Infrared observation of OC-C2H2, OC-(C2H2)2 and their isotopologues
A.J. Barclay, A. Mohandesi, K.H. Michaelian, A.R.W. McKellar, N. Moazzen-Ahmadia
IInfrared observation of OC-C H , OC-(C H ) and their isotopologues A.J. Barclay, a A. Mohandesi, a K.H. Michaelian, b A.R.W. McKellar, c and N. Moazzen-Ahmadi a a Department of Physics and Astronomy, University of Calgary, 2500 University Drive North West, Calgary, Alberta T2N 1N4, Canada b Natural Resources Canada, CanmetENERGY, 1 Oil Patch Drive, Suite A202, Devon, Alberta T9G 1A8, Canada c National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada
Abstract
The fundamental band for the OC-C H dimer and two combination bands involving the intermolecular bending modes and in the carbon monoxide CO stretch region are re-examined. Spectra are obtained using a pulsed supersonic slit jet expansion probed with a mode-hop free tunable infrared quantum cascade laser. Analogous bands for OC-C D and the fundamental for OC–DCCH as an impurity are also observed and analysed. A much weaker band in the same spectral region is assigned to a new mixed trimer, CO-(C H ) . The trimer band is composed uniquely of a -type transitions, establishing that the CO monomer is nearly aligned with the a -inertial axis. The observed rotational constants agree well with ab initio calculations and a small inertial defect value indicates that the trimer is planar. The structure is a compromise between the T-shaped structure of free acetylene dimer and the linear geometry of free OC-C H A similar band for the fully deuterated isotopologue CO-(C D ) confirms our assignment. Address for correspondence: Prof. N. Moazzen-Ahmadi, Department of Physics and Astronomy, University of Calgary, 2500 University Drive North West, Calgary, Alberta T2N 1N4, Canada. * Corresponding author. Tel: 1-403-220-5394 . Introduction There are a fair number of studies of the binary complex of carbon monoxide with acetylene. Initial studies were made through observation of 3 m infrared spectra of O C- HCCH and O C-HCCH which showed that the dimer is linear, and that the carbon atom of the CO monomer lies between the center of mass of CO and that of the entire complex [1,2]. The infrared rotational constants quickly led to detection of pure rotational spectra for several isotopologues [3,4,5]. This body of data confirmed that OC-C H is linear, with acetylene acting as the proton donor in forming the intermolecular bond. A second 3 m study of OC-HCCH was made by Beck et al. [6] with higher resolution and sensitivity. They observed extensive perturbations which were attributed to high density of states at 3300 cm -1 . These authors then argued that as density of states increases the probability of perturbation with nearby levels grows until at some point the states are so badly perturbed that the spectrum will appear to be random and chaotic. This claim was later proven to be incorrect by observation of infrared spectra of systems with higher density of states, such as deuterated species, which hardly show any perturbation [7]. It was then concluded that the extensive perturbations in the normal acetylene complex are due to a simple coincidence of energy levels, rather than any anomaly in coupling strengths or densities of states. Later infrared studies were made in the 4.7 m CO stretching region [8,9]. In contrast to the extensive perturbations observed in the 3 m region, spectra in the CO stretching fundamental showed only a single small perturbation. More recently, spectroscopic studies of OC-HCCH were extended by Rivera-Rivera et al. [10] to include the intermolecular bending modes and in the carbon monoxide CO stretch region. They used quantum cascade lasers to measure , + , + , and + (for consistency, we retain here their vibrational mode otation for OC-HCCH: is the C-O stretch ( -1 ), is the van der Waals stretch (
50 cm -1 ), and and are the van der Waals bends (
70 and 20 cm -1 )). Although Table 1 in their work [10] gives experimentally determined spectroscopic constants for the four vibrational states involved, Rivera-Rivera et al. do not provide a full analysis of + , only briefly mentioning that a preliminary analysis indicated significant perturbations in the upper state. We show below that, at least for J -values up to 11, this is not the case. There are virtually no high resolution spectroscopic data on larger clusters involving CO and other small linear molecules. One exception is the recent detection of CO-(CO ) [11] where a quasi T-shaped trimer structure is observed. This structure effectively combines the structures of the CO -CO dimer (planar slipped parallel) and the CO -CO dimer (T-shaped, with CO as the stem of the T, and adjacent C atoms). In this paper, we re-examine the , + , and + bands of OC-HCCH, and provide new data for the same three bands of OC-DCCD and the fundamental of OC-DCCH. We show that, although the bands for OC-HCCH exhibit small perturbations, they can be analysed to experimental accuracy using effective parameters. This is not possible for OC-DCCD because the upper state of + shows extensive perturbations for both e and f parity states, indicating strong coupling with a “dark” vibrational state, and resulting in a several perturbation-allowed lines which are clearly visible. Thanks to the high signal-to-noise ratio of our spectra, we were also able to observe a much weaker a -type band in the CO stretching fundamental region. A ro-vibrational analysis of this band indicates that it is due to a planar isomer of the mixed trimer OC-(C H ) . This conclusion is further confirmed by the presence of an analogous band for OC-(C D ) in the same spectral region and by ab initio calculations at MP2/cc-pvtz level. This structure, which orresponds to an asymmetric rotor with C s point group symmetry, preserves fairly closely the T-shaped geometry of acetylene dimer and the linear geometry of OC-HCCH complex. In many respects, this structure parallels previously reported planar isomers of OCS-(C H ) [12] and N O-(C H ) [13].
