N2 and Ar broadening and line mixing in the P and R branches of the v3 band of CH4

J. Quanr. Spectrosc. Radiat. Transfer Vol. 57. No. 2, pp. 157-176, 1997 Publishedby Ekvier Science Ltd. Printed in Great Britarn 0022-4073/97 517.00 + 0.00

Pergamon

PII: 80022-4073(%)00130-6

NZ AND Ar BROADENING AND R BRANCHES

AND LINE MIXING IN THE P OF THE v3 BAND OF CH, A. S. PINE

Optical Technology Division, National Institute of Standards and Technology, Gaithersburg. MD 20899. U.S.A. (Received

1.2June 1996)

Abstract-Nz- and Ar-broadened spectra of the allowed P- and R-branch manifolds for J < 10 in the v3 band of CH4, have been recorded from the Doppler limit to - 67 kPa at T = 295 K using a tunable difference-frequency laser spectrometer. The broadening coefficients exhibit larger variations among the tetrahedral components in the R-branch manifolds than in the P branch, which in turn are very similar to the Q branch previously measured [A.S. Pine, J. Chem. Phys. 97, 773 (1992)]. The broadenings for Ar are uniformly 88(l)% of those for NZ. Line intensities, pressure shifts and Dicke narrowing coefficients are also obtained. Strong line mixing among the blended tetrahedral components is observed, and an analysis is presented restricting line coupling among transitions with the same nuclear spin A, E or F symmetry with the sum of the mixing coefficients for a given symmetry in a J manifold constrained to zero. Published by Elsevier Science Ltd

1. INTRODUCTION

line shapes in methane are required for spectroscopic monitoring of the atmospheres of the Earth and the outer planets and some of their larger satellites. In an earlier tunable laser study’ of self and foreign gas broadening in the Q branch of the strong v3 band of CH.+, we found the broadening coefficients to depend systematically on the tetrahedral symmetry, C = A,, AZ, E, F, or F2, and order index, N, for a given J, as well as on the rotational J value. Several other broadening studies in other bands and branches of methane2-I6 have also noted a symmetry dependence, with some E transitions tending to be narrower than A or F, as had been calculated by Tejwani et a1;‘7-‘9and an order index variation had been observed by Rinsland et al’ for the v4 band. The J/C/N pattern of broadening coefficients for the v3 Q branch’ were found to be remarkably similar for the heavier buffer gases, Nz, O2 and Ar, differing only by a constant factor within the experimental precision of y 1.5%. The lighter buffers, H, and He, were also similar to each other, but not to the heavier. The similarity between N2 and Ar broadenings is even more apparent in the present v3 P and R branches measured here. For both buffers, there is better correspondence between the P and Q branches of v3 than with the R branch which exhibits somewhat greater C/N variations. Dicke narrowing of the Doppler distribution is also evident in the present measurements, here exhibiting a systematic transition dependence. In the previous v3 Q branch measurements,’ congestion and line overlap limited least-squares fitting of the spectra to pressures only up to N 13.3 kPa (100 torr). At pressures of 26.6 and 66.7 kPa, the fits were not convergent and linear extrapolations from the lower pressures produced significant deviations from the measurements. These instabilities and deviations were attributed,’ without proof, to line mixing, since such behavior was familiar from studies of Q branches of linear molecules such as N20,” C2H2,2’.22and HCN.“,” For the Q branch of methane, however, it was not clear if the dominant mixing arose from rotationally inelastic (AJ # 0) collisions, as for linear molecules, or from quasielastic (AJ = 0) collisions coupling the various tetrahedral components of a particular J level. Millot et al” observed inelastic line coupling between the Q(3) A2 and Q(4) A, lines in the Raman spectrum of the 2v2 band of CH,. Collisional

158

A. S. Pine

Line mixing due to quasielastic collisions can be isolated in the P and R branches where the J manifolds do not overlap at atmospheric pressures, but the weak centrifugal distortion and Coriolis splittings within a manifold do. Benner et a124.25 have since shown that the P and R branches of v3 of methane do exhibit rather strong line mixing based on multispectrum fits to high resolution Fourier-transform interferometer data. However, their analyses did not consider symmetry selection rules for the collisions or sum rules on the mixing coefficients, which we attempt to address here. In the present work, satisfactory fits are obtained if we prohibit collisional cross-relaxation between different nuclear spin A, E or F components and impose a zero sum of mixing coefficients among the manifold transitions of a given spin symmetry.26 2. EXPERIMENT

The methane P and R branch measurements were performed under similar conditions to the Q branch’ for consistency. Spectra of each P(J)and R(J)manifold for J < 10 were recorded with a linear-scan-controlled difference-frequency laser27-29having an instrumental line width of - 1 MHz. The laser was chopped at 800 Hz, split into two beams synchronously detected by reference and sample InSb photodiodes at T = 77 K feeding matched lock-in amplifiers with 40 msec time constants. The analog ratio of the transmitted to incident lock-in signals was recorded in order to reduce noise due to laser amplitude fluctuations. The spectra were scanned at 300 MHz, digitized at a 20 Hz rate, and stored in a computer for subsequent data processing and least-squares fitting. Wavenumber calibration was referenced to the FTIR measurements on methane by Brown30 and Tarrago et a13’with interpolation using transmission peaks of a confocal interferometer with a 0.050030625(50) cm-’ free-spectral-range recorded simultaneously on a 10 x finer grid for enhanced precision (note, estimated 20 uncertainties in parentheses are written in terms of last digits). A 1.5 cm-’ interval was scanned for each trace on a uniform grid of 3000 points, or about 18 points in a Doppler full width at half maximum (FWHM). The natural isotopic methane sample was of commercial ultra-high purity grade (nominal purity 299.97%) and the N2 and Ar buffers were claimed to be 299.9% pure. The measurements were performed at room temperature, T = 295(l) K, using a 69.5(2) cm long cell with CaF2 windows mounted at Brewster’s angle to reduce channeling on the unity transmittance baseline. For each allowed P(J)and R(J)manifold, a Doppler limited pure methane trace was recorded at low pressures, 15-23 Pa (0.11-O. 17 torr), to provide reference transition frequencies and relative intensities and to obtain a good estimate of the unity baseline. Then a premixed CH4/N2 or CH4/Ar sample was admitted to the cell at nominal pressures of 6.67, 13.33, 26.66 and 66.66 kPa (50, 100,200, 500 torr) and scanned with intervals of less than 10 min between traces. Pressures were measured simultaneously with two capacitance manometers with 133 and 1333 kPa ranges and nominal accuracies of 0.5%, but they generally agreed to 0.1% and the average value was used. The mixtures were prepared in a 6 1 spherical electropolished stainless steel chamber at a nominal concentration of l/750 for the R branch and l/500 for the weaker P branch. The actual concentrations are somewhat lower than the nominal since the buffer gas fill forces some of the methane out of the mixing chamber into the pressure gauges and connecting tubing. 3. DATA

ANALYSIS

AND FITTING

PROCEDURE

The line shape fitting is carried out on the absorption spectrum, U(O), obtained by applying Beer’s law to the transmission spectrum, S(w), normalized to the unity transmittance baseline, B(m), a(o) =

(llP,L)ln[B(o)lS(w)l.

