introduced to redress that imbalance and improve the ν8 simulation. However, with inclusion of the appropriate Coriolis coupling constant Ga1,8 in the global simulation II, the ν8 P/R intensity ratio becomes 1.26. This is commonly observed with Corioliscoupled modes (e.g., in CHClF242): enhancement of the Pbranch of the high frequency band and the R-branch of the low frequency band with corresponding reduction in the other branches is labeled “positive perturbation” by Mills.45 The effect is more pronounced in the wings due to the quantum number dependence of the wave function mixing.46,47 What is unusual about the present case is the slight decrease in the overall intensity of the weaker ν8 band at the expense of increased intensity in the ν1 and ν2 + ν3 regions. In the Coriolisinduced mixing, a portion of Ψ8 is lost in exchange for a wave function that is not purely Ψ1 in character (which would enhance the ν8 band), but a mixture of Ψ1, Ψ23, Ψ27, Ψ29, and Ψ355. 10951



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Table 7. Integrated Band Intensities from Experimental and Simulated Spectra of R12 measurement

temp./K

boundaries/cm−1

Sim I Sim II & IIIa MP2/aug-cc-pVTZb MP2/6-311+G(d,p)b B3LYP/aug-cc-pVTZb B3LYP/6-311+G(d,p)b QCISD/cc-pVTZc exp. (this work) Kagann et al. 1983 Varanasi and Chudamani 1988 Clerbaux et al. 1993 D’Amico et al. 2002 Myhre et al. 2006

150 150 150 296 300 287 297 295

1117, 1144 1117, 1144 1117, 1144 1130 ? 1130 1133 ?

a

1017 S for ν1, ν8/cm molecule−1

4.60, 5.07, 4.78, 5.64, 4.87,

3.16 3.67 3.07 3.88 3.51

4.60 4.62 4.50 4.71 4.60

± ± ± ± ±

0.16, 0.05, 0.08, 0.25, 0.13,

3.13 2.93 3.08 3.14 2.88

± ± ± ± ±

0.11 0.06 0.07 0.19 0.09

% ν1, ν2+ν3, ν8 in CF stretch 54.8, 54.6, 59.4, 58.0, 60.9, 59.2, 58.1, 54.2, 59.5, 61.2, 59.3, 60.0, 61.5,

7.1, 38.1 7.0, 38.4 -, 40.6 -, 42.0 -, 39.1 -, 40.8 -, 41.9 7.9, 37.9 -, 40.5 -, 38.8 -, 40.7 -, 40.0 -, 38.5

Using transition dipole ratio μ 08(c‑type)/μ 01(b‑type) = 0.77. bFrom the directly computed anharmonic IR intensities; see Table 3 and Supporting Information Table S1. cHarmonic IR intensities from ref 44. a

B3LYP/6-311+G(d,p). Again the MP2/aug-cc-pVTZ level proved very satisfactory.

The MP2/aug-cc-pVTZ calculations point to yet another Fermi resonance of large magnitude not yet accounted for: affecting ν8 and ν2 + ν9, with W8,29 = 10.6 cm−1. One effect of this resonance is to shift the respective levels by 2.0 cm−1, hence it is the major contributor to the anharmonic constant, x2,9 = −2.9 cm−1, and the deperturbed ν8 origin is 1159.1 cm−1. Another effect is to dilute the Ψ8 wave function such that |Ψ8|2 is reduced by 3.4%. 3.7. Comparisons with Theory and Other Work. Table 7 includes comparisons of both the overall magnitude and the proportions of band intensity across the CF stretching region (1050−1200 cm−1). With regards to proportions, previous studies12−15,20 have divided the CF stretch region according to the two fundamentals only, because the ν2 + ν3 band sandwiched in between ν1 and ν8 is far less evident at the warmer sample temperatures used in those studies. Differences in the selection of the ν1/ν8 boundary produce some variation in those proportions, but in general it appears that most of the underlying ν2+ν3 intensity has been allocated to ν1 (and it does indeed derive that intensity from ν1 via the Fermi resonance). The tabulated experimental proportions of ν8 (38.5−40.7%) are therefore only slightly overestimated, when compared with the better resolved 150 K spectrum (37.9%). The proportions of ν8 from theory are also somewhat higher, though the MP2/aug-ccpVTZ proportion may be adjusted from 40.6% to 39.0%, not far from experiment, if the leakage of ν8 intensity due to Fermi W8,29 and Coriolis ςa1,8 interactions is considered. Absolute band intensities cannot be obtained from our experiments due to the lack of accurate pressure measurement, but the consistency of the literature values allows the theoretical values to be assessed. Again, the MP2/aug-cc-pVTZ values are found to be most reliable. Use of a smaller 6-311+G(d,p) basis set (or DZP++)6 at the MP2 level leads to significant overprediction of the band strengths. The same trend was found with density functional theory at B3LYP level: although the vibrational wavenumbers were equally poor (systematically too low), the transition strengths were much improved by using the expanded aug-cc-pVTZ basis. Recently reported QCISD/ cc-pVTZ intensities44 are also somewhat high. A final indicator of the reliability of computed charge distributions is the permanent dipole moment, compared to the experimental value of 0.51 D:48 0.54 D for MP2/aug-cc-pVTZ, 0.71 D for MP2/6311+G(d,p), 0.42 D for B3LYP/aug-cc-pVTZ, 0.55 D for