2. Observed spectra
The spectra were recorded at the University of Calgary as described previously [14-16], using a pulsed supersonic slit jet apparatus and a Daylight Solutions quantum cascade laser. A typical gas mixture consisted of about 0.2 % CO and 0.2 % C H in helium carrier gas, and a jet backing pressure of 9 atmospheres were used. Spectral assignment and simulation were made using PGOPHER [17]. 2.1 OC-HCCH and OC-DCCD results The experimental spectra for the stretching fundamental (a - ro-vibrational band) of OC-HCCH (top trace) and OC-DCCD (third trace) are illustrated in Fig. 1. The simulated spectra (second and fourth trace) have a rotational temperature of 2.2 K. Due to the relatively low rotational temperature, we were able to observe and include only 24 lines for OC-HCCH and 25 for OC-DCCD in the final analyses. Figure 2 shows a segment of the experimental spectrum for the + combination band of OC-HCCH (top trace), a linear molecule - band with a characteristic Q -branch. We found no evidence for any sizeable perturbations, and the band can therefore be well simulated using effective parameters. The simulated spectrum for a rotational temperature of 2.2 K is shown in the second trace in Fig. 2. The corresponding experimental and simulated spectra for OC-DCCD are shown in the third and fourth traces, respectively. We assigned 35 lines for OC-HCCH and the same number for OC-DCCD. igure 1: Observed (first and third trace) spectra of the fundamental band for OC-HCCH and OC-DCCD. The simulated spectra (second and fourth trace) were made at a rotational temperature of 2.2 K Figure 2: Observed (first and third trace) spectra of the + combination band for OC-HCCH and OC-DCCD. The simulated spectra (second and fourth trace) were made at a rotational temperature of 2.2 K. The blank regions in the experimental spectra are CO monomer lines. Figure 3: Observed (first and third trace) spectra of the + combination band for OC-HCCH and OC-DCCD. The simulated spectra (second and fourth trace) were made at a rotational temperature of 2.2 K. The blank region in the OC-DCCD experimental spectrum is a CO monomer line. he combination band + is also a - band. A segment of this spectrum is shown in the top trace of Fig. 3. Here, the strong, unresolved and slightly red shaded feature at 2219.769 cm -1 is the Q -branch. Perhaps the striking difference between this Q -branch and the fully resolved Q -branch of the + band led Rivera-Rivera et al. [10] to conclude that + is badly perturbed. However, we are able to analyse this band with no difficulty using effective parameters and including 22 lines from the P and R branches. Since our effective rotational temperature is significantly lower than theirs, it remains possible that the perturbations mentioned by Rivera-Rivera et al. [10] affected only transitions with J -values higher than about 11. Spectroscopic constants for the , + , and + bands of OC-HCCH were retrieved by keeping the ground rotational constants fixed at their microwave values [5] and varying the rotational constants of the three excited vibrational states. A total of 81 frequencies were used in the analysis and 9 parameters were varied. The l -doubling parameter q for + was varied step-wise to reproduce the slightly red-shaded Q -branch in the top trace of Fig. 3. The rms error of the fit was 0.00052 cm -1 . The molecular parameters obtained are listed in Table 1 and detailed assignments are given in the supplementary material. Table 1. Molecular parameters for OC-HCCH (in cm -1 ). a Ground state
Excited state fundamental Excited state + combination Excited state + combination B b D J b b q c a Uncertainties (1 ) in parentheses are in units of the last quoted digit. b Held fixed at the value determined from rotational spectrum [5]. c Varied step-wise to reproduce the slight red-shaded Q-branch. See Fig. 3
The + combination band of OC-DCCD is strongly perturbed (see the third trace in Fig. 3). The clearest indication for this is in the P - and R -branches where the P -branch shows a rapid decrease in rotational spacing and eventual turn around at P (10) with a concomitant rapid increase in rotational spacing in the R -branch at higher J values. The rotational progression in the Q -branch is also very irregular. The indication is that the perturbing “dark” state lies at lower energy, and analysis of this band, including 38 transitions (with four perturbation allowed lines) reveals that the origin of the dark state is located about 2 cm -1 below the + band center. A total of 97 transitions for the four vibrational bands of OC-DCCD were used in the analysis and 17 parameters were varied. The fit had an rms error of 0.00076 cm -1, about twice the estimated (relative) experimental accuracy of 0.0003 cm -1 . The main contribution to the excess rms came rom transitions in the + band. The molecular parameters obtained are listed in Table 2 and detailed assignments are given in the supplementary material. Table 2. Molecular parameters for OC-DCCD (in cm -1 ). a Ground state
Excited state fundamental Excited state + combination Excited state + combination “Dark” state c B b D J b q a Uncertainties (1 ) in parentheses are in units of the last quoted digit. b Held fixed at the values determined from rotational spectrum [4]. c The interaction Hamiltonian connecting the dark state and + is given by H J l J l J J . The values for the interaction parameters were determined to be cm -1 , cm -1 , cm -1 . Figure 4: Observed (top trace) spectra of fundamental band for OC-(C H ) . The simulated spectrum (bottom trace) was made at a rotational temperature of 2.2 K and a 0.003 cm -1 Gaussian line width (FWHM).