(1)

Here Pais the partial pressure of the active molecule and L is the cell length. B(o)is interpolated from the Doppler-limited trace on a coarse grid of 200 points and can be adjusted interactively during the fitting procedure. Baseline variations can arise from drift in the fringes of the detector windows and filters in the separate beam paths and from beam steering due to the pressurization of the Brewster window cell. Manual adjustments of B(w) are typically less than l%, but

N2- and Ar-broadened

1.59

spectra of CH4

the uncertainties in the baseline remain an important source of error in the fitted line parameters. Spectra of the R(0) line broadened by Ar are shown in Fig. 1. The solid curve is the observed trace and the points are the fitted line shape; the observed-calculated residuals are displaced below the traces for visibility. The weak isotope line -0.1 cm-’ above the main line (R(1) of ‘CH,) and an even weaker “forbidden” line -0.06 cm-’ below are included in the fit. The low pressure, pure

CH4/Ar

v3 RO I

I

I

I1

I

P (AI-) kPa

0.0 O-C Gaussian ._.. O-C Rautian . . . . O-C Voigt

0

6.67 A/-

13.33 26.66

* -0.5

I I I I I I f I t I I , I_& , I I I I I 1 ,wi6; 3029.0

3028.9

3028.8

3028.7

3028.6

Wavenumberhm-1 Fig. 1. Absorbance spectra of the vj band R(0) line of CHI broadened by Ar (-) with the obs-calc residuals from fitted Gaussian and Rautian (. .) and Voigt (-) displaced vertically for visibility. The dots are not distinct when the vertical displacements are small.

A. S. Pine

160

methane trace is fit to a Gaussian profile with a width only -0.6% Doppler half width at l/e intensity,

higher than the calculated

0 = w, (2ks T/Mc~)“~.

(2)

Here w, is the transition frequency, k, is the Boltzmann constant and M is the methane molecular mass. The small excess width manifest by the barely observable residuals for the P(Ar) = 0 trace in Fig. 1 arises from a slight amount of self broadening and some instrumental effects dominated by the finite time constant and scan speed. When Ar is added, the line is well fit at all pressures by the Dicke-narrowed hard-collision Rautian profile,32 01(o) = (&,/&o)Re{r(x,

y + z>>,

r(x, y + 2) = w(x, Y + z)/]l - J&x,

y+

(3)

z>l,

exp( - t’) dr/[x - t + i(y + z)].

w(x, y + z) = (i/n)

s

(4)

(5)

Here S,,,is the integrated line strength, w(x, y + z) is the complex probability or error function (we use the Humlicek algorithm33 computationally), and the variables are given in dimensionless form scaled to the Doppler width, C, according to x = (w - 0,)/o,

y = ym/c, z = Pm/a,

(6)

where ymis the pressure-broadening parameter resulting from state- or phase-changing collisions and P,,, is the Dicke-narrowing parameter due to velocity-changing collisions. With no velocity-changing collisions, z = /I = 0, and the Rautian profile reduces to the Voigt profile, Re{ w(x, y)}. Residuals from Voigt fits to the Z?(O)line of methane are also shown in Fig. 1 by the light solid lines; they are most prominent at intermediate pressures and vanish at high pressure. Another Dicke-narrowed profile given by Galatry in the soft-collision limit34is not shown since it is almost indistinguishable from the Rautian here. In Fig. 2, we plot the fitted broadening parameters for the three line shapes compared to the weighted average from the Rautian to indicate their relative linearity with pressure. Although the differences are small, they are statistically significant, with the hard-collision Rautian yielding better results, as might be expected when the mass of the buffer gas is greater than the active molecule. Because of a strong correlation between the broadening and narrowing parameters in the fits, we have obtained the j3,, from the 6.67 kPa (50 torr) trace, where it is best determined, and scaled it linearly at higher pressures. This constraint is used for Bn,throughout the P and R branch fits, as it was for the Q branch.’ The Rautian profile yields excellent fits for J < 2, even when lines strongly overlap as shown for the Ar-broadened transmittance traces for R(2) in Fig. 3. Here the residuals are multiplied by three to show that there are no deviations beyond the noise level of the experiment. The weak isotopic R(3) lines are again included in the fit. The retrieved broadening and intensity parameters fit to individual traces are linear with pressure to better than 1%. Here we have constrained the relative integrated intensities of the E and F symmetry components to those measured in the Doppler traces. This constraint prevents intensity non-linearities due to parameter correlation at higher pressures when the lines are not distinctly resolvable. These relative intensity constraints are also used at higher J where the line strength ratios are usually within a few percent of the nuclear spin weights of 5: 3:2 for A :F: E transitions. The small deviations from the spin weights are mostly due to intensity sharing with perturbing levels from other members of the vibrational “pentadr’.3s~37 We also observe significant differences for the narrowing parameters, /I,,,, for the E and F components of R(2) as well as for the other J values, so we retain the transition dependence instead of averaging all the lines as we did for the Q branch.’ The differences in /I,,,are somewhat surprising since the velocity-changing collisions are kinematic and are not expected to depend on the internal rotation, vibration or spin state of the molecule to first order. We emphasize that, despite the strong overlap of the E and F symmetry components for the R(2) and P(2) manifolds at high pressures, it is not necessary to invoke line mixing to obtain good fits within the experimental noise level. This signifies the lack of collisional coupling or cross-relaxation

Nr and Ar-broadened

CH,/Ar

RO

v3

161

spectra of CH,

broadening

35

30

25

‘;

E 0 “:

2o

2

15

0

Voigt Galatry Rautian

V

10

q

x

5-

0

5

10

15

20

25

30

35

40

45

50

60

55

65

70

P/kPa Fig. 2. Pressure dependence of the broadening parameters from the Voigt, Galatry, and Rautian fits to the R(0) line where the straight line through the origin is the weighted average of the Rautian parameters.

between levels of different nuclear spin. At higher J, the manifolds have at least two transitions of the same symmetry, so that line mixing is possible. The Ar-broadening R(3) manifold fit with and without line mixing is shown in Fig. 4, indicating the systematic deviations obtained when the coupling between the two F symmetry components is ignored. We incorporate line mixing by modifying Eq. (3) in the form,26

4~) = (l/&c) c f%JRe{r(x, y + z)} + m

LIm{r(x,

y+

z)}],

(7)

where &,, is the mixing parameter for each transition, m, multiplying the dispersion-shaped imaginary part of the complex Rautian profile of Eq. (4). Here, S,,J,,, = N,,nmin the notation of the previous paper. 26In the weak line coupling or small overlap limit when the relaxation matrix elements, W,, , are much smaller than the separation, onr - wn, of the coupled transitions, Rosenkranz3’ has given a useful first-order perturbation theory approximation for the line mixing parameters,

L =2 1

P”

W”,/,&(W, - W”),

(8)

“fin

where the p,,, are the transition

moments. The off-diagonal

W,,,,, represent

thermally-averaged

A. S. Pine

162

collisional scattering cross sections or coherence transfer rates from line m to line n; the inverse scattering is related by detailed balance, W,, = Wn,,p,/pn, where the p,, are the populations of the lower energy levels of the transitions. Since the scattering rates are linear in pressure in the binary collision regime, the mixing parameters, cm, are also linear in pressure for the Rosenkranz first-order approximation, as are the line strengths, S,,,, the broadening parameters, y,,,, and the shifts, 6,, = CO,,- CO:,,where CO:,is the zero-pressure or Doppler-limited transition frequency. However, Eq. (7) is valid for line mixing to all orders at any overlap where all the parameters may,

1.0

CH4/Ar

v3 R2

Rautian 3 #

P (Ar) kPa -

6.67

P-.-

13.33

o-c x3 . . . .

