Article pubs.acs.org/JPCA
Microwave Studies on 1,4-Pentadiene: CH2CH−CH2−CHCH2; Transformations among the Three Rotational Isomers Eizi Hirota* The Graduate University for Advanced Studies, Hayama, Kanagawa 240-0193, Japan
Ryo Watanabe and Yoshiyuki Kawashima Department of Applied Chemistry, Faculty of Engineering, Kanagawa Institute of Technology, Atsugi, Kanagawa 243-0292, Japan
Toshiaki Shigemune, Juichi Matsumoto, and Kenji Murakami Department of Chemistry, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan
Asao Mizoguchi and Hideto Kanamori Department of Physics, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152-8551, Japan
Masakazu Nakajima and Yasuki Endo Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
Yoshihiro Sumiyoshi Department of Chemistry and Chemical Biology, Graduate School of Engineering, Gunma University, Aramaki, Maebashi, Gunma, 371-8510, Japan S Supporting Information *
ABSTRACT: In order to examine significant roles of conformations played in various research fields, a molecule with two internal-rotation axes of high symmetry, 1,4pentadiene, was studied in detail through the observation of its rotational spectra by using various types of microwave spectroscopy, Stark modulation and Fourier transform in the centimeter-wave region, direct absorption in the millimeter-wave region, and centimeter-/millimeter-wave combinations for double resonance, along with ab initio molecular orbital calculations. The molecule was confirmed to exist in three rotameric forms: skew−skew, cis−skew, and skew−skew′. For the cis−skew form, rotational spectra not only in the ground vibrational state, but also in three excited C-C torsional states were detected. Rotational and centrifugal distortion constants were precisely determined by the analysis of all the observed spectra, in addition to the relative energies of the three isomers and the torsional frequencies for the cis−skew form, as estimated from the observed spectral line intensities. The skew−skew form was found to be the most stable among the three isomers, the cis−skew form higher in energy than the skew−skew by 172 ± 66 cm−1, and the skew-skew′ form higher in energy than the cis−skew by 44 ± 26 cm−1. These experimental results were compared with those derived from a two-dimensional potential energy surface calculated by ab initio molecular orbital methods, in order to obtain a global view of molecular dynamics taking place on the surface, while paying attention to unique features of internal rotation characteristic of two dimensions.
I. INTRODUCTION Judicious recognition of the fact that the internal rotation about a single bond such as the C−C bond was not completely free, although isomers trapped in energy minima could not be well isolated, led to opening of a new research field: rotational © XXXX American Chemical Society
Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: December 17, 2012 Revised: March 13, 2013
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excited vibrational states. All the measurements were performed at dry ice temperature. Two other isomers expected to be present, however, could not be identified, presumably because of their too small dipole moments. It should be mentioned at this point that Chi Matsumura, who, at that time, was at the National Chemical Laboratory for Industry, kindly recorded the rotational spectra of 1,4-pentadiene for us using his automated-scan Stark modulation spectrometer for the frequency range from 30 to 35 GHz. A few lines thus observed were of some help in confirming assignment and were included in the analysis, Nearly 40 years later, we succeeded in observing the spectra of all the three rotational isomers using a Fourier transform microwave (FTMW) spectrometer set up at Kanagawa Institute of Technology.9 In the FTMW experiment, we diluted a 1,4pentadiene sample to 0.5% with Ar and introduced it into a Fabry−Perot cavity of the spectrometer through a 0.8 mm diameter orifice of a General Valve Series 9 pulsed nozzle at the repetition rate of 2 Hz and at the backing pressure of approximately 1.0∼1.5 atm. The frequency region covered by FTMW was from 6 to 25 GHz. The absorption signals were integrated 20 to 1000 times to attain a good signal-to-noise ratio for the measurement. Molecular beam spectroscopy sorts out only low-J lines, thus simplifying the spectrum and making the assignment easy, without sacrificing the sensitivity much, but rather improving it. However, the FTMW spectrometer at Kanagawa Institute of Technology was limited in frequency below 25 GHz, making the assignment of some transitions of the skew−skew form uncertain. We thus employed a double resonance spectrometer