Figure 5: Observed (top trace) spectra of fundamental band for OC-(C D ) . The simulated spectrum (bottom trace) was made at a rotational temperature of 2.2 K and a 0.003 cm -1 Gaussian line width (FWHM). The lines marked by black arrows are the transitions in the CO stretching fundamental band of OC-DCCH. .2 OC-(C H ) and OC-(C D ) results After accounting for the known dimer transitions in the fundamental bands, we were left with a large number of weak unassigned lines in the same spectral region for both OC-HCCH and OC-DCCD. This can be seen in the first and third traces in Fig. 1. The relatively strong feature between the rotational lines P(3) and P(4) of the fundamental, evident in both the OC-HCCH and OC-DCCD spectra, led us to conclude that this is the Q -branch of an a -type band of a complex containing CO and acetylene. We eventually assigned this band to a new mixed trimer, OC-(C H ) . The top trace in Fig. 4 shows a close-up of the top trace in Fig. 1. The strongest features (off scale) are the rotational lines of OC-HCCH. The broad feature at about 2149.04 cm -1 is the a -type Q -branch of the mixed trimer and the lines to higher frequency, whose intensities are magnified by a factor of 3, constitute the R -branch. The lower trace is the simulated spectrum with a rotational temperature of 2.2 K and a Gaussian line width of 0.003 cm -1 . The simulation indicates that this band consists uniquely of a -type transitions, and hence the a -inertial axis of the trimer must approximately coincide with the carbon monoxide C-O axis. Analogous spectra for OC-(C D ) shown in Fig. 5 lead to the same conclusion. Ultimately we assigned a total of 48 observed lines in terms of 52 transitions of CO-(C H ) , with values of J and K a ranging up to 11 and 4, respectively. These were used in a least-squares fit to determine the set of 7 parameters listed in Table 3. The average error in the fit was 0.00048 cm -1 . This fit was obtained without introducing any centrifugal distortion parameters. The assignments are given as Supplementary data. Similarly, we assigned 42 frequencies in terms of 49 transitions of OC-(C D ) with values of J and K a ranging up to 10 and 4, respectively. The least-squares fit gave an average error of 0.00045 cm -1 with a set of 7 parameters which are listed in Table 3. Again, no entrifugal distortion parameters were required. The assignments are given as Supplementary data. Table 3. Molecular parameters for CO-(C H ) and CO-(C D ) . a This work
MP2 /cc-pvtz CO-(C H ) CO-(C D ) CO-(C H ) CO-(C D ) / cm -1 A' / MHz 2668.8(64) 2536.1(69) B' / MHz 1405.04(57) 1315.34(52) C' / MHz 918.49(76) 862.12(31) A" / MHz 2661.4(64) 2528.4(69) 2715 2552 B" / MHz 1410.23(65) 1320.85(67) 1446 1351 C" / MHz 920.61(95) 863.23(33) 944 883 Δ" / amu Å a Uncertainties (1 ) in parentheses are in units of the last quoted digit. . Discussion and conclusions The lines marked by arrows in Fig. 5 are transitions in the CO stretching fundamental of OC-DCCH due to singly deuterated acetylene existing as an impurity in the C D sample. We assigned 17 transitions from this band. The analysis was made with the rotational parameters fixed at their microwave values [3]. The resulting parameters for the excited state are: cm -1 , ' 0.0463423(57) B cm -1 , D' 9.5(45) 10 cm -1 . The rms error of the fit was 0.00028 cm -1 . The assignments are given as Supplementary data. Several ab initio calculations have been reported for carbon monoxide–acetylene [18,19,20,21]. All verify that OC–HCCH is linear, but the reported intermolecular frequencies are not very consistent, with a large spread between the various theoretical values and significant differences from observed frequencies (see Table 1 of Ref. [10]). Perhaps the most reliable prediction for the intermolecular frequencies to date is that of Rivera-Rivera et al. [10], who used experimental rovibrational data involving together with other spectroscopic information to generate a four-dimensional morphed potential. This potential was then used to further characterize the structure and frequencies for other intermolecular modes. Their predictions for OC-HCCH were: e D cm -1 , D cm -1 , cm -1 (the hydrogen bond stretching frequency), and cm -1 (the higher frequency intermolecular bend). The experimental intermolecular frequencies from Ref. [10] and from the present work are listed in Table 4. Because the intermolecular and intramolecular modes do not couple strongly, we expect the intermolecular frequencies for in the ground vibrational state (20.48361(20) cm -1 ) and in the excited state (19.961(1) cm -1 ) to differ only slightly, as is indeed the case. So it is reasonable to assume that other excited state intermolecular frequencies isted in Table 4 are also close to their values in the ground vibrational state. We note that this assertion is valid for many other binary clusters [22]. Table 4. Observed intermolecular frequencies (in cm -1 ) for OC-HCCH and OC-DCCD in the excited state OC-HCCH OC-DCCD This work Ref. [10] a This work a The observed intermolecular frequency for in the ground vibrational state is 20.48361(20) cm -1 . As mentioned previously, the upper state of the + combination band of OC-DCCD is strongly perturbed, and our analysis indicates that the origin of the perturbing state is located at 2216 cm -1 . Our best guess for a perturbing state with correct symmetry is + + . This assignment would result in a value of cm -1 for the hydrogen bond stretching frequency, which seems reasonable for OC-DCCD since the predicted value for OC-HCCH in Ref. [10] is cm -1 . This (or indeed any other) vibrational assignment of the dark state does not explain the anomalously large values of B and q reported in Table 4 for this state. Explanation of this anomaly may have to wait for the availability of higher level ab initio calculations which fully explore the complete intermolecular potential surfaces for CO-C H and CO-C D . We are aware hat such a surface is under construction and to be published in the near future [23]. Such calculations may also help to explain why the O-bonded isomer, CO-HCCH, has not been experimentally detected. We are very confident that the spectra observed in Fig. 4 belong to the planar mixed trimer CO-(C H ) . This conclusion is supported by the small inertial defect of 0.72 amu Å , by the good fit to the observed spectra, by consistent isotope shifts, and by the observed a -type selection rules. For further verification, we made molecular structure calculations using the Gaussian-09 program. The calculations were carried out at the second order level of Moller-Plesset perturbation theory (MP2) in the same manner as those reported in Ref. [11] for CO-(CO ) . The resulting rotational parameters for OC-HCCH and OC-DCCD are listed in Table 4. They compare favorably with their experimental counterparts and help to confirm a planar structure. This structure and its inertial axes are illustrated in Fig. 6. As can be seen, the CO monomer lies close to the a -inertial axis, consistent with the observed a -type structure of the band. Although analysis of our results confirms the geometry shown in Fig. 6 and gives structural information for the trimer, they are not sufficient for determination of a unique experimental structure, which would require six or more rotational parameters. Here, we only have four independent rotational parameters. Finally, it should be noted that we observe no evidence for tunneling splitting in the spectra of the trimer and conclude that the large amplitude tunneling motion that exists in the free acetylene dimer is quenched by presence of the CO monomer. This is also the case for OCS-(C H ) [12] and N O-(C H ) [13]. Figure 6: The mixed CO-(C H ) trimer and its inertial axes. In conclusion, mid-infrared studies of a new planar isomer of the mixed trimer CO-(C H ) , are reported in the carbon monoxide CO stretch region using a mode-hop free tunable infrared quantum cascade laser. The trimer band is composed uniquely of a -type transitions, establishing that the CO monomer is nearly aligned with the a -inertial axis. The observed rotational constants agree well with ab initio calculations and a small value of the inertial defect indicates that the trimer is planar. This structure combines the T-shaped structure of free acetylene dimer and the linear geometry of free OC-C H Analysis of a similar band for the fully deuterated isotopologue CO-(C D ) confirms our assignment. In addition, the fundamental band of the linear dimer OC-C H , and two combination bands involving the intermolecular modes and , are re-examined. New spectra are observed for OC-C D , and its ntermolecular bending frequencies are determined by observation of combination bands. Finally, the fundamental band OC–DCCH, observed as an impurity in the OC-C D spectrum, is observed and analysed. Acknowledgements
The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. We also thank K. Esteki and J. Norooz Oliaee for help with the experiments.
