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The ground state torsion–rotation spectrum of propargyl alcohol (HCCCH2OH)
Journal of Molecular Spectroscopy 234 (2005) 149–156 www.elsevier.com/locate/jms
The ground state torsion–rotation spectrum of propargyl alcohol (HCCCH2OH) J.C. Pearson *, B.J. Drouin Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA Received 29 July 2005; in revised form 30 August 2005
Abstract The rotation–torsion spectrum of the asymmetric frame-asymmetric top internal rotor propargyl alcohol (HCCCH2OH) has been extended into the millimeter and submillimeter wave spectral regions. Over 2000 ground torsional state transitions have been measured and analyzed up to rotational quantum numbers J = 80 and Ka = 33 through a frequency of 633 GHz. The newly measured transitions were added to approximately 200 previously reported and now unambiguously assigned microwave transitions to comprise a data set of 2390 transitions which has been fit to 59 kHz using a reduced axis method (RAM) Hamiltonian. The ground state has been confirmed to consist of a symmetric and an antisymmetric gauche conformer with no spectroscopic evidence of stable trans conformer. A complete set of rotation and distortion constants through 6th order and a number of the 8th and one 10th order constants for the normal species are presented along with those determined from a re-analysis of the existing OD species data. The a and b symmetry Coriolis interaction constants and the gauche+ gauche tunnelling frequency of 652389.4 MHz has been determined for the OH species while the b symmetry Coriolis interaction and the 213 480 MHz tunnelling frequency were determined for the OD species. 2005 Elsevier Inc. All rights reserved.
1. Introduction Propargyl alcohol HCCCH2OH is the simplest stable unsaturated alcohol. The simple stable alcohols such as methyl, ethyl, n-propyl, isopropyl, and allyl are all known to exhibit large amplitude motions, which complicate or even dominate the rotational spectra. All the other small alcohols containing two or three carbons are known to exist in several different stable conformers due to the asymmetric internal rotation of the hydroxyl group [1–5]. Methyl, ethyl, isopropyl, syn-allyl, and most likely n-propyl alcohol all exhibit strong interactions between the internal motion and the overall rotation [3,5–7]. As in the other simple alcohols, the hydroxyl proton in propargyl alcohol is subject to a hindered large amplitude internal motion. The spectrum of propargyl alcohol is strongly influenced by the OH group tunnelling through the plane of the mol*
Corresponding author. Fax: +1 818 393 2430. E-mail address: [email protected] (J.C. Pearson).
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.08.013
ecule containing the heavy atoms. Fig. 1 shows the possible hydrogen configurations in propargyl alcohol. The barrier between the gauche confirmations of the OH rotation is quite low allowing this motion to be very rapid. In this paper, the ground state torsion–rotation spectrum of propargyl alcohol is presented. Several groups investigated the rotational spectrum of propargyl alcohol in the microwave region in the late 1960s. Bolton et al. [8] performed the first study of the main isotope and a number of other isotopes of propargyl alcohol in 1968. Kadzhar et al. [9,10] independently undertook similar studies. The first real clue to the complexity of the ground state spectrum was the result of the work of Hirota [11]. Hirota observed a number of higher JP/R (DJ = ± 1) branches and several Q (DJ = 0) branches at high Ka values for both the normal and the OD species in the spectral region below 50 GHz. The J and Ka assignments of these branches were confirmed with Stark effect patterns; however, it was not known if the transitions originated from the b- or c-component of the dipole. Unfortunately, the
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torsion–rotation constants for the OD species are presented from the re-analysis the work of Hirota [11]. The data should prove useful to radio astronomers searching for this species and in the analysis of internal energy redistribution in this species. Propargyl alcohol is now one of a very few asymmetric top-asymmetric frame internal rotors, which has been successfully analyzed to high J values. 2. Experimental
Fig. 1. Configuration diagram of propargyl alcohol gauche+ is the symmetric combination of gauche hydrogen relative to the plane of heavy atoms, gauche is the antisymmetric combination. No evidence supporting a stable trans configuration was found.
branches Hirota observed exhibit significant torsion–rotation perturbations and were not completely analyzed. The partial analysis and the high Ka values observed led Hirota to propose that the ground state was made up of a symmetric and antisymmetric gauche configurations separated by approximately 644 GHz. More recently, Pate [12] successfully measured a number of millimeter transitions including some b-type transitions (DKa = 1, DKc = 1) and determined gauche+ a and b dipole moments. In PateÕs study a simple asymmetric rotor analysis failed to account for the transitions above Ka = 7 suggesting strong torsion–rotation interactions. Propargyl alcohol is an excellent candidate for interstellar detection and potentially a good probe of the relative importance of gas phase ion driven chemical processes or dust grain surface driven chemical processes. As an unsaturated species, it should be formed on both dust and in the gas phase and therefore observable in both warm and cold interstellar regions. The chemical structure of propargyl alcohol is similar to a good number of well-known interstellar species. It could be derived from methyl alcohol by substitution of one methyl hydrogen with an acetylenic group. Additionally, molecules which could be suitably protonated in the gas phase or on dust grains like C3O are known to exist. The prospects for interstellar detection are greatly enhanced due to the tunnelling between the gauche+ and gauche substates. This tunnelling makes propargyl alcohol one of a very few polyatomic molecules, that exhibits a strong submillimeter spectrum even at low temperatures. The tunnelling also makes propargyl alcohol an attractive candidate for interstellar observation via absorption. The means of production, the submillimeter energy difference between ground state conformers and the substantial dipole moment could make propargyl alcohol detectable in a wide variety of different interstellar sources. In this paper, the ground state is confirmed to be composed of two gauche conformers and the analysis of the spectrum suggest no role for a trans configuration. The rotational dipole moments and the approximate effective torsion–rotational transition moments are discussed. The
The sample of HCCCH2OH was obtained from Matheson Coleman and Bell chemicals and required no further purification. The sample was directed into a double pass 1 meter long, absorption cell at a total pressure of 30 mTorr. A spectrometer with phase locked 80–120 GHz klystrons, point contact harmonic generators and tone burst modulation [13] was used to generate and modulate the millimeter and submillimeter wave radiation. The absorption spectrum was recorded with a Schottky diode or a 4.2 K InSb hot electron bolometer detector and digitized on a computer. Transitions have been measured through 633 GHz in frequency. The measurement accuracy is estimated to be between 50 and 150 kHz depending on the signal-to-noise and the line width. Fit residuals suggest the accuracy of most transitions is close to 50 kHz. The strongest low frequency lines are the most accurate as expected. The details of this spectrometer system can be found elsewhere [14]. Initial predictions were based on a fit of all the data of Hirota [11] and some additional transitions supplied by Pate [12] These predictions were sufficiently accurate to predict J values to 50 and Ka values between 6 and 20 for rapid assignment. The higher Ka a-type R branches (DJ = 1, DKa = 0 DKc = 1) diverged in a regular pattern and were assigned quickly once additional data were included. The low Ka a-type R branch lines were much more difficult to assign since the initial data set contained very limited information on the strong a-type DKa = 2 Coriolis interaction. Fortunately these lines are the strongest allowed transitions in the spectrum and were readily assigned once surveys of the spectral regions near 300 and 400 GHz were made. Additional measurements of high J low Ka transitions were then made to improve the analysis of the torsion rotation interactions. Lastly, the unassigned spectrum recorded by White [15] was assigned and incorporated into the analysis. A total of 2390 lines were used in the analysis including more than 2000 recorded between 84 and 633 GHz. The data set includes a-type and b-type transitions through J = 70 and Ka = 30 within each substate and J = 80 and Ka = 24 between the substates. All of these transitions including a very large number of highly perturbed ones have been fit to experimental accuracy. In these measurements, the strong lower frequency and quantum number a-type and c-type transitions are the most precise while the weak b-type, very high J > 60 c-type are the least precise. No additional OD data were recorded.
