The 2ν2 + ν3 and 2ν2 + ν1 bands of 16O3 at 4.1 μm: Line positions and intensities

JOURNAL

OF MOLECULAR

SPECTROSCOPY

139,343-352 (1990)

The 2~~ + v3 and 229 + v1 Bands of 1603 at 4.1 pm: Line Positions and Intensities CURTIS P.RINSLAND AND MARY ANN H. SMITH NASA Langley Research Center, Atmospheric Sciences Division, Mail Stop 401A. Hampton, Virginia 23665-5225

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

JEAN-MARIE

FLAUD AND CLAUDE CAMY-PEYRET

Laboratoire de Physique Mol&culaire et AtmosphMque, Universite’ Pierre et Marie Curie et C.N.R.S., Tour 13, 3’ &age, 4 place Jussieu, 75252 Paris Cede.x 05, France Fourier transform spectra of ozone have been recorded in the 4. l-pm region at a resolution of 0.010 cm-‘, allowing the first high-resolution study of the 2vz + V,and 2~2+ V, bands of the I603 molecule. The experimental rotational energy levels of the (021) and ( 120) vibrational states have been reproduced satisfactorily with a Hamiltonian that takes explicitly into account the Coriolis resonance affecting the levels, and a precise set of vibrational energies and rotational and coupling constants has been determined. In particular, the band centers vo(O21) = 2407.9345 cm-’ and vg( 120) = 2486.5766 cm-’ were obtained. Moreover, the transition moment constants of the 2~ + Yeand 2vz + u, bands were derived from a fit of 46 measured line intensities. From these parameters, a complete list of line positions, intensities, and lower state energies was generated for the two bands. In addition, the results for the (02 1) and ( 120) states obtained in this work have been combined with previous results for the (010) state to generate a complete list of line positions, intensities, and lower state energies for the 2~2 + u, - ~2and 2~2 + vi - Q hot bands of l6Oj in the 5.7~pm spectral region. The good quality of the new 4. l- and 5.7~pm line lists has been verified through comparisons of measured laboratory spectra with corresponding simulations. 8 1990 Academic Press, Inc.

INTRODUCTION

We report in this work the first extensive high-resolution study of the spectrum of 1603 in the 4.1~pm region, where the two weak bands 2~9 + u3 and 2~9 + vI are absorbing. Previous to this study, a medium-resolution spectrum covering this region ( 1) was recorded and analyzed to estimate the band center of the 2~ + u3 band. The absorption by both bands appears in the 0.04-cm-’ -resolution long-path low-pressure ozone laboratory atlas of Damon et al. (2)) but no analysis was reported. In addition to the first rotational assignments for both bands, this work also reports experimental measurements of individual line intensities in the two bands. 343

0022-2852190 $3.00 Copyright

0

1990 by Academic

All rights of reproduction

Press, Inc.

in any form reserved.

344

RINSLAND

EXPERIMENTAL

ET AL.