Appendix A. Supplementary data
Supplementary data associated with this article can be found below. eferences [1] M.D. Marshall, D.G. Prichard, J.S. Muenter, J. Chem. Phys. 90 (1989) 6049. [2] M.D. Marshall, J. Kim, T.A. Hu, L.H. Sun, J.S. Muenter, J. Chem. Phys. 94 (1991) 6334. [3]A.C. Legon, A.L. Wallwork, J.W. Bevan, Z. Wang, Chem. Phys. Lett. 180 (1991) 57. [4] M.A. Roehrig, S.G. Kukolich, Chem. Phys. Lett. 188 (1992) 232. [5] T.C. Germann, S.L. Tschopp, H.S. Gutowsky, J. Chem. Phys. 97 (1992) 1619. [6] R. D. Beck, A. G. Maki, S.-H. Tseng, R. O. Watts, J. Mol. Spectrosc. 158 (1993) 306. [7] I. Hunig, L. Oudejans, R. E. Miller, J. Mol. Spectrosc. 204 (2000) 148. [8] Y. Kawashima, K. Nishizawa, Chem. Phys. Lett. 253 (1996) 77. [9] J.A. Anstey, M.D. Brookes, A.R.W. McKellar, J. Mol. Spectrosc. 194 (1999) 281. [10] L.A. Rivera-Rivera, B.A. McElmurry, Z. Wang, I.I. Leonov, R.R. Lucchese, J.W. Bevan, Chem. Phys. Lett. 522 (2012) 17. [11] A.J. Barclay, A.R.W. McKellar, N. Moazzen-Ahmadi, Chem. Phys. Lett. 677 (2017) 127. [12] J. Norooz Oliaee, A.R.W. McKellar, N. Moazzen-Ahmadi, Chem. Phys. Lett. 512 (2011) 167. [13] S. Sheybani-Deloui, M. Yousefi, J. Norooz Oliaee, A.R.W. McKellar, N. Moazzen-Ahmadi, J. Mol. Spectrosc. 306 (2014) 6. [14] M. Dehghany, M. Afshari, Z. Abusara, C. Van Eck, N. Moazzen-Ahmadi, J. Mol. Spectrosc. 247 (2008) 123. [15] M. Rezaei, K.H. Michaelian, N. Moazzen-Ahmadi, J. Chem. Phys. 136 (2012) 124308. [16] M. Rezaei, S. Sheybani-Deloui, N. Moazzen-Ahmadi, K.H. Michaelian, A.R.W. McKellar, J. Phys. Chem. A 117 (2013) 9612. [17] C.M. Western, PGOPHER, a program for simulating rotational structure version 8.0, 2014, University of Bristol Research Data Repository, doi:10.5523/bris.huflggvpcuc1zvliqed497r2 [18] S.A.C. McDowell, A.D. Buckingham, Chem. Phys. Lett. 182 (1991) 551. [19] C.A. Parish, J.D. Augspurger, C.E. Dykstra, J. Phys. Chem. 96 (1992) 2069. [20] L. Adamowicz, Chem. Phys. Lett. 192 (1992) 199. [21] W.B. De Almeida, J.S. Craw, Chem. Phys. 169 (1993) 185. [22] N. Moazzen-Ahmadi, A.R.W. McKellar, Int. Rev. Phys. Chem. 32 (2013) 611. [23] R. Dawes, X.-G. Wang, T. Carrington, Jr., private communication.