at the University of Tokyo10 to observe transitions higher than 25 GHz and to confirm the assignment. In order to observe rotational spectra in much wider frequency range than that accessed by FTMW and also in excited torsional states, we used a millimeter-wave spectrometer at Tokyo Institute of Technology. It is equipped with a W-band source module HP83558A, which covers the frequency range 75∼110 GHz with the output power of a few milliwatts. The millimeterwave, modulated at 25 kHz, was collimated by a Teflon lens onto an absorption cell 2 m long and, after passing through the cell, was detected by an InSb detector cooled to liquid He temperature. The absorption signal thus detected was demodulated by a lock-in amplifier, SRS SR-850, at twice the modulation frequency (i.e., 2f detection) and was sent to a personal computer for recording and processing. The measurement was carried out by scanning the millimeter-wave frequency over 40 MHz in 2 s and by accumulating the signals thus obtained 70 times to attain a good signal-to-noise ratio (S/N). The accuracy of the frequency measurement was 100 kHz or better for an absorption line well isolated and recorded with a good S/N, but was somewhat less for a weak line, particularly when suffering from baseline distortion. The sensitivity of the spectrometer was tested by observing the J = 9−8 transition of 18O12C34S, which is as abundant as 8.5 × 10−5. The sample of 1,4-pentadiene was introduced in the absorption cell at the flow rate of 0.1 sccm (= mL/min), while maintaining the pressure in the cell to be about 10 mTorr. The cell was cooled to dry ice temperature.
isomerism during the 1930s. Rapid progress then followed in spectroscopic and other related methods resulting in a few empirical rules on the conformations, as summarized, for example, by Morino and Hirota.1 One typical example of such rules applies to the allylic system, XCH2−CHCH2, which normally exists in rotameric forms with either the C(3)−X or the C(3)−H eclipsing the CC bond. A pertinent case is the 1-butene molecule, which Kondo et al.2 established to exist in the cis and gauche (or better called “skew”) forms by microwave spectroscopy. It should be noted that these rules were primarily derived from the results on molecules with one internal-rotation axis, and extension of the rules to multiaxes systems is by no means straightforward and will be accomplished only after carrying out careful studies on such systems. The 1,4-pentadiene molecule was chosen in the present study as a step to fulfill such a goal. Very little had been known on the structure of 1,4-pentadiene. Berthier et al.3 derived the dipole moment from the dielectric constant of a benzene solution. Gallinella and Cadioli4 and Inagaki et al.5 recorded the vibrational spectra of 1,4-pentadiene. Although the two groups differed in assignment in a few places, both arrived at the same conclusion that three rotameric forms were present in the liquid phase with little energy differences among them. Inagaki et al. found all three forms abundant also in the gas phase. They performed a normal-coordinate analysis to infer that the three forms were cis−skew, skew−skew, and skew− skew′. Here the names of the rotameric forms were chosen according to the conformations about the two C−C bonds, and this nomenclature will be followed throughout the present paper. Cadioli and Gallinera6 estimated the molecular structure of the cis−skew form by using our preliminary results. Then two groups reported structural data obtained by electron diffraction.7,8 McClelland and Hedberg interpreted the diffraction pattern they recorded in terms of three rotamers and found that the cis−skew form was about 122 cm−1 higher in energy than the skew−skew and skew−skew′. The present study was started in late 1960s to scrutinize how well the conformation rules held for two-axes systems, by selecting 1,4-pentadiene as a test case because of its high symmetry. According to the rules, we expected three rotameric forms for this molecule, cis−skew, skew−skew, and skew−skew′, to be present as stable, while the cis−cis form would be too high in energy to be abundant for detection, because of steric repulsion between the two vinyl groups. We anticipated further that recent advancement of spectroscopic methods would make it possible for us to obtain information on how 1,4-pentadiene molecules behaved dynamically on the two-dimensional potential energy surface spanning the entire ranges of the internal-rotation angles about the two C−C bonds, by extensive measurements of rotational spectra combined with advanced molecular orbital calculations of internal-rotation potential energy surface.
