- Email: [email protected]
The rotational spectrum of CH3CN above 1000 GHz
JOURNAL OF MOLECULAR SPE’XROSCOPY
129,483-485 (1988)
NOTE The Rotational Spectrum of CH$N
above 1000 GHz
It is now possible to use ab initio methods to calculate with a good accuracy the anharmonic force field of a small molecule without heavy atoms: see, for instance, Ref. (I). To test this force field it is usual to calculate the vibrational energy levels and to compare them with experimental results. In some cases, it may be much easier to deduce this force field from sextic centrifugal force constants because they are very sensitive to the cubic and qua& force constants and, as ground state constants, are not affected by any resonance. One does not encounter great difficulties in determining sextic centrifugal distortion constants for an asymmetric top. However, for a linear molecule or a symmetric top, the task is much more difficult because in this case it is necessary to measure lines in the submillimeter-wave range, a region which is not easily accessible. In fact sextic constants for the simplet symmetric molecules have been determined only recently (2). In this respect methyl cyanide is a very interesting molecule, because it has only six atoms and its heaviest atom is N (mass: only 14 a.u.). However, a recent attempt to determine the sextic constant has failed although the spectrum was measured up to 900 GHz (3). For the measurement of higher J CH&N lines we used the submillimeter-wave spectrometer described in Ref. (4). The tunable submillimeter-wave radiation is produced by the nonlinear mixing of an optically pumped FIR laser with a microwave YIG source (2 to 4 GHz). The detection of the generated sidebands is achieved by a superheterodyne detection. Both mixer and heterodyne detector are comer cube Schottky diodes. The measured absorption lines corresponding to J = 69 + 68 for K between 0 and 7 and J = 57 + 56 for K between 0 and 8 are presented in Table I. For these last transitions (J = 56) we also report in Fig. 1 the experimental spectrum obtained in video detection. We used respectively the 1267.0815-GHz emission of CH2F2 pumped by the 9RO6 CO2 line and the 1042.1504-GHz CHzFl emission pumped by the 9R34 TABLE I Newly Observed J + 1 + J Transitions of CH3CN (in MHz) J
K
56 56 56 56 56 56 56 56 56 66 68
0 1 2 3 4 5 6 7 0 0 1
68 68 68 68 68 68
2 3 4 5 6 7
Exp.
1045852.9 1045833.4 1045775.2 1045677.6 1045541.3 1045366.1 1045151.8 1044899.4 1044607.7 1264442.5 1264419.6 1264350.2 1264233.4 1264070.5 1263863.1 1263607.2 1263307.4
483
E.-C. 0.196 0.198 -0.086 0.067 -0.002 -0.036 0.235 -0.097 0.270 0.143 -0.177 -0.428 0.320 0.815 -0.474 0.541 -0.634
0022-2852188 $3.00 Copyright
Q
1988 by Academic Pm% Inc.
AU rights of npiduction
in any form -d.
484
NOTE
s
,
IQ45
1045.0
GM
5
IW. I. Experimental spectrum of the J = 56 transitions for K between 0 and 7 (video detection).
CO;?line. At these frequencies the sensitivity of our spectrometer is lower than lo-’ cm-‘. To estimate the accumcy of the measurements, most of the lines were measured several times (4 to IO) after having completely detuned the spectrometer and redone the tuning. The frequency of some lines could also be independently estimated by using strong neighboring CHrF lines as reference spectrum (5). The accuracy is thought to be better than 300 kHz for the J = 56 lines and better than 500 kHz for the J = 68 lines (except for K > 4 where the accuracy is only 700 kHz). The frequency of a rotational transition J + 1, K + J, Kin the ground vibrational state may be written as v,, = 2B(J + 1) - 4D,(J + 1)’ - 2D,,(J + 1)K’ + H,(J + 1)3[(J + 2)’ - J3] + 4HJK(J + 1)3K2 + 2Hnr(J + 1)K“ + LIIIK(J + 1)3[(J+ 2)3 - J3]K2 + 4L,,&J
+ 1)‘K4 + 2L,-(J
+ 1)K6. (1)
A weighted least-squares method was used to fit the experimental frequencies of Table I and Ref. (3) to the parameters of Eq. (1). The weight of each transition was taken equal to the inverse square of the measurement accuracy. The derived parameters are listed in Table II, together with their standard deviations and their correlation coefficients. The three sextic constants have been accurately determined for the first time. In particular, the constant H, is now accurate enough to allow comparisons with ab initio calculations. Due to the high J transitions involved, it was necessary to take into account the octic term L,J,K. It was found that this term did improve the fit (reduced x2 = 0.38 instead of 0.60) and that this term could be significantly determined (L,&n(L,,& = 8.4). Furthermore, neglecting it has a sizable effect on HJ which becomes -0.347(28) 10S9MHz (instead of -0.203(28) lo-‘). On the other hand, the constant LJm is only marginally determined; -0.112(45) 10m8MHz, and has no influence on the quality of the fit (reduced x2 = 0.36). This constant was fixed at zero in the final least-squares fit.