DETAILS

AND

ANALYSIS

The spectra analyzed in this investigation were recorded in absorption at 0.0 1-cm -I resolution with the Fourier transform spectrometer located in the McMath solar telescope facility of the National Solar Observatory on Kitt Peak near Tucson, Arizona. Radiation emitted by a globar source was recorded with a liquid-nitrogen-cooled InSb detector. The absorption cell was a 7.6-cm-diameter Pyrex tube, 2.39 m long, with wedged potassium chloride windows and a Teflon valve. The two spectra used in the analysis were obtained at room temperature with nearly pure ozone samples generated using the silent electric discharge technique. One run measured ozone at - 15.5 Torr produced from ultra-high-purity natural oxygen. The other run recorded ozone at - 15.9 Torr generated from >99.98% pure 1602. Sample pressures were monitored continuously with a 0- to lOO-Torr Datametrics Barocel 570-A series pressure transducer during the - 1-hr period required to record each spectrum. Sample temperatures were also measured throughout the run by four thermocouples attached to the outside of the cell at approximately 50-cm intervals along its length. The measured temperature remained constant at 26°C during the recording of both spectra. The wavelength scale of each spectrum was calibrated using standards in the v3 band of 12C1602, as described in a previous investigation (3). For additional experimental details see Smith et al. (4). Since no data concerning the two bands 2v~+ v3and 2~ + vl of 1603were available, we started the analysis using a theoretical calculation (Table I) performed with vibrational energies and rotational coupling constants extrapolated from recent laboratory studies (3-8). In this way, it was possible to assign lines with medium J and low K, quantum numbers. These transitions were then used to refine some Hamiltonian constants, and a new calculation allowing better extrapolation was performed, leading to the assignment of additional lines. The process was pursued until it was not possible to assign new lines. The range of Jand K, observed for the (02 1) and ( 120) vibrational states is given in Table II. A few aspects of the analysis are worth noting: -Because of strong CO2 absorption in the low wavenumber region, it was not possible to observe the P branch of the 2v2 + v3 band for J’ higher than 26. -The intensities in the 2~ + v1 band decrease very rapidly with K” preventing the observation of transitions with Kh > 4. -The 2v2 + v3 and 2v2 + vi bands are very weak (see Figs. 1 and 2); consequently, the line positions could not be measured as precisely as in our previous studies (e.g., Refs. (3-5, 7)) and, on the average, the uncertainty in the positions is estimated to be of the order of 1.5 to 2 X lop3 cm-’ instead of 0.3 to 0.8 X 10m3cm-’ as obtained previously. ENERGY

LEVELS

AND

INTENSITIES

The final set of experimental energy levels has been fitted using a Hamiltonian (Table I), taking into account the Coriolis interaction affecting them; the corresponding vibrational energies and rotational and coupling constants are reported in Table III. The standard deviation of the fit is 1.6 X lop3 cm -‘, with 82% of the levels reproduced within 2 X 10e3 cm-’ ; this result is consistent with the experimental uncertainty (see previous section ) . As in previous investigations (3-5, 7)) it was not possible to deter-

160, BANDS

345

AT 4.1 pm

TABLE I Hamiltonian

Matrix

v = (021)

V’

Watson-type Hamiltonian H

vv Watson-type Hamiltonian H

HL

vv

= E, + [A' - 1 2

(Bv + C')] J; + 1 2

- A;J;

- AIK J;J’

- A: (~a)*

+ H;J;

+ HiJ

+ HIK J;

+ h;

J;J’

{J*,J* ) + hiJ z XY

+ L;J; + LiKJ J;J’

+ a[ {J’,J*

+ P; 5;”

H;,,, = h;,,,

+

{J,.J,}

= J,

+ PiKJ

+ h;:;”

with (AB} = AB + BA

J*

J;

(J’)’

- J; r

iJy

- 26;J;yJ1

+ LiJJ

(J*)Z

5;

J’ + a& [J;,Jiy}

J;(J’)’

+ ...

J’ + . . .

[Jt

(Bv - Cv) Jiy

+ H; (J*)’

t hlc iJ + hi:: [J;, v’v y

J’

(Bv + Cv) 3' + 1 2

~2 + 2hJ” J;~

(J;,Jiy}

P&J

” ‘c + hv”v {J,.J,

Jiy = J;

(J’)’

{J;.J;,l

+ PiKKJ J;J’

{J;,J;,}

+ Pi

+ LiJ

v'v'

- 6;: {J;,J;~}

{J;,J;~]

) + avKJ XY

z

(120)

Hermitic Conj.

Coriolis Interaction

H

=

- J:]

[J,,J,}]

(J’)’

+ L; (J’)*

(J’)’

+ 2R; Jly

(J’)’

RINSLAND

346

ET AL.