II. EXPERIMENTAL SECTION Samples of 1,4-pentadiene of a specified purity of 98% or higher were obtained from either Tokyo Kasei Co. or Aldrich Chemical Co. and were used without further purification. The rotational spectra of 1,4-pentadiene were recorded initially by using a Hughes-Wilson type, either sine-wave or square-wave, Stark modulation spectrometer installed at the Department of Chemistry, the University of Tokyo, and subsequently by a similar one at Kyushu University. Several absorption lines were observed and assigned to the cis−skew form, not only in the ground vibrational state, but also in three
III. ESTIMATION OF MOLECULAR STRUCTURE AND AB INITIO CALCULATIONS We designate the internal-rotation angles about the two C−C bonds as α1 and α2, which are taken to be zero at the cis conformation, namely, the conformation where the C−C bond eclipses the CC bond. Because of the symmetry of the B
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listed in Table 1; the ab initio parameters agree quite well with those empirically estimated.
1,4-pentadiene molecule, we need to consider only a quarter of the α1 and α2 space, as shown in Figure 1.
IV. OBSERVED SPECTRA AND ANALYSIS IV-1. cis−skew Form. (a). Ground Vibrational State. Because the dipole moment was estimated to be the largest for this isomer, searching for the rotational spectra started with this species in the frequency region 20−22 GHz, where Q-branches J2,J−2−J1,J−1 were expected to appear with well-resolved Stark components. In fact, a line observed at 21 154.98 MHz exhibited seven Stark components characteristic of Q-branches, which, when analyzed, gave J = 10.1 ± 0.5. This line was finally assigned to 102,8−101,9. Other members followed and were identified by a Q branch plot. Subsequently, R-branches (J+1)1,J+1−J0,J with J = 0−2 were detected to complete the rotational assignment. We checked the assignment also by double resonance; the intensity of 31,3−20,2 was decreased, when 21,1−20,2 was pumped. Later almost all the lines detected by Stark modulation in the centimeter-wave region were remeasured much more precisely (∼0.002 MHz) by FTMW. In the millimeter-wave region, we realized that Q branch transitions with K = 6−5 and 7−6 would appear in the region covered by our millimeter-wave source. It was quite easy to observe these transitions, because molecular constants were precisely determined by FTMW. A few R-branch transitions with small K values were also observed, which were found, together with the Q-branch lines, useful in determining sixth-order centrifugal distortion constants. Our observation was limited only to b-type transitions, while no attempt was made to detect other types of transitions, in view of the a and c dipole moment components being quite small. All the observed transitions, which are listed in Table S1, were simultaneously analyzed by an asymmetric-rotor rotational Hamiltonian in symmetric-top reduction including the centrifugal distortion terms up to the sixth order, and the molecular parameters thus obtained are listed in Table 2. The weight was chosen such that 1.0 was given to the lines measured by FTMW, 0.01 to those by millimeter-wave, and 0.0001 to those by conventional Stark modulation. The standard deviation of the fit was 0.0091 MHz. We analyzed the Stark effects measured for eight transitions by Stark modulation spectroscopy to determine the dipole moment components. The result is shown in Table 3. Only the b component was determined to be 0.3406 (16) D, whereas no significant values were obtained for both the a and c components. (b). Excited Vibrational States. We discovered three sets of satellites accompanying the ground-state spectra by conventional Stark modulation spectroscopy. It was, however, not possible to observe these satellites by FTMW, presumably because the effective temperature of the sample was too low, making the populations in excited vibrational states too small. It thus took us some time to identify millimeter-wave transitions, but finally we successfully detected and analyzed satellite spectra in the millimeter-wave region. The observed transitions are listed in Tables S2−S4, and the molecular constants derived from them are given in Table 2. As shown there, the standard deviation of the fit is 1 order of magnitude larger than that of the ground vibrational state, because high-precision FTMW data were not available. The changes of the rotational constants on vibrational excitation indicated that the three sets were reasonably assigned to the va = 1, va = 2, and vb = 1 states, where a and b denote the two lowest vibrational modes. We then measured the intensities of the vibrational satellites relative to the ground state lines to
Figure 1. Schematic phase diagram of the two-dimensional internal rotation in 1,4-pentadiene. The torsional coordinates are α1 and α2, and the positions of the three rotameric forms are indicated by ◇, ○, and △, respectively.