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
3. Theory Propargyl alcohol is a near prolate asymmetric top with a single large amplitude internal motion of the hydroxyl proton. The heavy atoms in propargyl alcohol fall in a plane and the three hydrogens bonded to the carbons are either in the plane or symmetric about the plane. As a result, the molecule has Cs symmetry as does the motion of the hydroxyl proton. From the Cs symmetry, the hydroxyl proton could be in the plane of the heavy atoms (trans or cis) or a symmetric or antisymmetric combination of out of the plane (gauche+ and gauche). Any trans, cis or gauche+ configuration is symmetric with respect to the plane while only the gauche configuration is antisymmetric. The Cs symmetry also dictates the selection rules allowing a and b-type transitions between configurations of the same symmetry and c-type transitions between configurations of different symmetries. As a result, only a- and b-type transitions can be observed within any possible configuration. A general Hamiltonian for a fixed-axis fixed-frame asymmetric top-asymmetric frame internal rotation problem has been proposed by Quade and co-workers [16–19]. It has been applied with varying degrees of success to a number of two ‘‘equivalent’’ substate asymmetric internal rotation problems [5,20–25]. In the case of propargyl alcohol, the formulation of the Hamiltonian used is often referred to as the reduced axis method [26]. The reduced axis Hamiltonian can be derived from the final transformed principal axis formulation of Quade [16], which is comprised of three parts H ¼ H R þ H TR þ H T ;
ð1Þ
where HR is the quasi-rigid-body rotational Hamiltonian, HT is the torsional Hamiltonian and HTR is the torsion–rotation interaction Hamiltonian. Explicitly the components are H R ¼ AðrÞ P 2a þ BðrÞ P 2b þ C ðrÞ P 2c ðrÞ
þ Dbc ðP b P c þ P c P b Þ þ DðrÞ ac ðP a P c þ P c P a Þ ðrÞ
þ Dab ðP a P b þ P b P a Þ; ðr1 ;r2 Þ
H TR ¼ Dbc
ðP b P c þ P c P b Þ 1
2
ðr ;r Þ þ Dac ðP a P c þ P c P a Þ ðr1 ;r2 Þ
þ Dab þM ðrÞ
H T ¼ DE .
ðP a P b þ P b P a Þ
ðr1 ;r2 Þ
1 ;r2 Þ
P a þ N ðr
1 ;r2 Þ
P b þ Oðr
P c; ð2Þ
Here r is the torsional substate identifier and terms with (r1, r2) are off diagonal in torsional substate. The Cs symmetry and the special case of two ‘‘equivalent’’ substates allow a number of simplifications to be made. The on diagonal (in torsional substate) Dbc and Dac are not allowed from the symmetry. The ‘‘equivalence’’ of the gauche states makes the on diagonal axis rotation Dab term zero since the two states share a common axis system [21].
151
The Cs symmetry and the even and odd symmetry of the two gauche substates observed prevents the off diagonal antisymmetric Dab and O terms in HTR from connecting them. Now a rotation around the c axis can be made to minimize either the linear or quadratic off diagonal terms [26]. The resulting reduced axis method Hamiltonian has one of the following forms: H R ¼ AðrÞ P 2a þ BðrÞ P 2b þ C ðrÞ P 2c H T ¼ DEðrÞ ðr1 ;r2 Þ
H TR ¼ Dbc
ðP b P c þ P c P b Þ ðr1 ;r2 Þ
þ Dac
ð3Þ
ðP a P c þ P c P a Þ þ
or 1 ;r2 Þ
H TR ¼ M ðr
1 ;r2 Þ
P a þ N ðr
Pb þ
Here as in Eq. (2), the torsional part of the Hamiltonian HT is the solution for the J = 0 problem where the resulting energy differences are treated as a parameter determined directly from the tunnelling splitting of the c-type spectra. The Dbc and Dac or M and N terms in Eq. (3) connect energy levels in the two different substates, which differ in Ka by 2 and 1 or 1 and 0, respectively. The validity of the transformation to the reduced axis is highly dependent on the actual tunnelling path taken by the hydroxyl proton. If the motion is a pure inversion and therefore a non-periodic motion, then on average there is no linear angular momentum and the unused HTR choice is exactly zero. However, if there is any tunnelling through both the trans and cis configurations, the motion is periodic and neither HTR choice can be made equal to zero. Since the trans barrier cannot be infinite, neither HTR term is exactly zero. However, the linear angular momentum contributions are typically completely correlated with other parameters in the absence of avoided crossings connected directly by these terms. As a result, transitions connecting energy levels well below the barrier and any trans levels can be effectively analyzed with either set of HTR terms but not both. At some point in the torsional manifold, this approximation will break down as it does in ethyl alcohol [24], however if the barrier is truly 2fold, it may be near the free rotor limit. Molecular distortion results in distortion on the torsion rotation terms in Eqs. (2) and (3). These can be expanded in terms of P2 or P 2a (i.e., DabJ or DabK). Ideally, the asymmetry constants coupled with the fundamental torsion rotation terms will facilitate fitting of interactions involving Ka states separated by more than 2. From a practical fitting perspective these higher order interactions are often critically dependent on the details of the distortion and can often be analyzed with fewer terms if an explicit DKa operator is included (i.e. for symmetric DKa = 3). 4. Analysis The 2390 measured transitions were fit to a Hamiltonian in the form of Eq. (3) which included a complete Watson S
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set of distortion constants through 6th order and all of the 8th order except l3 and l4 [27]. Distortion of the internal rotation and higher order torsion rotation effects were satisfactorily accounted for by multiplying either the Dbc and Dac or the M and N constant operators by expansions in P2 and P 2a denoted as DbcJ or DbcK. The M an N constants with their distortion successfully account for all the transitions, but the Dbc and Dac set had problems with a single avoided crossing between gauche+ Ka = 3 and gauche Ka = 6 at J = 46. Transitions connecting these levels could only be fit to about 1 MHz. As a result, an explicit b symmetry DKa = 3, ðP 3þ þ P 3 Þ interaction term was included in this analysis. In this case, P+ is defined as the normalized positive combination of Pb and iPc. The ðP 3þ þ P 3 Þ constant is, as one would expect, very highly correlated with the expansion of Dac in P 2n a (DacK, DabKK, etc.). The correlation is only broken by the previously mentioned level crossing. It was found that the DacK and ðP 3þ þ P 3 Þ were both required to fit all the spectra. However, when DacKK was included to extend the analysis the value of ðP 3þ þ P 3 Þ became ill determined and ðP 3þ þ P 3 Þ was still necessary to fit the level crossing. Therefore, the ðP 3þ þ P 3 ÞP 2a term was used instead of DacKK. This allows ðP 3þ þ P 3 Þ to fit the level crossing while ðP 3þ þ P 3 ÞP 2a is determined instead of DacKK. Observation of additional DKa = 3 level crossings would probably eliminate this fitting difficulty. The complete list of measured transition frequencies, quantum number assignments and the observed minus calculated for both analyses is given on Table 1. The four highly perturbed asymmetry doublet transitions where the quantum number assignment has changed between the analyses are denoted. Table 1 includes the result from
two fits one using the Dac and Dbc set and another using the M and N constants. It was attempted to fit both together but the correlations were always at least 0.9999 between Dbc and M as well as Dac and N. As a result, convergence was impossible to achieve. A complete set of predictions through J = 80 is available from the JPL spectral line catalog via anonymous FTP at http://spec.jpl.nasa.gov. The derived spectroscopic parameters as defined in Eq. (3) and the preceding paragraph are given in Table 2 for both fits. A difficult aspect of the analysis of propargyl alcohol arises from the interaction of the asymmetry terms in the Hamiltonian and the Coriolis interactions. The Coriolis terms connect single symmetric top K levels in two different vibrational or torsional states while the asymmetry mixes these K levels within a state. The asymmetry operators spread the effects of the Coriolis interaction to all the asymmetry mixed K levels in the appropriate Wang symmetry block of the Hamiltonian. The interaction between asymmetry and Coriolis operators results in two major implications; first, all the high J low Ka transitions are perturbed to some degree and second, the higher order Coriolis interactions have a very similar effect on lower order interactions coupled by higher order asymmetry operators. The first of these effects was prominently observed in the line positions connecting high J low Ka levels of propargyl alcohol while the second complicated the fitting process. The lack of level crossing in the currently available OD data set indicates that this indeterminacy remains in the parameter set. The rotation and distortion constants for the two OH substates are remarkably similar even to 8th order with the small differences due to the torsion and varying contri-
Table 1 Measured frequencies in MHz, quantum number assignments and residuals from model fits for propargyl alcohol J 0K 0 ;K 0
v
J K a ;K c
v
Unc
Reference
Fit #1
Fit #2
278,20 278,19 10,1 10,1 247,18 247,17 337,26 337,27 1610,6 1610,7
0 0 1 0 1 1 0 0 0 0
267,20 267,19 00,0 00,0 258,18 258,17 326,26 326,27 159,6 159,7
1 1 1 0 0 0 1 1 1 1
8762.220 8762.220 8912.180 8932.480 10053.550 10053.550 11304.780 11325.240 12367.810 12367.810
0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100
[11] [11] [11] [11] [11] [11] [11] [11] [11] [11]
0.005 0.036 0.106 0.028 0.027 0.017 0.162 0.165 0.013 0.013
0.006 0.037 0.106 0.028 0.027 0.017 0.161 0.167 0.011 0.011
11,0 1713,4 1713,5
1 0 0
10,1 1712,6 1712,5
1 1 1
28419.153 28478.315 28478.315
0.025 0.020 0.020
[12] [15]/[11] [15]/[11]
0.000 0.008 0.008
0.001 0.000 0.000
381,37 431,42 391,38 540,54 541,54 421,41 401,39
1 1 1 1 1 1 1
382,37 432,42 392,38 541,54 540,54 422,41 402,39
0 0 0 0 0 0 0
637743.445 637857.856 637936.884 637951.028 637960.110 637983.112 638033.400
0.100 0.100 0.100 0.100 0.100 0.100 0.100
A A A A A A A
0.005 0.022 0.004 0.112 0.109 0.015 0.008
0.019 0.002 0.020 0.077 0.074 0.038 0.031
a
c
Measured
Data sources are: (A) this work, Hirota [11], Pate [12], White [15], for full listing see supplemental material.