TABLE II Ground State Molecular Constants for Methyl Cyanide 9198.899378
B/MHZ
3.807786
DJlkHz
177.3953
DJKlkHz
(70) (120)
1.000
(35)
0.497
(2 8)
0.214
0.891 0.602
HJ/Hz
-0.000203
HJK/Hz
1.0220
(41)
0.150
HKJ’HZ
5.892
(36)
0.224
t-JJJK/mHz
-0.00889
No. Data
116
Note.
errors
Standard
1.000
0.341
(106)
in parentheses,
-0.077
shown
-0.050
1.000 -0.070 0.044
1.000 0.576
1.000
-0.280
0.797
-0.262
-0.422
1.000
-0.507
0.012
-0.623
-0.886
0.383
in units
of the
last digit.
1.000
NOTE
485
ACKNOWLEDGMENTS This work was supported by the Etablissement Public R&o& Nord/Pasde-Calais in the framework of the Centre Commun de Mesure de l’Unive.rsit~ de Lille I. F.X.B. thanks the CNRS for the research fellowship. REFERENCES 1. 2. 3. 4.
K. M. DUNN J. E. BOGGS,AND P. PuLAY, .I. Chem. Phys. 86,5088-5093 (1987). G. WLODARCZAK,D. B~UCHER,R. B~CQUET,AND J. DEMAISON,J. Mol. Spectrosc. 124,53-65 (1987). R. B~CQUET,G. WLODARCZAK,A. BAUER,AND J. DEMAISON,.I. Mol. Spectrosc. 127,382-389 (1988). G. PLW, F. X. BROWN, D. DANGOISSE,AND P. GLORIEUX, IEEE J. Quantum Electronics QE-23, 1388-1391 (1987). 5. F. X. BROWN, to be published. F. X. BROWN D. DANG~I~~E J. DEMAMN
Luboratoire de SpectroscopicHertzienne Associe’au CNRS Universitc! de Lille I, P5 F59655 Villeneuved*Ascq,Cidex, France Received January 4, 1988
129,483-485 (1988)
NOTE The Rotational Spectrum of CH$N
above 1000 GHz
It is now possible to use ab initio methods to calculate with a good accuracy the anharmonic force field of a small molecule without heavy atoms: see, for instance, Ref. (I). To test this force field it is usual to calculate the vibrational energy levels and to compare them with experimental results. In some cases, it may be much easier to deduce this force field from sextic centrifugal force constants because they are very sensitive to the cubic and qua& force constants and, as ground state constants, are not affected by any resonance. One does not encounter great difficulties in determining sextic centrifugal distortion constants for an asymmetric top. However, for a linear molecule or a symmetric top, the task is much more difficult because in this case it is necessary to measure lines in the submillimeter-wave range, a region which is not easily accessible. In fact sextic constants for the simplet symmetric molecules have been determined only recently (2). In this respect methyl cyanide is a very interesting molecule, because it has only six atoms and its heaviest atom is N (mass: only 14 a.u.). However, a recent attempt to determine the sextic constant has failed although the spectrum was measured up to 900 GHz (3). For the measurement of higher J CH&N lines we used the submillimeter-wave spectrometer described in Ref. (4). The tunable submillimeter-wave radiation is produced by the nonlinear mixing of an optically pumped FIR laser with a microwave YIG source (2 to 4 GHz). The detection of the generated sidebands is achieved by a superheterodyne detection. Both mixer and heterodyne detector are comer cube Schottky diodes. The measured absorption lines corresponding to J = 69 + 68 for K between 0 and 7 and J = 57 + 56 for K between 0 and 8 are presented in Table I. For these last transitions (J = 56) we also report in Fig. 1 the experimental spectrum obtained in video detection. We used respectively the 1267.0815-GHz emission of CH2F2 pumped by the 9RO6 CO2 line and the 1042.1504-GHz CHzFl emission pumped by the 9R34 TABLE I Newly Observed J + 1 + J Transitions of CH3CN (in MHz) J
K
56 56 56 56 56 56 56 56 56 66 68
0 1 2 3 4 5 6 7 0 0 1
68 68 68 68 68 68
2 3 4 5 6 7
Exp.
