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The millimetre-wave rotational spectrum of phenylacetylene
Journal of Molecular Spectroscopy 262 (2010) 82–88
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The millimetre-wave rotational spectrum of phenylacetylene Zbigniew Kisiel *, Adam Kras´nicki Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
a r t i c l e
i n f o
Article history: Received 26 April 2010 In revised form 24 May 2010 Available online 2 June 2010 Keywords: Rotational spectroscopy Millimetre-wave spectrum Excited vibrational states Coriolis interaction
a b s t r a c t The room-temperature rotational spectrum of phenylacetylene ðC6 H5 CBCHÞ, was studied at frequencies up to 340 GHz. Extensive new measurements, covering rotational transitions with quantum number values up to J ¼ 140 and K a ¼ 59, allowed determination of precise spectroscopic constants for the ground state and for the lowest two excited vibrational states, v 24 ¼ 1 and v 36 ¼ 1. The two excited states belong to the lowest B1 and B2 symmetry normal modes and their rotational transitions are very strongly perturbed by a-axis Coriolis resonance. A successful fit of the resonance is reported, resulting in fa24;36 ¼ 0:8403ð3Þ and DE ¼ E36 E24 ¼ 15:38994ð2Þ cm1 , in good agreement with results of ab initio computations. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Phenylacetylene is a fundamental hydrocarbon derivative of benzene and is implicated in chemical reaction networks associated with formation of polyaromatic hydrocarbons in combustion and in the interstellar medium (ISM) [1]. Many different studies on the formation of phenylacetylene at astrophysically relevant conditions have been carried out. It can be formed from benzene by impact shock [2] or collisions with the ethynyl radical [1]. It can also be formed by photochemical reactions from acetylene [3], vinylacetylene [4], or 1,3-butadiene [5]. Phenylacetylene has been formed in a mixture of gases simulating the atmosphere of Saturn’s moon Titan [6], and studies in Refs. [1,4,5] were, in fact, also motivated by the desire to explore the rich hydrocarbon chemistry expected to be present on Titan. Phenylacetylene is a polar molecule and is thus attractive as a potential radioastronomy marker of unsaturated, or even polyaromatic hydrocarbon chemistry, which is postulated to be relevant to the ISM on the basis of infrared spectroscopic signatures [7]. The available laboratory data concerning the rotational spectrum of phenylacetylene is insufficient for radioastronomical detection applications, especially at the promising mm-wave frequencies. The present work aims to remedy this situation, similar to our previous effort for a related benzene derivative, toluene [8]. The rotational spectrum of phenylacetylene was first studied by Zeil et al. [9], and their survey investigation was followed by a much more detailed study of Cox et al. [10]. Rotational constants were obtained for seven different isotopic species leading to a determination of the molecular structure. The electric dipole mo-
* Corresponding author. Fax: +48 22 8430926. E-mail address: [email protected] (Z. Kisiel). 0022-2852/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2010.05.007
ment, l ¼ la ¼ 0:656ð5Þ D, was also determined, and is appreciably higher than 0.375(10) D for toluene [11]. More recently, a much more extensive determination of the structure of phenylacetylene by rotational spectroscopy was carried out by Dreizler et al. [12] on the basis of rotational constants obtained for 39 different isotopic species. In that case the measurements were made by Fourier transform microwave spectroscopy on a supersonic expansion. Nevertheless, the frequency coverage of all of these investigations did not extend beyond 40 GHz and no excited vibrational state transitions were assigned. The present investigation improves on all of these counts as we report an analysis of the major features of the room-temperature rotational spectrum of phenylacetylene up to 340 GHz. 2. Experimental details All measurements were carried out with the two rotational spectrometers in Warsaw. The room-temperature spectrum was measured at frequencies 90–340 GHz with the broadband, source modulation spectrometer described in Ref. [13]. The spectrometer has presently been upgraded to the use of contemporary generation of zero-biased GaAs Schottky diode detectors and harmonic mixers from Virginia Diodes Inc. Two Istok BWO sources, OB-24 and OB-30, were used for measurements at 175–340 GHz. The region 90– 140 GHz was covered with a harmonic multiplication source, also from Virginia Diodes, which generated the 12th harmonic of the driving frequency from a microwave synthesizer. Measurements were performed on a commercial sample used without further purification and at a sample pressure of up to 10 mTorr. Additional measurements of some low-J transitions not covered in Ref. [12] were made in supersonic expansion, at 7–19 GHz, with the cavity Fourier transform microwave spectrometer (FTMW) in Warsaw
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[14]. This spectrometer is a coaxial waveguide version of the original design of Balle and Flygare [15], which has recently been upgraded to a simple computer aided single-step frequency downconversion [16]. The many individual millimetre wave spectra recorded during this work were combined into a single spectrum and subjected to analysis with the use of the AABS software package for Assignment and Analysis of Broadband Spectra [17]. The package provides a synchronised display of the experimental spectrum and of predictions for all vibrational and isotopic species relevant in a given spectrum. Flexible comparison between predictions and experiment allows the measured spectrum to be very rapidly reduced into datasets for several different fitting programs. A Loomis–Wood type display mode facilitates rapid graphical assignment. The package is freely available from the PROSPE website [18], and has been used in studies of many complex spectra, most recently those of ClONO2 [19], bromoform [20], and acrylonitrile [21]. The ground state data from previous work and from present measurements were fitted jointly by using the ASFIT/ASROT package [18], while the SPFIT/SPCAT package [22,23] was used for the analysis of vibrationally excited states. Frequency measurement uncertainties of 2 and 50 kHz were assumed for supersonic expansion, and room-temperature measurements, respectively.
3. Rotational spectrum The mm-wave region rotational spectrum for the ground state of phenylacetylene was predicted with accuracy sufficient for assignment by augmenting the rotational constants from previous work with quartic centrifugal distortion constants calculated from an ab initio harmonic force field. The high-J, a R-type transitions for a planar molecule are known to coalesce into strong bands, called type-II bands, with an interband frequency spacing of close to 2C. The nomenclature has been proposed by Borchert [24] who identified the initial stage of such band formation. The properties of this type of band were investigated in more detail in the spectrum of chlorobenzene [25], and a comprehensive classification was pro-
83
posed in Refs. [26,27]. An example type-II band in the spectrum of phenylacetylene is shown in Fig. 1. The strongest and leading line in a band of this type consists of doubly degenerate transitions with K a ¼ 0; 1. Successive lines along the band are for values of J decreasing, and of K a increasing in steps of 1. For positive DJK the lines normally evolve from the bandhead to higher frequencies, although the line pattern is quite sensitive to the value of the inertial defect. The changes on vibrational excitation are, nevertheless, fairly moderate and normally do not prevent assignment. A typical situation is depicted in Fig. 1 of Ref. [28] for fluorobenzene. In phenylacetylene, on the other hand, while the presence of strong satellite lines in the spectrum was obvious, their assignment was not possible until a prediction was made on the basis of the expected strong Coriolis perturbation between the two lowest excited vibrational states.