TABLE 11

Range of Observed Energy Levels

state Parameter

(021)

Number of Levels

(120)

95

02

.I max

26

49

&ax

10

4

mine simultaneously all the Coriolis coupling constants, so we fixed the h;Co2,j(120j coefficient of the operator iJYto the value used previously (5) for the (00 1) and ( 100) states of r60s. Using the equivalent width technique, intensities of 46 lines belonging to the two bands studied in this work were measured with a relative uncertainty of 20%, poorer than in our previous investigations (3-5, 7), because of the weakness of the bands. The exact amount of ozone in the cell was not known, so similarly to the study of the 3.6~pm region (4)) we calibrated the measured intensities with respect to intensities of lines in the 2y3, vl + v3, and 2v, bands of r603 at 4.8 pm ( 7). The calibration of the 4.8~pm intensities is, in turn, based on a calibration performed with respect to lines in the lo-pm region using an assumed value of (dpCL,/dq3)e= -0.2662 D (see Refs. 5 and 7 for more details). The experimental intensities obtained in the 4. l-pm region were then reproduced using the transition moment operators A-type band ( 2~ + ~3) , (ooo)(021)p;= (-0.701_, f 0.027) X 10-3&

+ (0.198 f 0.13) x 10-5(f[{&,

iJY) - {i&, ‘Ix}]>

B-type band (2~ + vr), @“‘c’)(021)~~ = (-O.562o +- 0.085) x 1O-3& + (0.335 rfr 0.17) x 10-4(L#+, JZ} + (0.570 -I- 0.14) x 10-Q2,

iJY}

with {A, B > = AB + BA, J, the component of J along the molecular axis cy, and 4, = aZol(direction cosine). All results are given in Debye. As is well known, the intensities are proportional to the square of the matrix elements of the dipole moment operator, and therefore it is not possible to determine the absolute signs of the transition moment constants from a least-squares fit of experimental line intensities. However, if the resonances are large enough, often one can obtain the relative signs of these constants without ambiguity. This was the case in our previous studies, but in the present one we observed that an almost equivalent, although slightly poorer intensity fit was obtained when the relative signs of the transition constants of the 2u2 + v3 and 2v2 + v, bands were changed. This problem arises because the intensities

r603 BANDS

+

2398

347

AT 4.1 pm

Measured Calculated

2399

WAVENUMBER

2400

(cm-‘)

FIG. 1. Laboratory (solid line) and best-fit calculated (plus symbols) spectra in the region of the 2~ + V, band (lower panel). The laboratory spectrum is a coadd of two spectra recorded at 0.0 1 cm-’ resolution with about 15.5 and 15.9 Torr of ozone in a 2.39-m absorption path at 26°C. Residuals (observed minus calculated) are shown in the upper panel. Note the expanded vertical scales used in both panels.

could not be measured with high precision, the resonances are not particularly strong for the observed levels, and the range of J and K, values covered by the present measurements is rather limited. Consequently, the transition moment constants given in this work are not as reliable as in our previous studies. Using the transition moment expansions deduced from the fit of the measured intensities and the wavefunctions derived from the diagonalization of the upper states (see Table I, III) and the ground state (5) Hamiltonians, a complete list of line positions, intensities, and lower state energies of the 2~2 + v3 and 2~ + v1 bands of 1603 has been computed ’ with an intensity cutoff of 1.O X 10e2’ cm-l /molecule cmm2 at 296 ’ A partition

function

Z( 296) = 3473 was used in the intensity

calculations.

348

RINSLAND ET AL.

0.99

2

5

v, 0.98

+

0.97 2508

I

I

I

Measured Calculated I

I

I

WAVENUMBER

I

I

2510

2509

(cm-‘)

FIG. 2. Laboratory (solid line) and best-fit calculated (plus symbols) spectra in the region of the 2uz + u, band (lower panel) and the residuals of the fit (upper panel). The laboratory spectrum is the same as that in Fig. 1.

