The Millimeter-Wave Spectrum and Structure of Vinyl Chloride

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

177, 232–239 (1996)

0137

The Millimeter-Wave Spectrum and Structure of Vinyl Chloride I. Merke,1 L. Poteau, G. Wlodarczak, A. Bouddou, and J. Demaison Laboratoire de Spectroscopie Hertzienne, URA CNRS 249, Baˆt. P5, Universite´ de Lille I, 59655 Villeneuve D’Ascq Cedex, France Received December 18, 1995; in revised form March 4, 1996; accepted March 7, 1996

The ground state rotational spectra of CH2|CH35Cl and CH2|CH37Cl have been measured in the millimeter-wave and submillimeter-wave ranges. These new data have been used to improve notably the accuracy of the rotational and centrifugal distortion constants. Finally an ab initio structure has been calculated and a near-equilibrium structure has been estimated using offsets derived empirically. q 1996 Academic Press, Inc. INTRODUCTION

Vinyl chloride, CH2|CHCl, is a major industrial product used mainly for PVC production. It is considered to be a carrier for chlorine transported into the troposphere and stratosphere. The a-type rotational spectrum of vinyl chloride was first assigned by Goldstein and Bragg in 1949 (1). One year later they investigated the chlorine quadrupole hyperfine structure (2). With the assignment of different deuterated isotopomers in 1960 Kivelson et al. (3) were able to determine a first structure of CH2|CHCl as well as chlorine quadrupole coupling constants and the dipole moment in a-direction: ma Å 1.42(2) D. In 1966 Savariraj (4, 5) recorded b-type transitions for the first time and assigned the 13C isotopomers. He determined rotational, quartic centrifugal distortion, and chlorine quadrupole coupling constants and performed double resonance experiments. In 1971 Gerry (6) refined the rotational, centrifugal distortion, and chlorine quadrupole coupling constants of the two most abundant species. In 1990 Hayashi and Inagusa (7) measured 20 isotopomers of vinyl chloride and determined for each isotopomer two diagonal quartic centrifugal distortion and chlorine quadrupole coupling constants. For the understanding of atmospheric spectra in the mmwave and far-infrared regions as well as for the analysis of high resolution infrared spectra, accurate spectroscopic spectra are required. Vinyl chloride pumped by CO2 lasers produces some powerful submillimeter continuous emissions. The observed frequencies are given in Ref. (8). To assign these emissions without ambiguity, it is also necessary to know accurate ground state rotational energies. Up to now investigations of vinyl chloride have been restricted to low J transitions and therefore no sextic centrifugal distortion 1 Current address: Institut fu¨r Physikalische Chemie, Rheinisch-Westfa¨lische Technische Hochschule, Templergraben 59, D-52056 Aachen, Germany.

constants have been reported. This induced us to extend the spectroscopic data base to high J and Ka values in the mmwave region. Another goal of this work was to determine a near equilibrium structure for vinyl chloride.

EXPERIMENTAL

The sample was obtained from Fluka and used without further purification. Transitions in the frequency region between 120 and 250 GHz were measured using a source modulated millimeter-wave spectrometer (9). A phase stabilized klystron (65–75) GHz supplies a harmonic generator with fundamental power. The radiation is then optically focused through a free space absorption cell. A superheterodyne detection was performed using the harmonic signal of a Gunn diode as local oscillator. Transitions in the frequency region between 360 and 450 GHz were measured with a BWO as radiation source used in the fundamental mode. The radiation was detected by a helium cooled InSb bolometer. The accuracy of the measurements is between 50 and 200 kHz depending on the width and intensity of the lines. Above 470 GHz, a far-infrared laser sidebands spectrometer was used. It is described in Ref. (10). This spectrometer is based on the generation of tunable sidebands by nonlinear mixing of a fixed FIR laser emission and a tunable 2–20 GHz radiofrequency radiation. This laser system enables us to cover 60% of the frequency range in the region 500–1500 GHz, and 30% in the region 1500–2500 GHz. Although a heterodyne receiver is used to detect the sideband signal, the ultimate sensitivity is only about 1006 cm01. For these last two reasons, it was not possible to measure b-type transitions involving higher Ka values which might have made the determination of all sextic centrifugal distortion constants feasible. The accuracy of the measurements is about 500 kHz. All measurements were made at room temperature and sample pressures of about 2 1 1002 mbar.

