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Research Paper RP1944Volume 41, December 1948Part of the Journal of Research of the National Bureau of Standards

Absorption Spectra of Methane in the Near InfraredBy Richard C. Nelson,

1Earle K. Plyler, and William S. BenedictA grating spectrometer with a PbS cell for detector has been used for the measurementof the infrared absorption bands of methane in the region of 1.66 /-t. Many lines of the P,0, and R branches of the 1.66-ju band have been observed.These are well resolved and a re of the correct structure and spacing for the F2 componentof 2 vz. The lines for values of / up to 10 are sharp^ showing no indication of splitting due tointeraction with neighboring state s or to centrifugal distortion. The rotational constantsobtained for this band are B' = 5.178, 3 = 0.0346. The la tter value is lower tha n in thevz fundam ental. Other bands observed are more, complex and irregular, presumably dueto mutual interaction.

In the infrared spectrum of methane there areat 3020.3 cm"1, and z>4 at 1306.2 cm"1. Because

v\ at 2914.2 cm"1 and v2 at 1526"1, are not active in the infrared, although

to give ban ds in the nea r infrared. M an y

2One of the unsettled

ban ds. Accordingly it was thoughtt further experimental da ta with higher resolu-would be of value. Th e presen t paper reports/*, and fromy, with particular emphasis on oneF2 com-3, at about 6,004 cm"1. Quite recen t

cM ath , M ohler, and G oldberg [2] hav e also2v z band under high resolution.In our studies, high resolution was obtained by

1 Research Associate, Northwestern University.2 Figures in brackets indicate the literature references at the end of this

structed by Cashman [3] as the detecting unit.One of the authors [4] has previously given adescription of the instrument and only a briefoutline of the arrangement will be repeated here.Figure 1 shows the plan of the optical parts ofthe spectrome ter. Th e system is designed ac-cording to the arrangement described by Pfund[5]. The paraboloidal mirrors have a focal lengthof 2 m and are 12 in. in diam eter. The g ratingh^s 15,000 lines per inch 'and the ruled surface is3 |by 5 in., giving a theoretical resolution in thefirst order of 75,000. An ellipsoidal m irror, witha conjugate focal ratio of 1:3, was used to focusthe energy from the exit slit onto the PbS cell.With this magnification, spectrometer slits 18 mmin length could be used with the PbS cell, whichpossessed a sensitive surface 7 mm long. Atxtngsten lamp was used as the source, and aquartz lens focused the filament on the entranceslit of the spectrom eter. The abs orption cell,which was 60 cm in length, was placed in front ofthie entranc e slit. A chopper, which interru ptsthe radiant energy approximately 1,000 times asepond, was placed imm ediately in front of the en-trance slit.

!For any selected region the grating was rotatedcontinuously. Th e driving mech anism has fivescanning speeds, and the Speedomax recorder hassr speeds for the chart, a selection which made itpcjssible to have dispersions of 50 to 0.02 A/mm onthe recording chart.A special narrow-band-pass amplifier was usedwith the PbS cell. Th e over-all voltage gain was615

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s,D

PARABOLOIDALMIRROR PLANE MIRROR

^ELLIPSOIDAL. ^ 1 MIRR OR

PbS CELL

PLANE MIRRORPARABOLOIDALMIRROR

FIGURE 1. Arrangement of the optical components of the spectrometer.approximately 1.8 X 108. The details of the am-plifier hav e been given in a prev ious pu blication [4].In the region around 1.66 n, runs were made attwo dispersion scales on the recorder chart.Measured wavelengths are largely based on tworuns made with slits 0.7 cm"1 spectral width, thedispersion on the chart being abo ut 15 cm~Vin.A commutator in the gear train driving thegrating actuated a pen that placed marks on thepaper corresponding to equal increments ofmotion of the nut upon the tangent screw, whichmoves the grating.Wavelengths were measured with reference tolines of the Hg spectrum . A record of the spec-trum in all orders over the desired region wasm ad e. Th en using the lines 15295.2, 5460.74(3d order), and 4358.35 A (4th order), a qua dra ticexpression was obtained for wavelength in termsof measurements on the scale impressed on therecord . An equation of the form Xi=Xo+