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
153
Table 2 Propargyl alcohol Hamiltonian parameters in MHz Fit #1
Fit #2
Gauche+ A B C DJ · 103 DJK · 102 DK d1 · 104 d2 · 105 HJ · 109 HJJK · 107 HJKK · 106 HK · 105 h1 · 109 h2 · 1010 h3 · 1010 LJ · 1014 LJJK · 1012 LJK · 1011 LJKK · 1010 LK · 109 l1 · 1014 l2 · 1015 PJJJKK · 1014 DE Dbc DbcJ · 105 DbcK · 104 DbcJJ · 1010 Dac DacJ · 104 DacK · 103
ðP 3þ þ P 3 Þ · 105 ðP 3þ þ P 3 ÞK · 106
Gauche
32527.93731(166) 32647.95734(175) 4700.248927(178) 4684.174412(170) 4232.216921(181) 4227.908512(172) 2.903958(110) 2.811131(106) 6.196600(252) 6.21770(32) 1.007490(32) 1.017754(39) 7.06958(34) 6.634496(316) 4.88530(150) 4.11124(98) 9.9820(308) 9.5393(306) 2.1775(47) 1.9889(51) 3.4208(63) 3.1476(78) 9.2561(232) 9.292(32) 4.3263(121) 4.0502(119) 7.016(81) 6.113(58) 1.1543(34) 0.89721(279) 2.650(277) 2.569(282) 1.742(52) 1.175(58) 3.382(144) 1.964(179) 4.017(70) 2.856(103) 7.18(135) 7.07(156) 2.137(130) 2.077(136) 6.02(109) 7.00(80) 2.512(159) 1.308(239) 652389.4199(209) 2.34009(37) 5.9587(90) 5.802(84) 2.452(126) 36.0109(113) 1.60026(87) 6.261(78)
Gauche+
DE M MJ · 102 MK MJJ · 106 MJK · 105 N NJ · 102 NK NJJ · 107 NKK · 103 NJK · 105 NJJ · 107 NKKK · 107 NKKJ · 108 NKJJ · 1010 NJJJ · 1012
Gauche
32544.9731(176) 32631.0683(175) 4701.97559(179) 4682.47384(181) 4232.130452(196) 4227.821866(186) 2.933541(192) 2.780560(212) 6.23325(55) 6.20076(68) 0.997188(169) 1.028360(169) 7.25088(106) 6.45053(112) 5.22123(237) 3.79551(187) 10.744(35) 8.882(38) 1.9453(120) 2.2812(144) 2.607(39) 4.183(36) 9.3686(251) 9.201(33) 4.7915(179) 3.6382(185) 8.003(93) 5.011(63) 1.3355(54) 0.7348(41) 4.750(306) 2.23(32) 1.259(58) 1.951(66) 3.091(224) 0.0216(32) 3.582(135) 0.4669(195) 10.00(155) 0.01120(184) 2.938(168) 1.750(171) 3.97(121) 6.71(83) 3.038(200) 0.427(303) 652389.4609(224) 3326.45(171) 4.833(45) 1.2644(162) 1.1115(193) 3.04(45) 1057.87(56) 3.7006(125) 1.6956(73) 7.611(131) 1.7328(247) 5.109(130) 7.611(131) 1.318(121) 3.97(40) 2.21(70) 9.49(58)
3.47(123) 8.893(59)
The fits included 2390 lines and have RMS (Fit #1) 59.6 kHz and RMS (Fit #2) 58.3 kHz.
butions from excited states. As a result of the similarity, only higher order terms, which were determined to have similar values in both substates were included in the analysis. A complete set of 8th order constants can be determined and does reduce the RMS of the fit slightly, but the l3 and l4 terms have very different values in the two torsional substates and some of the higher order Coriolis terms become undetermined. Removal of the undetermined Coriolis terms increases the RMS significantly without a significant change in the l3 and l4 terms. As a result, values for l3 and l4 are not given since their values appear to be an artifact of the torsion. The same is true to a lesser extent of h3, l1, and l2; however, these terms do have similar magnitudes in the two substates and were kept in the analysis. A slightly better reduced RMS is obtainable by adding a few
additional terms to one or the other torsional state. The quoted RMS uses the same constant set in both substates and results in a reduced RMS of 0.65 in both fits. The re-analysis of the existing propargyl alcohol OD data [11] was somewhat less satisfying since there is insufficient information to determine the a-type Dbc(PbPc + PcPb) or Pa Coriolis term. This Coriolis interaction will have a major effect on the higher J lower Ka energy levels, but it will have a minor effect on all the other constants determined. Some evidence of the contribution of the term is seen in the distortion constants where there are significant differences between gauche+ and gauche. As a result of these problems, a reduced RMS of only 2.4 was achieved. The unambiguously assigned HCCCH2OD transitions and the observed minus calculated are given in the
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supplemental material. Table 3 contains the rotation, distortion and interaction constants determined OD species. A number of attempts were made to try to determine simultaneously both sets of torsion rotation operators. Both sets were not simultaneously determinable, even with the full data set, suggesting that the OH motion prior to any level crossing of the same K can be effectively modeled by pure inversion to spectroscopic accuracy. The lowest same K crossing is predicted to occur between the gauche+ J1,J1 and gauche J1,J levels near J = 85 which is well above the J range transitions observed. In general, the lack of direct information on the DKa = 0 interaction typically precludes determination of both Pa and PbPc + PcPb. There is direct information on the b symmetry DKa = 1 interaction, Pb and PaPc + PcPa are both DKa = 1 interactions and can generally be interchanged. The failure to determine both sets of torsion–rotation constants simultaneously is by no means a proof of a pure inversion spectra, but it does suggest that the gauche torsional problem is localized away from the trans position. The similarity of all the distortion constants in either set is highly suggestive that the differences are what one would expect from coupling to excited vibrational modes given the 652 GHz energy difference between states and not the hidden effects of an unobserved periodic motion. This is clearly not the case in ethyl alcohol where the P4 distortion constants are drastically different and even opposite in sign in one case [24]. Attempts were also made to search for trans–gauche interactions similar to the ones which eventually dominate the higher J ethanol spectra [24,25]. No transitions involving levels through J = 80 and Ka = 33 were observed which could not be fit to spectroscopic accuracy. Once again this does not completely rule out a trans substate, but it suggests that if a trans state exists, it is at much higher energy and interacts very weakly if at all. The existence of a trans well, which is below the top of the torsional barrier and at much higher energy is inconsistent with the relatively low (400 cm1) barriers observed in other alcohols. A minimum in the trans position would also be expected to increase the importance of tunnelling through that position
Table 3 Deuterated propargyl alcohol Hamiltonian parameters in MHz
A B C DJ · 103 DJK · 102 DK dJ · 104 dK · 10 DE Dac DacK · 10 DacJ · 103
Gauche+
Gauche
29689.4(83) 4613.263(63) 4130.124(61) 4.189(234) 6.014(220) 3.76(99) 2.51(207) 2.63(34)
29730.7(60) 4600.874(46) 4127.556(49) 2.859(128) 4.500(228) 5.69(153) 7.351(161) 0.581(236) 213480.4(309) 78.80(87) 2.16(49) 1.433(234)
The fit includes 97 lines and has rrms 239.2 kHz.
and therefore the effects of undeterminable additional set of Coriolis terms, which is contrary to observations. 5. Barrier to internal rotation The barrier to internal rotation in propargyl alcohol can be calculated from the J = 0 torsional Hamiltonian, H ¼ Fp2 þ V ðaÞ;
ð4Þ
where F is inverse moment of inertia of the top and V(a) is the torsional potential which is XV n ð1 cosðnaÞÞ. ð5Þ V ðaÞ ¼ V 0 þ 2 The solution of Eq. (4) results in a series of torsional energy levels. In the general asymmetric top-asymmetric frame torsional problem, F is a function of torsional angle, but the equivalence of the gauche substates in propargyl alcohol requires F to be the same for each substate. As a result, an effective constant F gives a satisfactory solution to the torsional problem. The structure of the barrier determines the form of the solution. If the barrier is predominately 3fold, there will be a bound trans position and each torsional substate will be comprised of three torsional substates. However, if the barrier is predominately 2-fold then there will be no bound trans position and each torsional substate will consist of two substates. The lowest three Vn terms must be evaluated in order to obtain barrier to first order. A complete solution requires one tunneling energy per potential constant determined, e.g., ground state tunneling frequency, excited torsional state energy and excited state tunneling frequency, otherwise a unique solution cannot be determined. As a result, the available microwave tunnelling frequencies cannot determine the peak of the barrier at the trans position and information on the energy of the excited torsional states is needed. Nyquist reported a single hydroxyl torsion frequency for propargyl alcohol in liquid n-hexane at 192 cm1 for OH and 150 cm1 for OD [28]. To reproduce the microwave data, the first excited gauche+ and gauche states will be split significantly more than the ground state resulting in at least two and most likely four torsional bands from the ground state to the first excited state. However, the effect of the liquid n-hexane on the torsional frequencies is not well known. It is known that a large number of saturated alcohols exhibit a characteristic 210 ± 10 cm1 band in cyclohexane [29], which is relatively close to the gas phase excited OH torsional state energy. A numerical experiment using NyquistÕs values resulted in an unrealistically high V1 barrier term. The required V1 term was significantly larger than the available ab initio barrier which is expected to over estimate the barrier height [30]. Since the barriers for methanol and ethanol have been determined [25,31] and are close to 400 cm1 in height, the very large V1 was ruled out. As a result, little more can be said about the barrier than reported by Hirota [11].
