The electric dipole moment of methyl fluoride

JOURNAL

OF

MOLECULAR

SPECTROSCOPY

The Electric

83, 279-2X2 (1980)

Dipole

Moment

of Methyl

Fluoride’

The Stark effect of CH,F is extensively used as a calibration standard in laser Stark spectroscopy. The accepted value for the dipole moment of the ground vibrational state of CH,F is less accurate than the precision of laser Stark measurements, and questions have also been raised about the literature value. New molecular beam spectroscopy measurements have been made of the ratio of the Stark effect in the J = 1. K = 1 and ./ = 2, K = 2 CH,F states to that of the 0110 vibrational state of OCS. The results were ~,.,(CH:,F)/~,,,,,(OCS) = 2.638905(23) and CL~.~(CH,F)/~,,,,,(OCS) = 2.63894(10). This produces a dipole moment of I .85840 D with precision relative to OCS of 10 ppm and absolute accuracy of 43 ppm. INTRODUCTION

Infrared laser Stark spectroscopy, using CO,, CO, N20, and other fixedfrequency lasers, is a rapidly growing technique (I -7). The majority of laser Stark spectrometers use the Stark effect of methyl fluoride to calibrate the electric field intensity employed in the apparatus. In the first laser Stark study of CH,F (3 ) it was pointed out that the precision of the infrared measurement was greater than the quoted accuracy of the CH,F ground state dipole moment (8). Therefore, the accuracy of the dipole moment of the v3 vibrational state of CH,F was limited by the accuracy of the molecular beam measurement on the ground state. The initial laser Stark CHSF paper (3) also mentioned that the physically measured electrode spacing did not agree with the spacing obtained from the calibration using the ground-state CH,F moment. Even though the CH,F calibration was used, the lack of agreement raised questions about the accuracy of the ground state moment. Since that time other questions have been raised about the CH,F electric dipole moment; e.g., Amano and Schwendeman (9) questioned whether the CHRF moment was consistent with that of OCS, a frequently used standard for electric field calibration. The situation clearly made it desirable to reinvestigate the CH,F ground state. This is particularly true since the original molecular beam spectroscopy (8) on CH,F was done primarily as a study of hyperfine interactions. The dipole moment information in Ref. (8) is, in fact, somewhat vague, with references made to stray voltages and frequency shifts which varied from one spectrum to another. The dipole moment is not even mentioned in the abstract of this paper. It is not surprising that questions have been raised concerning the CH,F moment. Actually, the original Stark effect data were much better than the paper implied and the 1Supported

by NSF Grant

CHE77-12527

279

0022-2852/80/100279-04$02.00/O Copyright ,411 rights

ffi 1980 by Academic of reproduction

Press.

Inc.

in any form revsved.

280

MARSHALL

AND MUENTER

stray fields and frequency shifts related only to very weak rf field spectra obtained using many hours of signal averaging. To clear up any uncertainties and to obtain a more accurate calibration for laser Stark experiments, electric resonance spectra of CH3F have been reinvestigated. Since the laser Stark calibration uses the QI( 1) and QZ(2) transition, the Stark effect of the J = 1, K = 1, AM., = 1 and J = 2, K = 2, AMJ = 1 transitions were measured. EXPERIMENTAL