Supplementary Material for: Infrared observation of OC-C2H2, OC-(C2H2)2 and their isotopologues A.J. Barclay, A. Mohandesi, K.H. Michaelian, A.R.W. McKellar, N. Moazzen-Ahmadi Table A-1. Observed and calculated transitions in the C-O stretching fundamental band of OC-HCCH dimer (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 10 e 11 e 2148.3016 2148.3010 0.0007 9 e 10 e 2148.3973 2148.3971 0.0002 8 e 9 e 2148.4928 2148.4930 -0.0002 6 e 7 e 2148.6857 2148.6840 0.0017 5 e 6 e 2148.7796 2148.7791 0.0006 4 e 5 e 2148.8738 2148.8738 0.0000 3 e 4 e 2148.9682 2148.9683 -0.0000 2 e 3 e 2149.0622 2149.0624 -0.0002 1 e 2 e 2149.1561 2149.1563 -0.0002 0 e 1 e 2149.2495 2149.2498 -0.0003 1 e 0 e 2149.4354 2149.4359 -0.0005 2 e 1 e 2149.5279 2149.5285 -0.0006 3 e 2 e 2149.6202 2149.6208 -0.0006 4 e 3 e 2149.7123 2149.7127 -0.0004 5 e 4 e 2149.8045 2149.8043 0.0003 6 e 5 e 2149.8969 2149.8955 0.0014 7 e 6 e 2149.9856 2149.9864 -0.0008 8 e 7 e 2150.0765 2150.0770 -0.0004 9 e 8 e 2150.1669 2150.1672 -0.0003 10 e 9 e 2150.2579 2150.2570 0.0009 11 e 10 e 2150.3463 2150.3465 -0.0001 12 e 11 e 2150.4349 2150.4356 -0.0007 13 e 12 e 2150.5241 2150.5243 -0.0003 14 e 13 e 2150.6125 2150.6127 -0.0002 ************************************************
Table A-2. Observed and calculated transitions in nu3+nu9 combination band of OC-HCCH dimer in the region of C-O stretching fundamental (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 10 e 11 e 2168.4023 2168.4021 0.0002 9 e 10 e 2168.4731 2168.4730 0.0001 8 e 9 e 2168.5460 2168.5460 0.0000 7 e 8 e 2168.6213 2168.6213 0.0000 6 e 7 e 2168.6987 2168.6987 -0.0001 5 e 6 e 2168.7785 2168.7784 0.0001 4 e 5 e 2168.8605 2168.8603 0.0002 3 e 4 e 2168.9446 2168.9445 0.0000 2 e 3 e 2169.0309 2169.0310 -0.0000 1 e 2 e 2169.1196 2169.1197 -0.0001 1 f 1 e 2169.3066 2169.3066 -0.0000 2 f 2 e 2169.3120 2169.3121 -0.0001 3 f 3 e 2169.3203 2169.3203 0.0000 4 f 4 e 2169.3311 2169.3313 -0.0002 5 f 5 e 2169.3450 2169.3450 0.0000 6 f 6 e 2169.3613 2169.3614 -0.0000 7 f 7 e 2169.3805 2169.3804 0.0001 1 e 0 e 2169.3997 2169.3993 0.0003 8 f 8 e 2169.4019 2169.4022 -0.0002 9 f 9 e 2169.4268 2169.4266 0.0002 11 f 11 e 2169.4833 2169.4833 0.0000 2 e 1 e 2169.4970 2169.4971 -0.0001 12 f 12 e 2169.5154 2169.5155 -0.0000 3 e 2 e 2169.5968 2169.5970 -0.0002 4 e 3 e 2169.6993 2169.6992 0.0001 5 e 4 e 2169.8036 2169.8036 0.0000 6 e 5 e 2169.9101 2169.9102 -0.0001 7 e 6 e 2170.0189 2170.0190 -0.0001 8 e 7 e 2170.1298 2170.1299 -0.0001 9 e 8 e 2170.2431 2170.2430 0.0001
10 e 9 e 2170.3583 2170.3581 0.0002 11 e 10 e 2170.4747 2170.4753 -0.0006 12 e 11 e 2170.5950 2170.5946 0.0005 13 e 12 e 2170.7157 2170.7158 -0.0002 14 e 13 e 2170.8387 2170.8390 -0.0003 15 e 14 e 2170.9644 2170.9642 0.0002 ************************************************
Table A-3. Observed and calculated transitions in nu3+nu8 combination band of OC-HCCH dimer in the region of C-O stretching fundamental (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 10 e 11 e 2218.8297 2218.8294 0.0003 9 e 10 e 2218.9244 2218.9244 0.0000 8 e 9 e 2219.0178 2219.0193 -0.0015 7 e 8 e 2219.1149 2219.1140 0.0009 6 e 7 e 2219.2091 2219.2085 0.0006 5 e 6 e 2219.3034 2219.3029 0.0005 4 e 5 e 2219.3971 2219.3970 0.0001 3 e 4 e 2219.4907 2219.4909 -0.0002 2 e 3 e 2219.5842 2219.5846 -0.0004 1 e 2 e 2219.8639 2219.8643 -0.0003 1 e 1 e 2219.9568 2219.9570 -0.0002 2 e 2 e 2220.0495 2220.0495 -0.0000 3 e 3 e 2220.1421 2220.1417 0.0003 4 e 4 e 2220.2341 2220.2337 0.0003 5 e 5 e 2220.3266 2220.3255 0.0011 6 e 6 e 2220.4153 2220.4170 -0.0017 7 e 7 e 2220.5082 2220.5083 -0.0002 1 e 0 e 2220.5995 2220.5994 0.0001 8 e 8 e 2220.6904 2220.6903 0.0001 9 e 9 e 2220.7812 2220.7810 0.0002 11 e 11 e 2220.8713 2220.8714 -0.0001 ************************************************