232 0022-2852/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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ROTATIONAL SPECTRUM OF VINYL CHLORIDE

OBSERVED SPECTRA AND ANALYSIS

Vinyl chloride is a planar molecule with a quite strong dipole moment in a-direction and a small one in b-direction. Therefore the a-type spectrum is much stronger than the btype one. In the beginning we used the rotational and quartic centrifugal distortion constants with their standard deviations taken from Ref. (6) to predict transition frequencies and their estimated errors in the millimeter wave region. With the help of these predictions we easily assigned transitions with low J and Ka. By introducing these lines in a least-squares analysis in which the lines from Refs. (4–6) were also included, we got a new and improved set of constants which has been used to predict transition frequencies with higher centrifugal distortion contributions, usually lines with higher values of J and Ka. New measurements have been then carried out and the mentioned procedure has been repeated several times extending the measurements up to transitions with J values of 64 and Ka values of 20 for the 35Cl isotopomer and for J up to 39 and Ka up to 21 for the 37Cl isotopomer. In almost all transitions we observed chlorine quadrupole hyperfine structure. For the analysis of the centrifugal distortion, we used the hypothetical unsplit frequencies obtained by intensity weighted averaging of the strong hyperfine components. We used Watson’s A-reduction in the Ir-representation (11) for the fit H Å AP2z / BP2x / CP2y 0 DJP4 0 DJKP2P2z 0 DKP4z 0 2dJP2(P2x 0 P2y) 0 dK[P2z (P2x 0 P2y) / (P2x 0 P2y)P2z ] / FJP6 / FJKP4P2z / FKJP2P4z / FKP6z 4

2 x

CH2|CH35Cl); this is the reason why we did not keep it fixed at zero during the fits. Because vinyl chloride is a nearsymmetric top, we also tried Watson’s S-reduction. This time the high correlations between the sextic constants were removed, but nevertheless the two off-diagonal sextic constants h2 and h3 were not well determined in the analysis of the normal isotopomer, and not determined at all in the analysis of the 37Cl isotopomer. Watson (13) has recently proposed an empirical equation to predict the value of the inertial defect of a planar molecule. He has shown that the zero-point harmonic term is given approximately by Dharm Å 3K

/ 2fJP (P 0 P ) / fJKP2[P2z (P2x 0 P2y) / (P2x 0 P2y)P2z ] / fK[P4z (P2x 0 P2y) / (P2x 0 P2y)P4z ].

The measured frequencies of both isotopomers as well as the estimated uncertainties and the observed-minus-calculated values are listed in Table 1. Because of quite high correlation of fK with FJK and FKJ in the fits of both isotopomers we decided to fix fK to zero. fJK was not well determined, therefore it was also fixed to zero. The standard deviation of the fit did not significantly increase. The determined molecular constants of Eq. [1] are given in Table 2. As expected the centrifugal distortion constants of both isotopomers are quite similar. The least well determined parameter is FK: FK/s(FK) Å 6. In fact this parameter is highly correlated with both A and DK, the corresponding condition index (which is also the condition number in this case) being k Å 48 (12). So this parameter may not be reliable. However, its contribution is greater than 1 MHz for 4 lines, and greater than 100 kHz for 42 lines (in

D

1 1 1 1 / / 0 , vA vB vAB vC

r vA Å

r vC Å

16A3 0 vB Å taaaa

0

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r

16C3 vAB Å tcccc

16B3 0 tbbbb

r

[3]

16ABC 0 . tabab

Finally the total inertial defect is given by the following equation where the Coriolis contribution is empirically taken into account, D Å Dharm[1.0292 0 0.0911(N 0 3)],

[4]

where N is the number of atoms. The calculated value, D ˚ 2, is in extremely good agreement with the experÅ 0.102 uA ˚ 2, and confirms that the molecule imental value, 0.1084 uA is planar and that the determined constants are very likely correct. For planar molecules, there is a relation between the equilibrium quartic centrifugal distortion constants and, as a consequence, the planarity defect whose defining equation is

S

Dt Å 4 Tcc 0

D

T2 0 CT1 A/B

[5]

should be zero. In fact, for the ground state constants, it is significantly different from zero, Dt Å 00.319(14) 1 1004 MHz. This is why the centrifugal distortion constants were fitted neglecting the planarity constraint (Dt Å 0). Furthermore the planarity defect is negative as for all planar molecules measured so far and it has the right order of magnitude (14).

