ARTICLE pubs.acs.org/JPCA
Structure and Barrier to Methyl Group Internal Rotation for (CF3)2CFCF2OCH3 and Its Isomer n-C4F9OCH3 (HFE-7100) G. S. Grubbs, II and S. A. Cooke* Department of Chemistry, University of North Texas, 1155 Union Circle, Number 305070 Denton, Texas 6203-5017, United States
bS Supporting Information ABSTRACT: The hydrofluoroether C4F9OCH3 (methox ynonafluorobutane, HFE-7100) has been studied by chirped pulse Fourier transform microwave spectroscopy as vapor from the liquid participates in a supersonic expansion of argon. Two isomers are present, (CF3)2CFCF2OCH3 and n-C4F9OCH3, and in each case the rotational spectra of only one, dominating, conformer has been assigned. Rotational constants, centrifugal distortion constants, and barriers to methyl group internal rotation for the observed species have been experimentally determined for the first time. We note that Ray’s asymmetry parameter for the (CF3)2CFCF2OCH3 isomer is 0.007 083(1), indicating almost “perfect” asymmetry. Also, electronic structure calculations show an extremely short C(frame)-O ether bond length of 1.337 Å.
’ INTRODUCTION Ray’s asymmetry parameter1 provides a measure of a molecule’s asymmetry with regard to the relationship between the magnitudes of its molecular rotational constants, A, B, and C. There are two limiting cases, κ = -1 for a perfect prolate symmetric top, A > B = C, and κ = þ1, for a perfect oblate symmetric top, A = B>C. Asymmetry parameters are particularly useful when trying to write closed algebraic expressions for the energy levels of a rotating asymmetric molecule.2-4 The case of the “perfect” or “most’’ asymmetric molecule, where κ=0, provides a third limit where the resultant rotational spectrum bears the least resemblance to either of the oblate and prolate limits. Accordingly, the perfect asymmetric top provides a stiff challenge for transition quantum number assignment given the ensuing loss of patterns in the observed spectrum. We have, by chance, found a molecule in which κ ≈ 0 and the assigned rotational spectrum may be of interest with regard to the effectiveness of a chosen Hamiltonian.5 The molecule in question is a component of the commercial chemical HFE-7100. HFE-7100 is a 3M/Novec engineered fluid with chemical formula C4F9OCH3, i.e., methoxynonafluorobutane. The fluid is a mixture of two isomers, a branched chain isomer, (CF3)2CFCF2OCH3, and a straight chain isomer, CF3CF2CF2CF2OCH3. The compound has unusual properties such as a relatively high ratio of boiling point to surface tension, (334 K):(13.6 dyn/cm), which may be compared to the ratio (321 K):(17.6 dyn/cm) for CClF2CCl2F (CFC-113). The compound also has an extremely low toxicity. These properties have resulted in the compound being used as an effective electronics cleaner, refrigerant, and specialty solvent. It is particularly notable in its r 2011 American Chemical Society
low ozone depletion potential (ODP).6,7 Given the industrial application of this fluid, it is of use to determine spectroscopic constants which will assist in the environmental detection of the chemical. Furthermore, these molecules pose an interesting question concerning the barrier to methyl group internal rotation against a perfluorinated ether frame. This question has been previously discussed with regard to the protype species CF3OCH3.8 But, in general, is the barrier higher or lower than in the case of methyl group internal rotation against a non-fluorinated ether frame? And, what happens as the perfluorinated frame is lengthened? In this work we address these questions. Lastly, the variable nature of the C-O single bond length in both ethers and esters has been previously addressed by Allen and Kirby.9 Within an F-C-O linkage-containing system the electron withdrawing nature of fluorine can result in negative hyperconjugation between the lone pair orbital of oxygen and the antibonding orbital of the C-F bond.10 This so-called anomeric effect provides a good reason to anticipate an unusually short C-O bond in methoxynonafluorobutane. The matter is explored below.