26.66 66.66 4

-o.5"""""""'i""""' 3048.4 3048.3

3048.2

3048.1

eu W

3048.0

Wavenumberhm-1 Fig. 3. Transmittance spectra of the Y)band R(2) manifold of CH,, broadened residuals from fitted Rautian line shapes (. .) multiplied by 3 and displaced E symmetry line is on the left, F on the right.

by Ar (-_) with the obs-calc vertically for visibility. The

N2- and Ar-broadened

CH4/Ar

spectra of CHd

163

v3 R3 Rautian

0.5 cu

E IO w u *l-i

E

P (At-1

i! L” l-

kPa

0.0

I

Obs-Calc

x3

6.67 13.33 w

1 ine mixing..

I

. .

26.66

no mixinq

-0.5 3057.9

66.66

3057.8

3057.7

3057.6

Wavenumberhm-1 Fig. 4. Transmittance spectra of the v3band R(3) manifold of CH, broadened by Ar (-) with the obs-calc residuals from fitted Rautian line shapes with line mixing (. . .) and without line mixing (-) multiplied by 3 and displaced vertically for visibility. From left to right, the line symmetries are F, F, A.

in general, be non-linear with pressure. We have shown26 that the sum of the intensities, widths and shifts for coupled lines of the same transition moment and nuclear spin is conserved, and that the sum of their mixing parameters, Zngrn= (1/N&S,& = 0 to all orders. For quasielastic (AJ = 0) collisions, the pm are all equal, and if the transition moments, p,,,, are also equal, then the zero sum rule applies to the Cmthemselves. The lack of cross-relaxation and the zero sum for the mixing parameters among coupled lines implies-that Cm= 0 for a transition with no other component of the same symmetry in the manifold,

164

A. S. Pine

such as the A line in R(3) of Fig. 4, and that the &,,are equal in magnitude and opposite in sign for a doublet, such as the two F lines in R(3). We have imposed this zero sum rule in our fits by constraining C,,S,&, = 0 for all lines of a given A, E, or F symmetry in the manifold. The S, are included in the sums here since they are not exactly equal for a given symmetry because of the minor perturbations mentioned above. In Fig. 5, we display the R(6) and P(6) manifolds for Ar broadening to illustrate the critical effect of line mixing among the three F components and the two A components, and the negligible effect of the uncoupled but overlapped E component. Since the R(J) manifolds are more compact than the corresponding P(J), the line mixing becomes more apparent in the R branch at lower pressures. The residuals can be compared to those obtained in the multispectrum fit of the air-broadened P(6) manifold with unconstrained c,,,reported recently by Benner et al.25 We also have found that the line mixing parameters are strongly correlated to the other line parameters, particularly the shifts and the baseline adjustments, in the fits of real data. Therefore, we determine the cmfrom the higher pressure traces (66.66 kPa for J < 4 and 26.66 kPa for J 2 5) and scale them linearly with pressure elsewhere. This constraint, along with the relative intensity constraint noted above, may not be valid outside the Rosenkranz first-order approximation. 4. RESULTS

At each pressure, Pi, our fits yield position, o,, (and thereby shift, a,,,), intensity, S,, broadening, y,, narrowing, /I,,, and mixing, irn, parameters for each transition in the manifold subject to the constraints discussed in the previous section. In the mixing range where these parameters vary linearly with pressure, we can define a weighted average for a general pressure coefficient by (<) = Ciwi~~/Ciwi, where

wi =

(1/6(i)‘,

(9)

and & and S
(10)

These uncertainties provide an estimate of the combined standard errors in the trace fitting and the systematic errors due to baseline drift, pressure calibration, and to some extent, inadequacies in the line shape model or linear approximation. When several traces are averaged, the uncertainties are considerably larger than the la standard deviations in the individual fits. Thus, the averaged values may not reproduce the measured traces with the same quality as the individual fits. The pressure coefficients and uncertainties for all the allowed R(J) and P(J) transitions for both buffer gases are listed in Tables l-4. The pressure coefficients are labelled the same as their respective parameters, hopefully without causing confusion. A small correction for self broadening from the average of the Q-branch measurements’ is applied to the y(Ar) and y(N?) in Tables 1 and 3. For some lines in these P and R manifolds, the Rosenkranz first-order approximation is not valid at atmospheric pressures; so we restrict the averages for the shifts to P d 27 kPa. The broadenings and intensities seem reasonably linear and are averaged for P < 67 kPa for all but J 2 8 in the R branch where averages are limited to P < 27 kPa. The uncertainties for the intensities are generally ~0.3% for the stronger lines, with the reminder that the relative values in a manifold have been constrained to the Doppler-limited measurements. This precision implies that the pressure measurements, baseline adjustments and detector/lock-in/divider chain linearity are all valid to a few tenths of a percent. A correction factor of 1.044 is applied to the intensities to adjust for uncertainties in the methane concentration in accordance with prior Doppler-limited pure gas measurements.39 The broadening coefficients for the more isolated lines are determined to better than 1% in Tables 1 and 3, with systematic errors dominated by the line shape model. The shifts are small and almost always negative, and are usually determined to within 5%. A few of the more strongly blended lines have larger uncertainties, but even those blended at the Doppler limit can be curve-resolved to some degree in the present spectra.

I%- and Ar-broadened spectra of CH4

il1

A. S. Pine

166 Table Label J RO RI R2 R2 R3 R3 R3 R4 R4 R4 R4 R5 R5 RS RS R6 R6 R6 R6 R6 R6 RI R7 R7 R7 R7 RI R8 R8 R8 R8 R8 R8 R8 R9 R9 R9 R9 R9 R9 R9 R9 RIO RIO RlO RlO RlO RlO RlO RlO RlO RIO

C

N

Al Fl E F2 Fl F2 A2 Al Fl E F2 Fl F2 E Fl E F2 A2 F2 Fl Al Fl F2 A2 F2 E Fl Al Fl E F2 Fl E F2 Fl F2 E Fl Al Fl F2 A2 EF* A2 F2 Fl

I 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1

I 2 2 1 1

1 1 1 2 2 2 1 1 1 3 2 1 2 1

1 1

I I 2 2

F+ F+ Al Fl E F2

tcombined

1 1

I I

1. CH4 ~3 band R branch intensity, broadening and shift coefficientst at T = 295 K.

Wavenumber (cm-‘) 3028.75221 3038.49845 3048.16893 3048.15319 3057.76055 3057.72631 3057.68725 3067.30001 3067.26089 3067.23422 3067.16393 3076.72492 3076.67669 3076.56864 3076.54940 3086.08559 3086.07143 3086.03055 3085.89336 3085.86049 3085.83203 3095.37071 3095.35080 3095.17895 3095.13038 3095.10386 3095.06043 3104.58509 3104.57449 3104.56863 3104.33613 3104.28359 3104.22022 3104.20505 3113.71167 3113.70715 3113.42779 3113.41714 3113.37977 3113.30094 3113.27938 3113.26096 3122.76340 3122.76335 3122.44381 3122.43926 3122.37133 3122.36376 3122.33141 3122.29562 3 122.28454 3122.25721

Intensity (cm-?/MPa)

Y (Ar) (cm-‘/MPa)

Y (N) (cm-‘/MPa)

6 (Ar) (cm-‘/MPa)

6 (Nz) (cm-‘/MPa)