4. Ground state Measurements of ground state lines were extended up to 340 GHz with some care being taken to obtain a balanced coverage of the values of J and K a quantum numbers, as shown in Fig. 2. We have used Watson’s reduced asymmetric rotor Hamiltonian [29], in both A- and S-reductions. The results of fit are summarised in Tables 1 and 2, while complete listings and data files are given in Tables S1 and S2 of the electronic supplementary information. The present dataset allows determination of the complete sextic level Hamiltonian, with the exception of HK . The remaining two constants with only K dependance, namely A and DK , are also determined with smaller precision than other constants in the same order of the Hamiltonian. This is simply because the phenylacetylene is a rather prolate molecule ðj ¼ 0:85Þ, while we only have a R-type transitions at our disposal. A single, weak, a Q -type transition, 81;7 81;8 was actually measured in Ref. [12] and we have been able to confirm that measurement. We did not, however, succeed in confidently measuring further lines of this type, probably due to insufficient microwave excitation power in our FTMW spectrometer. The overall deviation of the fit close to 27 kHz for the
Fig. 1. Illustration of the strongest features visible in the room-temperature mm-wave rotational spectrum of phenylacetylene. The ground state transitions give rise to an n ¼ 2, type-II+ band of R-type transitions, which is characteristic of planar molecules. Values of J00 are indicated on the diagram and transitions away from the bandhead decrease in J and increase in K a . Similar bands for the two lowest excited vibrational states, v 24 ¼ 1 and v 36 ¼ 1, are strongly distorted by Coriolis perturbation between these states.
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ground state is very satisfactory and reflects the relatively rigid nature of the molecule, as well as improvements in the performance of our spectrometer. The S-reduction fit is slightly more successful, and also the values of correlation coefficients for this fit are generally lower (Tables S1 and S2). The quartic centrifugal distortion constants determined with both fits are in good agreement with values derived from various calculated harmonic force fields, see Table 3. 5. Vibrationally excited states
Fig. 2. Distribution plot of values of obs.–calc. differences in the S-reduction fit for the ground state of phenylacetylene. Circle diameters are proportional to the absolute value of the difference and the largest circles correspond to values of 0.20 MHz. The data subsets for Stark spectra from Ref. [10] and supersonic expansion FTMW spectra from Ref. [12] and the present work are marked.
A comprehensive study of the vibrational spectrum of phenylacetylene was carried out by King and So [31], who also proposed a normal mode assignment. This was correct except for the two lowest frequency vibrational modes, which were reassigned on the basis of additional information from laser fluorescence spectra [32]. The final picture was confirmed by ab initio calculations [33,34] and further normal mode analyses of phenylacetylene in comparison with related molecules [35,36]. Phenylacetylene is a molecule of C 2v symmetry and it has two low frequency B symmetry normal modes associated with distortion of the ACBCH group in relation to the phenyl ring, Fig. 3. Since there has been some confusion in the literature on the assignment of B1 and B2 symmetry for planar C 2v molecules, it is useful to recall a IUPAC recommendation on this matter [39]. Accordingly, the x-axis is chosen to be perpendicular to the plane of the molecule, such that the rv ðxzÞ in the present case becomes the ac inertial plane. The inplane and out-of-plane modes that are antisymmetric with respect to the C 2 operation are therefore assigned to the B2 and B1 species, respectively. The lowest frequency normal mode in phenylacetylene is the out-of-plane, B1 symmetry mode m24 , for which only an approxi-
Table 1 Spectroscopic constants for phenylacetylene obtained by using the A-reduced form of the rotational Hamiltonian. g.s.
Solution I
v 24 ¼ 1 a
A (MHz)
5680.3433(19)
ðA24 þ A36 Þ=2 (MHz) ðA24 A36 Þ=2 (MHz)
5679.62201(65) 3.60(13)
B (MHz) C (MHz)
1529.742116(24) 1204.955065(21)
B (MHz) C (MHz)
1531.433932(77) 1206.771426(61)
5679.62089(65) 3.16(14) 1532.609669(87) 1205.795275(72)
1531.433742(77) 1206.771561(61)
1532.609522(92) 1205.795396(75)
0.0429307(29) 0.99117(35) [0.2139] 0.0102342(18) 0.62358(24)
0.0431651(32) 0.94655(35) [0.2139] 0.0105225(22) 0.62421(20)
0.0429290(29) 0.99254(37) [0.2139] 0.0102324(18) 0.62342(24)
0.0431658(32) 0.94493(38) [0.2139] 0.0105219(23) 0.62420(21)
UJ (Hz) UJK (Hz) UKJ (Hz) UK (Hz)
0.00000189(36) 0.001659(20) 0.009308(72) [0.0] 0.00000071(15) 0.000822(16) 0.00760(38)
[0.00000189] 0.001474(12) 0.006207(57) [0.0] [0.00000071] 0.0008513(68) 0.00773(22)
[0.00000189] 0.001919(13) 0.012610(65) [0.0] [0.00000071] 0.0007352(69) 0.00997(26)
[0.00000189] 0.001481(12) 0.006801(57) [0.0] [0.00000071] 0.0008356(67) 0.00804(22)
[0.00000189] 0.001918(13) 0.012173(58) [0.0] [0.00000071] 0.0007489(70) 0.00972(26)
Ga (MHz) GJa (MHz) F bc (MHz) F Kbc (MHz) N lines b
rfit (kHz) rw c
c
v 36 ¼ 1
0.0422679(74) 0.982468(53) 0.2139(43) 0.0101710(27) 0.62427(37)
DE (MHz) DE (cm1)
a
v 24 ¼ 1
DJ (kHz) DJK (kHz) DK (kHz) dJ (kHz) dK (kHz)
/J (Hz) /JK (Hz) /K (Hz)
b
Solution II
v 36 ¼ 1
783 27.3 0.6156
461378.80(49) 15.389938(16) 9547.8(32) 0.0048495(89) 0.4761(26) 0.00000394(48) 1006 36.1 0.7216
461378.65(50) 15.389933(17) 9710.0(33) 0.0047536(79) 0.3518(24) 0.00000570(45) 1006 36.8 0.7367
Round parentheses enclose standard errors in units of the last quoted digit of the value of the constant, square parentheses enclose assumed values. The number of distinct frequency transitions used in the fit. Unitless deviation of the weighted fit.
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Table 2 Spectroscopic constants for phenylacetylene obtained by using the S-reduced form of the rotational Hamiltonian. g.s.