’ EXPERIMENTAL METHODS Methoxynonafluorobutane (99% pure, as a 50/50 mixture of two isomers) was purchased from Sigma-Aldrich Ltd. and used without further purification. The liquid sample was placed in a Received: October 30, 2010 Revised: December 15, 2010 Published: January 19, 2011 1086
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of the related compound C4F9OC2H5.19 Having generated a set of input geometries, optimizations and dipole moment calculations were performed (i) using the M06-2X density functional method20,21 and (ii) using an MP2 method.22 In both cases a 6-311G** basis set was used for all atoms.23,24 To achieve the second goal, a B3LYP/6-31G method25-28 was used to perform a relaxed potential energy scan as the COCH dihedral angle was stepped at 20 intervals.
’ RESULTS
Figure 1. Approximately 1 GHz portion of spectra collected. To show clearly the form of the spectrum of the highly asymmetric species (CF3)2CFCF2OCH3, those transitions assigned to the n-C4F9OCH3 species have been subtracted. Selected transitions have been labeled as JK-1Kþ10 rJK-1Kþ100 . At this scale the A-E torsional splittings are only just visible.
1/4 in. tube about 40 cm behind a solenoid valve. Argon held at backing pressures of 2 bar was bubbled through the liquid prior to passage through the solenoid valve and into a vacuum chamber held at approximately 10-5 Torr. This process resulted in a pulse of rotationally cold, ≈3 K, target molecules stabilized within a matrix of supersonically expanded argon. A chirped pulse, Fourier transform microwave (CP-FTMW) spectrometer was used to record the spectra of the target molecules between the frequency regions of 7.8 and 16.2 GHz. This instrument has been described in detail elsewhere11,12 and is based upon the chirp pulse experiment previously introduced by Pate and co-workers.13-15 Briefly, the instrument mixes a microwave pulse of frequency ν with a fast (5 μs) linear frequency sweep of DC-1 GHz generating a ν ( 1 GHz broadband pulse. The pulse is then amplified (5 W) using a solid-state amplifier and broadcast onto the supersonically expanding gas sample through a horn antenna. Following a delay of 0.2 μs a second antenna horn receives any free induction decay(s) (FID). The signal is then passed through an amplification stage and then proceeds to be directly digitized on a 12 GHz, 40 GS/s oscilloscope (Tektronix TDS6124 digital oscilloscope). Each experimental acquisition takes place at a rate of 4 Hz, and FIDs were averaged for approximately 60 000 acquisitions. Signal averaged regions of 2 GHz were obtained in 2-3 h. Linewidths for these experiments are approximately 80 kHz, and a 25 kHz uncertainty was attributed to frequency measurements. A 1 GHz portion of the spectra collected is shown in Figure 1.
’ QUANTUM CHEMICAL CALCULATIONS Quantum chemical calculations were performed following the spectral analyses detailed below. The calculations were performed (i) to identify the conformations of the molecular species for which spectra had been assigned and (ii) for comparative purposes to evaluate the barriers to internal rotation of the terminal -CH3 group. All calculations were performed using the Gaussian software suite.16 To achieve the first goal, optimizations were performed on both the branched and straight chain isomers. To locate different conformers, the starting geometries for the calculation can be very important. Starting geometries were generated using a rule-based, conformer generating tool called OMEGA.17,18 This approach proved very useful in a recent study
Spectral Analysis. Quantum number assignments for the observed transitions began through the identification of repeating patterns of, sometimes doubled, transitions spaced by approximately 850 MHz. With an assumed value of B þ C of 850 MHz an assignment of a-type transitions was eventually obtained. With a reasonable set of rotational constants it was possible to identify b-type transitions for the species in the collected rotational spectra. Given the magnitudes of the rotational constants, it was clear that this species must be the straight chain isomer, n-C4F9OCH3. Numerous transitions were doubled, or broadened, and, as expected, it was clear that effects of methyl group internal rotation were observable. A strategy similar to that employed by Krasnicki et al.29 was used in the analysis of