DETAILS

The molecular beam spectrometer used has been described previously (10). The beam was formed in a nozzle expansion using 5% commercial CH,F in argon. The nozzle was a 25pm-diameter pinhole without skimmer at room temperature and a 2-atm backing pressure was used. The signal-to-noise ratio produced was 50: 1 for the J = 1, K = 1 data and 20: 1 for the J = 2, K = 2 data using a 3-set time constant. To obtain this signal-to-noise ratio, it is necessary to use radio frequency fields which broaden the hyperhne components and, therefore, lower the resolution of the measurements. The J = 1, K = 1 measurements used a 3 mV/cm radiation field which produced a spectrum with features approximately 3 kHz wide. The J = 2, K = 2 spectrum is more complex and a 6 mV/cm field produced unresolved features 5 kHz wide. The former could be measured reproducibly to 100 Hz while the latter could be determined to a 500-Hz precision. All the measurements were taken in a strong field with respect to hyperfine splittings. This was determined both by experimentally observing spectra independent of the dc electric field and by calculating the hyperfine splittings using the parameters and computer program from Ref. (8). Hyperfine splittings at 15 V/cm agreed to within 50 Hz of truly high field splittings. Measurements were made with the earth’s magnetic field reduced to less than 100 mG. The frequencies used were the average of those obtained by sweeping the frequency in increasing and decreasing directions to average time constant errors. Making accurate frequency measurements is very easy relative to producing accurate electric fields and significant effort was expended in electric field calibration. The conventional use of OCS as a calibrant was not satisfactory since sufficient accuracy can be obtained only for fields greater than 500 V/cm. An accurate electrode spacing could be found, but a very accurate voltage divider would be needed and the presence of contact potentials and/or thermal emf’s would still have to be dealt with. The magnitude of the problem of extending a high-field calibration to low fields is made clear by considering that an absolute accuracy of a few hundred microvolts per centimeter was required. The calibration was done using the much faster Stark effect of the J = 1, I = + 1, M = 1 to J = 1, 1 = - 1, M = 1 transition in the Ol”O vibrational state of OCS (II). Since the ratio ~,,,,,,1~0,,,has been measured more accurately than pooo itself (II), this calibration will be consistent with common ground-state calibrations. The Stark coefficient for this I-doublet transition produces a secondorder frequency shift greater than 1 MHz for 15 V/cm and the transition frequency can be measured to an accuracy of better than 50 Hz.’ The OCS transition was measured immediately before and after the CH3F data were taken at a given ’ The instrumental

linewidth

is 1.5 kHz FWHM.

DIPOLE MOMENT

OF METHYL TABLE

FLUORIDE

281

I

Methyl Fluoride Stark Data”

ocs

13.78772

20.0000

25.0000

30.0000

14.56248

15.50182

16.57786

CH3F

1.1

6.99510(17)

9.33270(10)

11.67001(20)

14.00760(l)

CH3F

1.1

7.01710(4)

9.35452(6)

11.69192(6)

14.02940(7)

CH3F

1.1

7.02604(6)

9.36348(4)

11.70084(l)

14.03843(l)

CH3F

2,2

4.65288(31)

6.21135(4)

7.76960(3)

9.32820(19)

CH3F

2,2

4.66125(11)

6.21980(23)

7.77775(6)

9.33613(6)

CH3F

2,2

4.68453(12)

6.24290(28)

7.80004(82)

9.35943(19)

CH3F

2.2

4.69695(41)

6.25470(5)

7.81275(24)

9.37143(6)

ocs

13.78776

a. Frequencies are in MHz observed magnitudes.

14.56251

and numbers

15.50185

in parentheses

16.57793

are calculated

minus

voltage. Measurements were made at 1.5, 20, 25, and 30 V/cm. The electrode spacing was 1 cm and the voltages were supplied by an EDC 1030 voltage standard. To within the _50-Hz OCS measuring accuracy, the voltage source did not drift during the CH,F measurements, which required about 40 min for each voltage. The before and after OCS frequencies differed by approximately 35 Hz and the average frequency was used in calculating the field strengths. The J = 1, K = I transition frequencies ranged from 7.0 to 14.0 MHz and three narrow features of the broadened hyperfine structure were measured at each voltage. The J = 2, K = 2 transitions ranged from 4.7 to 9.4 MHz and four features were measured at each voltage. The larger Stark shifts and higher resolution for J = 1. K = 1 provided accuracy which was limited primarily by the electric field calibration. The J = 2, K = 2 transitions exhibited greater linewidth and smaller Stark shifts and the dipole moment accuracy was limited by the CHRF frequency measurements. The methyl fluoride and OCS calibration data are listed in Table I. The number in parentheses following each frequency is the residual found when the data are fit as described below. ANALYSIS

The average of the before and after OCS frequencies was used to obtain the field, E, from E = (v2 - ui)“‘lp. This expression is the exact solution of the twolevel Stark effect (12) for the I = 1, J = 1, M = 1 doublet and there are no higher corrections from AJ connections since J and M are the same for each level. v is the observed frequency, v0 is the zero-field frequency, and p is the moment of the 01’0 vibrational state of OCS. v,, was determined by fitting the OCS data to the electric field expression and extrapolating to zero. This value agreed with, but was more accurate than, a single zero-field measurement and it also agreed with the published value (II).