22.475 (101) 21.815 (84) 18.757 (35) 28.020 (53) 3 1.402 (24) 31.388 (24) 52.208 (41) 52.000 (100) 31.377 (61) 20.953 (41) 31.527 (61) 28.847 (56) 28.881 (56) 19.615 (39) 29.008 (56) 16.733 (27) 25.080 (41) 41.061 (68) 25.239 (42) 25.189 (41) 42.190 (70) 19.730 (63) 19.771 (63) 33.177 (104) 20.183 (64) 13.411 (42) 20.253 (64) 24.703 (75) 14.822 (45) 9.881 (30) 15.033 (46) 14.962 (46) 10.121 (31) 15.141 (46) 10.487 (11) 10.487 (I 1) 7.196 (8) 10.341 (I 1) 17.759 (20) 10.418 (11) 10.813 (13) 18.174(21) 11.597(17) 11.597(17) 6.533 (9) 6.533 (9) 1.250 (2) 1.250 (2) 12.130 (18) 6.031 (8) 4.832 (7) 7.223 (10)

0.4989 0.5563 0.5072 0.5783 0.5960 0.5855 0.5137 0.5144 0.5922 0.4757 0.5388 0.5301 0.5668 0.4664 0.5376 0.4905 0.5469 0.5008 0.5616 0.5414 0.5135 0.4808 0.5191 0.4673 0.5536 0.3730 0.5249 0.4205 0.4903 0.4736 0.4790 0.5165 0.4103 0.5173 0.4266 0.4708 0.4221 0.5053 0.4734 0.5165 0.5025 0.5077 0.3202 0.5402 0.3999 0.5732 0.6345 0.6345 0.4575 0.5369 0.2867 0.4987

0.5797 0.6383 0.5829 0.6618 0.6689 0.6561 0.5891 0.5918 0.6683 0.5420 0.6192 0.6008 0.6369 0.5361 0.6154 0.5518 0.6160 0.5683 0.6300 0.6124 0.5833 0.5472 0.5851 0.5319 0.6216 0.4284 0.5940 0.4827 0.5735 0.5296 0.5463 0.5812 0.4731 0.5884 0.4796 0.5330 0.4747 0.5742 0.5315 0.5724 0.5663 0.5716 0.3879 0.5956 0.4854 0.6058 0.7361 0.7361 0.5280 0.5967 0.3404 0.5588

- 0.0538 (7) -0.0496(11) -0.0468 (27) -0.0487 (22) -0.0596 (14) -0.0431 (13) -0.0537 (9) -0.0588 (13) -0.0588 (20) -0.0616 (18) -0.0468 (11) -0.0630(13) -0.0622 (13) -0.0521 (5) -0.0482 (1 I) -0.0665 (II) -0.0659 (14) -0.0694 (23) -0.0735 (20) - 0.0379 (55) -0.0444 (26) -0.0700 (4) -0.0616 (9) -0.0556(15) -0.0196 (26) - 0.0542 (8) -0.0399 (21) -0.0730 (12) -0.0810 (33) - 0.0695 (10) -0.0603 (17) - 0.0527 (47) -0.0497 (16) -0.0457 (24) -0.1001 (76) -0.0576(17) -0.0659 (10) -0.0725 (28) -0.0537 (7) -0.0794 (42) 0.0053 (50) -0.0430 (4) -0.0450 (87) - 0.0496 (68) -0.1147 (44) - 0.0364 (27) -0.0555 (32) -0.0570 (32) -0.0623 (32) -0.0048 (24) -0.0409 (27) -0.0271 (49)

-0.0593 (15) -0.0457 (15) -0.0491 (19) -0.0480 (18) -0.0505 (40) -0.0408 (1 I) -0.0464 (13) -0.0536 (11) -0.0481 (13) -0.0520 (9) -0.0410 (25) -0.0549 (9) -0.0536 (I 1) -0.0425 (28) -0.0427 (11) -0.0602 (38) -0.0558 (37) -0.0563 (25) -0.0665 (61) -0.0241 (40) -0.0369 (6) -0.0594 (18) -0.0550 (5) -0.0469 (6) -0.0527 (17) -0.0417 (6) -0.0360 (32) -0.0620 (102) -0.0593 (172) -0.0406 (12) -0.0519 (34) -0.0488 (24) -0.0394 (20) -0.0381 (5) -0.0783 (65) -0.0646 (8) -0.0612 (13) -0.0625 (17) -0.0471 (18) -0.0770 (35) 0.0097 (29) -0.0396 (38) -0.0362 (57) -0.0465 (I 18) -0.0921 (34) -0.0404 (36) -0.0414 (81) -0.041 I (87) -0.0556 (30) - 0.0088 (48) -0.0327 (56) -0.0162 (I 1)

(18) (9) (38) (36) (55) (59) (30) (22) (51) (43) (22) (22) (21) (46) (23) (74) (32) (3) (41) (59) (27) (52) (55) (32) (73) (57) (58) (49) (107) (103) (33) (20) (42) (39) (24) (26) (82) (29) (29) (58) (69) (40) (136) (231) (148) (46) (40) (40) (43) (67) (35) (74)

(17) (8) (26) (38) (19) (33) (14) (23) (53) (45) (33) (30) (45) (66) (23) (71) (49) (10) (78) (51) (20) (30) (47) (5) (76) (51) (68) (33) (70) (65) (12) (19) (13) (41) (49) (54) (8 1) (27) (34) (59) (73) (67) (99) (181) (101) (23) (38) (38) (27) (89) (42) (69)

uncertainties in parentheses in terms of last digits; see text.

The uncertainties in the Dicke narrowing and line mixing coefficients in Tables 2 and 4 represent the lo standard deviations of a single trace, since these parameters were constrained to vary linearly with pressure in the fits due to strong correlations with other parameters. As such, it is difficult to estimate the reliability of these uncertainties. However, judging their sensitivity to the interactive baseline adjustments, a factor of five increase in the uncertainties might be expected. This still leaves most of the coefficients and their transition dependence very well determined. The /I,,, and (“, of a few strongly blended high J transitions could not be determined reliably and were fixed to the values indicated in Tables 2 and 4. The Ar and N2 broadening coefficients for the various P,Q and R branch transitions are plotted in Fig. 6. The Q branch data are from Ref. 1. The F symmetry lines are plotted on the integer

N2- and Ar-broadened spectra of CH,

167

J, while the A lines are displaced to the left of their corresponding J and the E lines to the right in order to illustrate the species dependence to the broadenings. The broadenings show the same tendencies in the three branches with the R branch variations somewhat more exaggerated than the more similar P and Q branches. On average, using Eqs. (9) and (lo), the Q branch lines are 1.6 f 2.5% broader than the corresponding P lines, whereas the R lines are 3.8 f 4.3% narrower than the P. Usually, the sharpest line in a manifold has E symmetry, if one exists, or A, if not. However, not all of the E or A lines are narrower than the F for the same J. The systematic dependence of the F levels on the ground-state order index, N, is the same as shown previously for the Q branch.’