We take α as positive when we rotate the vinyl group clockwise, viewed from the methylene to the vinyl group. The rules mentioned earlier suggest three kinds of minima present in the potential energy surface, namely (α1, α2) = (120°, 0°):(cis− skew), (120°, 120°):(skew−skew), and (120°, −120°):(skew− skew′), where the angles denote approximate values. The names of the rotameric forms are given in parentheses. Before we started the microwave measurements, we estimated the molecular structure of 1,4-pentadiene by referring to the data on the related molecules such as 1-butene. The rotational constants thus estimated for the three rotamers are listed in Table 1, along with the dipole moment calculated by assuming the CH2CHCH2 group to be the same as that in propene.11 Table 1. Molecular Structure Parameters of 1,4-Pentadiene Empirically Estimated and Ab Initio Calculated. cis−skew Empirically Estimated A/MHz 11021.2 B/MHz 3280.3 C/MHz 2762.9 μa/D 0.09 μb/D 0.46 μc/D 0.09 MP2/6−311++G(d,p) A/MHz 10775.9 B/MHz 3199.3 C/MHz 2709.2 μa/D 0.04 μb/D 0.36 μc/D 0.02 camB3LYP/6−311++G(d,p) A/MHz 11358.1 B/MHz 3118.6 C/MHz 2667.7 a
skew−skew
skew−skew′
20219.1 2364.9 2344.5 0a 0.19 0a
13976.7 2610.0 2482.7 0a 0.35 0.13
19160.2 2372.5 2355.4 0a 0.12 0a
13609.9 2611.6 2471.1 0a 0.25 0.10
20258.3 2354.0 2336.0
14987.7 2522.7 2426.6
By symmetry.
Later we calculated these molecular parameters using ab initio molecular orbital methods: the Gaussian 09 package,12 as C
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Table 2. Molecular Constants of 1,4-Pentadiene in the cis−skew Form constant
GS
va = 1
va = 2
vb = 1
A/MHz B/MHz C/MHz DJ/MHz DJK/MHz DK/MHz d1/MHz d2/MHz HJ/kHz HJK/kHz HKJ/kHz HK/kHz h1/kHz h2/kHz h3/kHz σfit/MHz
11064.0170(15) 3154.67542(57) 2683.35228(49) 0.003 3068(48) −0.032 937(22) 0.142 790(80) −0.000 744 89(85) 0.000 032 03(45) −0.000 0100(74) −0.000 112(17) −0.001 08(32) 0.007 8(14) 0.000 0131(10) −0.000 002 22(75) −0.000 00015(17) 0.009 10
11093.0320(92) 3161.5855(56) 2684.5658(50) 0.003 369(24) −0.032 944(58) 0.144 98(32) −0.000 7614(64) 0.000 0279(18) 0.000 079(35) −0.000 170(68) −0.000 43(72) 0.020 3(43) 0.000 004(10) 0.000 0000(41) 0.000 0010(14) 0.113 13
11122.847(11) 3168.0513(64) 2685.4523(62) 0.003 344(29) −0.033 184(68) 0.146 89(45) −0.000 7707(62) 0.000 0202(19) 0.000 005(44) −0.000 520(39) 0.001 00(87) 0.021 7(63) −0.000 0294(83) 0.000 0136(47) 0.000 0044(17) 0.132 31
11079.7757(88) 3149.1121(58) 2685.3510(55) 0.003 414(26) −0.033 873(82) 0.148 92(43) −0.000 7580(50) 0.000 0362(17) 0.000 069(36) −0.000 201(56) 0.000 80(85) 0.011 8(64) 0.000 0113(72) −0.000 0036(38) 0.000 0014(11) 0.096 33
Table 3. Stark Effects and Dipole Moment of the cis−skew Form of 1,4-Pentadiene in the Ground Vibrational State.