Solution I
Solution II
v 24 ¼ 1
v 36 ¼ 1
A (MHz)
5680.3428(19)
ðA24 þ A36 Þ=2 (MHz) ðA24 A36 Þ=2 (MHz)
5679.61958(66) 3.16(15)
B (MHz) C (MHz)
1529.740864(24) 1204.956302(21)
B (MHz) C (MHz)
1531.42995(12) 1206.774758(83)
DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz)
0.0305185(32) 1.053136(36) 0.1557(43) 0.0101727(27) 0.0058781(34)
HJ (Hz) HJK (Hz) HKJ (Hz) HK (Hz) h1 (Hz) h2 (Hz) h3 (Hz)
0.00001258(14) 0.0012034(15) 0.007502(13) [0.0] 0.00000050(13) 0.00000737(15) 0.000001323(51)
DE (MHz) DE (cm1) Ga (MHz) GJa (MHz) F bc (MHz) N lines
1532.607433(91) 1205.797824(82)
1531.43009(12) 1206.774716(88)
1532.607195(98) 1205.797925(84)
0.031230(15) 1.0311(17) [0.1557] 0.0105613(21) 0.0059803(86)
0.031248(15) 1.0541(16) [0.1557] 0.0102080(32) 0.0058034(99)
0.031262(15) 1.0250(16) [0.1557] 0.0105533(23) 0.0059588(86)
0.00001139(48) 0.0009959(41) 0.004840(58) [0.0] [0.0000005] 0.00000427(32) 0.00000009(10)
0.00001392(48) 0.0013410(41) 0.009931(42) [0.0] [0.0000005] 0.00000903(30) 0.00000252(10)
0.00001221(46) 0.0009861(40) 0.004949(44) [0.0] [0.0000005] 0.00000517(31) 0.00000046(10)
0.00001302(46) 0.0013523(40) 0.009921(27) [0.0] [0.0000005] 0.00000819(30) 0.00000223(10)
461374.94(53) 15.389811(18)
461375.73(55) 15.389838(18)
9558.6(37) 0.004481(39)
9698.9(39) 0.004510(38)
0.4245(24) 0.00000835(21)
783 26.9 0.6065
v 36 ¼ 1
5679.61909(67) 2.69(16)
0.031278(15) 1.0482(17) [0.1557] 0.0101983(32) 0.0057792(99)
F Kbc (MHz)
rfit (kHz) rw
v 24 ¼ 1
0.3195(37) 0.00000773(19)
1006 38.2 0.7637
mate wavenumber (140 cm1) is available experimentally [32]. The next higher mode is the in-plane, B2 symmetry mode m36 , with a much more confident experimental wavenumber of 151.9 cm1 [32]. The next higher modes are m23 (B1 , 349 cm1), m16 (A2 , 418 cm1), and m13 (A1 , 465 cm1) [31], so that the most prominent excited state features in the room-temperature rotational spectrum will be constituted by transitions in v 24 ¼ 1 and v 36 ¼ 1. The two states are sufficiently close in energy that their mutual interaction has to be considered. Since B1 B2 ¼ A2 and A2 is the species containing the rotation about the z-axis, then Coriolis interaction about the a inertial axis will be possible. The Hamiltonian for the coupled fit of the two states is written in standard 2 2 block form:
1006 38.4 0.7679
H¼
Hð24Þ rot ð24;36Þ
HCor
ð24;36Þ
HCor
ð36Þ Hrot þ DE
! ;
ð1Þ
containing the pure rotational, Watsonian terms for the two vibrað24Þ tional states, Hrot and Hð36Þ rot , on the diagonal, augmented by the vibrational energy difference DE ¼ E36 E24 . The connecting, offdiagonal Coriolis term is given by
Table 3 Comparison of experimental and calculated values of selected force field dependent parameters for phenylacetylene.
DJ (kHz) DJK (kHz) DK (kHz) dJ (kHz) dK (kHz) fa24;36
DE (cm1) Di e (u Å2)
Exp.
Calculated
This work
B3LYPa
0.042268(7) 0.98247(5) 0.214(4) 0.010171(3) 0.6243(4) 0.8393(3) 15.38994(2) 0.07875(3)
0.0396 0.894 0.265 0.00954 0.568
MP2a 0.0391 0.902 0.239 0.00943 0.572
0.8296
0.8397
13.8 0.0939
19.6 0.0432
MP2b 0.0392 0.901 0.244 0.00946 0.571 0.8381 18.0(9.6d) 0.0486
Ref. [33]c 0.0420 1.0475 0.1474 0.0100 0.6493 0.84 16
a From unscaled harmonic force field evaluated with the 6-31G(d,p) basis set by using PC-GAMESS. b From unscaled harmonic force field evaluated with the 6-31G(d,p) basis set by using CFOUR [30]. c From multiscaled harmonic force field evaluated at the HF/4-21G level. d Value inclusive of anharmonic corrections. e Ground state inertia defect, Di ¼ Ic Ia Ib .
Fig. 3. Normal coordinate displacement vectors for the two lowest frequency normal modes in phenylacetylene. The plotted vectors are unweighted eigenvectors calculated with VIBCA and VECTOR [18] from the B3LYP/6-31G(d,p) harmonic force field evaluated with the PC-GAMESS Version [37] of the GAMESS package [38].
Z. Kisiel, A. Kras´nicki / Journal of Molecular Spectroscopy 262 (2010) 82–88
86 ð24;36Þ
HCor
¼ i Ga þ GJa P2 þ GKa P2z þ P z þ F bc þ F Jbc P 2 þ F Kbc P2z þ ðPx Py þ Py Px Þ:
ð2Þ
The coupling constant Ga is related to the Coriolis coefficient fa24;36 connecting the two modes by
Ga ¼ Afa24;36
hpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii ðx24 =x36 Þ þ ðx36 =x24 Þ :
ð3Þ
Results of ab initio computations in Ref. [33] and of those carried out presently allowed an initial estimate of Ga 9500 MHz to be made. Once this was incorporated into the predictions, the pattern of excited state lines, as marked Fig. 1, became discernible. Line intensities in the rotational spectrum of phenylacetylene carry nuclear spin statistical weights of 5:3, which arise from the presence of two pairs of symmetry equivalent hydrogens in the phenyl ring. Observation of a reversal in the weights between the ground state and excited states, shown in Fig. 4, provided confirmation of the assignment of the excited state lines to two B symmetry vibrational states. Once the initial assignment was made, the analysis turned out to be fairly straightforward, since the interaction between the two states was found to be very well described by only a limited number of constants in Eq. (2). It was possible to assign lines for a similar distribution of quantum number values to that shown in Fig. 2 for the ground state, except that owing to decreasing line intensity the upper limit on K a was around 50. The results of the final fits are summarised in Tables 1 and 2, and complete listings and data files for these fits are in Tables S3 and S4. In contrast to the ground state the A-reduced fits are slightly more successful than the S-reduced fits, in line with similar behaviour documented for several other molecules [21,40]. The deviations of the excited state fits are well below 40 kHz, and the relative invariance of the values of centrifugal distortion constants between the two excited sates and the ground state are evidence for the validity of the fitting model. Only DK (or DK ) and some sextic level constants could not be determined with confidence and were assumed at values from the ground state. Nevertheless, even though these fits were ultimately successful, we had to resolve several complications. First of all, there was considerable numerical instability when values of A24 and A36 were used as parameters of fit. It turned out that only their average was well determined while the difference was not. The adopted solution was to use the sum and difference of these rotational constants explicitly, as listed in Tables 1 and 2. This ensured numerical
Fig. 5. Dependence of deviation of the A-reduced coupled fit of rotational transitions in v 24 ¼ 1 and v 36 ¼ 1 vibrational states on the difference in rotational constant A between the two states. The two alternative solutions listed in Tables 1 and 2 are indicated.
stability but also revealed very limited sensitivity of the overall deviation of fit to the difference between the A rotational constants for the two excited states, as shown in Fig. 5. In particular, two alternative solutions, labelled I and II, could be identified and are listed in Tables 1 and 2. Solution I was preferred on the basis of standard deviation, but the discrimination from solution II was minimal, at a level of less than 1 kHz in the deviation of fit. By inspecting the predictions we found that many pairs of interacting energy levels in the two studied excited states were subject to considerable mixing. We therefore made a significant number of dedicated measurements targeted at transitions between such levels, and we were even able to measure several transitions that were identified by the quantum number assignment scheme of SPFIT as transitions between the two vibrational states (see Table S3). In spite of this, we were still not able to improve the discrimination between solutions I and II beyond that which is being reported. It
Fig. 4. Illustration of the effect of 5:3 nuclear spin statistical weights for phenylacetylene arising from the presence of two pairs of symmetry-equivalent protons. Each doublet consists of the 444;41 434;40 transition (left) and the 443;41 433;40 transition (right), which would be of similar intensity without the presence of statistical weights. The weights reverse between the ground state and the two excited states, confirming that the latter are both of B symmetry.
