JOURNAL OF T1l1H OPTICAL SOCIETY OF AMERICA

Pure Rotational Absorption Spectrum of Hydrogen Fluoride Vaporbetween 22 and 250 L

WALTER G. ROTHSCHILDScientific Laboratory, Ford Motor Company, Dearborn, 1f1icizigan

(Received 21 Maay 1963)

The first 11 successive pure rotational absorption lines of hydrogen fluoride vapor have been measuredin the far infrared between 22 and 250 ,u with a commercial grating spectrometer. Most of these transitionsare reported here for the first time. The rotational constant B and the centrifugal stretching constant Dcalculated from the observed transitions amount to Bo=20.55940.006 cm-', Do=0.00211±0.00004 cm-',within their 95% confidence limit. These values agree extremely well with the ones obtained from reportedrotation-vibration and pure rotational spectra. The experimental procedures are described. It is shownthat the window material of the cell, polyethylene, gives rise to an extraneous band at 389.1 cm-' by areaction with the sample.

INTRODUCTION

UP to the present, eight individual transitions ofthe pure rotational spectrum of hydrogen fluoride

vapor, which has its most intense lines in the far in-frared between 448 cm-l (22.3 Az) and 40 cm-' (250 ,),have been reported in the literature. In 1927, Czernylmeasured the transitions J= 1, 3, and 4 (the quantumnumber J is that of the lower level). Recently, Kuipers,Smith, and Nielsen2 have determined the J=10, 11,and 12 and, in emission, the J= 14 and 15 transitions.They worked at elevated temperatures to cause suffi-cient depolymerization in the hydrogen fluoride samplesand to increase the populations of the high rotationalstates. Concurrently with the work reported here,3

Mason and Nielsen4 have measured the pure rotationalspectrum of hydrogen fluoride.

It is the purpose of this paper to report the measure-ments of the 11 successive pure rotational absorptionlines J= 0 to 10 of HF vapor at room temperature and tocompare the resulting rotational constants with thecorresponding values obtained from some representativestudies on the fine structure of rotation-vibration bandsreported in the literature.

EXPERIMENTAL

The HF sample (anhydrous grade, 99.9% minimum,the Matheson Company, Inc.,) was contained in a10-cm Ni cell with high-density polyethylene windowsof about 1.3 mm thickness. Total vapor pressuresranged from 50 to 456 mm Hg. The cell was kept at theambient temperature of the instrument. The spectrawere taken with a Perkin-Elmer far-infrared double-beam spectrometer, Model 301.' The spectral rangecovered by the instrument is 50-660 cm-'; this placesthe ground-state rotational transition of HF (at 41.30

' M. Czerny, Z. Physik 44, 235 (1927).2 G. A. Kuipers, D. F. Smith, and A. H. Nielsen, J. Chem.

Phys. 25, 275 (1956).3W. G. Rothschild, Bull. Ain. Phys. Soc. 8, 326 (1963).

A. A. Mason and A. H. Nielsen, Bull. Am. Phys. Soc. 7, 575(1962); 8, 555 (1963).

5 C. C. Helms, H. W. Jones, A. J. Russo, and E. H. Siegler,Jr., Spectrochim. Acta 19, 819 (1963).

cm-l) outside the instrumental range. However, onlyminor modifications and an additional grating of 4lines/mm are required to extend the instrumental rangeto 35 cm-' (see below).

All gratings were calibrated in the single-beam modewith the rotational spectrum of atmospheric watervapor.6' 7 The calibrations were evaluated by a linearleast-square calculation since the grating drive is linearin wavenumber. Between 11 and 22 water lines wereemployed throughout the respective wavelength regionof each grating. The 4-lines/mm grating was an excep-tion because of the sparsity of isolated intense transi-tions of water in this range.

The extension of the instrumental range to approxi-mately 35 cm-' was performed with the techniquedescribed by M5ller and McKnight.' A 4-lines/mmgrating blazed at an angle of 26°45' and used in thefirst order served as the dispersion element. The instru-ment was converted to single-beam operation sincethis increased the energy by a factor of 2. The totalfilter combination used consisted of a CsI chopper, onecoarse and two fine scatter plates, two 3-lines/mmpolyethylene echelette transmission-filter gratings in-stalled in the mercury-lamp area and the beam-com-bining area, respectively, and a quartz-black polyethy-lene transmission filter.

