The ν1 and ν3 bands of 16O3: Line positions and intensities

17 ( 1987)

JOURNAL OF MOLECULAR SPECTROSCOPY lu,209-2

The vl and v3 Bands of 1603: Line Positions and intensities J.-M.

RAUD

AND

C. CAMY-PEYRET

Laboratoire de Physique Molkulaire et Atmospht%ique, Universite Pierre et Marie Curie et CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France

V. MALATHY DEW Department of Physics, College of William and Mary, Williamsburg, Virginia 23185

AND C.

P. RINSLAND AND M. A. H. SMITH

Atmospheric Sciences Division, NASA Langley Research Center, Hampton, Virginia 23665

Using 0.005 cm-’ resolution Fourier transform spectra of samples of ozone, the Y,and y3bands of 160j have been reanalyzed to obtain accurate line positions and an extended set of upper state rotational levels (J up to 69, K, up to 20). Combined with the available microwave data, these upper state rotational levels were satisfactorily fitted using a Hamiltonian which takes explicitly into account the strong Coriolis interaction affecting the rotational levels of these two interacting states, In addition, 350 relative line intensities were measured from which the rotational expansions of the transition moment operators for the Y,and vj states have been deduced. Finally, a complete listing of line positions, intensities, and lower state energies of the Y, and vr bands of 160r has been generated. 0 1987 Academicpre~5,Inc. INTRODUCTION

Because of the importance of the ozone molecule in the earth’s atmosphere, the vibration-rotation spectrum of this molecule has been the subject of numerous studies. The most recent investigations include the microwave investigations in Refs. (I-4) the study of the far-infrared spectrum (5), and the high-resolution infrared studies of the regions of the u2 band (68) the vl and v3 bands (4, 9-12), the v1 + v3 band (13), the 2y3, q + v3, and 21, bands (14), and the vI + v2 + v3 band (15). To improve the existing line parameters for the lo-pm region, which is often used in remote sensing studies, we have recorded spectra at 0.005 cm-’ resolution covering this interval with the McMath Fourier transform spectrometer at the National Solar Observatory on Kitt Peak in Arizona. We have reanalyzed the v1 and v3 bands of 1603 from these spectra, and present in this paper molecular parameters which can be used to calculate improved line positions and intensities for these two interacting bands. EXPERIMENTAL

DETAILS AND ANALYSIS

The absorption cell used in our experiments consisted of a 50-cm-long, 5.08-cmdiameter Pyrex tube with Teflon valves. Slightly wedged (5- 10 mrad) potassium chlo209

0022-2852187 Copyright 0

$3.00

1987 by Academic Pm% Inc. All rightsof wmduction in any form mered.

F-LAUD ET AL.

210

ride windows were used in order to prevent channeling arising from multiple reflections. The sample pressures ranged from 0.37 to 23.2 Torr of which three scans, listed in Table I, were selected for the analysis. During the experiment, the pressures and temperatures were monitored continuously using 0- 10 and 0- 100 Torr Barocel pressure heads and either a thermocouple or a mercury-in-glass thermometer placed in contact with the absorption cell. The vI band lines of 14N2’60 between 1255 and 1282 cm-‘, as reported by Olson et al. (16) were used to calibrate the wavelength scale of the spectra. The ozone samples were prepared using nearly pure (>99.98%) 1602 or natural O2 samples. The standard technique of silent electric discharge was used in generating the ozone, For additional experimental details see Flaud et al. (I 7) and Rinsland et al. (18). Using the results of previous studies of the IJ~and v3 bands of 1603 (4, 9-l 1), it was rather easy to start the analysis of the spectra. Following the initial assignments, a first calculation was performed using a Hamiltonian, taking explicitly into account the Coriolis interaction between the rotational levels of the two interacting vibrational states (100) and (00 1) (see Table II). A first set of vibrational energies, rotational and coupling constants, was then obtained allowing us to calculate extrapolated levels and to extend the assignments. The process was repeated until almost all of the lines expected to be observable in the laboratory data were assigned. The interfering lines belonging to the hot bands were identified using the results of Ref. (10) whereas lines belonging to the v1and v3bands of the isotopic species 160’80’60 and ‘60’60’80 were located in the natural O3 spectra with the aid of the results given in Refs. (I 7-19). The lo-pm spectral region of O3 is very crowded, even at the high resolution reached by the McMath Fourier transform spectrometer, and, in order to derive the most accurate energy levels, great care was taken to select only well-isolated and unblended transitions for the analysis. In this respect, the availability of spectra recorded over a range of ozone pressures proved to be very useful. Finally, about 2600 lines belonging to the vI and v3bands of 1603were used to derive the experimental upper state rotational energy levels (up to J = 69 and K, = 20). LINE POSITIONS