Z. Kisiel, A. Kras´nicki / Journal of Molecular Spectroscopy 262 (2010) 82–88 Table 4 Comparison of experimental and calculated vibrational changes (MHz) in rotational constants. Exp.a c
Calc.b
0.7213(20)
0.668
A24 A0 B24 B0 C 24 C 0
4.32(13) 1.69182(8) 1.81846(8)
5.02d 1.572 1.716
A36 A0 B36 B0 C 36 C 0
2.88(13) 2.86755(9) 0.84021(7)
3.74d 2.646 0.752
A A0
a
Values from A-reduction, solution I. Calculated with CFOUR [30] at the MP2/6-31G(d,p) level. A ¼ ðA24 þ A36 Þ=2. d Deperturbed values obtained by subtracting contributions in Eqs. (4) and (5), from the calculated effective values A24 A0 ¼ 173:45 and A36 A0 ¼ 172:09 MHz, see text. b
c
should be mentioned that we did not encounter any lines that were not accounted for in the fits, in that they were either badly shifted or missing, and the fits encompass all transitions that we would have been expected to measure. In an attempt to discriminate more confidently between solutions I and II we turned to anharmonic force field calculations, which are increasingly being used in derivation of semi-experimental equilibrium structures. Although the performance of such calculations for molecules of the size of phenylacetylene has not yet been benchmarked, there are indicators that practicable levels of calculation may already be useful [41]. We used the CFOUR package [30] to calculate the vibrational changes in rotation constants, and the results are summarised in Table 4. We note that the agreement with experiment for B and C rotational constants is excellent, confirming the assignment of the lower vibrational level to v 24 ¼ 1 and of the upper to v 36 ¼ 1. The situation for the A rotational constant is more involved since CFOUR calculates vibrational changes between effective values inclusive of the effects of perturbation, as described, for example, by Eq. 17.7.2 of Ref. [42]. The deperturbed values, in the sense of those obtained from the coupling fits made here, can be obtained by subtracting the contributions to ðAv A0 Þ from the fa24;36 term given by
2A2 a 2 3x224 þ x236 f ; x24 24;36 x224 x236 2A2 a 2 3x236 þ x224 ¼ f : x36 24;36 x236 x224
dðA24 A0 Þ ¼ daA24 ¼
ð4Þ
dðA36 A0 Þ ¼ daA36
ð5Þ
It can be seen from Table 4 that application of Eqs. (4) and (5) leads to values of ðAv A0 Þ which are both satisfactorily close to experiment, and also unambiguously prefer solution I, in which A24 < A36 . 6. Conclusion The present investigation considerably extends the coverage of the known rotational spectrum of the phenylacetylene molecule, as is evident from Fig. 2. The reported spectroscopic constants should allow accurate prediction of the rotational spectrum well into the submillimetre-wave region. The analysis of the strong Coriolis coupling between m24 and m36 modes turned out to be entirely satisfactory, although selection between the two alternative solutions could only be made with confidence on the basis of calculation of the vibrational changes in rotational constants. It is useful to restate the word of warning made in Ref. [19] that in more complex situations a given fit that is acceptable according to the criteria of satisfactory reproduction of the spectrum may not necessarily be the physically most meaningful solution.
87
The comparison of the various force field dependant quantities determined presently for phenylacetylene with the results from different calculations (Table 3) shows good agreement. We note that none of the routine diagnostic-level calculations is outstandingly better than others. For example, the MP2 results are more consistent with the experimental fa24;36 , while the DFT result is better for the inertial defect. The MP2/6-31G(d,p) results illustrate the level of consistency between two independent computational packages. We also find a remarkable agreement of the current experimental results with those based on a very rudimentary HF/ 4-21G calculation by Csaszar et al. [33]. The Scaled Quantum Mechanics technique used in that work and based on a combination of results for benzene and acetylene appears to have worked very well. Finally, the use of m36 from Ref. [32] and the present value of DE, allows an estimate of 136.5 cm1 for the wavenumber of the m24 fundamental. Acknowledgments The authors thank Bolesław Kozankiewicz for the sample of phenylacetylene, and also Frank De Lucia and Heinrich Mäder for help with equipment problems. Financial support from the Polish Ministry of Science and Higher Education, Grant No. N-N2020541-33, is gratefully acknowledged. 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://library.osu.edu/sites/ msa/jmsa_hp.htm). References [1] B. Jones, F. Zhang, P. Maksyutenko, A.M. Mebel, R.I. Kaiser, J. Phys. Chem. A 114 (2010) 5256–5262. [2] K. Mimura, M. Ohashi, R. Sugisaki, Earth Planet. Sci. Lett. 133 (1995) 265–269. [3] G.R. Floyd, R.H. Prince, W.W. Duley, J. R. Astron. Soc. Can. 67 (1973) 299–305. [4] J.A. Stearns, T.S. Zwier, E. Kraka, D. Cremer, Phys. Chem. Chem. Phys. 8 (2006) 5317–5327. [5] J.J. Newby, J.A. Stearns, C.-P. Liu, T.S. Zwier, J. Phys. Chem. A 111 (2007) 10914– 10927. [6] B.N. Tran, J.C. Joseph, M. Force, R.G. Briggs, V. Vuitton, J.P. Ferris, Icarus 177 (2005) 106–115. [7] Y.J. Pendleton, L.J. Allamandola, Astrophys. J. Suppl. Ser. 138 (2002) 75–98. [8] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, H. Mäder, J. Mol. Spectrosc. 227 (2004) 109–113. [9] W. Zeil, M. Winnewisser, H.K. Bodenseh, H. Buchert, Z. Naturforsch. 15a (1960) 1011–1013. [10] A.P. Cox, I.C. Ewart, W.M. Stigliani, J. Chem. Soc. Faraday Trans. II 71 (1975) 504–514. [11] H.D. Rudolph, H. Dreizler, A. Jaeschke, P. Wendling, Z. Naturforsch. 22a (1970) 940–944. [12] H. Dreizler, H.D. Rudolph, B. Hartke, J. Mol. Struct. 698 (2004) 1–24. [13] I. Medvedev, M. Winnewisser, F.C. De Lucia, E. Herbst, E. Białkowska-Jaworska, L. Pszczółkowski, Z. Kisiel, J. Mol. Spectrosc. 228 (2004) 314–328. [14] Z. Kisiel, J. Kosarzewski, L. Pszczółkowski, Acta Phys. Pol. A 92 (1997) 507–516. [15] T.J. Balle, W.H. Flygare, Rev. Sci. Instrum. 52 (1981) 33–45. [16] A. Kras´nicki, L. Pszczółkowski, Z. Kisiel, J. Mol. Spectrosc. 260 (2010) 57–65. [17] Z. Kisiel, L. Pszczółkowski, I.R. Medvedev, M. Winnewisser, F.C. De Lucia, E. Herbst, J. Mol. Spectrosc. 233 (2005) 231–243. [18] Z. Kisiel, PROSPE – Programs for ROtational SPEctroscopy. Available from:. [19] Z. Kisiel, E. Białkowska-Jaworska, R.A.H. Butler, D.T. Petkie, P. Helminger, I.R. Medvedev, F.C. De Lucia, J. Mol. Spectrosc. 254 (2009) 78–86. [20] Z. Kisiel, A. Kras´nicki, L. Pszczółkowski, S.T. Shipman, L. Alvarez-Valtierra, B.H. Pate, J. Mol. Spectrosc. 257 (2009) 177–186. [21] Z. Kisiel, L. Pszczółkowski, B.J. Drouin, C.S. Brauer, S. Yu, J.C. Pearson, J. Mol. Spectrosc. 258 (2009) 26–34. [22] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377. [23] H.M. Pickett, SPFIT/SPCAT package. Available from: . [24] S.J. Borchert, J. Mol. Spectrosc. 57 (1975) 312–315. [25] Z. Kisiel, J. Mol. Spectrosc. 144 (1990) 381–388. [26] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, J. Mol. Spectrosc. 177 (1996) 240–250.