Table 2. CH4 VTband R branch Dicke narrowing and line mixing coeficientst T=295K. Label / RO RI R2 R2 R3 R3 R3 R4 R4 R4 R4 R5 R5 R5 R5 R6 R6 R6 R6 R6 R6 R7 R7 R7 R7 R7 R7 R8 R8 R8 R8 R8 R8 R8 R9 R9 R9 R9 R9 R9 R9 R9 RlO RlO RlO RIO RIO RIO RlO RlO RIO RIO

C Al Fl E F2 Fl F2 A2 Al Fl E F2 Fl F2 E FI E F2 A2 F2 FI Al Fl F2 A2 F2 E Fl Al Fl E F2 Fl E F2 Fl F2 E Fl Al Fl F2 A2 EF* A2 F2 Fl F+ F+ Al Fl E F2

N 1 1 1 1

1 I 1 1

1 I I 2

1 1 I 1 2 1

I I I 2 2 1 1

1 1 1 2 2 2

I 1

1 3 2

1 2 1 1 1 1 1 2 2

I 1 1 1

B(Ar) (cm-‘/MPa)

P(W) (cm-‘/MPa)

0.2932 (36) 0.1832 (28) 0.2603 (36) 0.2156 (27) 0.2252 (27) 0.2263 (27) 0.2845 (15) 0.2460 (13) 0.22 18 (26) 0.2622 (30) 0.2190 (21) 0.2441 (27) 0.1885 (24) 0.2872 (34) 0.2417 (26) 0.3595 (62) 0.2450 (41) 0.2175 (18) 0.1947 (34) 0.2207 (34) 0.2643 (20) 0.2743 (37) 0.2311 (38) 0.2969 (20) 0.2322 (39) 0.3397 (41) 0.2447 (36) 0.3186 (30) 0.2772 (77) 0.2772 (77) 0.2880 (34) 0.1999 (34) 0.3213 (49) 0.2046 (37) 0.2817 (95) 0.28 17 (95) 0.3495 (128) 0.2733 (103) 0.2712 (35) 0.1772 (60) 0.2103 (62) 0.2605 (39) 0.2097 (fix) 0.2097 (fix) 0.2097 (fix) 0.2097 (fix) 0.2097 (fix) 0.2097 (fix) 0.2997 (61) 0.2097 (fix) 0.2097 (fix) 0.2097 (fix)

0.2604 (44) 0.1490 (60) 0.1961 (55) 0.1945 (46) 0.1642 (39) 0.1804 (39) 0.2300 (21) 0.2501 (23) 0.2122 (44) 0.2382 (49) 0.2358 (39) 0.2341 (43) 0.23 12 (42) 0.2897 (55) 0.2322 (41) 0.2989 (95) 0.2428 (69) 0.2022 (28) 0.1832 (53) 0.2218 (55) 0.2299 (30) 0.2237 (48) 0.2068 (52) 0.2169 (25) 0.2354 (55) 0.2776 (53) 0.2580 (51) 0.2564 (38) 0.2403 (114) 0.2403 (114) 0.2282 (44) 0.1999 (47) 0.2650 (63) 0.2219 (54) 0.2474 (95) 0.2474 (95) 0.2857 (114) 0.2205 (96) 0.2373 (30) 0.1313 (53) 0.1985 (59) 0.2805 (38) 0.2023 (fix) 0.2023 (fix) 0.2023 (fix) 0.2023 (fix) 0.2023 (fix) 0.2023 (fix) 0.2464 (58) 0.2023 (fix) 0.2023 (fix)

i(Ar) (I/MPa)

i(N2) l/MPa)

-2.892 (30) 2.892 (30)

- 3.282 (38) 3.282 (38)

- 1.299 (8)

- 1.535 (11)

1.292 (8) -0.480 (15) - 1.190(15)

1.528 (11) -0.473 (15) -1.378(15)

1.659(19) -0.394 (23) -1.614(11) -5.234 (381 5.636 i45j 1.569(11) - 1.123 (23) 0.026 (23) -2.193

1.844 (23) -0.638 (34)

- 1.780 (19j - 5.227 f60) 5.858 il7j 1.735 (19) - 1.531 (30) 0.308 (30)

(19)

-2.496 (19)

3.251 (38)

3.679 (49)

-0.424 (19) 0.000 (fix) -0.015 (23) -4.096 (26) 4.475 (38) -0.582 (15) 0.000 (fix)

-0.826 0.000 -0.161 -3.980 0.000 4.904 -0.578 0.000

-0.034 (41) -4.141 (23) -8.384 (173) 8.665 (176) 4.051 (23) 0.000 (fix) -0.912(11) -0.882 (34) 0.000 (fix) 0.000 (fix) 0.000 (fix) 0.871 (1 I) - 5.598 (68) 0.000 (fix) 5.466 (79)

-0.619 (41) - 4.400 (23) -8.512 (191) 9.349 (195) 4.299 (23) 0.000 (fix) -1.137(11) -2.038 (38) 0.000 (fix) 0.000 (fix) 0.000 (fix) l.O89(ll) -4.756 (75) 0.000 (fix) 5.818 (83)

0.000

ifixj

(19) (fix) (23) (30) (fix) (41) (11) (fix)

at

A. S. Pine

168 Table PI P2 P2 P3 P3 P3 P4 P4 P4 P4 P5 P5 P5 P5 P6 P6 P6 P6 P6 P6 PJ PJ PJ PJ PJ PJ P8 P8 P8 P8 P8 P8 P8 P9 P9 P9 P9 P9 P9 P9 P9 PlO PlO PI0 PlO PlO PlO PlO PlO PI0 tcombined

Fl E F2 Fl F2 A2 Al Fl E F2 Fl F2 E Fl E F2 A2 F2 Fl Al Fl F2 A2 F2 E Fl Al Fl E F2 Fl E F2 Fl F2 E FI Al Fl F2 A2 E F2 A2 F2 Fl Al Fl E F2

1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 2 2 2 1 1 1 3 2 1 2 1 1 1 1 2 3 1 2 2 I 1 1 1

3. CHI VI band 3009.01137 2999.06041 2998.99401 2989.03346 2988.93251 2988.79521 2979.01123 2978.91986 2978.84805 2978.65041 2968.85517 2968.73616 2968.47358 2968.40324 2958.68253 2958.65083 2958.53633 2958.23291 2958.12001 2958.01722 2948.47406 2948.42137 2948.10792 2947.91206 2947.81095 2941.66797 2938.25180 2938.21536 2938.19258 2937.76717 2937.49500 2931.30814 2931.23456 2927.96353 2927.93210 2927.42910 2927.31261 2921.07614 2926.88509 2926.78294 2926.70022 2917.66285 2917.65255 2917.62902 2917.06607 2916.96612 2916.75373 2916.39624 2916.30178 2916.20155

uncertainties

P branch

intensity,

4.087 (75) 7.607 (34) 11.363 (51) 16.025 (61) 15.902 (61) 26.497 (100) 30.125 (48) 18.019 (29) 11.999 (20) 17.947 (29) 11.734 (50) 17.769 (50) 11.635 (32) 17.554 (50) 10.539 (39) 15.168 (51) 26.141 (96) 15.551(57) 15.660 (57) 26.130 (96) 12.879 (26) 12.765 (26) 20.706 (42) 12.557 (25) 8.478 (18) 12.683 (26) 16.117 (73) 9.702 (44) 6.500 (29) 9.433 (43) 9.591(43) 6.343 (28) 9.562 (43) 6.920 (9) 6.912 (9) 4.517 (6) 6.682 (9) 11.375 (16) 6.748 (9) 6.808 (9) 11.387(16) 2.980 (10) 4.703 (15) 7.663 (26) 4.475 (15) 4.432 (15) 7.416 (25) 4.466 (15) 3.033 (10) 4.559 (16)

in parentheses

broadening

and shift coefficientst

0.4999 (49) 0.5666 (41) 0.5608 (34) 0.5930 (19) 0.5829 (39) 0.5355 (24) 0.5646 (20) 0.6004 (30) 0.5228 (33) 0.5449 (30) 0.5685 (29) 0.5904 (28) 0.4948 (32) 0.5391 (40) 0.5285 (42) 0.5649 (39) 0.5368 (25) 0.5769 (34) 0.5499 (51) 0.5124 (28) 0.5178 (28) 0.5377 (32) 0.5164 (15) 0.5621 (12) 0.4119 (38) 0.5269 (19) 0.4576 (35) 0.4974 (40) 0.4897 (59) 0.5087 (31) 0.5423 (35) 0.4147 (41) 0.5180 (23) 0.4467 (23) 0.4725 (22) 0.463 1 (53) 0.5127 (23) 0.4994(12) 0.5208 (44) 0.5135 (41) 0.5050 (16) 0.4020 (16) 0.4338 (73) 0.4378 (44) 0.4771 (34) 0.5040 (42) 0.4915 (29) 0.5039 (43) 0.3062 (42) 0.5066 (21)