In order to derive precise rotational levels for the (100) and (001) vibrational states, we decided first to fit simultaneously the microwave (1-4) and far infrared (5) data to obtain a unique set of rotational constants for the ground state. This was done using TABLE I Characteristics of the Spectra spectrum

Pressure

NO

(Ton-1

(K)

(cm)

1

23.2

293.1

50.0

2

8.1

295.7

50.0

3

1.09

293.1

50.0

Temperature

Path Length

211

Y, AND vg BANDS OF I603 TABLE II Hamiltonian Matrices ”

=

(100)

Watson-type Hamiltonian

" = (000)

v'= 1001)

Watson-type Hermitic conj.

Hamiltonian H YY

Ii YY Coriolis interaction FY'"

ii "V

Watson-type Hamiltonian HY'"'

=E Y +[,.-,(,v+Cv)]J,+,(,v+Cv)Jp+~(Bv-Cy)J~~

-A;J:-A;KJ;J'-A; 0z,z-S~iJ~,J~,)-2S~J~~J'

a Watson-type Hamiltonian (Table II), and the values are given in Table III. The statistical weights used in this calculation were those given in Refs. (4, 5), and the observed line positions were reproduced within their stated experimental uncertainties. Then adding the observed wavenumbers of the rq and v3 lines to the rotational energy levels of the ground state computed with the constants of Table III, we deduced the energies of the rotational levels of the (100) and (001) vibrational states. These last levels together with the available microwave data for these states (4) were least-squares fitted using again the Hamihonian matrix given in Table II. The results are very satisfactory since the infrared and microwave data are reproduced within their exper-

212

FLAUD

ET AL.

TABLE III Rotational

Constants

of the Ground

AV

3.553666502 3 * 0.00000023

B"

0.4452832070

C" A”

0.394751807S (0.2116872,

Y

f 0.000000027

f

0.0000069)

10.'

x

l-O.184846o

+ 0.00006)

A:

(0.454169

f 0.000035)

x lo-' x 10-b

syII

(0.323240,

+ 0.000040)

x 10-g

8Y

(0.697903,

f 0.000022)

x 10-7

n:

(0.39896

f 0.00087)

x 10“ x 10-n

I

2

H: T H:

(-0.185929

t 0.00047)

(-O.6468

* 0.037)

x 10 -"

(0.3215

+ 0.013)

x lo-'*

h:

(0.2293

+ 0.0033)

1

I

h: h: L: L:x,

(-o.757S

L"

(-0.325

I

L: 1: p: PilKJ

the results standard

J

* 0.049)

(0.1755

0

l-o.1177o (O.2739

RI,

All

f 0.000000030

A"

111

to one

State of ‘60’60’60

10.299

I .

x 10-0 x 10‘"

f 0.0011)

x lo-'*

+ 0.0031)

x 1O“O

+ 0.043)

x lo-'=

f 0.037)

x 10

f

0.071)

-15

x 10 -1'

(0.181z

f 0.056)

(o.333o

f 0.033)

x lo-*'

(0.1895

f 0.093)

x lo-'3

are given

in me'.

x 10-l*

The errors

correspond

deviation.

imental uncertainties (standard deviations of 0.33 X 1O-3 cm-’ for the infrared data and 0.11 MHz for the microwave data). The corresponding vibrational energies, rotational and coupling constants are given in Table IV. As noticed in previous works (4, 20), it was not possible to determine simultaneously all the coupling constants, and consequently /z&,,,~, the coefficient of the operator iJy, was given a fixed value. This value has been derived from the potential function given in Ref. (21) and is compatible with the values of the same constant obtained for 160180160 (I 7) and ‘*o’60180 (22). LINE

INTENSITIES

The intensities of 350 lines belonging to the vi and v3 bands of 1603 were measured from three spectra, the characteristics of which are given in Table I. However, since the exact amount of ozone was not known for each spectrum, we have used lines measured in the different spectra to calibrate each spectrum against the other in order

213

Y, AND v3 BANDS OF ‘b, TABLE IV Vibrational Energies, Rotational and Coupling Constants for the (100) and (00 1) Vibrational States of 1603 * 0.000023

1103.13728 J

1042.08398

f: 0.00000054

3.50055300

0.44273646az

a 0.000000069

0.441296035,

0.392568221n

f 0.000000063 0.000010)