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[27] Z. Kisiel, L. Pszczółkowski, J. Mol. Spectrosc. 178 (1996) 125–137. [28] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, J. Mol. Spectrosc. 232 (2005) 47–54. [29] J.K.G. Watson, in: J.R. Durig (Ed.), Vibrational Spectra and Structure, vol. 6, Elsevier, New York/Amsterdam, 1977, pp. 1–89. [30] CFOUR, A quantum chemical program package written by J.F. Stanton, J. Gauss, M.E. Harding, P.G. Szalay with contributions from A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, Y.J. Bomble, O. Christiansen, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W.J. Lauderdale, D.A. Matthews, T. Metzroth, D.P. O’Neill, D.R. Price, E. Prochnow, K. Ruud, F. Schiffmann, S. Stopkowicz, J. Vázquez, F. Wang, J.D. Watts and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A.V. Mitin and C. van Wüllen. For the current version, see. [31] G.W. King, S.P. So, J. Mol. Spectrosc. 36 (1970) 468–487. [32] A.R. Bacon, J.M. Hollas, T. Ridley, Can. J. Phys. 62 (1984) 1254–1263.
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Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
The millimetre-wave rotational spectrum of phenylacetylene Zbigniew Kisiel *, Adam Kras´nicki Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
a r t i c l e
i n f o
Article history: Received 26 April 2010 In revised form 24 May 2010 Available online 2 June 2010 Keywords: Rotational spectroscopy Millimetre-wave spectrum Excited vibrational states Coriolis interaction
a b s t r a c t The room-temperature rotational spectrum of phenylacetylene ðC6 H5 CBCHÞ, was studied at frequencies up to 340 GHz. Extensive new measurements, covering rotational transitions with quantum number values up to J ¼ 140 and K a ¼ 59, allowed determination of precise spectroscopic constants for the ground state and for the lowest two excited vibrational states, v 24 ¼ 1 and v 36 ¼ 1. The two excited states belong to the lowest B1 and B2 symmetry normal modes and their rotational transitions are very strongly perturbed by a-axis Coriolis resonance. A successful fit of the resonance is reported, resulting in fa24;36 ¼ 0:8403ð3Þ and DE ¼ E36 E24 ¼ 15:38994ð2Þ cm1 , in good agreement with results of ab initio computations. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Phenylacetylene is a fundamental hydrocarbon derivative of benzene and is implicated in chemical reaction networks associated with formation of polyaromatic hydrocarbons in combustion and in the interstellar medium (ISM) [1]. Many different studies on the formation of phenylacetylene at astrophysically relevant conditions have been carried out. It can be formed from benzene by impact shock [2] or collisions with the ethynyl radical [1]. It can also be formed by photochemical reactions from acetylene [3], vinylacetylene [4], or 1,3-butadiene [5]. Phenylacetylene has been formed in a mixture of gases simulating the atmosphere of Saturn’s moon Titan [6], and studies in Refs. [1,4,5] were, in fact, also motivated by the desire to explore the rich hydrocarbon chemistry expected to be present on Titan. Phenylacetylene is a polar molecule and is thus attractive as a potential radioastronomy marker of unsaturated, or even polyaromatic hydrocarbon chemistry, which is postulated to be relevant to the ISM on the basis of infrared spectroscopic signatures [7]. The available laboratory data concerning the rotational spectrum of phenylacetylene is insufficient for radioastronomical detection applications, especially at the promising mm-wave frequencies. The present work aims to remedy this situation, similar to our previous effort for a related benzene derivative, toluene [8]. The rotational spectrum of phenylacetylene was first studied by Zeil et al. [9], and their survey investigation was followed by a much more detailed study of Cox et al. [10]. Rotational constants were obtained for seven different isotopic species leading to a determination of the molecular structure. The electric dipole mo-
* Corresponding author. Fax: +48 22 8430926. E-mail address: [email protected] (Z. Kisiel). 0022-2852/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2010.05.007
ment, l ¼ la ¼ 0:656ð5Þ D, was also determined, and is appreciably higher than 0.375(10) D for toluene [11]. More recently, a much more extensive determination of the structure of phenylacetylene by rotational spectroscopy was carried out by Dreizler et al. [12] on the basis of rotational constants obtained for 39 different isotopic species. In that case the measurements were made by Fourier transform microwave spectroscopy on a supersonic expansion. Nevertheless, the frequency coverage of all of these investigations did not extend beyond 40 GHz and no excited vibrational state transitions were assigned. The present investigation improves on all of these counts as we report an analysis of the major features of the room-temperature rotational spectrum of phenylacetylene up to 340 GHz. 2. Experimental details All measurements were carried out with the two rotational spectrometers in Warsaw. The room-temperature spectrum was measured at frequencies 90–340 GHz with the broadband, source modulation spectrometer described in Ref. [13]. The spectrometer has presently been upgraded to the use of contemporary generation of zero-biased GaAs Schottky diode detectors and harmonic mixers from Virginia Diodes Inc. Two Istok BWO sources, OB-24 and OB-30, were used for measurements at 175–340 GHz. The region 90– 140 GHz was covered with a harmonic multiplication source, also from Virginia Diodes, which generated the 12th harmonic of the driving frequency from a microwave synthesizer. Measurements were performed on a commercial sample used without further purification and at a sample pressure of up to 10 mTorr. Additional measurements of some low-J transitions not covered in Ref. [12] were made in supersonic expansion, at 7–19 GHz, with the cavity Fourier transform microwave spectrometer (FTMW) in Warsaw
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[14]. This spectrometer is a coaxial waveguide version of the original design of Balle and Flygare [15], which has recently been upgraded to a simple computer aided single-step frequency downconversion [16]. The many individual millimetre wave spectra recorded during this work were combined into a single spectrum and subjected to analysis with the use of the AABS software package for Assignment and Analysis of Broadband Spectra [17]. The package provides a synchronised display of the experimental spectrum and of predictions for all vibrational and isotopic species relevant in a given spectrum. Flexible comparison between predictions and experiment allows the measured spectrum to be very rapidly reduced into datasets for several different fitting programs. A Loomis–Wood type display mode facilitates rapid graphical assignment. The package is freely available from the PROSPE website [18], and has been used in studies of many complex spectra, most recently those of ClONO2 [19], bromoform [20], and acrylonitrile [21]. The ground state data from previous work and from present measurements were fitted jointly by using the ASFIT/ASROT package [18], while the SPFIT/SPCAT package [22,23] was used for the analysis of vibrationally excited states. Frequency measurement uncertainties of 2 and 50 kHz were assumed for supersonic expansion, and room-temperature measurements, respectively.
3. Rotational spectrum The mm-wave region rotational spectrum for the ground state of phenylacetylene was predicted with accuracy sufficient for assignment by augmenting the rotational constants from previous work with quartic centrifugal distortion constants calculated from an ab initio harmonic force field. The high-J, a R-type transitions for a planar molecule are known to coalesce into strong bands, called type-II bands, with an interband frequency spacing of close to 2C. The nomenclature has been proposed by Borchert [24] who identified the initial stage of such band formation. The properties of this type of band were investigated in more detail in the spectrum of chlorobenzene [25], and a comprehensive classification was pro-
83
posed in Refs. [26,27]. An example type-II band in the spectrum of phenylacetylene is shown in Fig. 1. The strongest and leading line in a band of this type consists of doubly degenerate transitions with K a ¼ 0; 1. Successive lines along the band are for values of J decreasing, and of K a increasing in steps of 1. For positive DJK the lines normally evolve from the bandhead to higher frequencies, although the line pattern is quite sensitive to the value of the inertial defect. The changes on vibrational excitation are, nevertheless, fairly moderate and normally do not prevent assignment. A typical situation is depicted in Fig. 1 of Ref. [28] for fluorobenzene. In phenylacetylene, on the other hand, while the presence of strong satellite lines in the spectrum was obvious, their assignment was not possible until a prediction was made on the basis of the expected strong Coriolis perturbation between the two lowest excited vibrational states.