0.5892 0.6546 0.6499 0.6762 0.6685 0.6212 0.6478 0.6805 0.5943 0.6252 0.6415 0.6629 0.5672 0.6165 0.6032 0.6371 0.6067 0.6527 0.6267 0.5896 0.5863 0.6096 0.5872 0.6302 0.4715 0.5979 0.5271 0.5680 0.5551 0.5817 0.6105 0.4784 0.5883 0.5093 0.5378 0.5270 0.5816 0.5615 0.5833 0.5778 0.5676 0.4594 0.4983 0.5058 0.5420 0.5692 0.5554 0.5642 0.3577 0.5644

(33) (46) (20) (14) (36) (20) (19) (30) (18) (24) (23) (33) (33) (34) (43) (32) (19) (34) (53) (23) (21) (28) (21) (22) (40) (17) (27) (69) (39) (33) (32) (24) (18) (26) (18) (73) (43) (21) (61) (45) (20) (49) (41) (19) (55) (10) (10) (24) (33) (47)

at 7’ = 295 K.

-0.0875 -0.0869 -0.0885 -0.0839 -0.0119 -0.0763 -0.0811 -0.0788 - 0.0869 -0.0719 -0.0812 -- 0.0721 -0.0815 -0.0653 -0.0823 -0.0756 -0.0660 - 0.0794 -0.0653 -0.0602 -0.0738 -0.0600 -0.0827 -0.0748 -0.0802 -0.0697 -0.0771 -0.0632 -0.0666 -0.0710 -0.0108 -0.0715 -0.0608 -0.0698 -0.0613 -0.0159 -0.0699 -0.0675 -0.0772 -0.0627 -0.0637 -0.0714 - 0.0632 -0.0545 -0.0654 -0.0625 -0.0762 -0.0808 -0.0692 -0.0538

(41) (7) (19) (11) (11) (19) (1) (8) (9) (7) (7) (20) (12) (10) (11) (3) ’ (8) (9) (8) (19) (15) (31) (17) (16) (3) (6) (12) (7) (11) (7) (7) (9) (12) (22) (7) (3 1) (14) (11) (11) (18) (22) (22) (52) (14) (10) (10) (18) (59) (16) (31)

-0.0712 (14) -0.0810 (6) -0.0152 (10) -0.0734 (9) - 0.0666 (20) - 0.0109 (4) -0.0743 (5) -0.0725 (11) -0.0789 (16) -0.0678 (10) -0.0741 (2) - 0.0675 (8) -0.0800 (12) -0.0614 (1Oj -0.0724 (31 -0.0616 (I>) -0.0597 (15) -0.0750 (16) -0.0643 (19) -0.0511(16) -0.0690 (3) -0.0596 (10) -0.0761 (14) -0.0681 (8) -0.0737 (15) -0.0663 (14) -0.0681 (17) -0.0574 (17) -0.0621 (3Oj -0.0718 (20) -0.0641 (8) -0.0674 (22) -0.0591 (20) -0.0588 (26) - 0.0555 (20) -0.0713 (4) -0.0650 (21) -0.0606 (11) -0.0734 (28j - 0.0579 (8) -0.0533 (12) -0.0705 (45) -0.0512 (70) - 0.0492 ( 10) -0.0549 (14) -0.0562 (25) -0.0678 (19) - 0.0748 (42) - 0.0602 ( 19) -0.0563 (40)

in terms of last digits; see text.

5. DISCUSSION

5.1. Intensities The integrated intensities listed in Tables 1 and 3 are more extensive than given in our previous Doppler-limited study of the v3 band strength of methane39 and, together with the Q branch measurements reported earlier,’ provide a reasonably complete set of line strengths for the allowed methane transitions up to J = 10. The relative uncertainties of the intensities in either the P or R branch is <0.3%, though the absolute uncertainty due to possible systematic errors is estimated to be -2%, primarily limited by the scaling correction of the concentration of methane in the premixed sample to that of the prior pure methane data. 39Note that the P and R intensities here have also been corrected for isotopic abundance (0.98893(5) for 12CH4);whereas the Q were not.’ Our constraint on the relative integrated intensities within a manifold is only strictly valid in the range of the Rosenkranz first-order line mixing26,3*approximation.

N2- and Ar-broadened

spectra

of CR

169

5.2. Broadening coeficients

The J, symmetry, and order dependencies of the broadening coefficients for methane have been qualitatively predicted by Tejwani et a1’7-‘9using Anderson-TsacSurnutte@,4’ theory extended to octopole and hexadecapole moments and dispersion and induction interactions.42.43The dependence of J primarily results from the increasing AJ energy gaps with J for inelastic collisions, compensated in part by the increased number of quasielastic channels. The symmetry effects principally arise from the lack of cross-relaxation between different nuclear spin configurations and the fewer E or A levels than F levels available for collisional transitions. The order dependence is probably related to the symmetric-top wavefunction expansion K values as noted by Tejwani et a1.19

Table Label J

4. CH4 YJ band

C

N

PI P2 P2 P3 P3 P3 P4 P4 P4 P4 P5 P5 P5 P5 P6 P6 P6 P6 P6 P6 P7 P7 P7 P7 P7 P7 P8 P8 P8 P8 P8 P8 P8 P9 P9 P9 P9 P9 P9 P9 P9 PI0 PI0 PI0 PlO PlO PlO PlO PlO PI0

Fl E F2 FI F2 A2 Al Fl E F2 FI F2 E Fl E F2 A2 F2 FI Al Fl F2 A2 F2 E Fl Al Fl E F2 Fl E F2 FI F2 E Fl Al Fl F2 A2 E F2 A2 F2 Fl Al Fl E F2

1

tlo

uncertainties

1 1 1

1 1 1 1

1 1 2 1 1

1 1 2 1 1 1 1 2 2

1 1

I I 1 2 2 2 1 1 1 3 2 1 2 1 1 1 1 2 3

1 2 2

1 1 1 1

P branch

Dicke narrowing T=295K.