4. DISCUSSION AND CONCLUSIONS The present analysis of the ν1 polyad serves to illustrate both the limitations of rovibrational analysis and its benefits. Despite dealing with a severely entangled set of vibrational levels mixed by Coriolis and Fermi resonances, it was possible (with much effort) to make substantial progress in assigning and fitting rovibrational transitions of C35Cl2F2. However, the set of around 4000 assigned lines was not as comprehensive as could be attained in less perturbed band systems (e.g., 6180 were assigned for ν8 and 8739 for ν223). Some high quantum number ranges were unassignable due to the perturbations and associated dilution of the transition strength. The situation with C35Cl37ClF2 was even worse: the near coincidence of interacting levels and the additional resonance interactions brought about through the reduction in symmetry from C2v to Cs made rovibrational assignments untenable. Even if a comprehensive set of assignments could be made, fitting all the transitions in a completely rigorous manner would require treatment of all 11 interacting levels in the vicinity of ν1, ν8, ν2 + ν3, ν2 + ν7, ν2 + ν9, ν3 + 2ν5, ν3 + ν4 + ν7, ν3 + ν4 + ν9, ν4 + 2ν7, ν4 + 2ν9 and ν4 + ν7 + ν9. Clearly it is not practical to employ such a Hamiltonian to routinely model band profiles for comparison with atmospheric spectra. In such cases, it is necessary to resort to sets of spectra measured at different temperatures and pressures. On the positive side, a great deal has been learned about this important atmospheric molecule. In the process of the rovibrational analysis, unravelling the identity and interactions of the vibrational levels led to reassessment of the fundamental vibrational assignments for ν3, ν7, and ν9. With the far IR spectra of these weak and overlapping fundamentals being difficult to interpret, obtaining band origins for the ν2 + ν3, ν2 + ν7, and ν2 + ν9 combinations was crucial to determining the fundamental wavenumber values. This in turn points to the need for a re-evaluation of the force field; previous studies27,35,49 were limited to the harmonic level and relied on now superseded values for the fundamentals. In this work, the MP2/aug-cc-pVTZ level of theory was found to produce excellent results for CCl2F2. With some tuning, e.g., to the CF stretching constants, it should be possible to adapt this anharmonic force field to generate a highly accurate potential. 10952



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Notes

The present analysis has increased understanding of the molecular physics that affects the distribution of IR absorption in the CF stretch region, and consequently the Global Warming Potential (GWP) of R12. The resonance induced mixing leaves the overall intensity preserved, but it results in shifted bands, changes in the relative band strengths via intensity stealing (e.g., enhancing the ν2 + ν3 combination) and altered balance of P/R branches. In doing so, the radiative efficiency of R12 is affected since in this spectral region the IR flux is greater at the low wavenumber end, e.g., by ≈ 27% between 1165 and 1095 cm−1.50 Thus, a simplistic model that did not account for such effects would differ from the more realistic GWPs determined from experimental spectra. Resonance-induced mode mixing also has implications for intramolecular vibrational−rotational energy redistribution.51 For example, short pulse excitation into “ν1” may couple to the nearby interacting levels and hence readily populate the ν2, ν3, ν5, ν7, and ν9 modes. Some studies have explored dynamics or reactivity of CCl2F2 via excitation in this spectral region, as it is readily accessible via CO2 laser sources. For example, recent work examined the energy distribution of molecules undergoing multiphoton excitation using the R(30) CO2 laser line at 1084.6 cm−1.52 Multiphoton dissociation schemes employing IR radiation for 13C isotopic enrichment from CCl2F2 have been reported.7−11 From Tables 1 and 2, it is evident that large 13 C isotopic shifts occur for the ν1, ν6, and ν8 modes. Such shifts provide the possibility of selective IR excitation. However, at least with regards to absorption of the first photon, ν6 and ν8 suffer from overlapping absorptions from combination modes ν3 + ν7 and ν2 + ν3 of the more abundant 12C species. The ν1 Q-branch for 13C is clearly evident in the 150 K spectrum of Figure 1b: the band is centered at 1073.7 cm−1, with maximum absorbance at 1075 cm−1. King and Stephenson reported high yields of 13CF2 near 1075 cm−1, but found that isotopic selectivity was enhanced closer to 1057 cm−1.7 Other studies since then have explored the temperature dependence of isotope separation,9 or have employed mixtures with O210 or HI.11 It is worth noting that the ν1 band of the 13C species is unlikely to suffer from the same degree of resonance mixing, being further separated from the interacting states. It should therefore be much more amenable to high-resolution analysis.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was generously supported by the Australian Synchrotron through far IR beam-time access. Quantum chemical calculations were performed via the NCI Australia National Facility, through the National Computational Merit Allocation Scheme.