4. Ground state Measurements of ground state lines were extended up to 340 GHz with some care being taken to obtain a balanced coverage of the values of J and K a quantum numbers, as shown in Fig. 2. We have used Watson’s reduced asymmetric rotor Hamiltonian [29], in both A- and S-reductions. The results of fit are summarised in Tables 1 and 2, while complete listings and data files are given in Tables S1 and S2 of the electronic supplementary information. The present dataset allows determination of the complete sextic level Hamiltonian, with the exception of HK . The remaining two constants with only K dependance, namely A and DK , are also determined with smaller precision than other constants in the same order of the Hamiltonian. This is simply because the phenylacetylene is a rather prolate molecule ðj ¼ 0:85Þ, while we only have a R-type transitions at our disposal. A single, weak, a Q -type transition, 81;7 81;8 was actually measured in Ref. [12] and we have been able to confirm that measurement. We did not, however, succeed in confidently measuring further lines of this type, probably due to insufficient microwave excitation power in our FTMW spectrometer. The overall deviation of the fit close to 27 kHz for the
Fig. 1. Illustration of the strongest features visible in the room-temperature mm-wave rotational spectrum of phenylacetylene. The ground state transitions give rise to an n ¼ 2, type-II+ band of R-type transitions, which is characteristic of planar molecules. Values of J00 are indicated on the diagram and transitions away from the bandhead decrease in J and increase in K a . Similar bands for the two lowest excited vibrational states, v 24 ¼ 1 and v 36 ¼ 1, are strongly distorted by Coriolis perturbation between these states.
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ground state is very satisfactory and reflects the relatively rigid nature of the molecule, as well as improvements in the performance of our spectrometer. The S-reduction fit is slightly more successful, and also the values of correlation coefficients for this fit are generally lower (Tables S1 and S2). The quartic centrifugal distortion constants determined with both fits are in good agreement with values derived from various calculated harmonic force fields, see Table 3. 5. Vibrationally excited states
Fig. 2. Distribution plot of values of obs.–calc. differences in the S-reduction fit for the ground state of phenylacetylene. Circle diameters are proportional to the absolute value of the difference and the largest circles correspond to values of 0.20 MHz. The data subsets for Stark spectra from Ref. [10] and supersonic expansion FTMW spectra from Ref. [12] and the present work are marked.
A comprehensive study of the vibrational spectrum of phenylacetylene was carried out by King and So [31], who also proposed a normal mode assignment. This was correct except for the two lowest frequency vibrational modes, which were reassigned on the basis of additional information from laser fluorescence spectra [32]. The final picture was confirmed by ab initio calculations [33,34] and further normal mode analyses of phenylacetylene in comparison with related molecules [35,36]. Phenylacetylene is a molecule of C 2v symmetry and it has two low frequency B symmetry normal modes associated with distortion of the ACBCH group in relation to the phenyl ring, Fig. 3. Since there has been some confusion in the literature on the assignment of B1 and B2 symmetry for planar C 2v molecules, it is useful to recall a IUPAC recommendation on this matter [39]. Accordingly, the x-axis is chosen to be perpendicular to the plane of the molecule, such that the rv ðxzÞ in the present case becomes the ac inertial plane. The inplane and out-of-plane modes that are antisymmetric with respect to the C 2 operation are therefore assigned to the B2 and B1 species, respectively. The lowest frequency normal mode in phenylacetylene is the out-of-plane, B1 symmetry mode m24 , for which only an approxi-
Table 1 Spectroscopic constants for phenylacetylene obtained by using the A-reduced form of the rotational Hamiltonian. g.s.
Solution I
v 24 ¼ 1 a
A (MHz)
5680.3433(19)
ðA24 þ A36 Þ=2 (MHz) ðA24 A36 Þ=2 (MHz)
5679.62201(65) 3.60(13)
B (MHz) C (MHz)
1529.742116(24) 1204.955065(21)
B (MHz) C (MHz)
1531.433932(77) 1206.771426(61)
5679.62089(65) 3.16(14) 1532.609669(87) 1205.795275(72)
1531.433742(77) 1206.771561(61)
1532.609522(92) 1205.795396(75)
0.0429307(29) 0.99117(35) [0.2139] 0.0102342(18) 0.62358(24)
0.0431651(32) 0.94655(35) [0.2139] 0.0105225(22) 0.62421(20)
0.0429290(29) 0.99254(37) [0.2139] 0.0102324(18) 0.62342(24)
0.0431658(32) 0.94493(38) [0.2139] 0.0105219(23) 0.62420(21)
UJ (Hz) UJK (Hz) UKJ (Hz) UK (Hz)
0.00000189(36) 0.001659(20) 0.009308(72) [0.0] 0.00000071(15) 0.000822(16) 0.00760(38)
[0.00000189] 0.001474(12) 0.006207(57) [0.0] [0.00000071] 0.0008513(68) 0.00773(22)
[0.00000189] 0.001919(13) 0.012610(65) [0.0] [0.00000071] 0.0007352(69) 0.00997(26)
[0.00000189] 0.001481(12) 0.006801(57) [0.0] [0.00000071] 0.0008356(67) 0.00804(22)
[0.00000189] 0.001918(13) 0.012173(58) [0.0] [0.00000071] 0.0007489(70) 0.00972(26)
Ga (MHz) GJa (MHz) F bc (MHz) F Kbc (MHz) N lines b
rfit (kHz) rw c
c
v 36 ¼ 1
0.0422679(74) 0.982468(53) 0.2139(43) 0.0101710(27) 0.62427(37)
DE (MHz) DE (cm1)
a
v 24 ¼ 1
DJ (kHz) DJK (kHz) DK (kHz) dJ (kHz) dK (kHz)
/J (Hz) /JK (Hz) /K (Hz)
b
Solution II
v 36 ¼ 1
783 27.3 0.6156
461378.80(49) 15.389938(16) 9547.8(32) 0.0048495(89) 0.4761(26) 0.00000394(48) 1006 36.1 0.7216
461378.65(50) 15.389933(17) 9710.0(33) 0.0047536(79) 0.3518(24) 0.00000570(45) 1006 36.8 0.7367
Round parentheses enclose standard errors in units of the last quoted digit of the value of the constant, square parentheses enclose assumed values. The number of distinct frequency transitions used in the fit. Unitless deviation of the weighted fit.
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Table 2 Spectroscopic constants for phenylacetylene obtained by using the S-reduced form of the rotational Hamiltonian. g.s.