Table 4. Vibrational Energy of the Three Vibrational States of the cis−skew Form of 1,4-Pentadiene Determined by Relative Intensity Measurements
Stark coefficient [10−7 MHz/(volt/cm)2] transition
M
obs
obs, calc
11,0−10,1 21,1−20,2
1 2 1 3 2 4 3 2 1 5 4 3 2 0 1 0 2 1 0
175.6 201.6 14.9 194.8 69.00 164.1 114.75 80.25 59.13 126.88 82.88 49.38 32.88 69.38 92.88 22.88 97.38 −10.13 −46.38
0.0 −1.8 −1.7 3.0 −0.54 1.3 −0.31 −0.75 −1.39 0.75 0.80 1.56 0.54 0.45 −3.32 −1.21 1.64 −0.50 −0.53
31,2−30,3 41,3−40,4
51,4−50,5
11,1−00,0 21,1−10,1 31,3 − 20,2
μa2 = −0.00076(16) D2 μb2 = 0.1160(11) D2 μc2 = −0.00063(88) D2
[transition frequency in MHz/observed intensity/ relative intensity] transition
GS
va = 1
va = 2
vb = 1
191,19−180,18
103981.18 27.68 1.000 109315.38 12.85 1.000 109220.68 17.93 1.000
104040.86 13.07 0.472 109378.06 5.76 0.448 109286.44 9.19 0.513 0.478 102.(7)
104088.54 6.85 0.247 109428.24 3.14 0.244 109339.34 4.65 0.259 0.250 193.(12)
104046.98 8.43 0.305 109383.34 3.64 0.283 109281.28 6.03 0.336 0.308 164.(10)
201,20−190,19
200,20−191,19
average energy/cm−1
0.0
IV-2. skew−skew Form. The Q-branch series J1,J −1−J0,J were expected to appear in a narrow frequency region around 18 GHz, because the asymmetry parameter of this form would be quite small. Although Stark modulation did not allow us to observe such lines, we could detect them by FTMW. Then we supplemented Q-branch transitions with R-branch lines such as 111−000 and 212−101. However, it was quite difficult to extend the measurement by the FTMW spectrometer of Kanagawa Institute of Technology to transitions with K equal to 2 and larger, because the A rotational constant was quite large. We then realized that we had access to the two series: J2,J−1−J+11,J and J2,J−2−J+11,J+1. Even with these series included in the analysis, it was difficult to determine rotational and quartic centrifugal distortion constants simultaneously. We thus decided to employ the doubleresonance method, which was developed at the University of Tokyo10 and was successfully employed to extend the frequency coverage of FTMW to the millimeter-wave region. The combinations of the monitor and pump transitions we employed are listed in Table 5. In parallel with double resonance, we also tried to extend the frequency coverage to higher frequency, 75∼110 GHz by the mm-wave spectrometer. However, the skew−skew form has a small dipole moment and a large A rotational constant, making it difficult to find a good candidate of high-K lines. Finally, we arrived at two Q-branch series: J3,J−3−J2,J−2 and J3,J−2−J2,J−1 with
μt ≅ μb = 0.3406(16) D
estimate the vibrational energies, where three R-branch transitions were chosen because they looked most appropriate among others for the intensity comparison. As listed in Table 4, the vibrational energies of the three vibrational states were determined to be 102 ± 7, 193 ± 12, and 164 ± 10 cm−1, respectively, by assuming T = 200 K (kT = 139 cm−1), which are to be compared with the two lowest modes calculated by ab initio methods: (87.1 and 141.1) by MP2/6−311 and (90.1 and 152.4) by camB3LYP, in cm−1. The agreement between the observed and calculated values is fairly good, although the former are slightly larger than the latter. Reference to the torsional frequencies, 84.6 and 164.5 cm−1, respectively, in the skew and cis forms of 3-fluoropropene,13,14 suggests that the a and b modes roughly correspond to the C−C torsion at the skew and cis conformations, respectively. D
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overlapped and were difficult to resolve clearly; unless information on the assignment was available from other transitions, it would be almost impossible to identify the individual members. The latter series were much more clearly observed and provided a clue to the analysis of the former series. All the observed transitions were summarized in Table S6, and were analyzed to derived molecular parameters, which are given in Table 6. The weight for lines measured by FTMW was 1.0, whereas it was reduced to 0.01 for millimeter-wave lines and 0.0001 for those measured by Stark modulation, and the standard deviation of the fit was 0.00494 MHz.