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0 0

180

160

120

11.4 11.0 10.6 10.2 9.8 9.4 9.0 8.6 8.2 7.8 7.4 7.0 6.6 6.2 5.8 5.4 5.0 4.6 4.2SCALE NUMBER

FIGURE 2. Absorption spectrum of the 1.66-p band C H 4 .Th e cell was 60 cm in length and the gas at atmospheric pressure.0 5

3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5SCALE NUMBERFIGUKE 3 . Center of the 1.66-y. band, showing fine structure states of the zero branch.

2 .4 2 .3

lines. These lines m ay be pa rt of a comb ina-the absorption of the gas was measured w ith1, the zero branc h showedstruc ture . Figure 3 shows the central partthe ban d. Th e gas was at atmospheric pressuree observations. When a smaller pressure

Q branch was obtained, but theintense compon ents were not prese nt.

The intensities given are measured to within 2percen t. The stronger lines ma y actually be moreintense tha n the measurem ents indicate. Th at is,the finite slit widths may make it impossible tofind the maximum absorption at the center of thelines. All faint lines th at measure less than 3 per-cent are arbitrarily marked 2 percent in intensity.The intensity figures in the table denote the per-centage absorption of the minimum point of thelines.617

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All the obse rved lines of appre ciable inte nsity forthe region are listed in table 1. W ave numbe rs ofsome of the lines are m ark ed for identification. Asufficient number of lines are numbered on the fig-ure so that the tables can be related to the experi-m en tal results. Th e ba nd for the 1.10- to 1.13-/*region, shown in figure 4, does no t hav e th e reg ularstructure as observed in the 2vz band. The wave-lengths and intensities of all the lines are given intable 2.The 2J>3 band gives sufficient data for calculatingsome of the consta nts of me than e. Th e only linesin the CH 4 absorption that can be given a definiteinterp reta tion are listed in table 3. These are thestrongest lines in the region, and form a bandconsisting of P, Q, and R branches of simplestructure, the band bearing a marked resemblanceto the vz fundamental. The vibrational transitioninvolved, 2v3, is the first overtone of that funda-me ntal. Th e theory of the structure of this bandhas been given by Johnston and Dennison, [6] andby Shaffer, Nielsen, and Tho m as [7]. Th e first-named authors have pointed out that the upperlevel is six-fold degenerate in the zeroth-orderapproximation, but that the first-order Coriolisinteraction due to the internal angular momentumof the vibration removes the degeneracy, givingsix different energies for each value of the rota-t ional quantum number J. At

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1 6 0

[30

100

1 7 0

1 4 0

no 18421.3cm"11 1 1

6 0 9

- \ ^ N""' \

pi46J9 61 .8809.0cm-11 1 1 1 1

1METHANE +

/ f \- 1 . f y 'If 46.2

seoi .ecm-'

WATER

V V

WATER

r\N

VAPOR

-

VAPOR

3.5 3. 2 2.9 2. 6 2. 3 2.0SCALE 1.7N U M B E R 1.4 0 . 8 0 .5 0 .2

4. Upper curve shows the absorption of water vapor in the atmosphere; lower curve is the absorption of methaneinterposed on the, atmospheric absorption.2. Wavelength, wave number, and intensity of

observed lines in the 1.16-fx regionWavenumber4cm r18656.58645.28637.68628. 68616.6