B(Ar) (cm-‘/MPa)

B(N) (cm-‘/MPa)

0.2647 (127) 0.1395 (38) 0.1668 (27) 0.1814(36) 0.2058 (37) 0.2411 (22) 0.2130 (14) 0.1874 (24j 0.2294 (31) 0.2610 (23) 0.2101 (20) 0.1991 (21) 0.2346 (31) 0.2513 (19) 0.2551 (48) 0.2246 (34) 0.2389 (20) 0.2224 (36) 0.2379 (34) 0.2671 (19) 0.2441 i36j 0.2165 (38) 0.2519 (24) 0.1861 (39j 0.3235 (46) 0.2385 (38) 0.2679 (26) 0.2479 (47) 0.2740 (71) 0.2230 (46) 0.2611 (55) 0.2868 (58) 0.1870 (45) 0.2882 (41) 0.2393 (41) 0.3138 (68) 0.2367 (47) 0.2446 (27) 0.1906 (50) 0.2006 (54) 0.2066 (26) 0.2097 (fix) 0.2097 (fix) 0.2869 (53) 0.3078 (100) 0.2777 (104) 0.2715 (61) 0.2481 (100) 0.3591 (97) 0.2406 (98)

0.2172 (234) 0.1397 (69) 0.1865 (51) 0.1814(56) 0.1937 (58) 0.233 1 (34) 0.1984 (20) 0.1890 (35) 0.1953 (42) 0.2339 (32) 0.1741 (29) 0.2295 (34) 0.2073 (46) 0.2199 (30) 0.2459 (53) 0.2013 (37) 0.1982 (20) 0.2398 (41) 0.2339 (38) 0.2484 (21) 0.2237 (41) 0.2032 (43) 0.2423 (27) 0.1666 (44) 0.2783 (50) 0.2158 (43) 0.2629 (34) 0.2236 (60) 0.2302 (88) 0.2209 (62) 0.2663 (72) 0.2456 (72) 0.2005 (60) 0.2232 (61) 0.2147 (65) 0.3132 (113) 0.2299 (78) 0.2421 (45) 0.1969 (87) 0.2160 (90) 0.202 1 (43) 0.2023 (fix) 0.2023 (fix) 0.2349 (59) 0.2838 (118) 0.1642 (105) 0.2026 (66) 0.1377 (98) 0.2809 (101) 0.2821 (127)

in parentheses

and

line mixing

i(Ar) (l/MPa)

coefficients?

i(N) (WPa)

-0.568 (6) 0.573 (6)

-0.728 (15) 0.732 (15)

-0.286

-0.326

(3)

(3)

0.284 (3) - 0.032 (3) -0.246 (3)

0.328 (3) -0.053 (5) -0.436 (5)

0.283 (5)

0.494 (6)

-0.158 (50) -0.461 (3) -l/%44(6) 1.593 (8) 0.461 (3) -0.334 (19) -0.124 (19)

-0.183 (5) -0.521 (3) - 1.576 (6) 1.751 (8) 0.521 (3) -0.304(19) -0.071 (19)

-0.616

-0.827

(11)

(I 1)

1.078 (26)

1.199 (30)

-0.233 (19) -0.150(19) -0.225 (I I) -0.778 (I 1) 0.154(19) 1.240 (26) -0.199 (15) -0.173 (15)

-0.173 (23) -0.301 (23) 0.086 (15) - 1.229 (15) 0.304 (23) 1.323 (30) -0.473 (19) -0.402(19)

-0.364 (15) -0.898 (8) -2.502 (19) 3.216 (34) 0.898 (8) 0.000 (fix) 0.000 (fix) -0.733 (15) - 1.075 (30) 0.068 (30) 0.759 (15) -0.135 (26) 0.000 (fix) 1.120(53)

-0.267 -0.999 -2.449 3.577 0.999 0.000 0.000 -0.612 - 1.405 -0.143 0.631 - 0.590 0.000 2.097

in terms of last digits; see text.

(19) (11) (19) (38) (11) (fix) (fix) (15) (30) (30) (15) (26) (fix) (49)

at

170

A. S. Pine

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N1- and Ar-broadened

spectra of CH4

171

More recently, Neshyba et al” and Gabard4’ have applied the semiclassical line broadening theory of Robert and Bonamy46 to methane perturbed by Nz and Ar buffer gases using more realistic electrostatic octopole and hexadecapole moments for CH4, supplemented by atom-atom Lennard-Jones 6-12 dispersive and repulsive potentials which dominate the broadening. The Neshyba et al@ CH4/N, calculations exhibit good average agreement with less symmetry our vj band Q-branch broadening coefficients,’ but with considerably dependence than observed experimentally. For CH.,/Ar, Gabard45 has obtained similar results (- 10% too low on average) with the FTIR measurements of broadening in v4 by Rinsland et al’ and our tunable laser measurements in the vi Q branch’ and P and R branches here. The Gabard4’ calculations exhibit the correct J/C/N and branch trends for the broadening coefficients, although, again, the measured variations in the Y,,, between the branches and within a given J manifold are more exaggerated. Some refinement of the anisotropic part of the model potential, incorporation of the imaginary part of the Sz scattering function, and a better treatment of the collision dynamics45 may be necessary to improve the agreement with the data. The Ar and N, broadening patterns in Fig. 6 are strikingly similar for a given branch, so their ratios are compared in Fig. 7. For the 164 corresponding J/C/N line pairs for the vj band P, Q and R branches measured here, the weighted average ratio using Eqs. (9) and (10) is (;$Ar)/y(N?)) = 0.879 f 0.010. The small spread represents an upper limit to the measurement precision x j’ 2. The average Ar/N2 width ratio here is nearly identical to the value of 0.877 f 0.017 found for 72 line pairs in the v4 band by Rinsland et a1.9 The similarity of the Ar and Nz broadening coefficients for corresponding methane transitions is rather remarkable considering the different multipolar symmetries of the interaction potentials for the two buffers and the availability of rotational exchange on collisions with Nz. Certainly no rotational resonances are evident in the Nz broadening data. Since a single empirical scale factor for (?;(Ar)/y(N*)) = 0.879 ) 0.010 well represents the P, Q, and R branches of v3 (and v~),~and we previously obtained (y(O?)/y(N*)) = 0.937 f 0.015 for the Q branch of v~,we might expect that the air (-79% N2 + 21% 02) broadening coefficients will be x99% of those for Nz. This is consistent with the recent v3 P and R branch measurements of Benner et al,” though their r.m.s. deviation was several percent. In Fig. 7, we also compare our v3 P and R branch Nz broadenings with the most recent values reported by Benner et al.” On average, their P branch measurements are 2.3 + 4.0% higher than ours and their R branch values are 1.6 f 3.1% higher. Their measurements of the allowed R branch transitions were limited to J < 4 because of the complications of line mixing, and their J = 4 Fl line is suspiciously low. The Ar broadenings for the R branch of v4 measured by Rinsland et al9 are also compared in Fig. 7 with our present v3 band data, and we find excellent agreement (99.3 + 2.0%) throughout. Thus, there seems to be less vibrational dependence than branch dependence within a given vibration. This suggests that the stronger J/C/N variations in the R branch arise from the larger inelastic gaps when J’ > J”, rather than from any perturbations of the excited state wavefunctions for the diad and pentad levels. We note that the splittings of the tetrahedral components of the J manifolds are much larger in v4 than v~, which reduces the complications from line mixing. 5.3. Shift coeflcients An examination of the shift coefficients in Tables 1 and 3 indicates that the Ar shifts are generally larger than the Nz, contrary to the widths, but with a larger spread and a few exceptions. There are no obvious correspondences between the branches, J values, symmetries or order indices. In the least-squares fits, the shifts were highly correlated with the line mixing parameters and exhibited significant non-linearities at higher pressure. Therefore, the 67 kPa data were not used in the determination of the shift coefficients. Primarily for this reason, a linear extrapolation of the tabulated results above the 27 kPa trace using Eq. (7) may produce significant deviations from the measured spectra, particularly for the high J R branch. This is illustrated in Fig. 8 for the observed R(7) and P(7) manifolds compared to the simulated (not fitted) spectra from Tables 14 with an without line mixing.