the internal rotation. Initially fits were performed separately on the A and E torsional sublevels using Pickett’s SPFIT/SPCAT program.30 The SPFIT/SPCAT software was used within the framework of the AABS package,31 from the PROSPE Web site,32 which permits rapid spectral assignments. The A sublevel was fit to a standard Watson A-type reduced Hamiltonian.33 The Watson A-type reduced Hamiltonian was chosen because of the anticipated large asymmetry of the molecule. The E sublevel was treated using a method in which internal rotation is treated as a perturbation.34,35 It was apparent during the fitting procedure that the internal rotation axis must lie close to the ab plane for nC4F9OCH3, as only the following terms in the internal rotation Hamiltonian were necessary to be added to Watson’s reduced Hamiltonian for the E sublevel:
Hint ¼ ðDa þ DKa Pz 2 ÞPa þ Db Pb
ð1Þ
in which Da and Db represent first-order correction terms within the perturbation approach and DKa is a centrifugal distortion term for Da. The results of this fitting procedure are presented in Table 1. Having assigned quantum numbers to the observed spectral transitions, two further fits were performed using software that treats the A and E sublevels simultaneously, namely, XIAM36 and ERHAM.37 In the former, i.e., XIAM, a combined axis method (CAM) is used in which the internal rotation component of the Hamiltonian takes the following form: Hint ¼ Feff ðp - FPa Þ2 þ V3 =2ð1 - cos 3RÞ
ð2Þ
where p is the angular momentum operator for the methyl rotor, F relates the moments of inertia of the molecule to the moment of inertia of the methyl rotor, V3 is the 3-fold barrier height, and R is the torsional angle. Feff is an effective rotational constant for the methyl top and may be related to the rotational constant F0 for the methyl top using either eq 9 of Hougen et al.38 or eq 3 of Ouyang and Howard.39 In the latter software, i.e., ERHAM, an effective Hamiltonian approach is used in which matrix elements for both the internal 1087
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Table 1. Spectroscopic Constants from Effective Fits for Torsional Sublevels in the Ground State of n-C4F9OCH3 “A”
parameter
“E” a
A/MHz
1129.776 16(34)
Table 3. Spectroscopic Constants from Effective Fits for Torsional Sublevels in the Ground State of (CF3)2CFCF2OCH3 “A”
parameter
1129.710 50(30)
“E” a
B/MHz C/MHz
438.338 90(16) 413.062 19(17)
438.337 29(16) 413.062 79(17)
A/MHz
765.202 09(73)
765.164 27(69)
B/MHz
636.565 44(42)
636.565 27(32)
ΔJ/Hz
10.91(23)
9.66(23)
C/MHz
506.120 49(49)
506.119 38(44)
ΔJK/Hz
-27.35(61)
-20.41(38)
ΔJ/Hz
10.7(16)
11.5(16)
ΔJK/Hz ΔK/Hz
38.1(64) -27.7(78)
32.4(64) -23.5(74)
ΔK/Hz
76.9(22)
67.3(20)
δJ/Hz
0.258(89)
0.87(13)
δk/Hz
121(11)
δJ/Hz
1.44(78)
1.81(40)
Da/MHz
-5.4527(17)
δk/Hz
7.6(52)
11.2(58)
DKa /kHz Db/MHz
0.178(13) 1.179(84)
Da/MHz
-4.3898(19)
Dc/MHz
0.7076(15)
475
Nb
215
trans obsc
μa, μc
rmsd
0.227
Nb
474
trans obs
μa, μb
rmsd
0.493
c
0.508
a
Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b Number of observed trand sitions used in the fit. c Dipole type Root P of the transitions observed. 2 mean square deviation of the fit, [ [((obs - calc)/error) ]/Nlines]1/2.
Table 2. Ground-State Spectroscopic Constants and Related Properties for n-C4F9OCH3 from Programs That Perform Fits to Both A and E Torsional Sublevels Simultaneously, Namely, XIAM and ERHAM parameter
XIAM
ERHAM a
A/MHz
1129.732 50(15)
B/MHz
438.337 988(65)
438.337 947(65)
C/MHz
413.062 478(65)
413.062 547(66)
ΔJ/Hz ΔJK/Hz
10.997(86) -27.1(24)
11.01(88) -27.1(24)
1129.732 53(13)
ΔK/Hz
75.15(83)
75.19(84)
δJ/Hz
0.158(33)
0.158(32)
δk/Hz
110.0(38)
109.7(38)
V3/cm-1
336(1)
IR/(u Å2)
3.1861(92)
3.1838(94)
F/GHz — (a,i) /deg
158.62(46) 21.56(30)
159.78(47) 21.62(30)
β /deg
8.71
8.73(14)
F
0.006 701
0.006 694(11)
Nb
949
894
rmsc
0.557
0.557
EE - EA/MHz
681.8(10)
a
Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b Number of observed transitions used in the fit. c Root mean square deviation of the fit, P [ [((obs - calc)/error)2]/Nlines]1/2.
rotation energy and the rotational operators are expressed as Fourier series. The determinable spectroscopic parameters are the coefficients of the Fourier series, which for the internal rotation energy, are represented using the ε symbols, the F parameters, and the angles between the internal rotor axes and the reference axes.