1045852.9 1045833.4 1045775.2 1045677.6 1045541.3 1045366.1 1045151.8 1044899.4 1044607.7 1264442.5 1264419.6 1264350.2 1264233.4 1264070.5 1263863.1 1263607.2 1263307.4
483
E.-C. 0.196 0.198 -0.086 0.067 -0.002 -0.036 0.235 -0.097 0.270 0.143 -0.177 -0.428 0.320 0.815 -0.474 0.541 -0.634
0022-2852188 $3.00 Copyright
Q
1988 by Academic Pm% Inc.
AU rights of npiduction
in any form -d.
484
NOTE
s
,
IQ45
1045.0
GM
5
IW. I. Experimental spectrum of the J = 56 transitions for K between 0 and 7 (video detection).
CO;?line. At these frequencies the sensitivity of our spectrometer is lower than lo-’ cm-‘. To estimate the accumcy of the measurements, most of the lines were measured several times (4 to IO) after having completely detuned the spectrometer and redone the tuning. The frequency of some lines could also be independently estimated by using strong neighboring CHrF lines as reference spectrum (5). The accuracy is thought to be better than 300 kHz for the J = 56 lines and better than 500 kHz for the J = 68 lines (except for K > 4 where the accuracy is only 700 kHz). The frequency of a rotational transition J + 1, K + J, Kin the ground vibrational state may be written as v,, = 2B(J + 1) - 4D,(J + 1)’ - 2D,,(J + 1)K’ + H,(J + 1)3[(J + 2)’ - J3] + 4HJK(J + 1)3K2 + 2Hnr(J + 1)K“ + LIIIK(J + 1)3[(J+ 2)3 - J3]K2 + 4L,,&J
+ 1)‘K4 + 2L,-(J
+ 1)K6. (1)
A weighted least-squares method was used to fit the experimental frequencies of Table I and Ref. (3) to the parameters of Eq. (1). The weight of each transition was taken equal to the inverse square of the measurement accuracy. The derived parameters are listed in Table II, together with their standard deviations and their correlation coefficients. The three sextic constants have been accurately determined for the first time. In particular, the constant H, is now accurate enough to allow comparisons with ab initio calculations. Due to the high J transitions involved, it was necessary to take into account the octic term L,J,K. It was found that this term did improve the fit (reduced x2 = 0.38 instead of 0.60) and that this term could be significantly determined (L,&n(L,,& = 8.4). Furthermore, neglecting it has a sizable effect on HJ which becomes -0.347(28) 10S9MHz (instead of -0.203(28) lo-‘). On the other hand, the constant LJm is only marginally determined; -0.112(45) 10m8MHz, and has no influence on the quality of the fit (reduced x2 = 0.36). This constant was fixed at zero in the final least-squares fit.
TABLE II Ground State Molecular Constants for Methyl Cyanide 9198.899378
B/MHZ
3.807786
DJlkHz
177.3953
DJKlkHz
(70) (120)
1.000
(35)
0.497
(2 8)
0.214
0.891 0.602
HJ/Hz
-0.000203
HJK/Hz
1.0220
(41)
0.150
HKJ’HZ
5.892
(36)
0.224
t-JJJK/mHz
-0.00889
No. Data
116
Note.
errors
Standard
1.000
0.341
(106)
in parentheses,
-0.077
shown
-0.050
1.000 -0.070 0.044
1.000 0.576
1.000
-0.280
0.797
-0.262
-0.422
1.000
-0.507
0.012
-0.623
-0.886
0.383
in units
of the
last digit.
1.000
NOTE
485
ACKNOWLEDGMENTS This work was supported by the Etablissement Public R&o& Nord/Pasde-Calais in the framework of the Centre Commun de Mesure de l’Unive.rsit~ de Lille I. F.X.B. thanks the CNRS for the research fellowship. REFERENCES 1. 2. 3. 4.
K. M. DUNN J. E. BOGGS,AND P. PuLAY, .I. Chem. Phys. 86,5088-5093 (1987). G. WLODARCZAK,D. B~UCHER,R. B~CQUET,AND J. DEMAISON,J. Mol. Spectrosc. 124,53-65 (1987). R. B~CQUET,G. WLODARCZAK,A. BAUER,AND J. DEMAISON,.I. Mol. Spectrosc. 127,382-389 (1988). G. PLW, F. X. BROWN, D. DANGOISSE,AND P. GLORIEUX, IEEE J. Quantum Electronics QE-23, 1388-1391 (1987). 5. F. X. BROWN, to be published. F. X. BROWN D. DANG~I~~E J. DEMAMN
Luboratoire de SpectroscopicHertzienne Associe’au CNRS Universitc! de Lille I, P5 F59655 Villeneuved*Ascq,Cidex, France Received January 4, 1988