K and maximum values of J and K, of 50 and 12 for the 2~ + u3 band and 60 and 9 for the 2~ + v1 band. The sum of the intensities (in cm-‘/molecule cm-’ at 296 K units) and the number of lines in the list are 4.11 X 10ez2 and 862 lines for the 2~2 + v3 band and 3.73 X 1O-22 and 1042 lines for the 2~2 + vl band. Since both bands are quite weak, lines below the intensity cutoff contribute significantly to the total band intensity. A calculation without any intensity cutoff yields sums closer to the actual values. The resulting calculated integrated band intensities (in cm-’ /molecule cme2 at 296 K units) are 4.35 X 1O-22 for the 2~2 + v3 band and 4.08 X 1O-22 for the 2v2 + vl band. No previous intensity measurements have been reported for these bands. Figs. 1 and 2 show comparisons of the laboratory and calculated spectra for two regions. The observed features of the 2v2 + v3 and 2v2 + v1 bands are reproduced very

349

1603 BANDS AT 4.1 pm TABLE III Vibrational Energies and Rotational and Coupling Constants for the Interacting States (02 1) and ( 120) of I603 Vibrational and Rotational Constants

(021)

(120)

2407.9344, f 0.000064

2486.5766, f 0.000078

3.6056457,, k 0.0000071

3.666844,, + 0.000031

0.4384710,, + 0.0000015

0.4401173,, f 0.0000010

0.38595780,, ?.0.00000091

0.38793935,, f 0.00000024

(0.24683,, + 0.00019) x 10-j

(0.275500 f 0.0017) x 10-3

(-0.13864a f 0.0029) x 10-Z

(-0.2018,, t 0.0057) x lo+

(0.47379,, + 0.00025) x 1O-6

(0.469179 f 0.0012) x 10-e

(0.534853 f 0.0041) x 10-5

(0.328,, + 0.017) x 1O-5

(0.62698, f 0.0013) x 10-7

(0.7656,, ?r 0.0097) x lo-'

(0.254,, + 0.014) x 1O-7

(0.254,, f 0.014) x 10.'

(-0.792,, ? 0.035) x 1o-8

(-0.792,, + 0.035) x 10-E

Coupling Constants

- (-0.10551,,2+ 0.00063) x 10-l hC~021~~120~ h'C~021~~120~ - -0.470

All the results are in cm-' and the quoted errors correspond to one standard deviation. Constants without ermrs were held fixed during the fit.

well by the calculations. Note that the maximum line center absorption is less than 2%. No unassigned lines remain in this region of the spectra. Operational satellites often include channels in the 4.3~pm spectral region for performing vertical temperature soundings. Advanced sounders with accuracies of - 1.5 K are planned and will use narrow band channels in this region to measure air-surface temperature differences as well as the vertical temperature profile in the lower troposphere ( 9). Because the signals from these channels will include radiance from the 2~ + v3 and 2~ + v1 ozone bands, our new data should be useful for deriving a proper correction for the ozone contribution. HOT BANDS OF 1603 AT 5.7 pm

350

RINSLAND ET AL.

1.oo

x .-

E aI -P

-c

__

Calculated

(2~2

+ v3 -

v2 Only)

I8

0.95

. -Measured 0 . H20 1681.5

Calculated (All O3 Lines

Included) 1682.5

1682.0

Wavenumber

(cm-‘)

FIG. 3. Laboratory (solid line) and best-fit calculated (open diamonds) spectra in the region of the 219 + Y) - v2 hot band (lower panel). The laboratory spectrum was recorded at 0.005 cm-’ resolution with about 23.7 Torr of ozone in a 50-cm absorption path at 28°C. The strongest absorptions in the region are produced by lines of the ~2 + vg band. The upper panel shows a simulation calculated with only the hotband line list. The vertical scale is the same in both panels.