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
6. Dipole moments The dipole moments of an internal rotor with Cs symmetry can be expressed as and expansion in sine or cosine components. The sine terms connect torsional states of different symmetry and the cosine terms connect torsional states of the same symmetry. Linear terms represent the pure rotation within a given state. The first order contributions of the dipole are ! l ¼ l0 þ l1 cosðaÞ þ l0 þ l1 cosðaÞ þ l1 sinðaÞ. ð6Þ a
a
b
b
c
The effective transition moment for any transition is given by hJ 0 ; K 0 ; M 0 ; w0T j! l jJ ; K; M; wT i;
ð7Þ
where |J,K,Mæ is the rotational wavefunction and |wTæ is that the torsional wavefunction. Here the zero terms of la and lb result from the usual rotational contributions within each state. Since the spectrum is composed of two equivalent gauche states that act as a pure inversion, Eq. (7) can be simplified as follows: h0þ j cosðaÞj0þ i h0 j cosðaÞj0 i Const; h0þ j sinðaÞj0 i ¼ h0 j sinðaÞj0þ i Const;
ð8Þ
where WT is either ground state gauche+ (0+) or gauche (0). The result is a fixed symmetric (a-type and b-type) dipole in each gauche state and a fixed effective inversion dipole between the ground gauche+ and gauche states. No K dependence of line strength was observed in propargyl alcohol and the expected intensity in the c-type transitions appears to be constant to experimental accuracy, which is about 10% in intensity, suggesting the approximation made in Eq. (8) is consistent with experimental observations. The effective a-type and b-type dipole moments in the gauche+ substate were measured by Pate [12] and determined to be 1.037(2) Debye for la and 0.147(4) Debye for lb. The a-dipole is in agreement with the 0.99 Debye determined by Kadzhar et al. [9]. The dipole was determined from low J and low K transitions known to be well isolated from the other substate. It can be expected that the gauche state will have nearly identical a-type and b-type dipole moment with any difference due to rotation–vibration intensity borrowing being slightly different for the two sub-states due to the 21.7 cm1 energy difference. Since the only published c-dipole measurement is clearly too small for the observed intensities (0.177 Debye from [9]), we compared observed c-type intensities with a-type intensities for lines observed within 25 MHz. The best agreement was found with lc effective of 0.75(8) Debye corresponding to the c-type dipole moment multiplied by the torsional overlap integral. 7. Conclusions Propargyl alcoholÕs ground state has been confirmed to be composed of two gauche states separated by
155
652.3894 GHz inversion frequency in the OH species and 213.48 GHz in the OD species. The two torsional substates of the ground state are strongly coupled with a and b symmetry Coriolis interactions. Because either the linear or the quadratic Coriolis terms can be used to fit the spectrum equally well, it can be concluded that the torsional wave function does not sample the trans position and that the tunnelling of the proton is effectively an inversion. Complete determination of the potential barrier will require a spectroscopic determination of the energy of the first excited stateÕs gauche+ and gauche levels. This coupled with K-dependent measurement of the dipole components would facilitate determination of the sine and cosine-dependent parts of the dipole moment. The analysis presented here is more than adequate for astronomical searches and assignments. The large tunnelling splitting of the ground state is a simple example of a class of large molecule that is highly suitable for detection by far infrared astronomy. The required feature is a dipole moment involved in a large amplitude motion that will result in strong large amplitude motion transitions involving the lowest energy levels of the ground state at relatively high frequencies. In large molecules this provides an opportunity to observe much of the column density even in cold regions where detection of absorption features may be the best or only way to achieve detection with radio astronomy techniques. Acknowledgments This research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors thank Brooks Pate for providing his unpublished results and Herb Pickett and Ed Cohen for many insightful discussions on the torsion–rotation problem. Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa_hp.htm). References [1] Y. Sasada, M. Takano, T. Satoh, J. Mol. Spectrosc. 38 (1971) 33–42. [2] A.A. Abdurakhamanov, E.I. Veliyulin, R.A. Ragmova, L.M. Imanov, J. Struct. Chem. 22 (1981) 28. [3] E. Hirota, J. Phys. Chem. 83 (1979) 1457. [4] H. Badawi, P. Lorencak, K.W. Hillig II, M. Imachi, R.L. Kuczkowski, J. Mol. Struct. 162 (1987) 247–254. [5] S. Melandri, P.G. Favero, W. Caminati, Chem. Phys. Lett. 223 (1994) 541–545. [6] R.M. Lees, J.G. Baker, J. Chem. Phys. 48 (1968) 5299–5318. [7] J.C. Pearson, K.V.L.N. Sastry, M. Winnewisser, E. Herbst, F.C. De Lucia, J. Phys. Chem. Ref. Data 24 (1995) 1–32. [8] K. Bolton, N.L. Owen, J. Sheridan, Nature 217 (1968) 164.
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[9] Ch. O. Kadzhar, G.A. Abdullaev, L.M. Imanov, Izv. Acad. Sci. Azerb. SSR. Ser. Fiz.-Tekn. Mat. Nauk No. 3, 26 (1969). [10] Ch. O. Kadzhar, G.A. Abdullaev, L.M. Imanov, Izv. Acad. Nauk. SSR. Fiz.-Tekh. Mat. Nauk No. 1, 38 (1973). [11] E. Hirota, J. Mol. Spectrosc. 26 (1968) 335–350. [12] B.H. Pate, private communication (1995). [13] J.F. Alder, J.G. Baker, in: N.W. Barnett (Ed.), Quantitative Millimetre Wavelength Spectrometry, Royal Society of Chemistry, Cambridge, UK, 2002. [14] R.R. Friedl, M. Birk, J.J. Oh, E.A. Cohen, J. Mol. Spectrosc. 170 (1995) 383–396. [15] W.F. White, NASA Technical Note D-7904 121 (1975). [16] C.R. Quade, C.C. Lin, J. Chem. Phys. 38 (1963) 540–550. [17] C.R. Quade, J. Chem. Phys. 44 (1966) 2512–2523. [18] C.R. Quade, J. Chem. Phys. 47 (1967) 1073–1090. [19] J.V. Knopp, C.R. Quade, J. Chem. Phys. 48 (1968) 3317–3324. [20] E. Hirota, T. Kirooka, Y. Morino, J. Mol. Spectrosc. 26 (1968) 351– 367. [21] P. Meakin, D.O. Harris, E. Hirota, J. Chem. Phys. 51 (1969) 3775–3788.
[22] R.E. Schmidt, C.R. Quade, J. Chem. Phys. 62 (1975) 3864–3874. [23] H.M. Pickett, D.G. Scroggin, J. Chem. Phys. 61 (1974) 3954–3958. [24] J.C. Pearson, K.V.L.N. Sastry, E. Herbst, F.C. De Lucia, J. Mol. Spectrosc. 175 (1996) 246–261. [25] J.C. Pearson, K.V.L.N. Sastry, E. Herbst, F.C. De Lucia, Astrophys. J. 480 (1997) 420–431. [26] H.M. Pickett, J. Chem. Phys. 56 (1972) 1715–1723. [27] W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. [28] R.A. Nyquist, Spectrochim. Acta 27A (1971) 2513–2523. [29] S.M. Craven, Application of Far-Infrared Spectroscopy to the Study of the Structure and Dynamics of Organic Molecules—Alcohols Air Force Materials Laboratory Technical Report AFML-TR-71-192 (1971). [30] E.L. Stewart, U. Mazurek, J.P. Bowen, J. Phys. Org. Chem. 9 (1996) 66–78. [31] G. Moruzzi, B.P. Winnewisser, M. Winnewisser, I. Mukhopadhyay, F. Strumia, in: Microwave, Infrared and Laser Transitions of Methanol, CRC Press, Boca Raton, FL, 1995.