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[2]

˚ 2 is the usual conversion facwhere K Å 505379.1 MHzruA tor and the effective vibrational frequencies are given in terms of the quartic centrifugal distortion constants tabgd by

[1]

2 y

S

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TABLE 1 Experimental Rotational Transitions (MHz) of Vinyl Chloride

Note. s Å uncertainty of the transition in kHz; o 0 c Å observed 0 calculated frequency in MHz; the frequencies under 100 GHz are taken from Ref. (6). 234

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TABLE 1 —Continued

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MERKE ET AL.

TABLE 1 —Continued

STRUCTURE

The substitution structure (rs) of vinyl chloride was first determined by Kivelson et al. (3). Later Hayashi and Inagusa (7) measured the microwave spectra of 20 isotopic species and refined the rs structure. However, the b-coordinates of the chlorine and Htrans atoms are so small that the solutions of the Kraitchman equations are not reliable. Quite recently, Coffey et al. (15) calculated an ab initio structure which was empirically corrected in order to obtain r0 values. They found a good agreement with the experimental r0 structure. However both r0 and rs structures are empirical, making comparisons with other molecules risky. This is the reason why we undertook the determination of a new structure as near as possible to the equilibrium structure. We used the procedure described below and which was previously used for CH3CN (16) and CH3CGCH (17).

To estimate the experimental re structure, we used the r rm method developed by Berry and Harmony (18). The ground state moments of inertia I 0g are first scaled by a factor 2r 0 1, Irm,g(i) Å (2rg 0 1)I 0g(i)

where rg Å rg(1) Å

I sg(1) I 0g(1)

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i Å 1 Å parent.

[7]

The ‘‘substitution moments’’ of the parent molecule I sg(1) are calculated from the substitution coordinates. As usual the experimental rotational constants were used without

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[6]

g Å a,b,c i Å all isotopomers,

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ROTATIONAL SPECTRUM OF VINYL CHLORIDE

237

TABLE 2 Molecular Constants for the Ground State of Vinyl Chloride

magnetic correction nor centrifugal distortion correction, because these corrections are at least an order of magnitude smaller than the vibrational correction. Furthermore, it was checked that these corrections have no significant effect on the derived structure. For substitutions on a principal plane or axis, Kraitchman equations may give negative values for the squares of the coordinates. These negative contributions must also be included to obtain I sg(1). Then Harmony suggests to correct the moments of the deuterated isotopic species to account for overscaling. This ‘‘Laurie’’ correction is equivalent to an elongation of the C{D bond by an amount ˚ . For instance, for the c-axis, dr Å 0.0028 A D (Irm,c)corr Å (Irm,c)D / 2mD ∑ (aidai / bidbi),

[8]

i

and analogously for the a and b axes by cyclic permutation of a, b, and c. ai, bi, and ci are the cartesian coordinates of the D atoms and dai, dbi, and dci the components of dr. After the subsequent r0-type least-squares fit to the scaled moments, this correction, Eq. [8], leads to a structure where ˚ comthe C{H bond is longer by approximately 0.0056 A

pared with the results obtained without this correction. Furthermore, this correction has been shown (19) to remain restricted to the C{H bond length, hardly affecting the rest of the structure. This method has been applied to several molecules containing hydrogen atoms (16–21). It has been found to be quite reliable for heavy-atom coordinates, but the results for the C{H bond lengths are sometimes inaccurate. Since the molecule is planar, the three moments of inertia of each isotopic species provide only two independent relations. The substitution coordinates may be calculated using either the planar Kraitchman equations and two moments of inertia (e.g., Ia and Ib or Ib and Ic) or the full Kraitchman equations for a nonplanar molecule (22). As a result of the zero-point vibrations, each method is expected to give (hopefully) slightly different substitution coordinates, but only one r rm structure. This may be used as a consistency test. The rs and r rm coordinates were calculated using these different methods. The results are reported in Table 3. For the sake of comparison the ro, rs, and re,I structures are also given. The re,I structure (23) is equivalent to the substitution structure but it is less sensitive to small coordinates, so it is generally more reliable. As expected the heavy-atom coordi-

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MERKE ET AL.