(0.217494,. (-0.21569,6

(0.35570&,

0.00019) 0.000098)

(0.4189690

0.00058) 0.0011)

(-0.16976g,

x lo-'

(0.658775,,

(-0.2040S3

(0.208072gS

x 10-J

0.000053)

6

0.3909982750 x 10-a

0.000121

(0.461480S1

(0.456697 1*

x 10-B x 10“ x 10“

f 0.000000053 i: 0.000000048 + 0.000012)

x 10 -=

+ 0.00012)

x 10“

* 0.000034)

x 10-6

(O.296O9Io

* 0.00020)

(0.759512

?1 0.000064)

II

(o.390356, (-o.1a02S0

x 10-a

+ 0.00000052

f 0.00080) + 0.0012)

x lo-' x lo-' x lo-' x 10-u

(-0.312,‘

0.014)

x 10-10

(0.15*,

?r 0.15)

(0.423,,

0.013)

x lo“2

(o.17040,

+ 0.0070)

(o.97mn

0.12)

x 10-9

(0.248 ?I

f 0.013)

t-o.7g9,

0.13)

x 10“'

~-0.1141~~

* 0.0074)

x 1O“O

(O.2355,0

* 0.0021)

x10-'%

(-0.1141**

f 0.0015)

0.038)

(0.916,, ~-o.121aa,5

x lo-l3

0.00089)

(0.308,S

0.025)

-0.3251

lo-'=

x lo-"

(0.317

x lo-"

0.13)

0.333 0.1895

x 10-11

* 0.17)

0.333

x 10-I'

lo-'8

0.1895

x lo-'0

=

~r.3 given

deviation.

* 0.000080~

x 10-Z

-0.470

( 0.756Ee0 , * SC = (-o.105a50b . . . tc h 001.,00 = ( 0.58 ,* *

the results

x 10 -'*

constants

(-0.996301,,

h 001.100

one standard

x lo-‘0 x 10“'

x lo-"

lo-"

LOO h’ f --~01.~00 = "C h 001,100 =

x lo-'* x 10-a

+ 0.032)

(0.21,,

Coupling

x 10 -11

x lo-'"

0.2994

(0.14,,

hi.1:

3,

-0.3251

lo-"

0.2994

All

f 0.000023

.

3.55669374S

in cm-' Parameters

f 0.0031)

x 10 -b

f 0.00039) 0.24)

x 10-6

x lo-'

and the quoted with

errors

no errors

were

correspond held

to

fixed.

to obtain a consistent set of relative intensities. These relative intensities were then reproduced using the method extensively described in Refs. (23,24). The transformed transition moment operators of the zq and v3 bands are expanded in the following way:

214

FLAUD ET AL.

B-type band (000) ( 1OO)pL: = (000) ( 1OO)pu;& + (OOO)(lOO)~clh{i~y,Jz}+(ooo)(loo)~;{f#&, iJy}+ * * *

A-type band (000) (loo)& = (000) (00 l)&#& +(000)(001)PLb4((&,

&I - {i&J, .L})+(OOo) (OOl)Pb~({&, iJy) + {GJ,, JX})+ * - -

with {A, B} = AB + BA 4, = aza (direction cosine)

J, = component of J along the molecular axis CY. Together with the wavefunctions derived from the diagonalization of the Hamiltonian matrices of the upper states and the ground state, the previous expansions were used to reproduce the observed line intensities leading to the determination of the transition moment constants “‘~j given in Table V. We have also quoted in this table the theoTABLE V Transition Moment Constants of the Y, and vg Bands of I603 YY’

’

pLJ

v3band

PLI

PLI

PLI

vlband

r‘l

p.

standard values

-0.188232

-0.188232

0.636

x 1O-4

0.636

x lo-'

0.170

x lo-’

0.170

x lo-*

-0.154

x 10-l

-0.18

x lo-'

I-0.15450%

+ 0.00061)

(-0.1802,

f 0.0052)

are in Debye

deviation.

have been

Theoretical

(0.190,

“8 All the results

Experimental

+ 0.033)

in the line

x lo-'

without

intensity

Statistical O,
x 10-3

(D) and the quoted

For the constants

used

x 10-l

6%

0.549

errors

x lo-"

correspond

to one

errors,

the theoretical

calculation

(see text).