The ground state torsion–rotation spectrum of propargyl alcohol (HCCCH2OH) J.C. Pearson *, B.J. Drouin Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA Received 29 July 2005; in revised form 30 August 2005
Abstract The rotation–torsion spectrum of the asymmetric frame-asymmetric top internal rotor propargyl alcohol (HCCCH2OH) has been extended into the millimeter and submillimeter wave spectral regions. Over 2000 ground torsional state transitions have been measured and analyzed up to rotational quantum numbers J = 80 and Ka = 33 through a frequency of 633 GHz. The newly measured transitions were added to approximately 200 previously reported and now unambiguously assigned microwave transitions to comprise a data set of 2390 transitions which has been fit to 59 kHz using a reduced axis method (RAM) Hamiltonian. The ground state has been confirmed to consist of a symmetric and an antisymmetric gauche conformer with no spectroscopic evidence of stable trans conformer. A complete set of rotation and distortion constants through 6th order and a number of the 8th and one 10th order constants for the normal species are presented along with those determined from a re-analysis of the existing OD species data. The a and b symmetry Coriolis interaction constants and the gauche+ gauche tunnelling frequency of 652389.4 MHz has been determined for the OH species while the b symmetry Coriolis interaction and the 213 480 MHz tunnelling frequency were determined for the OD species. 2005 Elsevier Inc. All rights reserved.
1. Introduction Propargyl alcohol HCCCH2OH is the simplest stable unsaturated alcohol. The simple stable alcohols such as methyl, ethyl, n-propyl, isopropyl, and allyl are all known to exhibit large amplitude motions, which complicate or even dominate the rotational spectra. All the other small alcohols containing two or three carbons are known to exist in several different stable conformers due to the asymmetric internal rotation of the hydroxyl group [1–5]. Methyl, ethyl, isopropyl, syn-allyl, and most likely n-propyl alcohol all exhibit strong interactions between the internal motion and the overall rotation [3,5–7]. As in the other simple alcohols, the hydroxyl proton in propargyl alcohol is subject to a hindered large amplitude internal motion. The spectrum of propargyl alcohol is strongly influenced by the OH group tunnelling through the plane of the mol*
Corresponding author. Fax: +1 818 393 2430. E-mail address: [email protected] (J.C. Pearson).
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.08.013
ecule containing the heavy atoms. Fig. 1 shows the possible hydrogen configurations in propargyl alcohol. The barrier between the gauche confirmations of the OH rotation is quite low allowing this motion to be very rapid. In this paper, the ground state torsion–rotation spectrum of propargyl alcohol is presented. Several groups investigated the rotational spectrum of propargyl alcohol in the microwave region in the late 1960s. Bolton et al. [8] performed the first study of the main isotope and a number of other isotopes of propargyl alcohol in 1968. Kadzhar et al. [9,10] independently undertook similar studies. The first real clue to the complexity of the ground state spectrum was the result of the work of Hirota [11]. Hirota observed a number of higher JP/R (DJ = ± 1) branches and several Q (DJ = 0) branches at high Ka values for both the normal and the OD species in the spectral region below 50 GHz. The J and Ka assignments of these branches were confirmed with Stark effect patterns; however, it was not known if the transitions originated from the b- or c-component of the dipole. Unfortunately, the
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torsion–rotation constants for the OD species are presented from the re-analysis the work of Hirota [11]. The data should prove useful to radio astronomers searching for this species and in the analysis of internal energy redistribution in this species. Propargyl alcohol is now one of a very few asymmetric top-asymmetric frame internal rotors, which has been successfully analyzed to high J values. 2. Experimental
Fig. 1. Configuration diagram of propargyl alcohol gauche+ is the symmetric combination of gauche hydrogen relative to the plane of heavy atoms, gauche is the antisymmetric combination. No evidence supporting a stable trans configuration was found.
branches Hirota observed exhibit significant torsion–rotation perturbations and were not completely analyzed. The partial analysis and the high Ka values observed led Hirota to propose that the ground state was made up of a symmetric and antisymmetric gauche configurations separated by approximately 644 GHz. More recently, Pate [12] successfully measured a number of millimeter transitions including some b-type transitions (DKa = 1, DKc = 1) and determined gauche+ a and b dipole moments. In PateÕs study a simple asymmetric rotor analysis failed to account for the transitions above Ka = 7 suggesting strong torsion–rotation interactions. Propargyl alcohol is an excellent candidate for interstellar detection and potentially a good probe of the relative importance of gas phase ion driven chemical processes or dust grain surface driven chemical processes. As an unsaturated species, it should be formed on both dust and in the gas phase and therefore observable in both warm and cold interstellar regions. The chemical structure of propargyl alcohol is similar to a good number of well-known interstellar species. It could be derived from methyl alcohol by substitution of one methyl hydrogen with an acetylenic group. Additionally, molecules which could be suitably protonated in the gas phase or on dust grains like C3O are known to exist. The prospects for interstellar detection are greatly enhanced due to the tunnelling between the gauche+ and gauche substates. This tunnelling makes propargyl alcohol one of a very few polyatomic molecules, that exhibits a strong submillimeter spectrum even at low temperatures. The tunnelling also makes propargyl alcohol an attractive candidate for interstellar observation via absorption. The means of production, the submillimeter energy difference between ground state conformers and the substantial dipole moment could make propargyl alcohol detectable in a wide variety of different interstellar sources. In this paper, the ground state is confirmed to be composed of two gauche conformers and the analysis of the spectrum suggest no role for a trans configuration. The rotational dipole moments and the approximate effective torsion–rotational transition moments are discussed. The
The sample of HCCCH2OH was obtained from Matheson Coleman and Bell chemicals and required no further purification. The sample was directed into a double pass 1 meter long, absorption cell at a total pressure of 30 mTorr. A spectrometer with phase locked 80–120 GHz klystrons, point contact harmonic generators and tone burst modulation [13] was used to generate and modulate the millimeter and submillimeter wave radiation. The absorption spectrum was recorded with a Schottky diode or a 4.2 K InSb hot electron bolometer detector and digitized on a computer. Transitions have been measured through 633 GHz in frequency. The measurement accuracy is estimated to be between 50 and 150 kHz depending on the signal-to-noise and the line width. Fit residuals suggest the accuracy of most transitions is close to 50 kHz. The strongest low frequency lines are the most accurate as expected. The details of this spectrometer system can be found elsewhere [14]. Initial predictions were based on a fit of all the data of Hirota [11] and some additional transitions supplied by Pate [12] These predictions were sufficiently accurate to predict J values to 50 and Ka values between 6 and 20 for rapid assignment. The higher Ka a-type R branches (DJ = 1, DKa = 0 DKc = 1) diverged in a regular pattern and were assigned quickly once additional data were included. The low Ka a-type R branch lines were much more difficult to assign since the initial data set contained very limited information on the strong a-type DKa = 2 Coriolis interaction. Fortunately these lines are the strongest allowed transitions in the spectrum and were readily assigned once surveys of the spectral regions near 300 and 400 GHz were made. Additional measurements of high J low Ka transitions were then made to improve the analysis of the torsion rotation interactions. Lastly, the unassigned spectrum recorded by White [15] was assigned and incorporated into the analysis. A total of 2390 lines were used in the analysis including more than 2000 recorded between 84 and 633 GHz. The data set includes a-type and b-type transitions through J = 70 and Ka = 30 within each substate and J = 80 and Ka = 24 between the substates. All of these transitions including a very large number of highly perturbed ones have been fit to experimental accuracy. In these measurements, the strong lower frequency and quantum number a-type and c-type transitions are the most precise while the weak b-type, very high J > 60 c-type are the least precise. No additional OD data were recorded.
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
3. Theory Propargyl alcohol is a near prolate asymmetric top with a single large amplitude internal motion of the hydroxyl proton. The heavy atoms in propargyl alcohol fall in a plane and the three hydrogens bonded to the carbons are either in the plane or symmetric about the plane. As a result, the molecule has Cs symmetry as does the motion of the hydroxyl proton. From the Cs symmetry, the hydroxyl proton could be in the plane of the heavy atoms (trans or cis) or a symmetric or antisymmetric combination of out of the plane (gauche+ and gauche). Any trans, cis or gauche+ configuration is symmetric with respect to the plane while only the gauche configuration is antisymmetric. The Cs symmetry also dictates the selection rules allowing a and b-type transitions between configurations of the same symmetry and c-type transitions between configurations of different symmetries. As a result, only a- and b-type transitions can be observed within any possible configuration. A general Hamiltonian for a fixed-axis fixed-frame asymmetric top-asymmetric frame internal rotation problem has been proposed by Quade and co-workers [16–19]. It has been applied with varying degrees of success to a number of two ‘‘equivalent’’ substate asymmetric internal rotation problems [5,20–25]. In the case of propargyl alcohol, the formulation of the Hamiltonian used is often referred to as the reduced axis method [26]. The reduced axis Hamiltonian can be derived from the final transformed principal axis formulation of Quade [16], which is comprised of three parts H ¼ H R þ H TR þ H T ;
ð1Þ
where HR is the quasi-rigid-body rotational Hamiltonian, HT is the torsional Hamiltonian and HTR is the torsion–rotation interaction Hamiltonian. Explicitly the components are H R ¼ AðrÞ P 2a þ BðrÞ P 2b þ C ðrÞ P 2c ðrÞ
þ Dbc ðP b P c þ P c P b Þ þ DðrÞ ac ðP a P c þ P c P a Þ ðrÞ
þ Dab ðP a P b þ P b P a Þ; ðr1 ;r2 Þ
H TR ¼ Dbc
ðP b P c þ P c P b Þ 1
2
ðr ;r Þ þ Dac ðP a P c þ P c P a Þ ðr1 ;r2 Þ
þ Dab þM ðrÞ
H T ¼ DE .