8606. 58601. 68587. 2

W a v e -lengthA11548.911563.911574.011586.211602.3

11615. 911622. 611642.0

Absorp-t ionPercent3030201520

303525

Wavenumbercm -18567. 78546. 58523. 78509.08489.68460.98421.3

Wave-lengthA11668.511697.5

11728.811749.011775.9 '11815.911871.4

Absorp-t ionPercent1515

1055210

The centrifugal splittingof the particular vibra-in question, and is proportional to( J + 1 ) 2 . The resonance splitting, proportionalis very dependent on the vibrationalin the */4 fundamental [8], the split-is experimentally observable as low as J=3,s been well accounted for [11] by the second-In the vz fundam ental [8] however,so in the 2v3 band here studied, the

experimental observation is t h a t the lines of theP and R branches are sharp and narrow, and agreein position and intensity with the predictions ofthe first-order theory, except for relatively smallcorrection for centrifugal stretching, up to e / = l l .This shows that the second-order interactionsleading to splitting are of comparatively minorimportance in 2vz. Presumably such interactionsare much more important for the other overtoneand combination bands in the region, resultingin bands of much more complex structure whichwe are unable to interpret .

The following equations represent the observedlines to the required accuracy:B branch: v=vQ+B'[(J+l) (J+2) +( J ) ] S ' ' J ( J ) ZQ branch: v=vo+B'[(J(J+l)-6fl-B"J{J+l)P branch: v=vo+B /[(J-l)J-2UJ+2)\-B"J(J+1)+4DJ\ j

(1)

of Met hane 619

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20 40 60 80 100 120 140 160 180 200 220

FIGUKE 5. Plot of the experim ental d ata for the determ inationof the molecular constants.

Upper plot is based on eq 3, and the lower plot is based on eq 2.The following combinations of eq. 1 are usefulin deriving the values of the constants:

(2)(3)

In these equations, v0 is the band origin, B' andB" are the effective reciprocal moments of inertiafor the upper and ground vibrational levels, re-spectively, J is the rotational quantum number ofthe lower level, f is the constant representing theangular momentum due to the upper-state vibra-, tion, and D is the constant representing the correc-tion due to centrifugal stretchin g. As explainedabove, the effect of the centrifugal forces is both,to stretch the molecule, resulting in an equal low-ering of all levels of equal J, and to distort it, re-sulting in a splitting of those levels. W e have cal-

culated both effects for the ground vibrationstate, making use of the published formulas [7the former effect is larger by a factor of about Hence it is permissible, for lines where the expermental splitting is unobservable, to make use ofsingle constant D to correct for the centrifugstretching, as is the common practice with ditomic or linear molecules.In Figure 5 are plotted the values of the lefhand sides of eq 2 and 3 as a function of J(J+1The points fall quite well on straight lines, up 7=11, the slopes and intercepts yielding the folowing com binations of constants: J5 '(l + f)

5.357 cm "1, Z?=1.9X10"4 cm "1, y o + B '(l 3f) 6010.45 cm"1, (B' B" ) = 0.066 cm" 1.The value of D is not well determined by the daof figure 5; the slope as drawn is the theoreticalcalculated valu e, and also fits the d at a for th e fundamental.In order to obtain the values of the individuconstants, use is made of data from other banto obtain B ", the rotational constant of the grounstate , common to all ban ds. By working up an analogous way the data of Nielsen and Nielse[8] on the vz fundamental, and of Dickinson, Dilloand R ase tti [9] on the R am an lines of the samband, we obtain B"=5.244 cm"1. (This compares favorably with the value proposed by Chil[10], 5.252 cm "1, from an analysis of the vz andfundamentals. The perturbations in the lattband, however, make it somewhat less suitabfor a precise eva lua tion ). Th is yields for thesub-band of 2 v3, B r=5.178 cm"1, f=0.034j,0=6005.81 cm"1. Th e corresponding values fv3 are ' = 5.207 cm "1, f=0.0536, *>0=3018.cm "1. If there were only harm onic terms in tpotential energy, the value of f for the two banshould be the sam e. Th e observed difference far beyond the experimental error and must due to anharmonic terms in the potential energ