MARSHALL

282

AND MUENTER

The CHBF transitions are M = 1 + M = 0 and there are small second-order corrections to the Stark effect (12). The largest contribution was 390 Hz. The calculated second-order contributions were subtracted from the observed frequencies to generate effective frequencies obeying the linear Stark effect. A linear least-squares fit of the CH3F effective frequencies to the OCS determined electric fields produced a very precise ratio of the CH,F moment to the OCS moment. Initially, each measured feature for both the J = 1, K = 1 and J = 2, K = 2 transitions were fit individually to a dipole moment ratio and zero-field intercept. Then all the J = 1, K = 1 data were fit to a dipole moment ratio and three intercepts and the J = 2, K = 2 data were fit to a moment ratio and four intercepts. The individually obtained ratios agreed with the combined moments well within one standard deviation as did the intercepts. The most accurate results are from the combined fits, which yield ~l,l(CH,F)I~u,,,(OCS) = 2.638905(23) and ~2,2(CH3F)I~U,,,(OCS) = 2.63894( 10). The uncertainties quoted are one standard deviation. The ratios, intercepts, and OCS frequencies were used to calculate CH3F frequencies. The calculated minus the observed frequencies are listed in parentheses in Table I. The ratios provide moments3 of pl,l = 1.85840(2) and p2,2 = 1.85842(6), where the uncertainties quoted reflect only the precision relative to OCS. The absolute accuracy of the CH3F moments depend on the accuracy of the OCS moment, which is 0.004%. The final absolute uncertainty is 0.004% for pI,,(CHJF) and 0.006% for p&CH3F). Since the ratio of pO,,,,(OCS)/ I~.,,,,,(OCS) is known to 10 ppm, the CH3F measurements are completely consistent with any calibration based on the ground-state moment of OCS. CONCLUSIONS

The dipole moment of CH3F has been remeasured specifically for use in calibrating infrared laser Stark spectrometers. The new values obtained are in complete agreement with previous results and are an order of magnitude more accurate. RECEIVED:

August 27, 1979 REFERENCES

I. R. G. BREWER, M. J. KELLY, AND A. JAVAN, Phys. Rev. Lert. 23, 559-563

(1969).

2. F. SHIMIZU, J. Chem. Phys. 52, 3572-3576 (1970). 3. S. M. FREUND, G. DUXBURY. M. RGMHELD, J. T. TIEDJE, AND T. OKA, J. Mol. Specfrosc. 52, 38-57 (1974). 4. J. W. C. JOHNS AND A. R. W. MCKELLAR, J. Chem. Phys. 63, 1682-1685 (1975). 5. C. YAMADA AND E. HIROTA, J. Mol. Specfrosc. 64, 31-46 (1977). 6. C. L. CALDOW. G. DUXBURY, AND L. A. EVANS, J. Mol. Spectrosc. 69, 239-253 (1978). 7. T. AMANO AND R. H. SCHWENDEMAN, J. Chem. Phys. 68, 530-537 (1978). 8. S. C. WOFSY, J. S. MUENTER, AND W. A. KLEMPERER, J. Chem. Phys. 55, 2014-2019 (1971). 9. T. AMANO AND R. H. SCHWENDEMAN, Paper WG6, 33rd Symp. Mol. Structure, 1978. 10. J. S. MUENTER, J. Chem. Phys. 56, 5409-5412 (1972): B. FABRICANT, D. KRIEGER, AND J. S. MUENTER, J. Chem. Phys. 67, 1576- 1586 (1977). Il. J. REINARTZ, W. MEERTS, AND A. DYMANUS, Chem. Phys. Letf. 16, 576-580 (1972). I2. C. H. TOWNES AND A. L. SCHAWLOW. “Microwave Spectroscopy,” Chap. 10, McGrawHill, New York,

1955.

‘I To obtain CHJF moments x IO-” erg’sec,

c = 2.99792458

from the ratios, the following x 10”’ cm/set,

constants

and p,,,,, = 0.70423(3)

D.

were used: h = 6.626176