Solution I
Solution II
v 24 ¼ 1
v 36 ¼ 1
A (MHz)
5680.3428(19)
ðA24 þ A36 Þ=2 (MHz) ðA24 A36 Þ=2 (MHz)
5679.61958(66) 3.16(15)
B (MHz) C (MHz)
1529.740864(24) 1204.956302(21)
B (MHz) C (MHz)
1531.42995(12) 1206.774758(83)
DJ (kHz) DJK (kHz) DK (kHz) d1 (kHz) d2 (kHz)
0.0305185(32) 1.053136(36) 0.1557(43) 0.0101727(27) 0.0058781(34)
HJ (Hz) HJK (Hz) HKJ (Hz) HK (Hz) h1 (Hz) h2 (Hz) h3 (Hz)
0.00001258(14) 0.0012034(15) 0.007502(13) [0.0] 0.00000050(13) 0.00000737(15) 0.000001323(51)
DE (MHz) DE (cm1) Ga (MHz) GJa (MHz) F bc (MHz) N lines
1532.607433(91) 1205.797824(82)
1531.43009(12) 1206.774716(88)
1532.607195(98) 1205.797925(84)
0.031230(15) 1.0311(17) [0.1557] 0.0105613(21) 0.0059803(86)
0.031248(15) 1.0541(16) [0.1557] 0.0102080(32) 0.0058034(99)
0.031262(15) 1.0250(16) [0.1557] 0.0105533(23) 0.0059588(86)
0.00001139(48) 0.0009959(41) 0.004840(58) [0.0] [0.0000005] 0.00000427(32) 0.00000009(10)
0.00001392(48) 0.0013410(41) 0.009931(42) [0.0] [0.0000005] 0.00000903(30) 0.00000252(10)
0.00001221(46) 0.0009861(40) 0.004949(44) [0.0] [0.0000005] 0.00000517(31) 0.00000046(10)
0.00001302(46) 0.0013523(40) 0.009921(27) [0.0] [0.0000005] 0.00000819(30) 0.00000223(10)
461374.94(53) 15.389811(18)
461375.73(55) 15.389838(18)
9558.6(37) 0.004481(39)
9698.9(39) 0.004510(38)
0.4245(24) 0.00000835(21)
783 26.9 0.6065
v 36 ¼ 1
5679.61909(67) 2.69(16)
0.031278(15) 1.0482(17) [0.1557] 0.0101983(32) 0.0057792(99)
F Kbc (MHz)
rfit (kHz) rw
v 24 ¼ 1
0.3195(37) 0.00000773(19)
1006 38.2 0.7637
mate wavenumber (140 cm1) is available experimentally [32]. The next higher mode is the in-plane, B2 symmetry mode m36 , with a much more confident experimental wavenumber of 151.9 cm1 [32]. The next higher modes are m23 (B1 , 349 cm1), m16 (A2 , 418 cm1), and m13 (A1 , 465 cm1) [31], so that the most prominent excited state features in the room-temperature rotational spectrum will be constituted by transitions in v 24 ¼ 1 and v 36 ¼ 1. The two states are sufficiently close in energy that their mutual interaction has to be considered. Since B1 B2 ¼ A2 and A2 is the species containing the rotation about the z-axis, then Coriolis interaction about the a inertial axis will be possible. The Hamiltonian for the coupled fit of the two states is written in standard 2 2 block form:
1006 38.4 0.7679
H¼
Hð24Þ rot ð24;36Þ
HCor
ð24;36Þ
HCor
ð36Þ Hrot þ DE
! ;
ð1Þ
containing the pure rotational, Watsonian terms for the two vibrað24Þ tional states, Hrot and Hð36Þ rot , on the diagonal, augmented by the vibrational energy difference DE ¼ E36 E24 . The connecting, offdiagonal Coriolis term is given by
Table 3 Comparison of experimental and calculated values of selected force field dependent parameters for phenylacetylene.
DJ (kHz) DJK (kHz) DK (kHz) dJ (kHz) dK (kHz) fa24;36
DE (cm1) Di e (u Å2)
Exp.
Calculated
This work
B3LYPa
0.042268(7) 0.98247(5) 0.214(4) 0.010171(3) 0.6243(4) 0.8393(3) 15.38994(2) 0.07875(3)
0.0396 0.894 0.265 0.00954 0.568
MP2a 0.0391 0.902 0.239 0.00943 0.572
0.8296
0.8397
13.8 0.0939
19.6 0.0432
MP2b 0.0392 0.901 0.244 0.00946 0.571 0.8381 18.0(9.6d) 0.0486
Ref. [33]c 0.0420 1.0475 0.1474 0.0100 0.6493 0.84 16
a From unscaled harmonic force field evaluated with the 6-31G(d,p) basis set by using PC-GAMESS. b From unscaled harmonic force field evaluated with the 6-31G(d,p) basis set by using CFOUR [30]. c From multiscaled harmonic force field evaluated at the HF/4-21G level. d Value inclusive of anharmonic corrections. e Ground state inertia defect, Di ¼ Ic Ia Ib .
Fig. 3. Normal coordinate displacement vectors for the two lowest frequency normal modes in phenylacetylene. The plotted vectors are unweighted eigenvectors calculated with VIBCA and VECTOR [18] from the B3LYP/6-31G(d,p) harmonic force field evaluated with the PC-GAMESS Version [37] of the GAMESS package [38].
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86 ð24;36Þ
HCor
¼ i Ga þ GJa P2 þ GKa P2z þ P z þ F bc þ F Jbc P 2 þ F Kbc P2z þ ðPx Py þ Py Px Þ:
ð2Þ
The coupling constant Ga is related to the Coriolis coefficient fa24;36 connecting the two modes by
Ga ¼ Afa24;36
hpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii ðx24 =x36 Þ þ ðx36 =x24 Þ :
ð3Þ
Results of ab initio computations in Ref. [33] and of those carried out presently allowed an initial estimate of Ga 9500 MHz to be made. Once this was incorporated into the predictions, the pattern of excited state lines, as marked Fig. 1, became discernible. Line intensities in the rotational spectrum of phenylacetylene carry nuclear spin statistical weights of 5:3, which arise from the presence of two pairs of symmetry equivalent hydrogens in the phenyl ring. Observation of a reversal in the weights between the ground state and excited states, shown in Fig. 4, provided confirmation of the assignment of the excited state lines to two B symmetry vibrational states. Once the initial assignment was made, the analysis turned out to be fairly straightforward, since the interaction between the two states was found to be very well described by only a limited number of constants in Eq. (2). It was possible to assign lines for a similar distribution of quantum number values to that shown in Fig. 2 for the ground state, except that owing to decreasing line intensity the upper limit on K a was around 50. The results of the final fits are summarised in Tables 1 and 2, and complete listings and data files for these fits are in Tables S3 and S4. In contrast to the ground state the A-reduced fits are slightly more successful than the S-reduced fits, in line with similar behaviour documented for several other molecules [21,40]. The deviations of the excited state fits are well below 40 kHz, and the relative invariance of the values of centrifugal distortion constants between the two excited sates and the ground state are evidence for the validity of the fitting model. Only DK (or DK ) and some sextic level constants could not be determined with confidence and were assumed at values from the ground state. Nevertheless, even though these fits were ultimately successful, we had to resolve several complications. First of all, there was considerable numerical instability when values of A24 and A36 were used as parameters of fit. It turned out that only their average was well determined while the difference was not. The adopted solution was to use the sum and difference of these rotational constants explicitly, as listed in Tables 1 and 2. This ensured numerical
Fig. 5. Dependence of deviation of the A-reduced coupled fit of rotational transitions in v 24 ¼ 1 and v 36 ¼ 1 vibrational states on the difference in rotational constant A between the two states. The two alternative solutions listed in Tables 1 and 2 are indicated.
stability but also revealed very limited sensitivity of the overall deviation of fit to the difference between the A rotational constants for the two excited states, as shown in Fig. 5. In particular, two alternative solutions, labelled I and II, could be identified and are listed in Tables 1 and 2. Solution I was preferred on the basis of standard deviation, but the discrimination from solution II was minimal, at a level of less than 1 kHz in the deviation of fit. By inspecting the predictions we found that many pairs of interacting energy levels in the two studied excited states were subject to considerable mixing. We therefore made a significant number of dedicated measurements targeted at transitions between such levels, and we were even able to measure several transitions that were identified by the quantum number assignment scheme of SPFIT as transitions between the two vibrational states (see Table S3). In spite of this, we were still not able to improve the discrimination between solutions I and II beyond that which is being reported. It
Fig. 4. Illustration of the effect of 5:3 nuclear spin statistical weights for phenylacetylene arising from the presence of two pairs of symmetry-equivalent protons. Each doublet consists of the 444;41 434;40 transition (left) and the 443;41 433;40 transition (right), which would be of similar intensity without the presence of statistical weights. The weights reverse between the ground state and the two excited states, confirming that the latter are both of B symmetry.