Figure 1 shows the rotational water spectrum takenin this way between 35 and 50 cml. The region wasscanned at 0.23 cm-'/min and a time constant of 40sec with the slits about one-half open (width 5.5mm=0.76 cm-' at 41 cm-'). The assignments and linestrengths (g cm-2 at 300'K) were taken from Bene-dict's tables.7 Although this spectral region has appearedseveral times elsewhere in the literature,9" 0 it is repro-duced here as the first example of the application of

6 L. R. Blaine, E. K. Plyler, and W. S. Benedict, J. Res. Nat].Bur. Std. (U. S.) 66A, 223 (1962).

V W. S. Benedict, Table of the Water Vapor Spectrum (un-published).

I K. D. Muller and R. V. McKnight, J. Opt. Soc. Am. 53,760 (1963).

9 E. K. Plyler and L. R. Blaine, J. Res. Natl. Bur. Std. (U. S.)60, 55 (1958).

10 H. Yoshinaga, S. Fujita, S. Minami, A. Mitsuishi, R. A.Oetjen, and Y. Yamada, J. Opt. Soc. Am. 48, 315 (1958).

20

VOLUME11 54, NUMBER 1 JANUARY 1964

January1964 ROTATIONAL SPECTRUM OR

90TABLE I. Observed and calculated vacuum wavenumbers of thepure rotational transitions of HF between f=0 and 10.

Apparent SpectralTransition Vacuum wavenumbers (cm-') half-width slitwidth

JJ- Observed Calc. - Obs. (cm-') (cm-')

01 41.30±t0.71 -0.17 1.3 0.81--2 82.35±0.25 -0.18 2.2 1.623 122.834±0.28 +0.30 3.5 2.134 163.92±0.13 +0.01 2.9 1.745 204.50±0.12 +0.03 2.6 1.156 244.97±40.16 -0.09 2.1 1.56-4 284.98±0.13 -0.05 1.9 1.57->8 324.52±0.22 +0.10 2.0 1.589 363.89±0.18 -0.02 1.2 0.79-*10 402.77±0.18 -0.03 1.6 1.4

10-*11 441.05±0.29 +0.01 0.8

Moller andto spectra."1

80 I-

70 I-

U 60z

a:

t- 40

H

H

X 30McKnight's echelette transmission filters

J=9-1

J=8-9

I-.

1-

20HRESULTS AND TREATMENT OF THE DATA

The measured wavenumbers of the rotational transi-tions of HF, together with their apparent half-widthsand spectral slitwidths, are compiled in Table I. Theirexperimental uncertainty is the propagated probableerror computed from the uncertainties of the linearcalibration curve (this contributes two error terms)and the error in the wavelength reproducibility. Thelatter contribution is the largest for the 20-, 30-, and40-lines/mm gratings, which have very small calibrationerrors. This is in contrast to the 4-lines/mm grating,for which the calibration error is predominant. In allcases where wavenumbers of a given transition had beenmeasured with two gratings the final result was con-sistently within the combined experimental error deter-mined from the individual errors.

100

90 /

so 91 1\I A7-3 t2)8' 0 IL JI202, 12)

Spectral Width 32 - 625

70 (187.4)

60

514 - 523

50 (4837)z

Q: 24~- 431 (1824)140 (2 o2 ii (1625)5

30 ,~-3,, (5962)3 -? 0-ill

20 1 I . I

35 40 45 50WAVENUMBER (cm-')

FIG. 1. Rotational spectrum of atmospheric water vapor be-tween 50 and 35 cm-' obtained by means of a modified Perkin-Elmer 301 (see text). The numbers in parentheses are the linestrengths at 300°K in g-cm-'. The level assignment is given inthe K.-,Ki notation.

1" See Ref. 3.

10 I

0

J=l0OII

0

410

l

350 370 390 410 430 450

WAVENUMBER (cm-')

FIG. 2. The rotational transitions J=8, 9, and 10 of hydrogenfluoride and the extraneous vibrational band at 389.1 cm-'.

The energy expression, which contains sufficientterms to represent the data satisfactorily, is"2

F(J)=Bo(J+1)J-Do(J+1)YJ', (1)

where Bo is the rotational constant and Do is thecentrifugal stretching constant, averaged over theground vibrational state. The next higher-order pertur-bation term Ho(J+ 1)3J3 is estimated to contribute lessthan 1 part in 5000, or 0.06 cm'l, to the transitionJ= 8 and approximately 0.16 cm'- to J= 10. The pre-cision of the wavelength measurements and the fewtransitions of sufficiently high J do not warrant theinclusion of the term Ho(J+1)'J3 into the expressionfor the energy.