In our investigation of the spectrum of i603 at 5.7 pm (3), we reported that weak unassigned absorption features could be observed in addition to the lines of the two main bands, v2 + v3 (band center = 1726.5225 cm-‘) and vI + v2 (band center = 1796.2619 cm-‘). Several of these unassigned lines were marked in Figs. 2 and 3 of Ref. (3). These features are about 5% as strong as the strongest lines of the v2 + v3 and vI + v2 bands, and we mentioned that the unassigned lines were believed to be transitions of the 2v2 + v3 - v2 and the 2v2 + vI - v2 hot bands of 1603. In the present work, we confirm this conjecture. From the vibrational energies and the rotational and coupling constants of the (02 1) and ( 120) states, as reported in Table III of the present investigation, and the corresponding parameters of the (010) state from Ref. (8), a listing of positions,

1603 BANDS AT 4.1 pm

351

1 .oo

v

-

x a_

cn c Q> -I-,

-c

-

0.95

I

Calculated

I I

(2~2

+ vl

-

v2 Only)

I

1 .oo

x .m

c

0.95

al 4-J

-

SI

-Measured Q Calculated (All 03 Lines

Included)

0.90 1804.5

1804.6

1804.7

Wavenumber

1804.8

1804.9

1805.0

(cm-l)

FIG. 4. Laboratory (solid line) and best-fit calculated (open diamonds) spectra in the region of the 219 t V, - v2 hot band (lower panel). The laboratory spectrum was recorded at 0.005 cm-’ resolution with about 23.7 Torr of ozone in a 50-cm absorption path at 28°C. The strongest absorptions in the region are produced by lines of the v, + “2 band. The upper panel shows a simulation calculated with only the hotband line list. The vertical scale is the same in both panels.

intensities, and lower state energies for the 2v2 + v3 - v2 and the 2v2 + v1 - v? hot bands of 1603 has been calculated. The intensities were computed with the transition moment operators of the v2 + v3 and vI + v2 bands multiplied by fi to account for the vibrational matrix element. The calculations were performed with an intensity cutoff of 1.O X 10e2’ cm-’ /molecule cm-2 at 296 K with maximum values of J and K, of 50 and 12 for the 2v2 + v3 - v2 band and 60 and 9 for the 2v2 + vI - v2 band, respectively. The sum of the intensities (in cm-’ /molecule cm -2 at 296 K units) and total number of lines in the list are 3.42 X 10P2’ and 1365 lines for the 2v2 + v3 - v2 band and 1.37 X 10e21 and 1621 lines for the 2~2 + vI - v2 band, respectively. The calculated integrated band intensities (in cm -’ /molecule cm -2 at 296 K units) derived without an intensity cutoff in the calculations are 3.45 X 10e2’ for the 2v2 + v3 - v2

RINSLAND ET AL.

352

band and 1.40 X 10P21 for the 2u2 + v1 - v2 band. The computed band centers are 1707.0034 cm-’ for the 2v2 + v3 - ~2 band and 1785.6456 cm-’ for the 2v2 + v1 - v2 band. Figures 3 and 4 compare measured and calculated spectra in regions selected to illustrate the hot-band lines. Figure 3 shows the same spectral region and laboratory data as plotted in Fig. 2 of Ref. (3). Lines of the 212 + v3 - v2 hot band are observed in this region. Figure 4 illustrates a region from the same spectrum containing several lines of the 2v2 + vl - v2 hot band. The best-fit calculated spectra in both figures have been generated from a line parameters listing that includes the 2v2 + v3 - v2 and 2v2 + vI - v2 hot-band lines in addition to the v2 + v3 and v1 + v2 band lines from Ref. (3). In all cases, the observed hot-band features are reproduced satisfactorily with the new line parameters, thereby improving our knowledge of ozone absorption in the 5.7-pm region. ACKNOWLEDGMENTS The authorsthank CharlesT. Solomon of NASA Langleyand JeremyWagner and Claude Plymate of the National Solar Observatory(NSO) for their help with the laboratoryexperiment,Greg Ladd for the computerprocessingof the data at NSO, and D. ChrisBennerof William and Mary and CarolynH. Sutton of ST SystemsCorporationfor theirassistancein the processingof the spectraat NASA Langley.Research at the College of William and Mary was supportedunder CooperativeAgreementNCCl-80 with NASA. NSO is operated by the Association of Universitiesfor Researchin Astronomy, Inc., under contract with NSF. RECEIVED:

September 20, 1989 REFERENCES

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