Z. Kisiel, A. Kras´nicki / Journal of Molecular Spectroscopy 262 (2010) 82–88 Table 4 Comparison of experimental and calculated vibrational changes (MHz) in rotational constants. Exp.a c
Calc.b
0.7213(20)
0.668
A24 A0 B24 B0 C 24 C 0
4.32(13) 1.69182(8) 1.81846(8)
5.02d 1.572 1.716
A36 A0 B36 B0 C 36 C 0
2.88(13) 2.86755(9) 0.84021(7)
3.74d 2.646 0.752
A A0
a
Values from A-reduction, solution I. Calculated with CFOUR [30] at the MP2/6-31G(d,p) level. A ¼ ðA24 þ A36 Þ=2. d Deperturbed values obtained by subtracting contributions in Eqs. (4) and (5), from the calculated effective values A24 A0 ¼ 173:45 and A36 A0 ¼ 172:09 MHz, see text. b
c
should be mentioned that we did not encounter any lines that were not accounted for in the fits, in that they were either badly shifted or missing, and the fits encompass all transitions that we would have been expected to measure. In an attempt to discriminate more confidently between solutions I and II we turned to anharmonic force field calculations, which are increasingly being used in derivation of semi-experimental equilibrium structures. Although the performance of such calculations for molecules of the size of phenylacetylene has not yet been benchmarked, there are indicators that practicable levels of calculation may already be useful [41]. We used the CFOUR package [30] to calculate the vibrational changes in rotation constants, and the results are summarised in Table 4. We note that the agreement with experiment for B and C rotational constants is excellent, confirming the assignment of the lower vibrational level to v 24 ¼ 1 and of the upper to v 36 ¼ 1. The situation for the A rotational constant is more involved since CFOUR calculates vibrational changes between effective values inclusive of the effects of perturbation, as described, for example, by Eq. 17.7.2 of Ref. [42]. The deperturbed values, in the sense of those obtained from the coupling fits made here, can be obtained by subtracting the contributions to ðAv A0 Þ from the fa24;36 term given by
2A2 a 2 3x224 þ x236 f ; x24 24;36 x224 x236 2A2 a 2 3x236 þ x224 ¼ f : x36 24;36 x236 x224
dðA24 A0 Þ ¼ daA24 ¼
ð4Þ
dðA36 A0 Þ ¼ daA36
ð5Þ
It can be seen from Table 4 that application of Eqs. (4) and (5) leads to values of ðAv A0 Þ which are both satisfactorily close to experiment, and also unambiguously prefer solution I, in which A24 < A36 . 6. Conclusion The present investigation considerably extends the coverage of the known rotational spectrum of the phenylacetylene molecule, as is evident from Fig. 2. The reported spectroscopic constants should allow accurate prediction of the rotational spectrum well into the submillimetre-wave region. The analysis of the strong Coriolis coupling between m24 and m36 modes turned out to be entirely satisfactory, although selection between the two alternative solutions could only be made with confidence on the basis of calculation of the vibrational changes in rotational constants. It is useful to restate the word of warning made in Ref. [19] that in more complex situations a given fit that is acceptable according to the criteria of satisfactory reproduction of the spectrum may not necessarily be the physically most meaningful solution.
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The comparison of the various force field dependant quantities determined presently for phenylacetylene with the results from different calculations (Table 3) shows good agreement. We note that none of the routine diagnostic-level calculations is outstandingly better than others. For example, the MP2 results are more consistent with the experimental fa24;36 , while the DFT result is better for the inertial defect. The MP2/6-31G(d,p) results illustrate the level of consistency between two independent computational packages. We also find a remarkable agreement of the current experimental results with those based on a very rudimentary HF/ 4-21G calculation by Csaszar et al. [33]. The Scaled Quantum Mechanics technique used in that work and based on a combination of results for benzene and acetylene appears to have worked very well. Finally, the use of m36 from Ref. [32] and the present value of DE, allows an estimate of 136.5 cm1 for the wavenumber of the m24 fundamental. Acknowledgments The authors thank Bolesław Kozankiewicz for the sample of phenylacetylene, and also Frank De Lucia and Heinrich Mäder for help with equipment problems. Financial support from the Polish Ministry of Science and Higher Education, Grant No. N-N2020541-33, is gratefully acknowledged. 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://library.osu.edu/sites/ msa/jmsa_hp.htm). References [1] B. Jones, F. Zhang, P. Maksyutenko, A.M. Mebel, R.I. Kaiser, J. Phys. Chem. A 114 (2010) 5256–5262. [2] K. Mimura, M. Ohashi, R. Sugisaki, Earth Planet. Sci. Lett. 133 (1995) 265–269. [3] G.R. Floyd, R.H. Prince, W.W. Duley, J. R. Astron. Soc. Can. 67 (1973) 299–305. [4] J.A. Stearns, T.S. Zwier, E. Kraka, D. Cremer, Phys. Chem. Chem. Phys. 8 (2006) 5317–5327. [5] J.J. Newby, J.A. Stearns, C.-P. Liu, T.S. Zwier, J. Phys. Chem. A 111 (2007) 10914– 10927. [6] B.N. Tran, J.C. Joseph, M. Force, R.G. Briggs, V. Vuitton, J.P. Ferris, Icarus 177 (2005) 106–115. [7] Y.J. Pendleton, L.J. Allamandola, Astrophys. J. Suppl. Ser. 138 (2002) 75–98. [8] Z. Kisiel, E. Białkowska-Jaworska, L. Pszczółkowski, H. Mäder, J. Mol. Spectrosc. 227 (2004) 109–113. [9] W. Zeil, M. Winnewisser, H.K. Bodenseh, H. Buchert, Z. Naturforsch. 15a (1960) 1011–1013. [10] A.P. Cox, I.C. Ewart, W.M. Stigliani, J. Chem. Soc. Faraday Trans. II 71 (1975) 504–514. [11] H.D. Rudolph, H. Dreizler, A. Jaeschke, P. Wendling, Z. Naturforsch. 22a (1970) 940–944. [12] H. Dreizler, H.D. Rudolph, B. Hartke, J. Mol. Struct. 698 (2004) 1–24. [13] I. Medvedev, M. Winnewisser, F.C. De Lucia, E. Herbst, E. Białkowska-Jaworska, L. Pszczółkowski, Z. Kisiel, J. Mol. Spectrosc. 228 (2004) 314–328. [14] Z. Kisiel, J. Kosarzewski, L. Pszczółkowski, Acta Phys. Pol. A 92 (1997) 507–516. [15] T.J. Balle, W.H. Flygare, Rev. Sci. Instrum. 52 (1981) 33–45. [16] A. Kras´nicki, L. Pszczółkowski, Z. Kisiel, J. Mol. Spectrosc. 260 (2010) 57–65. [17] Z. Kisiel, L. Pszczółkowski, I.R. Medvedev, M. Winnewisser, F.C. De Lucia, E. Herbst, J. Mol. Spectrosc. 233 (2005) 231–243. [18] Z. Kisiel, PROSPE – Programs for ROtational SPEctroscopy. Available from:
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