Table A-4. Observed and calculated transitions in the C-O stretching fundamental band of OC-DCCD dimer (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 11 e 12 e 2148.4928 2148.4930 -0.0002 9 e 10 e 2148.6760 2148.6762 -0.0002 8 e 9 e 2148.7673 2148.7674 -0.0001 7 e 8 e 2148.8583 2148.8584 -0.0001 6 e 7 e 2148.9490 2148.9491 -0.0001 5 e 6 e 2149.0394 2149.0395 -0.0001 4 e 5 e 2149.1296 2149.1296 0.0000 3 e 4 e 2149.2195 2149.2195 -0.0000 2 e 3 e 2149.3091 2149.3091 0.0000 1 e 2 e 2149.3983 2149.3983 0.0000 0 e 1 e 2149.4873 2149.4873 -0.0000 1 e 0 e 2149.6644 2149.6644 0.0001 2 e 1 e 2149.7525 2149.7525 0.0000 3 e 2 e 2149.8403 2149.8402 0.0001 4 e 3 e 2149.9277 2149.9277 0.0000 5 e 4 e 2150.0149 2150.0148 0.0001 6 e 5 e 2150.1017 2150.1016 0.0001 7 e 6 e 2150.1882 2150.1882 0.0001 8 e 7 e 2150.2744 2150.2743 0.0000 9 e 8 e 2150.3602 2150.3602 -0.0000 10 e 9 e 2150.4460 2150.4458 0.0002 11 e 10 e 2150.5312 2150.5310 0.0002 12 e 11 e 2150.6161 2150.6159 0.0002 13 e 12 e 2150.7006 2150.7006 0.0001 14 e 13 e 2150.7847 2150.7849 -0.0001 ************************************************
Table A-5. Observed and calculated transitions in nu3+nu9 combination band of OC-DCCD dimer in the region of C-O stretching fundamental (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 10 e 11 e 2167.6845 2167.6848 -0.0002 9 e 10 e 2167.7577 2167.7579 -0.0002 8 e 9 e 2167.8325 2167.8327 -0.0002 7 e 8 e 2167.9092 2167.9093 -0.0001 6 e 7 e 2167.9874 2167.9875 -0.0002 5 e 6 e 2168.0674 2168.0675 -0.0001 4 e 5 e 2168.1491 2168.1493 -0.0002 3 e 4 e 2168.2326 2168.2327 -0.0002 2 e 3 e 2168.3179 2168.3179 -0.0000 1 f 2 e 2168.4959 2168.4958 0.0001 1 f 1 e 2168.5002 2168.5002 0.0001 2 f 2 e 2168.5068 2168.5067 0.0001 3 f 3 e 2168.5156 2168.5155 0.0001 4 f 4 e 2168.5265 2168.5265 0.0001 5 f 5 e 2168.5397 2168.5396 0.0001 6 f 6 e 2168.5549 2168.5548 0.0000 7 f 7 e 2168.5723 2168.5723 0.0001 1 e 0 e 2168.5841 2168.5840 0.0001 8 f 8 e 2168.5919 2168.5918 0.0001 9 f 9 e 2168.6136 2168.6134 0.0001 11 f 11 e 2168.6371 2168.6372 -0.0001 2 f 1 e 2168.6631 2168.6630 0.0001 12 e 12 e 2168.6762 2168.6761 0.0001 3 f 2 e 2168.6906 2168.6909 -0.0002 4 e 3 e 2168.7701 2168.7700 0.0001 5 e 4 e 2168.8657 2168.8656 0.0001 6 e 5 e 2168.9630 2168.9629 0.0001 7 e 6 e 2169.0619 2169.0619 -0.0000 8 e 7 e 2169.1626 2169.1625 0.0000 9 e 8 e 2169.2649 2169.2648 0.0001
10 e 9 e 2169.3688 2169.3688 0.0001 11 e 10 e 2169.4743 2169.4744 -0.0000 12 e 11 e 2169.5817 2169.5815 0.0001 13 e 12 e 2169.6904 2169.6902 0.0002 14 e 13 e 2169.8005 2169.8005 0.0000 ************************************************
Table A-6. Observed and calculated transitions in nu3+nu8 combination band of OC-DCCD dimer in the region of C-O stretching fundamental (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 8 f 8 e 2217.4334 2217.4346 -0.0012 Perturbation allowed transition 9 e 10 e 2217.4420 2217.4439 -0.0018 8 e 9 e 2217.4647 2217.4658 -0.0011 10 e 11 e 2217.4894 2217.4890 0.0005 7 e 8 e 2217.5192 2217.5191 0.0001 6 e 7 e 2217.5883 2217.5876 0.0008 5 e 6 e 2217.6651 2217.6642 0.0009 9 f 9 e 2217.7092 2217.7068 0.0023 Perturbation allowed transition 4 e 5 e 2217.7460 2217.7456 0.0005 3 e 4 e 2217.8299 2217.8298 0.0001 10 f 10 e 2217.8914 2217.8911 0.0003 2 e 3 e 2217.9155 2217.9159 -0.0004 11 f 11 e 2217.9837 2217.9862 -0.0026 1 e 2 e 2218.0025 2218.0032 -0.0007 12 f 12 e 2218.0375 2218.0363 0.0011 1 f 1 e 2218.1810 2218.1811 -0.0002 2 f 2 e 2218.1828 2218.1837 -0.0008 3 f 3 e 2218.1876 2218.1880 -0.0004 4 f 4 e 2218.1949 2218.1950 -0.0001 5 f 5 e 2218.2062 2218.2061 0.0001 6 f 6 e 2218.2245 2218.2243 0.0002 7 f 7 e 2218.2565 2218.2564 0.0001 1 e 0 e 2218.2685 2218.2692 -0.0008 8 f 8 e 2218.3192 2218.3190 0.0002 2 e 1 e 2218.3590 2218.3593 -0.0003 3 e 2 e 2218.4510 2218.4506 0.0004 9 f 9 e 2218.4554 2218.4544 0.0010 4 e 3 e 2218.5447 2218.5436 0.0011 10 e 9 e 2218.6142 2218.6133 0.0009 Perturbation allowed transition 5 e 4 e 2218.6410 2218.6396 0.0014