Table 5. Double-Resonance Experiments Carried out for the skew−skew Form of 1,4-Pentadiene monitor transition
detected transition (frequency in MHz)
21,1−20,2 31,2−30,3 41,3−40,4 51,4−50,5 61,5−60,6 71,6−70,7 81,7−80,8 21,1−20,2 11,0−10,1 31,2−30,3 21,1−20,2 51,4−50,5 41,3−40,4 51,4−50,5
22,0−21,1 (52780.3515) 32,1−31,2 (52752.8010) 42,2−41,3 (52716.1399) 52,3−51,4 (52670.4381) 62,4−61,5 (52615.7773) 72,5−71,6 (52552.2560) 82,6−81,7 (52479.9866) 32,2−21,1 (66835.0889) 21,2−10,1 (26946.7625) 41,4−30,3 (36249.7868) 31,3−20,2 (31603.0103) 42,3−51,4 (29245.7087) 51,5−40,4 (40887.0978) 61,6−50,5 (45514.9506)
V. DISCUSSION AND FUTURE STUDIES V-1. Molecular Constants and Molecular Structure. We could reproduce the observed spectra by using an asymmetricrotor rotational Hamiltonian in symmetric-top reduction including the sixth-order centrifugal distortion terms, as shown in Tables 2 (cis−skew) and 6 (skew−skew and skew−skew′). Our data sets contained transitions of J as large as, or even larger than, 30 and K equal to 7, but still the sixth centrifugal distortion constants were only marginally determined, and we would probably require higher J and K transitions to be observed and eighth or higher order centrifugal terms to be included for more precise determination of the sixth terms, which would not be easily realized. This is really unfortunate, because we have extended our observations to the millimeter-wave region, in order to obtain some information on the internal-rotation potential energy surface through detection of the effects of resonance on rotational spectra. So far, no such perturbations have been found. Rotational and quartic centrifugal distortion constants, on the other hand, were well determined. We compare the observed quartic centrifugal terms with those calculated by MP2/cc-pVTZ Gaussian 03 after optimizing the structural parameters; the experimental and theoretical results generally agree with each other quite well, but some systematic discrepancies are noticed in a few cases, as shown in Table 7. We also derived three structural parameters by fitting the calculated rotational constants to the observed values, whereas others were fixed to those derived from an electron diffraction experiment reported in ref 8. The results are given in Table 8. The atoms in the molecule were numbered as H2C(1) C(2)H−C(3)H2−C(4)HC(5)H2. For the cis−skew form, our parameters agree with the electron diffraction values, as they should, because our rotational constants had been included in the analysis of ref 8. For the skew−skew and skew−skew′ forms, our results differ considerably from those of electron diffraction, but agree quite well with the camB3LYP/6−311++G(d,p) values. V-2. Internal-Rotation Dynamics. We have estimated the relative energies of three potential minima, skew−skew, cis−skew, and skew−skew′, by comparing the intensities of rotational spectra of the three rotameric forms in the respective ground state. We focused attention to the millimeter-wave spectra, because we thought the spectra in this region were observed in a straightforward way and thus were least affected by impedance mismatch of microwave circuitry in the spectrometer. Unfortunately, there is only a small number of spectral lines for both the skew−skew and skew−skew′ forms in the millimeter-wave region that are amenable to intensity measurements. Furthermore these lines are not necessarily close to the spectra of the cis−skew form, which are a little more abundant than those of the former two. The measurement was based upon the following intensity formula for a rotational transition:15