ðP a P b þ P b P a Þ
ðr1 ;r2 Þ
1 ;r2 Þ
P a þ N ðr
1 ;r2 Þ
P b þ Oðr
P c; ð2Þ
Here r is the torsional substate identifier and terms with (r1, r2) are off diagonal in torsional substate. The Cs symmetry and the special case of two ‘‘equivalent’’ substates allow a number of simplifications to be made. The on diagonal (in torsional substate) Dbc and Dac are not allowed from the symmetry. The ‘‘equivalence’’ of the gauche states makes the on diagonal axis rotation Dab term zero since the two states share a common axis system [21].
151
The Cs symmetry and the even and odd symmetry of the two gauche substates observed prevents the off diagonal antisymmetric Dab and O terms in HTR from connecting them. Now a rotation around the c axis can be made to minimize either the linear or quadratic off diagonal terms [26]. The resulting reduced axis method Hamiltonian has one of the following forms: H R ¼ AðrÞ P 2a þ BðrÞ P 2b þ C ðrÞ P 2c H T ¼ DEðrÞ ðr1 ;r2 Þ
H TR ¼ Dbc
ðP b P c þ P c P b Þ ðr1 ;r2 Þ
þ Dac
ð3Þ
ðP a P c þ P c P a Þ þ
or 1 ;r2 Þ
H TR ¼ M ðr
1 ;r2 Þ
P a þ N ðr
Pb þ
Here as in Eq. (2), the torsional part of the Hamiltonian HT is the solution for the J = 0 problem where the resulting energy differences are treated as a parameter determined directly from the tunnelling splitting of the c-type spectra. The Dbc and Dac or M and N terms in Eq. (3) connect energy levels in the two different substates, which differ in Ka by 2 and 1 or 1 and 0, respectively. The validity of the transformation to the reduced axis is highly dependent on the actual tunnelling path taken by the hydroxyl proton. If the motion is a pure inversion and therefore a non-periodic motion, then on average there is no linear angular momentum and the unused HTR choice is exactly zero. However, if there is any tunnelling through both the trans and cis configurations, the motion is periodic and neither HTR choice can be made equal to zero. Since the trans barrier cannot be infinite, neither HTR term is exactly zero. However, the linear angular momentum contributions are typically completely correlated with other parameters in the absence of avoided crossings connected directly by these terms. As a result, transitions connecting energy levels well below the barrier and any trans levels can be effectively analyzed with either set of HTR terms but not both. At some point in the torsional manifold, this approximation will break down as it does in ethyl alcohol [24], however if the barrier is truly 2fold, it may be near the free rotor limit. Molecular distortion results in distortion on the torsion rotation terms in Eqs. (2) and (3). These can be expanded in terms of P2 or P 2a (i.e., DabJ or DabK). Ideally, the asymmetry constants coupled with the fundamental torsion rotation terms will facilitate fitting of interactions involving Ka states separated by more than 2. From a practical fitting perspective these higher order interactions are often critically dependent on the details of the distortion and can often be analyzed with fewer terms if an explicit DKa operator is included (i.e. for symmetric DKa = 3). 4. Analysis The 2390 measured transitions were fit to a Hamiltonian in the form of Eq. (3) which included a complete Watson S
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set of distortion constants through 6th order and all of the 8th order except l3 and l4 [27]. Distortion of the internal rotation and higher order torsion rotation effects were satisfactorily accounted for by multiplying either the Dbc and Dac or the M and N constant operators by expansions in P2 and P 2a denoted as DbcJ or DbcK. The M an N constants with their distortion successfully account for all the transitions, but the Dbc and Dac set had problems with a single avoided crossing between gauche+ Ka = 3 and gauche Ka = 6 at J = 46. Transitions connecting these levels could only be fit to about 1 MHz. As a result, an explicit b symmetry DKa = 3, ðP 3þ þ P 3 Þ interaction term was included in this analysis. In this case, P+ is defined as the normalized positive combination of Pb and iPc. The ðP 3þ þ P 3 Þ constant is, as one would expect, very highly correlated with the expansion of Dac in P 2n a (DacK, DabKK, etc.). The correlation is only broken by the previously mentioned level crossing. It was found that the DacK and ðP 3þ þ P 3 Þ were both required to fit all the spectra. However, when DacKK was included to extend the analysis the value of ðP 3þ þ P 3 Þ became ill determined and ðP 3þ þ P 3 Þ was still necessary to fit the level crossing. Therefore, the ðP 3þ þ P 3 ÞP 2a term was used instead of DacKK. This allows ðP 3þ þ P 3 Þ to fit the level crossing while ðP 3þ þ P 3 ÞP 2a is determined instead of DacKK. Observation of additional DKa = 3 level crossings would probably eliminate this fitting difficulty. The complete list of measured transition frequencies, quantum number assignments and the observed minus calculated for both analyses is given on Table 1. The four highly perturbed asymmetry doublet transitions where the quantum number assignment has changed between the analyses are denoted. Table 1 includes the result from
two fits one using the Dac and Dbc set and another using the M and N constants. It was attempted to fit both together but the correlations were always at least 0.9999 between Dbc and M as well as Dac and N. As a result, convergence was impossible to achieve. A complete set of predictions through J = 80 is available from the JPL spectral line catalog via anonymous FTP at http://spec.jpl.nasa.gov. The derived spectroscopic parameters as defined in Eq. (3) and the preceding paragraph are given in Table 2 for both fits. A difficult aspect of the analysis of propargyl alcohol arises from the interaction of the asymmetry terms in the Hamiltonian and the Coriolis interactions. The Coriolis terms connect single symmetric top K levels in two different vibrational or torsional states while the asymmetry mixes these K levels within a state. The asymmetry operators spread the effects of the Coriolis interaction to all the asymmetry mixed K levels in the appropriate Wang symmetry block of the Hamiltonian. The interaction between asymmetry and Coriolis operators results in two major implications; first, all the high J low Ka transitions are perturbed to some degree and second, the higher order Coriolis interactions have a very similar effect on lower order interactions coupled by higher order asymmetry operators. The first of these effects was prominently observed in the line positions connecting high J low Ka levels of propargyl alcohol while the second complicated the fitting process. The lack of level crossing in the currently available OD data set indicates that this indeterminacy remains in the parameter set. The rotation and distortion constants for the two OH substates are remarkably similar even to 8th order with the small differences due to the torsion and varying contri-
Table 1 Measured frequencies in MHz, quantum number assignments and residuals from model fits for propargyl alcohol J 0K 0 ;K 0
v
J K a ;K c
v
Unc
Reference
Fit #1
Fit #2
278,20 278,19 10,1 10,1 247,18 247,17 337,26 337,27 1610,6 1610,7
0 0 1 0 1 1 0 0 0 0
267,20 267,19 00,0 00,0 258,18 258,17 326,26 326,27 159,6 159,7
1 1 1 0 0 0 1 1 1 1
8762.220 8762.220 8912.180 8932.480 10053.550 10053.550 11304.780 11325.240 12367.810 12367.810
0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100
[11] [11] [11] [11] [11] [11] [11] [11] [11] [11]
0.005 0.036 0.106 0.028 0.027 0.017 0.162 0.165 0.013 0.013
0.006 0.037 0.106 0.028 0.027 0.017 0.161 0.167 0.011 0.011
11,0 1713,4 1713,5
1 0 0
10,1 1712,6 1712,5
1 1 1
28419.153 28478.315 28478.315
0.025 0.020 0.020
[12] [15]/[11] [15]/[11]
0.000 0.008 0.008
0.001 0.000 0.000
381,37 431,42 391,38 540,54 541,54 421,41 401,39
1 1 1 1 1 1 1
382,37 432,42 392,38 541,54 540,54 422,41 402,39
0 0 0 0 0 0 0
637743.445 637857.856 637936.884 637951.028 637960.110 637983.112 638033.400
0.100 0.100 0.100 0.100 0.100 0.100 0.100
A A A A A A A
0.005 0.022 0.004 0.112 0.109 0.015 0.008
0.019 0.002 0.020 0.077 0.074 0.038 0.031
a
c
Measured
Data sources are: (A) this work, Hirota [11], Pate [12], White [15], for full listing see supplemental material.