TABLE 3 Comparison of Different Structures of Vinyl Chloridea

nates are consistent but the C{H bond lengths show rather large variations. It also seems to indicate that the three C{H bond lengths are different. Another way to obtain a near-equilibrium structure is to use ab initio calculations. It is well established that the angles from ab initio calculations are generally in good agreement with the experimental equilibrium values, at least with a sufficiently large basis set. For the bond lengths, on the other hand, an empirical correction is necessary. The method assumes that errors for a given bond length will be roughly constant from molecule to molecule provided that a sufficiently large basis set is used and that the electron correlation is taken into account, at least at the MP2 level. It is particularly reliable for C{H bond lengths (24). It was also applied with success for the CC, CN (12), CF (25), and C|O (21) bond lengths. This method has not yet been applied to C{Cl bonds (at least to determine equilibrium structures). For this purpose, we have calculated at the MP2 level the structures of chlorine derivatives for which an accurate re (or r rm) structure has been determined. All calculations were made with Gaussian 92 (26). Different basis sets were used: 6-31G**, 6-311 / G(d, p), and 6-311 / G(2d, p). They give compatible results (after offset correction, see below) for the CH and CC bonds, but for the CCl bond, the 6-311 / G(2d, p) basis set seems to be more reliable (this is expected for a second-row atom like chlorine). The results are collected in Table 4. Although the number of experimental values is ˚ , and there is a small, their range is rather large, 0.16 A very good correlation between experimental and calculated values, r Å 0.998. There are not enough data and they are not accurate enough to check whether the correction dr Å re(exp.) 0 r(ab initio) is constant or not; its median value ˚ . It may be used as offset to correct the ab is 00.017 A initio bond length. Alternatively, a linear regression of the

experimental data as a function of the ab initio ones (stan˚ ) allows us to estimate the ‘‘true’’ dard deviation 0.003 A equilibrium value for the C{Cl bond length in vinyl chloride. Both methods are in close agreement. The lengths of the C{H and C|C bonds calculated at the MP2/6-31G** and MP2/6-311 / G(d, p) levels were corrected with the previously estimated offsets (12). The derived equilibrium structure as well as the ‘‘original’’ ab initio structures are shown in Table 5. For the heavy-atom coordinates, there is very good agreement between the re and the r rm structures. But large differences are found for the C{H bond lengths. This result is rather general and it seems extremely difficult

TABLE 4 Equilibrium C{Cl Bond Lengths (in A˚)

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ROTATIONAL SPECTRUM OF VINYL CHLORIDE

TABLE 5 Equilibrium Structure of Vinyl Chloridea

to obtain reliable H-coordinates using only the ground state moments of inertia. The equilibrium geometry of C-chlorophosphaethyne (ClCGP) has been recently determined from the equilibrium rotational constants of the 35Cl and 37Cl isotopomers (27). But it is not accurate because the system of equations is illconditioned, as it is usual for a linear triatomic molecule. In ˚ . The estimated ab initio particular, re(C{Cl) Å 1.634(6) A (with offset correction) equilibrium length is re(C{Cl) Å ˚ . Using this value as an additional datum in the least1.641 A ˚ gives squares fit with an estimated accuracy of 0.002 A ˚ and re(CGP) Å 1.548(2) A ˚ . This re(C{Cl) Å 1.639(2) A new structure is compatible with the older one, but it is probably more reliable. ACKNOWLEDGMENTS This work has been supported in part by the European Programme Human Capital and Mobility (Network Contract ERBCHRXCT 93-0157). I. M. is also grateful to this program for financial support.

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