According to eq 3, there should be a constadifference of 5 '( l+ 3 f) = 5 .7 2 cm"1 betwe[B(J)+P(J)]/2 and Q(J). This is very nearwhat is observed, although the lines in thebranch, being not quite fully resolved, are nknown with great accuracy. The re is , howeva slight bu t definite anomaly near J = 9 , as showby the differences in tab le 3. I t would appethat the Q branch is weakly perturbed by anothvibrational level with zero internal angular mmentum and a different value of B', so that cro620 Journal of Resear

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TABLE 3. Identified lines in the 2v$ band of CH 4

J

01234567891011121314 '15

Ob-servedcm ~l6015.86026.46036.86047.06057.36067.26077.16086.96096.46106.16114.76123.86133.26 1 4 2 . 26150.36158.3

Calcu-lated

cmr 16016.176026.386036.83. 6047.106057.256067.236077.056 0 8 6 . 716096.196 1 0 5 . 526114.666123.616132.396140.946149.336 1 5 7 . 52

Ob-servedcm ~l

6004.26003.96003.46002.76001.96000.85999.65998.45 9 9 7 . 55995.65994.65992.9

Calcu-lated

cm~ l

6004.606004.346003.946003.416002.756001.966001.045999.985 9 9 8 . 755997.475996.025994.445 9 9 2 . 72

P(J)Ob-servedCW" 1

5994.25983.35972.25961.05949.65938.35926.75915.05903.45891.65 8 7 9 . 55866.95854.4

Calcu-lated

cm *1

5994.225 9 8 3 . 255972.145960.935 9 4 9 . 585938.135 9 2 6 . 595914.945903.205891.365879.435867.435855.35

F2 component occurs near this point.A x sublevel of 23, or possibly some other combination band withi symmetry.In addition to the good agreement between the

P and R

J" = 5 andgth of those with J"=6 is markedly apparent .The ultimate goal of a study of the CH 4 spec-

effective f 's of all ob servable overto ne and

of a poten tial function. From th e small num berof completely interpreted bands this is not yetpossible, although the present work is a short stepin tha t direction. Fu rthe r experimental studyunder high resolution of CH 4 and its deuteratedderivatives, and further theoretical studies usinga poten tial function of somewhat greater simplicitythan that of Shaffer, Nielsen and Thomas [7], arerequ ired. A simplification of the experim entalband structure may be expected if measurementsare made at low temperatures.References

[1] Gerhard Herzberg, Molecular spectra and molecularstructure (D. Van Nostrand Co., New York, N . Y.,1945).[2] Marcel V. Migeotte, Phy s. Rev. 73, 519 (1948); R. R.M cM ath, O. C. Mohler, and L . Goldberg, Phys.Rev. 73, 1203 (1948).[3] R. J. Cashman, Proc. Nat. Elec. Conf. 2 (Chicago,1946).[4] R. C. Nelson and W. R. Wilson, Proc. Nat. Elec.Conf. 3 (Chicago, 1947).[5] A. H. Pfund, J. Opt. Soc. Am. & Rev. Sci. Instr. 14,337 (1927).[6] D. M. Dennison and M. Johnston, Phys. Rev. 47,93 (1935).[7] W. H. Shaffer, H. H. Nielsen, and L . H. T homas,Phys. Rev. 56, 895, 1051 (1939).[8] A. H. Nielsen and H. H. Nielsen, Phys. Rev. 54, 118(1938). '[9] R. G. Dickinson, R. P. Dillon, and F. Rasetti, Phys.Rev. 34, 582 (1929).[10] W. H. J. Childs, Proc. Roy. Soc. (London) 153, 555(1936).[11] H. A. Jahn, Proc. Roy. Soc. [A], 168, 469, 495 (1938);H. A. Jahn and W. H. J. Childs, Proc. Roy. Soc,[A], 169, 451 (1939).WASHINGTON, October 1, 1948.

on Spectra of M ethan e 621