0.254
a
Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b Number of observed trand sitions used in the fit. c Dipole type P of the transitions observed. Root mean square deviation of the fit, [ [((obs - calc)/error)2]/Nlines]1/2.
The parameters determined using the XIAM and ERHAM codes are presented in Table 2. Approximately 900 lines were recorded for the first species with energy levels spanning J = 3-37, K-1 = 0-17, and Kþ1 = 0-30. Having completed the assignment of the first species, the assigned spectrum was subtracted from the observed spectra and the assignment/fitting procedure outlined above was repeated for an identified second species. From the magnitudes of the rotational constants it was clear that this second species was probably the branched chain isomer (CF3)2CFCF2OCH3, and subsequent quantum chemical calculations confirmed this. Effective spectroscopic parameters for the separate A and E sublevels for this species are presented in Table 3. For (CF3)2CFCF2OCH3 it is apparent that the internal rotation axis must lie close to the ac plane as only the following terms in the internal rotation Hamiltonian were necessary to be added to Watson’s reduced Hamiltonian for the E sublevel:
-227.26(33)
ε1/MHz
213
Hint ¼ Da Pa þ Dc Pc
ð3Þ
The results of the fitting procedure to the A and E sublevels simultaneously are presented in Table 4. Approximately 420 lines were recorded for the second species with energy levels spanning J = 5-15, K-1 = 0-12, and Kþ1 = 0-15. Output files for the computer programs used in the spectral analyses, which also provide the frequencies of the transitions observed together with the quantum number assignments, are available in the Supporting Information. The three methods used in the spectral analyses of the data collected in this work all provide comparable results indicating that the spectroscopic parameters obtained are reliable. A very useful comparison of the SPFIT and XIAM approaches has been provided by Ouyang and Howard.39 Also a recent review of the practical treatment of methyl internal rotors has been provided by Kleiner.40 Isomer and Conformer Identification. Quantum chemical calculated structural parameters for both isomers are presented in Tables 5 and 6. Good agreement between the calculated rotational constants of the lowest energy conformer of the branched chain 1088
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Table 4. Ground-State Spectroscopic Constants and Related Properties for (CF3)2CFCF2OCH3 from Programs That Perform Fits to Both A and E Torsional Sublevels Simultaneously, Namely, XIAM and ERHAM parameter
XIAM
B/MHz
636.565 806(62)
C/MHz
506.119 371(81)
ΔJ/Hz
n-C4F9OCH3
ERHAM
765.176 82(19) a
A/MHz
Table 6. Comparison of Selected Experimental and Calculated Structural Properties for the Two Observed Isomers of Methoxynonafluorobutane
11.90(26)
parameter
765.176 79(13)
2b
expt
calc c
(CF3)2CFCF2OCH3 a
expt
calc
636.565 643(62)
Ia/uÅ
447.34396(6)
447.449
660.4735(2)
652.810
506.119 492(81)
Ib/(u Å2)
1152.9437(2)
1142.351
793.91479(8)
784.456
11.77(28)
Ic/(u Å2)
1223.4929(2)
1211.307
998.5372(2)
985.028
964.54630(3)
953.104
565.98923(2)
558.337
ΔJK/Hz
31.74(99)
31.9(11)
Pa d/(u Å2)
ΔK/Hz
-23.1(13)
-23.4(14)
δJ/Hz δk/Hz
2.457(73) 12.34(87)
2.479(75) 12.10(93)
Pb/(u Å2) Pc/(u Å2)
258.94659(2) 188.39736(3)
258.202 189.247
432.54794(2) 227.92555(3)
426.691 226.119
κe
-0.929464(1)
-0.929
0.007085(1)
0.00484
V3/cm
-1
320.6(9) -256.17(69)
ε1/MHz IR/(u Å2)
3.2325(87)
F/GHz
156.34(42)
157.30(42)
— (a,i) /deg
14.63(21)
14.65(21)
β /deg
10.15
10.17(21)
F EE - EA/MHz
0.004811
0.004 804(13) 768.5(20)
Nb
428
412
rmsc
0.260
0.252
3.2283(86)
a
Taken from the MP2/6-311G** geometry for conformer B; see Table 5. b Principal moment of inertia. c Numbers in parentheses give standard errors (1σ, 67% confidence level) P in units of the least significant figure. d Second moment of inertia Pa = i miai2 and similarly for Pb and Pc. e κ = (2B - A - C)/(A - C).