10 f 10 e 2218.7237 2218.7246 -0.0009 Perturbation allowed transition 7 e 6 e 2218.8497 2218.8489 0.0008 11 e 10 e 2218.8699 2218.8727 -0.0028 8 e 7 e 2218.9723 2218.9728 -0.0005 12 e 11 e 2219.0624 2219.0605 0.0019 9 e 8 e 2219.1266 2219.1279 -0.0013 10 e 9 e 2219.3513 2219.3500 0.0013 ************************************************ Table A-7. Observed and calculated transitions in the C-O stretching fundamental band of OC-DCCH dimer (units of 1/cm). ************************************************ J' symm J" symm Obs. Calc. Obs-Calc ************************************************ 7 e 8 e 2148.813 2148.8133 -0.0003 6 e 7 e 2148.908 2148.9084 -0.0004 5 e 6 e 2149.002 2149.0032 -0.0004 4 e 5 e 2149.098 2149.0978 0.0005 3 e 4 e 2149.191 2149.1920 -0.0001 2 e 3 e 2149.286 2149.2860 0.0002 1 e 2 e 2149.379 2149.3796 0.0000 0 e 1 e 2149.472 2149.4730 -0.0003 1 e 0 e 2149.658 2149.6587 0.0003 4 e 3 e 2149.934 2149.9347 0.0000 5 e 4 e 2150.026 2150.0261 -0.0001 6 e 5 e 2150.117 2150.1172 0.0001 7 e 6 e 2150.208 2150.2079 0.0002 8 e 7 e 2150.298 2150.2984 0.0000 9 e 8 e 2150.388 2150.3885 0.0004 10 e 9 e 2150.478 2150.4783 0.0000 11 e 10 e 2150.567 2150.5679 -0.0002 ************************************************
Table A-8. Observed and calculated transitions in the C-O stretching fundamental band of OC-(C2H2)2 trimer (units of 1/cm). ************************************************** J' Ka' Kc' J" Ka" Kc" Observed Calculated Obs-Calc ************************************************** 8 3 6 9 3 7 2148.3235 2148.3235 0.0000 7 2 5 8 2 6 2148.3559 2148.3561 -0.0002 7 2 5 8 2 6 2148.3562 2148.3561 0.0001 5 2 3 6 2 4 2148.5083 2148.5081 0.0002 5 3 2 6 3 3 2148.5223 2148.5223 0.0000 4 2 2 5 2 3 2148.5948 2148.5947 0.0001 4 2 3 5 2 4 2148.6421 2148.6431 -0.0010 3 3 1 4 3 2 2148.7094 2148.7085 0.0008 3 2 2 4 2 3 2148.7154 2148.7162 -0.0008 3 0 3 4 0 4 2148.7425 2148.7424 0.0002 2 1 1 3 1 2 2148.7685 2148.7687 -0.0001 2 0 2 3 0 3 2148.8047 2148.8046 0.0001 2 1 2 3 1 3 2148.8175 2148.8173 0.0002 1 1 0 2 1 1 2148.8519 2148.8523 -0.0005 1 1 1 2 1 2 2148.8861 2148.8851 0.0010 7 3 5 7 3 4 2148.9366 2148.9363 0.0003 0 0 0 1 0 1 2148.9473 2148.9463 0.0010 6 3 4 6 3 3 2148.9806 2148.9814 -0.0008 1 0 1 0 0 0 2149.1021 2149.1016 0.0005 2 1 2 1 1 1 2149.1633 2149.1630 0.0003 2 0 2 1 0 1 2149.1752 2149.1750 0.0002 2 1 1 1 1 0 2149.1950 2149.1954 -0.0004 3 1 3 2 1 2 2149.2296 2149.2299 -0.0003 3 0 3 2 0 2 2149.2419 2149.2418 0.0001 3 2 1 2 2 0 2149.2711 2149.2714 -0.0003 3 1 2 2 1 1 2149.2775 2149.2777 -0.0001 4 1 4 3 1 3 2149.2947 2149.2946 0.0000 4 0 4 3 0 3 2149.3031 2149.3030 0.0001 4 2 3 3 2 2 2149.3303 2149.3311 -0.0008 5 2 4 4 2 3 2149.4020 2149.4022 -0.0001 6 0 6 5 0 5 2149.4212 2149.4215 -0.0003
5 1 4 4 1 3 2149.4261 2149.4270 -0.0009 5 2 3 4 2 2 2149.4483 2149.4486 -0.0003 6 2 5 5 2 4 2149.4704 2149.4704 -0.0000 7 1 7 6 1 6 2149.4812 2149.4804 0.0008 7 0 7 6 0 6 2149.4812 2149.4812 -0.0001 6 1 5 5 1 4 2149.4912 2149.4911 0.0001 6 3 4 5 3 3 2149.4970 2149.4975 -0.0004 6 3 3 5 3 2 2149.5214 2149.5216 -0.0002 8 0 8 7 0 7 2149.5411 2149.5412 -0.0001 8 1 8 7 1 7 2149.5411 2149.5409 0.0003 7 1 6 6 1 5 2149.5501 2149.5499 0.0002 7 3 5 6 3 4 2149.5720 2149.5720 0.0001 7 4 3 6 4 2 2149.5917 2149.5909 0.0008 9 1 9 8 1 8 2149.6010 2149.6011 -0.0001 9 0 9 8 0 8 2149.6010 2149.6012 -0.0002 7 3 4 6 3 3 2149.6134 2149.6134 -0.0001 8 2 6 7 2 5 2149.6781 2149.6776 0.0005 8 3 5 7 3 4 2149.7025 2149.7025 0.0000 9 4 6 8 4 5 2149.7394 2149.7394 -0.0000 9 2 7 8 2 6 2149.7394 2149.7388 0.0006 10 2 8 9 2 7 2149.7947 2149.7952 -0.0005 ************************************************** Table A-9. Observed and calculated transitions in the C-O stretching fundamental band of OC-(C2D2)2 trimer (units of 1/cm). ************************************************** J' Ka' Kc' J" Ka" Kc" Observed Calculated Obs-Calc ************************************************** 7 2 6 8 2 7 2148.7031 2148.7052 -0.0021 8 0 8 9 0 9 2148.7031 2148.7030 0.0001 8 1 8 9 1 9 2148.7031 2148.7032 -0.0001 6 5 2 7 5 3 2148.7351 2148.7351 0.0000 6 3 4 7 3 5 2148.7351 2148.7350 0.0001
6 1 5 7 1 6 2148.7521 2148.7512 0.0008 7 1 7 8 1 8 2148.7617 2148.7615 0.0002 7 0 7 8 0 8 2148.7617 2148.7611 0.0006 6 1 6 7 1 7 2148.8194 2148.8199 -0.0006 6 0 6 7 0 7 2148.8194 2148.8189 0.0005 5 2 4 6 2 5 2148.8302 2148.8307 -0.0004 4 2 2 5 2 3 2148.8522 2148.8517 0.0004 4 2 3 5 2 4 2148.8971 2148.8968 0.0003 4 0 4 5 0 5 2148.9333 2148.9330 0.0003 3 0 3 4 0 4 2148.9896 2148.9894 0.0001 3 1 3 4 1 4 2148.9982 2148.9983 -0.0001 2 1 1 3 1 2 2149.0143 2149.0144 -0.0001 2 2 0 3 2 1 2149.0230 2149.0228 0.0002 2 0 2 3 0 3 2149.0479 2149.0479 0.0000 2 1 2 3 1 3 2149.0601 2149.0601 0.0000 1 1 0 2 1 1 2149.0929 2149.0929 -0.0001 1 0 1 2 0 2 2149.1115 2149.1115 0.0000 1 1 1 2 1 2 2149.1239 2149.1236 0.0003 5 2 3 5 2 4 2149.3397 2149.3394 0.0003 3 1 2 3 1 3 2149.3431 2149.3435 -0.0005 2 1 2 1 1 1 2149.3836 2149.3842 -0.0006 2 1 1 1 1 0 2149.4143 2149.4143 0.0001 3 1 3 2 1 2 2149.4467 2149.4470 -0.0003 3 0 3 2 0 2 2149.4581 2149.4583 -0.0002 3 2 2 2 2 1 2149.4726 2149.4725 0.0001 4 1 4 3 1 3 2149.5080 2149.5079 0.0001 4 0 4 3 0 3 2149.5159 2149.5160 -0.0001 4 2 3 3 2 2 2149.5420 2149.5417 0.0003 5 2 4 4 2 3 2149.6085 2149.6086 -0.0001 5 2 3 4 2 2 2149.6506 2149.6511 -0.0005 6 2 5 5 2 4 2149.6726 2149.6729 -0.0003 7 0 7 6 0 6 2149.6836 2149.6840 -0.0005 7 1 7 6 1 6 2149.6836 2149.6831 0.0004 6 1 5 5 1 4 2149.6927 2149.6926 0.0001 6 3 4 5 3 3 2149.6977 2149.6976 0.0001 6 2 4 5 2 3 2149.7297 2149.7294 0.0003 7 2 6 6 2 5 2149.7349 2149.7348 0.00016 1 5 7 1 6 2148.7521 2148.7512 0.0008 7 1 7 8 1 8 2148.7617 2148.7615 0.0002 7 0 7 8 0 8 2148.7617 2148.7611 0.0006 6 1 6 7 1 7 2148.8194 2148.8199 -0.0006 6 0 6 7 0 7 2148.8194 2148.8189 0.0005 5 2 4 6 2 5 2148.8302 2148.8307 -0.0004 4 2 2 5 2 3 2148.8522 2148.8517 0.0004 4 2 3 5 2 4 2148.8971 2148.8968 0.0003 4 0 4 5 0 5 2148.9333 2148.9330 0.0003 3 0 3 4 0 4 2148.9896 2148.9894 0.0001 3 1 3 4 1 4 2148.9982 2148.9983 -0.0001 2 1 1 3 1 2 2149.0143 2149.0144 -0.0001 2 2 0 3 2 1 2149.0230 2149.0228 0.0002 2 0 2 3 0 3 2149.0479 2149.0479 0.0000 2 1 2 3 1 3 2149.0601 2149.0601 0.0000 1 1 0 2 1 1 2149.0929 2149.0929 -0.0001 1 0 1 2 0 2 2149.1115 2149.1115 0.0000 1 1 1 2 1 2 2149.1239 2149.1236 0.0003 5 2 3 5 2 4 2149.3397 2149.3394 0.0003 3 1 2 3 1 3 2149.3431 2149.3435 -0.0005 2 1 2 1 1 1 2149.3836 2149.3842 -0.0006 2 1 1 1 1 0 2149.4143 2149.4143 0.0001 3 1 3 2 1 2 2149.4467 2149.4470 -0.0003 3 0 3 2 0 2 2149.4581 2149.4583 -0.0002 3 2 2 2 2 1 2149.4726 2149.4725 0.0001 4 1 4 3 1 3 2149.5080 2149.5079 0.0001 4 0 4 3 0 3 2149.5159 2149.5160 -0.0001 4 2 3 3 2 2 2149.5420 2149.5417 0.0003 5 2 4 4 2 3 2149.6085 2149.6086 -0.0001 5 2 3 4 2 2 2149.6506 2149.6511 -0.0005 6 2 5 5 2 4 2149.6726 2149.6729 -0.0003 7 0 7 6 0 6 2149.6836 2149.6840 -0.0005 7 1 7 6 1 6 2149.6836 2149.6831 0.0004 6 1 5 5 1 4 2149.6927 2149.6926 0.0001 6 3 4 5 3 3 2149.6977 2149.6976 0.0001 6 2 4 5 2 3 2149.7297 2149.7294 0.0003 7 2 6 6 2 5 2149.7349 2149.7348 0.0001