The frequencies of the transitions are then given by

F(J+ 1)-F(J) = 1(cm-')= 2B 0 (J+ 1)-4Do(J+ 1)3. (2)

Equation (2) was evaluated with a linear least-square calculation. The measured wavenumber of eachindividual transition was weighted proportionally tothe inverse square of its probable error (see Table I).The resulting values of Bo and Do are shown in Table II,whereas the differences between the calculated wave-numbers from Eq. (2) and the observed wavenumbers

12 G. Herzberg, Spectra of Diatomic Mllolecules (D. Van NostrandCompany, Inc., Princeton, New Jersey, 1955), 2nd ed., p. 107.

, . . . . .

OF HYDROGEN FLUORIDE VAPOR

I

22 WALTER G. ROTHSCHILD

TAABLE II. Comparison of some rotational constants of HFobtained from pure rotational and from rotation-vibrationspectra.

Constant" Reference

Bo =20.55940.006 cm-l This work

20.57

20.559±0.002

20.55340.006

Do=0.00211 ±-0.000040.00212-40.000020.0021140.00005

Remarks

Pure rotational spectrumfrom J=0 to 10

1 Calculated from three ro-tational transitions oflow J (assumed Do=0.0021)

14 Fine structure of H2 -F 2Ilame emission spectrum

2 Fline structue of the 0+-1and the 0s-2 as wellas five pure rotationallines of high .J

This work142

-All experimental uncertainties given in terms of the 95%, confidencelimnit.

are entered in Table I. The uncertainties attached toB and D are the computed 95% confidence limits."3

Table II also gives a comparison between the molecu-lar constants of HF determined from pure rotationaland from rotation-vibration spectra. The agreementbetween the values of Bo and Do obtained bv the differ-ent techniques is very good. The precision indicesreported here are equal to the one given by Kuipersel al.2 although, at the present, wavelength measure-ments in the far infrared are less precise than wave-length determinations in the infrared region.

EXTRANEOUS BAND AT 389.1 cin-'

Figure 2 shows that part of the rotational spectrumof HF where the intensities of the absorption lines

13 L. G. Parratt, Probability and Experimzental Errors in Science(John Wiley & Sons, Inc., New York, 1961), pp. 126-31. Thenormal equations of y=ax-bx 3 have to be formed, where yrepresents wavenumber and x equals J+-1, a=2B, b=4D. Thecomputation of the 95% confidence limits was carried out byomitting the transitions x= 1, 2, and 3 and assigning equal weightsto the remaining y's. This greatly facilitates the computation ofthe standard deviation besides resulting in a more conservativevalue.

14 D. E. Mann, B. A. Thrush, D. R. Lide, Jr., J. J. Ball, andN. Acquista, J. Chem. Phys. 34, 420 (1961).

decrease rapidly with increasing J because of thelowered fractions of the rotational population. Thereappears an extraneous band between J=8 and J=9.The insert to Fig. 2 shows the appearance of the bandafter the absorption cell had been equipped with afresh set of polyethylene windows. The P, Q, R struc-ture of the band is well delineated and the Q branch,at 389.0, cm-', is very sharp. As can be seen, the HFhas mostly disappeared. The total pressure in the cellafter completion of the scan, however, was only slightlyless than the initial pressure of 441 nun Hg. Successivescans employing the previously installed windowsshowed a certain "aging" of the window material, whichresulted in a weaker intensity of the extraneous bandand a stronger intensity of the rotational lines of HFwith successive fillings of the cell. The upper curve inFig. 2 was taken after four repeated fillings and evacua-tions of the cell and shows the spectrum at about thesame total pressure of 441 mm Hg.

An identification of the band is not within the scopeof this paper. Apparently, it belongs to a decompositionproduct due to the attack of HF or a reactive impuritycontained in it, on polyethylene.

CONCLUSION

It has been shown here that the rotational constantsB and D of hydrogen fluoride determined from the far-infrared rotational absorption spectrum agree extremelyclosely with the ones obtained from extensive rotation-vibration spectra in the infrared.

Furthermore, it has been shown that polyethylene,which is one of the few as well as extensively usedwindow materials in the far infrared, can give riseto extraneous bands by a reaction with the samplematerial.

ACKNOWLEDGMENTS

I anm very grateful to Dr. E. E. Weaver for the prep-aration of the hydrogen fluoride samples. I deeplyappreciate the help and advice of Dr. K. D. Mbller,Fairleigh Dickinson University, Teaneck, New Jersey.Thanks are due Mr. R. H. Bohnsack for machining theabsorption cell.

22 Vol. 54