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
153
Table 2 Propargyl alcohol Hamiltonian parameters in MHz Fit #1
Fit #2
Gauche+ A B C DJ · 103 DJK · 102 DK d1 · 104 d2 · 105 HJ · 109 HJJK · 107 HJKK · 106 HK · 105 h1 · 109 h2 · 1010 h3 · 1010 LJ · 1014 LJJK · 1012 LJK · 1011 LJKK · 1010 LK · 109 l1 · 1014 l2 · 1015 PJJJKK · 1014 DE Dbc DbcJ · 105 DbcK · 104 DbcJJ · 1010 Dac DacJ · 104 DacK · 103
ðP 3þ þ P 3 Þ · 105 ðP 3þ þ P 3 ÞK · 106
Gauche
32527.93731(166) 32647.95734(175) 4700.248927(178) 4684.174412(170) 4232.216921(181) 4227.908512(172) 2.903958(110) 2.811131(106) 6.196600(252) 6.21770(32) 1.007490(32) 1.017754(39) 7.06958(34) 6.634496(316) 4.88530(150) 4.11124(98) 9.9820(308) 9.5393(306) 2.1775(47) 1.9889(51) 3.4208(63) 3.1476(78) 9.2561(232) 9.292(32) 4.3263(121) 4.0502(119) 7.016(81) 6.113(58) 1.1543(34) 0.89721(279) 2.650(277) 2.569(282) 1.742(52) 1.175(58) 3.382(144) 1.964(179) 4.017(70) 2.856(103) 7.18(135) 7.07(156) 2.137(130) 2.077(136) 6.02(109) 7.00(80) 2.512(159) 1.308(239) 652389.4199(209) 2.34009(37) 5.9587(90) 5.802(84) 2.452(126) 36.0109(113) 1.60026(87) 6.261(78)
Gauche+
DE M MJ · 102 MK MJJ · 106 MJK · 105 N NJ · 102 NK NJJ · 107 NKK · 103 NJK · 105 NJJ · 107 NKKK · 107 NKKJ · 108 NKJJ · 1010 NJJJ · 1012
Gauche
32544.9731(176) 32631.0683(175) 4701.97559(179) 4682.47384(181) 4232.130452(196) 4227.821866(186) 2.933541(192) 2.780560(212) 6.23325(55) 6.20076(68) 0.997188(169) 1.028360(169) 7.25088(106) 6.45053(112) 5.22123(237) 3.79551(187) 10.744(35) 8.882(38) 1.9453(120) 2.2812(144) 2.607(39) 4.183(36) 9.3686(251) 9.201(33) 4.7915(179) 3.6382(185) 8.003(93) 5.011(63) 1.3355(54) 0.7348(41) 4.750(306) 2.23(32) 1.259(58) 1.951(66) 3.091(224) 0.0216(32) 3.582(135) 0.4669(195) 10.00(155) 0.01120(184) 2.938(168) 1.750(171) 3.97(121) 6.71(83) 3.038(200) 0.427(303) 652389.4609(224) 3326.45(171) 4.833(45) 1.2644(162) 1.1115(193) 3.04(45) 1057.87(56) 3.7006(125) 1.6956(73) 7.611(131) 1.7328(247) 5.109(130) 7.611(131) 1.318(121) 3.97(40) 2.21(70) 9.49(58)
3.47(123) 8.893(59)
The fits included 2390 lines and have RMS (Fit #1) 59.6 kHz and RMS (Fit #2) 58.3 kHz.
butions from excited states. As a result of the similarity, only higher order terms, which were determined to have similar values in both substates were included in the analysis. A complete set of 8th order constants can be determined and does reduce the RMS of the fit slightly, but the l3 and l4 terms have very different values in the two torsional substates and some of the higher order Coriolis terms become undetermined. Removal of the undetermined Coriolis terms increases the RMS significantly without a significant change in the l3 and l4 terms. As a result, values for l3 and l4 are not given since their values appear to be an artifact of the torsion. The same is true to a lesser extent of h3, l1, and l2; however, these terms do have similar magnitudes in the two substates and were kept in the analysis. A slightly better reduced RMS is obtainable by adding a few
additional terms to one or the other torsional state. The quoted RMS uses the same constant set in both substates and results in a reduced RMS of 0.65 in both fits. The re-analysis of the existing propargyl alcohol OD data [11] was somewhat less satisfying since there is insufficient information to determine the a-type Dbc(PbPc + PcPb) or Pa Coriolis term. This Coriolis interaction will have a major effect on the higher J lower Ka energy levels, but it will have a minor effect on all the other constants determined. Some evidence of the contribution of the term is seen in the distortion constants where there are significant differences between gauche+ and gauche. As a result of these problems, a reduced RMS of only 2.4 was achieved. The unambiguously assigned HCCCH2OD transitions and the observed minus calculated are given in the
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supplemental material. Table 3 contains the rotation, distortion and interaction constants determined OD species. A number of attempts were made to try to determine simultaneously both sets of torsion rotation operators. Both sets were not simultaneously determinable, even with the full data set, suggesting that the OH motion prior to any level crossing of the same K can be effectively modeled by pure inversion to spectroscopic accuracy. The lowest same K crossing is predicted to occur between the gauche+ J1,J1 and gauche J1,J levels near J = 85 which is well above the J range transitions observed. In general, the lack of direct information on the DKa = 0 interaction typically precludes determination of both Pa and PbPc + PcPb. There is direct information on the b symmetry DKa = 1 interaction, Pb and PaPc + PcPa are both DKa = 1 interactions and can generally be interchanged. The failure to determine both sets of torsion–rotation constants simultaneously is by no means a proof of a pure inversion spectra, but it does suggest that the gauche torsional problem is localized away from the trans position. The similarity of all the distortion constants in either set is highly suggestive that the differences are what one would expect from coupling to excited vibrational modes given the 652 GHz energy difference between states and not the hidden effects of an unobserved periodic motion. This is clearly not the case in ethyl alcohol where the P4 distortion constants are drastically different and even opposite in sign in one case [24]. Attempts were also made to search for trans–gauche interactions similar to the ones which eventually dominate the higher J ethanol spectra [24,25]. No transitions involving levels through J = 80 and Ka = 33 were observed which could not be fit to spectroscopic accuracy. Once again this does not completely rule out a trans substate, but it suggests that if a trans state exists, it is at much higher energy and interacts very weakly if at all. The existence of a trans well, which is below the top of the torsional barrier and at much higher energy is inconsistent with the relatively low (400 cm1) barriers observed in other alcohols. A minimum in the trans position would also be expected to increase the importance of tunnelling through that position
Table 3 Deuterated propargyl alcohol Hamiltonian parameters in MHz
A B C DJ · 103 DJK · 102 DK dJ · 104 dK · 10 DE Dac DacK · 10 DacJ · 103
Gauche+
Gauche
29689.4(83) 4613.263(63) 4130.124(61) 4.189(234) 6.014(220) 3.76(99) 2.51(207) 2.63(34)
29730.7(60) 4600.874(46) 4127.556(49) 2.859(128) 4.500(228) 5.69(153) 7.351(161) 0.581(236) 213480.4(309) 78.80(87) 2.16(49) 1.433(234)
The fit includes 97 lines and has rrms 239.2 kHz.
and therefore the effects of undeterminable additional set of Coriolis terms, which is contrary to observations. 5. Barrier to internal rotation The barrier to internal rotation in propargyl alcohol can be calculated from the J = 0 torsional Hamiltonian, H ¼ Fp2 þ V ðaÞ;
ð4Þ
where F is inverse moment of inertia of the top and V(a) is the torsional potential which is XV n ð1 cosðnaÞÞ. ð5Þ V ðaÞ ¼ V 0 þ 2 The solution of Eq. (4) results in a series of torsional energy levels. In the general asymmetric top-asymmetric frame torsional problem, F is a function of torsional angle, but the equivalence of the gauche substates in propargyl alcohol requires F to be the same for each substate. As a result, an effective constant F gives a satisfactory solution to the torsional problem. The structure of the barrier determines the form of the solution. If the barrier is predominately 3fold, there will be a bound trans position and each torsional substate will be comprised of three torsional substates. However, if the barrier is predominately 2-fold then there will be no bound trans position and each torsional substate will consist of two substates. The lowest three Vn terms must be evaluated in order to obtain barrier to first order. A complete solution requires one tunneling energy per potential constant determined, e.g., ground state tunneling frequency, excited torsional state energy and excited state tunneling frequency, otherwise a unique solution cannot be determined. As a result, the available microwave tunnelling frequencies cannot determine the peak of the barrier at the trans position and information on the energy of the excited torsional states is needed. Nyquist reported a single hydroxyl torsion frequency for propargyl alcohol in liquid n-hexane at 192 cm1 for OH and 150 cm1 for OD [28]. To reproduce the microwave data, the first excited gauche+ and gauche states will be split significantly more than the ground state resulting in at least two and most likely four torsional bands from the ground state to the first excited state. However, the effect of the liquid n-hexane on the torsional frequencies is not well known. It is known that a large number of saturated alcohols exhibit a characteristic 210 ± 10 cm1 band in cyclohexane [29], which is relatively close to the gas phase excited OH torsional state energy. A numerical experiment using NyquistÕs values resulted in an unrealistically high V1 barrier term. The required V1 term was significantly larger than the available ab initio barrier which is expected to over estimate the barrier height [30]. Since the barriers for methanol and ethanol have been determined [25,31] and are close to 400 cm1 in height, the very large V1 was ruled out. As a result, little more can be said about the barrier than reported by Hirota [11].