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(1) Hartmann, D. L.; Klein Tank, A. M. G.; Rusticucci, M. ; Alexander, L. V.; Brönnimann, S.; Charabi, Y.; Dentener, F. J.; Dlugokencky, E. J.; Easterling, D. R.; Kaplan, A. et al. Observations: Atmosphere and Surface. In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P. M., Eds.; Cambridge University Press: Cambridge, U.K./New York, 2013. (2) Rigby, M.; Prinn, R. G.; O’Doherty, S.; Montzka, S. A.; McCulloch, A.; Harth, C. M.; Mühle, J.; Salameh, P. K.; Weiss, R. F.; Young, D.; et al. Re-evaluation of the Lifetimes of the Major CFCs and CH3CCl3 Using Atmospheric Trends. Atmos. Chem. Phys. 2013, 13, 2691−2702. (3) Advanced Global Atmospheric Gases Experiment. http://agage. eas.gatech.edu/ (accessed August 18, 2014). (4) Harries, J. E.; Brindley, H. E.; Sagoo, P. J.; Bantges, R. J. Increases in greenhouse forcing inferred from the outgoing longwave radiation spectra of the Earth in 1970 and 1997. Nature 2001, 410 (6826), 355− 357. (5) 5. Myhre, G.; Shindell, D.; Bréon, F.-M.; Collins, W.; Fuglestvedt, J.; Huang, J.; Koch, D.; Lamarque, J.-F.; Lee, D.; Mendoza, B. et al. Anthropogenic and Natural Radiative Forcing. In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P. M., Eds.; Cambridge University Press: Cambridge, U.K./New York, 2013. (6) Bera, P. P.; Francisco, J. S.; Lee, T. J. Identifying the Molecular Origin of Global Warming. J. Phys. Chem. A 2009, 113, 12694−12699. (7) King, D. S.; Stephenson, J. C. Intrinsic Isotopic Selectivity Factors: CO2 TEA Laser Photolysis of CF2C12. J. Am. Chem. Soc. 1978, 100, 7151−7155. (8) Ritter, J. J. Isotopically Selective CO2 Transverse Excitation Laser Induced Chemical Reactions of C12CF2 and Br2CF2 with Olefins. J. Am. Chem. Soc. 1978, 100, 2441−2444. (9) Chou, J.-S. J.; Grant, E. R. Enhanced isotope separation in CF2C12 by infrared multiphoton dissociation at elevated temperatures. J. Chem. Phys. 1981, 74, 5679−5685. (10) Nip, W. S.; Hackett, P. A.; Willis, C. Carbon-13 Isotopic Selectivity in the Infrared Multiphoton Photolysis of CF2C12−O2 Mixtures. Can. J. Chem. 1981, 59, 2703−2707. (11) Laptev, V. B.; Ryabov, E. A. Production of Highly Enriched Carbon-13 by IR Multiphoton Dissociation of Dichlorodifluoromethane Mixed with Hydrogen Iodide. High Energy Chem. (Translation of Khimiya Vysokikh Energii) 2000, 34, 193−199. (12) Kagann, R. H.; Elkins, J. W.; Sams, R. L. Absolute Band Strengths of Halocarbons F-11 and F-12 in the 8- to 16-μm Region. J. Geophys. Res. C 1983, 2, 1427−1432. (13) Varanasi, P.; Chudamani, S. Infrared Intensities of Some Chlorofluorocarbons Capable of Perturbing the Global Climate. J. Geophys. Res. 1988, 93, 1666−1668. (14) Clerbaux, C.; Colin, R.; Simon, P. C.; Granier, C. Infrared Cross Sections and Global Warming Potentials of 10 Alternative Hydrohalocarbons. J. Geophys. Res. 1993, 98, 491−497. (15) Myhre, G.; Stordal, F.; Gausemel, I.; Nielsen, C. J.; Mahieu, E. Line-by-Line Calculations of Thermal Infrared Radiation Representa-

ASSOCIATED CONTENT

S Supporting Information *

Supporting Information figures illustrate identity scrambling in the heavily mixed Ψ1 wave functions and include a note on the fitting procedure used to cope with this, and show additional IR spectra in selected regions. Supplementary tables present vibrational wavenumber values computed at various levels of ab initio theory, spectroscopic constants from a one state fit of ν2 + ν3, and a comparison of experimental rotational and centrifugal distortion constants for C35 Cl2 F2 with the anharmonic MP2/aug-cc-PVTZ values. A full list of authors of refs 1, 2, 5, 31, and 32 is also provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

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

Max-Planck-Institut für Struktur and Dynamik der Materie, 22761, Hamburg, Germany. 10953



Article

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The Limits of Rovibrational Analysis: The Severely Entangled Î½1

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