172

A. S. Pine

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N2- and Ar-broadened

173

spectra of CH,

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174

A. S. Pine

R(7) and P(7) manifolds compared to the simulated (not fitted) spectra from Tables 14 with an without line mixing. 5.4. Dicke narrowing coeficients In our previous study of the v3 Q branch of methane,’ we were able to fit the medium pressure spectra with negligible residuals using the Rautian profile with narrowing parameters, /I,,,, constrained to be equal for all lines. This average fl was then related to an “optical” diffusion constant which was found to be well correlated with (but roughly twice) the mass diffusion constants of methane in each buffer gas. In the current P and R branch spectra, however, we obtain significant differences in the /?,,,, as can be seen in Tables 2 and 4, and constraints to equate or average these parameters produce unacceptable residuals, even within a given J manifold. Though the average value of the retrieved p,,, from the P and R branches is of the same magnitude as found in the Q branch, the /&Ar)/b(N,) ratio is systematically somewhat higher than before. Since the diffusion or velocity-changing collision effects are usually dominated by the isotropic it is surprising that the /3,,,are so transition dependent. part of the intermolecular potential, ‘.32.34 There does seem to be a tendency for the A and E symmetry transitions to have a distinctly higher fintthan the F, which may suggest some influence of the nuclear spin. Such a spin diffusion effect would not be monotonic since L = 0: 1:2 for the E: F:A levels respectively. The trend in /?,,,is essentially opposite to that of y,,,; such an anticorrelation has been derived by Looney4’ considering that the effect of velocity change on the line profile may be preempted by any prior state or phase interruption in the same collision. Another possible effect that can mimic Dicke narrowing4’ is the speed-dependent Voigt profile4”S0 which considers the relative kinetic energy dependence of the collision cross sections over the thermal distribution. This could depend on the internal rotational and spin level since it is affected by the energy gaps and available states. The speed-dependent Voigt profile can also produce line shape asymmetries and non-linear shifts at higher pressures, difficult to distinguish from line mixing. However, it is difficult to reconcile these fl,,, variations with the much smaller differences observed in the Q branch. 5.5. Line mixing coejicients The R and P manifold spectra in Figs. 4, 5, and 8 clearly demonstrate the influence of line mixing We find here that the individual on the overlapped contours, as had been noted by Benner et al. 24,25 spectra can be fit to within the experimental noise level using the Dicke-narrowing line mixing profile of Eq. (7) with no mixing between lines of different nuclear spin A : F: E symmetry and the sum of mixing parameters of a given symmetry constrained to zero for these quasielastic collisions.26 We note in Tables 2 and 4 that the mixing coefficients are universally negative for the highest frequency transition of the manifold and positive for the lowest. This generally results in a collapse or narrowing of the manifold, which can be anticipated from the first-order Rosenkranz approximation, Eq. (8), since the off-diagonal line coupling collision rates, W,,, are always negative. We also find that the mixing coefficients are larger in magnitude for the eight-fold clusters on the low frequency edge of the manifolds than for the six-fold clusters on the high edge. This effect is most prominent for the F-symmetry transitions in the R(7) and P(7) manifolds shown in Fig. 8 where the higher F lines are closer together and are more overlapped, but show smaller “no mixing” residuals. Steinfeld and coworkers5’-” have observed a propensity to preserve the n-fold cluster for state-to-state inelastic collisions in various tetrahedral molecules, and Parson” has rationalized this with approximate calculations in a cluster basis. Gabard45 has calculated a number of individual inelastic and quasielastic line coupling cross sections for CH4/Ar indicating similar behavior. As noted in the fitting procedure, parameter correlation due to the finite signal-to-noise ratio, baseline uncertainties, and extraneous weak isotopic and forbidden lines led us to adopt several linearity constraints-namely, we linearly scaled the Dicke narrowing and line mixing coefficients determined at one pressure each and fixed the relative integrated line intensities within a manifold. These would be legitimate constraints within the Rosenkranz approximation, Eq. (8) valid for I[,,,1< 0.1. However, some of the retrieved mixing coefficients given in Tables 2 and 4 yield c,,, outside this range at atmospheric pressures, and we in fact observe strong non-linearities in the shifts at -67 kPa. This may result in rather poor predictions at higher pressure, particularly for

N2- and Ar-broadened

spectra of CHI

175

the R branch as shown in Fig. 8. The P branch is generally better behaved since the overlap and line mixing is reduced. Slight systematic non-linearities ( < 1%) in the broadening parameters due to inadequacies in the Rosenkranz approximation and the Rautian Dicke narrowing model also are evident in the residuals for the predicted spectra, even at lower pressures as seen in Fig. 8. Another method to reduce parameter correlation is to simultaneously fit spectra at several distinct pressures using a line shape model with the appropriate pressure dependence. Benner et a124,25 have demonstrated this using multispectrum fits of their FTIR measurements of methane. They incorporated line mixing in the linear Rosenkranz approximation with no coupling selection rules or sum rules. As we have seen here, however, the Rosenkranz approximation is not always valid for pressures > 30 kPa, particularly for the high J R branch, and the collisional selection and sum rules are valid at all pressures, In order to extend the model beyond the Rosenkranz limit, one might consider fitting the linear W,,,. relaxation matrix elements directly to the spectra. Inverting the W-matrix is rapid and convenient using available personal computers. However, for k coupled lines, there are k(k - 1)/2 independent W,, (considering detailed balance) and only k - 1 determinable c,,,mixing parameters (imposing the zero sum rule) at any pressure since Eq. (7) is valid to all orders. Therefore, doublets can be fully specified, but there are more unknowns than data when k > 3. This is true even for multispectrum fits if all the pressures are lower than the Rosenkranz limit. However, at higher pressures, non-linearities in the <,,,and the other broadening parameters may provide enough data to determine the W,,, directly in multispectrum fits. Another approach, of course, is to calculate reliable W,,,, theoretically by improving the interaction potential and the dynamics. Such theoretical modeling can be well tested by the current spectra and results. Alternatively, one might develop an empirical rate law, such as the energy gap or ECS scaling laws used for linear molecules,2’t23 to model all the W,,,, with a reduced set of parameters. Important modifications would be required for spherical tops to account for symmetry selection rules, anharmonic and Coriolis splittings, and vibrational degeneracy, as it has already been demonstrated that simple energy gap laws do not work.5w53 6. CONCLUSIONS

We have obtained a reasonably complete and precise set of intensity, broadening and shift coefficients for the allowed P and R branch manifolds of the v3 band of CH, in Ar and N, buffers to complement our previous Q branch measurements. ’ It was essential to incorporate Dicke narrowing and line mixing in order to fit the overlapped spectral profiles. Non-linear pressure dependencies of the retrieved line shape parameters indicate that the Rosenkranz first-order approximation for the line mixing coefficients is not applicable above w 30 kPa for J 2 6 in the R branch or J 2 9 in the P branch. The nearly constant ratio observed for y(Ar)/ y(N2) = 0.879 + 0.010 is encouraging as a measure of the experimental precision, as a means to estimate other transitions and buffers from limited measurements, and as a guide for collision cross section calculations for molecule-molecule interactions. Acknowledgements-The theoretical narrowing

calculations coefficients.

author is grateful to Dr T. Gabard for a copy of his thesis and some helpful comments on his and to Dr J. P. Looney for his suggestion about the anti-correlation between the broadening and This work was supported by the NASA Upper Atmosphere Research Program.

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