J.C. Pearson, B.J. Drouin / Journal of Molecular Spectroscopy 234 (2005) 149–156
6. Dipole moments The dipole moments of an internal rotor with Cs symmetry can be expressed as and expansion in sine or cosine components. The sine terms connect torsional states of different symmetry and the cosine terms connect torsional states of the same symmetry. Linear terms represent the pure rotation within a given state. The first order contributions of the dipole are ! l ¼ l0 þ l1 cosðaÞ þ l0 þ l1 cosðaÞ þ l1 sinðaÞ. ð6Þ a
a
b
b
c
The effective transition moment for any transition is given by hJ 0 ; K 0 ; M 0 ; w0T j! l jJ ; K; M; wT i;
ð7Þ
where |J,K,Mæ is the rotational wavefunction and |wTæ is that the torsional wavefunction. Here the zero terms of la and lb result from the usual rotational contributions within each state. Since the spectrum is composed of two equivalent gauche states that act as a pure inversion, Eq. (7) can be simplified as follows: h0þ j cosðaÞj0þ i h0 j cosðaÞj0 i Const; h0þ j sinðaÞj0 i ¼ h0 j sinðaÞj0þ i Const;
ð8Þ
where WT is either ground state gauche+ (0+) or gauche (0). The result is a fixed symmetric (a-type and b-type) dipole in each gauche state and a fixed effective inversion dipole between the ground gauche+ and gauche states. No K dependence of line strength was observed in propargyl alcohol and the expected intensity in the c-type transitions appears to be constant to experimental accuracy, which is about 10% in intensity, suggesting the approximation made in Eq. (8) is consistent with experimental observations. The effective a-type and b-type dipole moments in the gauche+ substate were measured by Pate [12] and determined to be 1.037(2) Debye for la and 0.147(4) Debye for lb. The a-dipole is in agreement with the 0.99 Debye determined by Kadzhar et al. [9]. The dipole was determined from low J and low K transitions known to be well isolated from the other substate. It can be expected that the gauche state will have nearly identical a-type and b-type dipole moment with any difference due to rotation–vibration intensity borrowing being slightly different for the two sub-states due to the 21.7 cm1 energy difference. Since the only published c-dipole measurement is clearly too small for the observed intensities (0.177 Debye from [9]), we compared observed c-type intensities with a-type intensities for lines observed within 25 MHz. The best agreement was found with lc effective of 0.75(8) Debye corresponding to the c-type dipole moment multiplied by the torsional overlap integral. 7. Conclusions Propargyl alcoholÕs ground state has been confirmed to be composed of two gauche states separated by
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652.3894 GHz inversion frequency in the OH species and 213.48 GHz in the OD species. The two torsional substates of the ground state are strongly coupled with a and b symmetry Coriolis interactions. Because either the linear or the quadratic Coriolis terms can be used to fit the spectrum equally well, it can be concluded that the torsional wave function does not sample the trans position and that the tunnelling of the proton is effectively an inversion. Complete determination of the potential barrier will require a spectroscopic determination of the energy of the first excited stateÕs gauche+ and gauche levels. This coupled with K-dependent measurement of the dipole components would facilitate determination of the sine and cosine-dependent parts of the dipole moment. The analysis presented here is more than adequate for astronomical searches and assignments. The large tunnelling splitting of the ground state is a simple example of a class of large molecule that is highly suitable for detection by far infrared astronomy. The required feature is a dipole moment involved in a large amplitude motion that will result in strong large amplitude motion transitions involving the lowest energy levels of the ground state at relatively high frequencies. In large molecules this provides an opportunity to observe much of the column density even in cold regions where detection of absorption features may be the best or only way to achieve detection with radio astronomy techniques. Acknowledgments This research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The authors thank Brooks Pate for providing his unpublished results and Herb Pickett and Ed Cohen for many insightful discussions on the torsion–rotation problem. Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa_hp.htm). References [1] Y. Sasada, M. Takano, T. Satoh, J. Mol. Spectrosc. 38 (1971) 33–42. [2] A.A. Abdurakhamanov, E.I. Veliyulin, R.A. Ragmova, L.M. Imanov, J. Struct. Chem. 22 (1981) 28. [3] E. Hirota, J. Phys. Chem. 83 (1979) 1457. [4] H. Badawi, P. Lorencak, K.W. Hillig II, M. Imachi, R.L. Kuczkowski, J. Mol. Struct. 162 (1987) 247–254. [5] S. Melandri, P.G. Favero, W. Caminati, Chem. Phys. Lett. 223 (1994) 541–545. [6] R.M. Lees, J.G. Baker, J. Chem. Phys. 48 (1968) 5299–5318. [7] J.C. Pearson, K.V.L.N. Sastry, M. Winnewisser, E. Herbst, F.C. De Lucia, J. Phys. Chem. Ref. Data 24 (1995) 1–32. [8] K. Bolton, N.L. Owen, J. Sheridan, Nature 217 (1968) 164.
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[9] Ch. O. Kadzhar, G.A. Abdullaev, L.M. Imanov, Izv. Acad. Sci. Azerb. SSR. Ser. Fiz.-Tekn. Mat. Nauk No. 3, 26 (1969). [10] Ch. O. Kadzhar, G.A. Abdullaev, L.M. Imanov, Izv. Acad. Nauk. SSR. Fiz.-Tekh. Mat. Nauk No. 1, 38 (1973). [11] E. Hirota, J. Mol. Spectrosc. 26 (1968) 335–350. [12] B.H. Pate, private communication (1995). [13] J.F. Alder, J.G. Baker, in: N.W. Barnett (Ed.), Quantitative Millimetre Wavelength Spectrometry, Royal Society of Chemistry, Cambridge, UK, 2002. [14] R.R. Friedl, M. Birk, J.J. Oh, E.A. Cohen, J. Mol. Spectrosc. 170 (1995) 383–396. [15] W.F. White, NASA Technical Note D-7904 121 (1975). [16] C.R. Quade, C.C. Lin, J. Chem. Phys. 38 (1963) 540–550. [17] C.R. Quade, J. Chem. Phys. 44 (1966) 2512–2523. [18] C.R. Quade, J. Chem. Phys. 47 (1967) 1073–1090. [19] J.V. Knopp, C.R. Quade, J. Chem. Phys. 48 (1968) 3317–3324. [20] E. Hirota, T. Kirooka, Y. Morino, J. Mol. Spectrosc. 26 (1968) 351– 367. [21] P. Meakin, D.O. Harris, E. Hirota, J. Chem. Phys. 51 (1969) 3775–3788.
[22] R.E. Schmidt, C.R. Quade, J. Chem. Phys. 62 (1975) 3864–3874. [23] H.M. Pickett, D.G. Scroggin, J. Chem. Phys. 61 (1974) 3954–3958. [24] J.C. Pearson, K.V.L.N. Sastry, E. Herbst, F.C. De Lucia, J. Mol. Spectrosc. 175 (1996) 246–261. [25] J.C. Pearson, K.V.L.N. Sastry, E. Herbst, F.C. De Lucia, Astrophys. J. 480 (1997) 420–431. [26] H.M. Pickett, J. Chem. Phys. 56 (1972) 1715–1723. [27] W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984. [28] R.A. Nyquist, Spectrochim. Acta 27A (1971) 2513–2523. [29] S.M. Craven, Application of Far-Infrared Spectroscopy to the Study of the Structure and Dynamics of Organic Molecules—Alcohols Air Force Materials Laboratory Technical Report AFML-TR-71-192 (1971). [30] E.L. Stewart, U. Mazurek, J.P. Bowen, J. Phys. Org. Chem. 9 (1996) 66–78. [31] G. Moruzzi, B.P. Winnewisser, M. Winnewisser, I. Mukhopadhyay, F. Strumia, in: Microwave, Infrared and Laser Transitions of Methanol, CRC Press, Boca Raton, FL, 1995.