analysis 61.4 % of the lines

6 < 6 < 12 %

21.4 %

12 d 6 < 24 %

13.7 %

24 4 8 < 34 %

3.5 %

215

Y, AND us BANDS OF 160s

retical values of these constants derived using the formulae of Ref. (24) and the ozone dipole moment expansion given in Ref. (17). It is interesting to note that: (i) The correcting rotational constants appearing in the expansion of the transformed transition moment operator of the vg band were fixed to their theoretical values. In fact, it was not possible to determine these values from our experimental set of intensities because their contribution is weak for the lines which were measured. (ii) There is excellent agreement between the experimental and theoretical values of (000) (100) &. As already noticed in Ref. (4), this term is essential to reproduce correctly the vl line intensities. The agreement is less satisfactory for the other correcting term, but this is explainable because the contribution of this last term is weaker, and consequently it is not well determined from our limited set of intensities. Overall, the fit is very satisfactory since 82.8% of the intensities are reproduced within a relative error less than 12% (see the statistical analysis of Table V for more details). As mentioned previously, it has not been possible to measure absolute intensities from our laboratory spectra. Many measurements of integrated band intensities (25, 26) or of individual line intensities (27, 28) of ozone have been performed in the lopm region, but the consistency in the results is not better than about 10%. Consequently, we have decided to scale our intensities using the value given in Refs. (4, 17, 28) @p,/c3q,), = -0.2662

D.

0.a 2

0.6

Z (3 0.4 ?iT

0 1006.0

1006.5

WAVENUMBER

1007.0

(cm-‘)

FIG. 1. Comparison between a weakly apodized laboratory spectrum (solid line) recorded with -0.37 Torr of 160j in a 50-cm absorption path and a calculated spectrum (plus symbols) generated with the line parameters described in the text. Residuals (observed minus calculated) are plotted on expanded vertical scale in the upper panel and are expressed as a percentage of the peak measured intensity in the interval. Some absorption by hot band transitions of 1603occurs this interval and has been simulated with the line parameters from the 1982 AFGL compilation. The mixing ratio of 0s in the laboratory sample has been adjusted in matching the measured and calculated spectra. There are simultaneously high K. v3 lines and resonating high K, v, lines in this region.

216

FLAUD ET AL.

0.90 1224.0

1225.0

1224.5

WAVENUMBER

(cm-‘)

FIG. 2. Comparison of a weakly apodized laboratory spectrum (solid line) recorded with a23.2 Torr of natural OJ in a 50-cm absorption path and a calculated spectrum (plus symbols) generated with the line parameters described in the text. The format is the same as in Fig. 1. There are very high K, Y, lines in this region.

Finally, a complete spectrum of the u1 and v3 bands of I603 has been computed’ with an intensity cutoff of 0.1 X 1O-24cm-‘/molecule cme2 at 296 K. In this computation maximum values of 89 and 23 were considered for J and K, as well as a maximum lower state energy of 3500 cm-‘. Total band intensities of 0.5403 X lo-l8 and 0.14 13 X lo-l6 cm-‘/molecule cmm2 at 296 K were obtained respectively for the y1 and v3 bands of 1603. The total band intensity obtained for u3 compares very well with the value of 0.1475 X lo-l6 cm-‘/molecule cme2 at 300 K derived by Secroun et al. (26) from the anomalous dispersion of ozone at 10 pm. A listing of 14 026 line positions, intensities, and lower state energies was derived, and to check its quality we have compared portions of synthetic spectra with the measured laboratory spectra. As can be seen from Figs. 1 and 2, the agreement between observation and calculation is very good. However, for atmospheric calculations, it should be recalled that the absolute intensities calculated in this work (as well as those for the ul and v3 bands of ‘60’80’60 (I 7) and ‘60’60’80 (19)) have been obtained using (dpz/c3q3)e= -0.2662 D. If this value is to be changed, all of the intensities will have to be multiplied by the square of the ratio of the two values. ACKNOWLEDGMENTS The authors thank Bumie Williams of NASA Langley and Rob Hubbard and Mike Brown of the National Solar Observatory (NSO) for their help with the laboratory equipment; Greg Ladd of NSO for the computer

’ A partition function Z(296) = 3473 has been used in the intensity calculations.

Y, AND v3 BANDS OF I603

217

processing of thedata;and D. ChrisBennerof Wiiam and Mary and CarolynH. Suttonof SASC Technologies for their assistancein the processingof the spectraat NASA Langley. Researchat the College of William and Mary was supportedunder CooperativeAgreementNCCI-80 with NASA. J.-M. FIaudand C. CamyPeyretacknowledgepartialsupportof their researchwork under this cooperative agreement. The National

Solar Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. The computational work was performed at the Centre Inter R&ional de Calcul Electronique, CNRS, 9 1405 Orsay, France. RECEIVED:

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