a
Numbers in parentheses give standard errors (1σ, 67% confidence level) in units of the least significant figure. b Number of observed P transitions used in the fit. c Root mean square deviation of the fit, [ [((obs - calc)/error)2]/Nlines]1/2.
Table 5. Calculated Properties for Two Isomers of Methoxynonafluorobutane n-C4F9OCH3 parameter A a/MHz
conf A
conf B
conf B(MP2)
(CF3)2CFCF2OCH3
894.40
1132.84
1129.47
774.16
B/MHz
554.98
447.00
442.40
644.24
C/MHz μa/D
513.06 -1.84
420.91 -2.45
417.22 -2.72
513.06 -2.66
μb/D
-2.26
1.59
-1.65
0.09
μc/D
-0.86
-0.10
-0.07
1.43
— (a,i) /deg
47.3
21.7
21.8
10.8
281
266
V3 b/cm-1 a
Rotational constants and dipole moment components were calculated using the M06-2X/6-311G** method except for the column headed conf B(MP2) for which the parameters were calculated at the MP2/6-311G** level of theory. b Calculated from the B3LYP/6-31G method.
isomer, (CF3)2CFCF2OCH3, and the experimental rotational constants of Table 4 was found. The calculated structure of this isomer is shown in Figure 2. Notably Ray’s asymmetry parameter, κ = (2B - A - C)/(A - C), is equal to 0.007 085(1) for this molecule, indicating near perfect asymmetry. The identification of the conformer observed for the straight chain, n-C4F9OCH3, isomer was less straightforward. At the M06-2X/6-311G** level of theory the lowest energy conformer, labeled conformer A in Table 5, had very poor agreement with the experimental rotational constants of Tables 2 and 3. A considerably better match of the n-C4F9OCH3 isomer’s rotational constants, and also the angle between the internal rotor
Figure 2. Calculated structure of the lowest energy conformer of (CF3)2CFCF2OCH3.
and the a-axis, could be made with the second lowest M06-2X/6311G** conformer, labeled conformer B in Table 5. We note that, at the M06-2X/6-311G** level of theory, conformers A and B were found to be almost degenerate, separated by just 7 cm-1. In other words, working within the M06-2X regime, we would have expected to observe spectra from both conformer A and conformer B. However, spectra resembling that produced from the rotational constants of conformer A in Table 5 were absent in our observations. As indicated in the Quantum Chemical Calculations, further calculations were performed at the MP2 level. At the MP2/6-311G** level of theory conformer B of Table 5 was now found to be the lowest energy conformer, some 344.5 cm-1 below the equivalent MP2/6-311G** conformer A of Table 5. Given (i) the very good agreement of the calculated structural parameters of conformer B from Table 5 with those experimentally determined in Tables 3 and 4 and that (ii) at the MP2/6311G** level of theory conformer B is the lowest energy nC4F9OCH3 conformer, we are confident that the observed straight chain isomer, n-C4F9OCH3, is indeed conformer B from Table 5. The calculated structures of conformer B and, for completeness, conformer A are presented in Figure 3. The calculated principal coordinates for all atoms are available in the Supporting Information. 1089
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Table 7. Selected Geometric Parameters of C4F9OCH3, CF3OCH3, CH3OCH3, and C2H5OCH3 r(Cm-O) a/Å n-C4F9OCH3
c,d
r(Cf-O)b/Å
— (COC)/deg
1.436
1.337
115
(CF3)2CFCF2OCH3 c CF3OCH3 e
1.439 1.426(9)
1.337 1.347(9)
115 115.5(4)
CH3OCH3 f
1.415(1)
1.415(1)
111.8(2)
CH3CH2OCH3 g
1.415(6)
1.404(7)
111.5(4)
a
The C(methyl)-O bond length. b The C(frame)-O bond length. c From the M06-2X/6-311G** method. d Conformer B from Table 5. e Reference 8. f Reference 44. g Reference 42.