J ≥ 24. Although these lines were quite weak due to the small dipole moment, we still could detect high-J members by carefully searching the spectra and finally arrived at the assignments consistent with the results of the double-resonance experiment. We then analyzed all the observed spectral data listed in Table S5 simultaneously, with giving the weight of 1.0 to the lines observed by FTMW and double resonance and of 0.01 or 0.001 to millimeter-wave transitions, in favorable and unfavorable conditions, respectively. The molecular constants thus determined are given in Table 6; the standard deviation of the fit was 0.00421 MHz. Table 6. Molecular Constants of the skew−skew and skew−skew′ Forms of 1,4-Pentadiene constant
skew−skew
skew−skew′
A/MHz B/MHz C/MHz DJ/MHz DJK/MHz DK/MHz d1/MHz d2/MHz HJ/kHz HJK/kHz HKJ/kHz HK/kHz h1/kHz h2/kHz h3/kHz σfit/MHz
19949.0019(16) 2351.78741(19) 2332.76933(21) 0.001 1557(21) −0.050 198(27) 0.8100(15) 0.000 018 31(56) 0.000 006 69(31) −0.000 0020(45) −0.000 354(46) 0.0119(65) −0.94(33) −0.000 0022(13) −0.000 0033(25) −0.000 0029(21) 0.004 21
14611.9860(11) 2537.75132(39) 2430.61940(38) 0.002 6394(70) −0.068 638(13) 0.638 95(12) −0.000 594 78(47) 0.000 017 07(23) −0.000 017(38) −0.000 289(18) −0.006 13(46) 0.066 3(44) 0.000 006 9(15) 0.000 001 54(51) 0.000 000 12(11) 0.004 94
IV-3. skew−skew′ Form. Again the Q-branch series J1,J−1−J0,J gave a first clue to the observation and assignment of the spectra; this series appeared in the 12−14 GHz region. The Q−branch series was supplemented by the R branch lines J+11,J+1−J0,J, as in the case of other forms. Although the spectra of this form were not as strong as those of the cis−skew form, it was not difficult to detect some transitions involving levels of K = 2, and we could detect and make assignment even for some c-type transitions. We could identify Q-branch transitions with both K = 4−3 and 5−4 in the millimeter-wave region covered by our spectrometer. Since the former appeared very crowded, several members were E
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Table 7. Observed and Calculated Quartic Centrifugal Distortion Constants of the Three Rotameric Forms of 1,4-Pentadiene skew−skew
a
cis−skew
skew−skew′
constant
obs
calca
obs
calca
obs
calca
DJ/MHz DJK/MHz DK/MHz d1/kHz d2/kHz
0.0011557(21) −0.050198(27) 0.8100(15) 0.01831(56) 0.00669(31)
0.0012419 −0.050538 0.7454 −0.00739 0.00686
0.0033068(48) −0.032937(22) 0.142790(80) −0.74489(85) 0.03203(45)
0.0034011 −0.030754 0.123191 −0.76353 0.03249
0.0026394(70) −0.068638(13) 0.63895(12) −0.59478(47) −0.01707(23)
0.0027472 −0.061025 0.48887 −0.51171 0.00313
Gaussian MP2/cc-pVTZ.
Table 8. Molecular Structure of the Three Rotameric Forms of 1,4-Pentadienea skew−skew
cis−skew
skew−skew′
parameter
present
EDb
calcc
present
EDb
calcc
present
EDb
calcc
∠C−C−C ∠CC−C α1 α2
110.9 124.3 118.9 118.9
108.9(19) 125.5(6) 122.2(78) 122.2(78)
112.4 125.1 118.2 118.2
113.2 (125.5)d 117.0 4.2
113.1(11) 125.5(6) 116.9(7) 4.3(69)
115.5 125.1 119.2 11.2
111.9 123.4 123.3 −123.3
108.9(19) 125.5(6) 128.6(84) −128.6(84)
112.8 125.0 123.0 −123.0
Structural parameters common to all the three rotamers were fixed to those reported in ref 8: r(C−C) = 1.508(2) Ǻ , r(CC) = 1.334(2) Ǻ , r(C−H) = 1.090(2) Ǻ ,