Figure 3. Calculated structure of two conformers of n-C4F9OCH3.
In Table 6 we have compared the calculated moments of inertia, second moments, and asymmetry parameters from the chosen conformers with the experimental values. The good agreement between parameters provides further reassurance that the correct conformer for each isomer has been identified. It appears that for the hydrofluoroethers presented in this work, and elsewhere,6 electronic structure calculations can reliably be performed using an MP2 method. However, the relatively large size of these molecules results in these calculations being quite expensive. The structural data presented here should be of use with regard to a comparative density functional study. We also comment on one further, important aspect that we have neglected to account for in our quantum chemical calculations and that concerns the possibility of high barriers to interconversion between conformers. In such cases the lowest energy conformer can be prohibited from being populated in a supersonic expansion. Accurate calculations of zero-point energy corrected Gibb’s free energies, at the temperature prior to the supersonic expansion, 298 K, and also the interconversion barriers, would shed further light on the matter.
’ DISCUSSION For n-C4F9OCH3 we determine a barrier to the 3-fold internal rotation of the methyl group of 336(1) cm-1. For (CF3)2CFCF2OCH3 a slightly lower barrier of 320.6(9) cm-1 is found. The B3LYP/6-31G calculations, detailed in Table 5, support a difference of 15 cm-1 between the two barriers. These barriers may be compared to the methyl group internal rotation barriers in dimethyl ether (CH3)2O, methyl ethyl ether C2H5OCH3, and trifluoromethoxymethane CF3OCH3, where the barriers have been determined as 951.05(70),41 890(16),42 and 386(10)
cm-1,8 respectively. The considerably small barrier in C4F9OCH3 compared to both the hydroethers and, to a lesser extent, one hydrofluoroether is notable. This finding may be explained by an appeal to the geometries of the ethers concerned; see Table 7. We find that for both isomers of C4F9OCH3 the CH3-O bond length is longer than the other ethers in Table 7, i.e., 1.436 Å compared to 1.415(6) Å, respectively. Also, the COC angle in C4F9OCH3 is about 4 more “open”, i.e., more obtuse, than in C2H5OCH3. Simply put, the -CH3 group in C4F9OCH3 is more free of the hindrances of the frame than in, for example, C2H5OCH3, and accordingly the barrier to internal rotation is lower in the former hydrofluoroethers. The extremely short C(frame)-O bond length, 1.337 Å, is notable in both isomers of C4F9OCH3. Although this is a calculated value, a survey of the literature indicates that this may be the shortest ever C-O bond length in an ether. Typical C-O single bonds are usually about 1.43 Å.43 The variable nature of the C-O single bond in ethers has been discussed by Allen and Kirby.9 These authors interpret the C-O bond length in R1-O-R2 systems through appeals to the electronegativities, as determined through pKa measurements, of the R1 and R2 group alcohols. In the case of a highly electronegative R2 group then there will be a considerable contribution of an ionic valence bond tautomer, of the þtype Rþ1 OR2 , to the structure of the ether. This has alternatively been discribed as a negative hyperconjugation effect involving orbital interaction between the lone pair on the oxygen and the antibonding, σ*, orbital of the C-F bond(s).10 This is clearly the case in the present work where the electronegative perfluoroalkyl chain causes a tautomeric contribution to the structure of CHþ3 OC4F9, resulting in a relatively long C(methyl)-O bond length and a remarkably short C(frame)-O bond length.
’ CONCLUSIONS Analysis of the pure rotational spectra of (CF3)2CFCF2OCH3 and n-C4F9OCH3 has led to newly determined spectroscopic parameters. Low barriers to methyl group internal rotation have been rationalized for the title compounds by noting that the C(methyl)-O bond length is quite long and the C-O-C angle quite open, i.e. more obtuse, compared to other methyl ethers. The (CF3)2CFCF2OCH3 molecule is almost perfectly asymmetric and will provide a pedagogic example with regard to the quantum mechanical treatment of the asymmetric rotor. ’ ASSOCIATED CONTENT
bS
Supporting Information. All measured transition frequencies and quantum number assignments for both molecules. This material 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]. Phone: þ1 940 369 8832. Fax: þ1 940 565 4318.
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