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Line positions and intersities for the ν1 + ν2 and ν2 + ν3 bands of 16O3
JOURNAL OF MOLECULAR SPECTROSCOPY
125, 174-183 ( 1987)
Line Positions and Intensities for the v1 + v2 and v2 + u3 Bands of 1603 V. MALATHY DEW Department of Physics, College of Williamand Mary, Williamsburg,Virginia23185 J.-M. FLAUD AND C. CAMY-PEYRET Laboratoire de Physique Molkculaireet Atmosphkrique,Tour 13. 3’ &age, UniversitkPierre et Marie Curie et CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France AND C.
P. RINSLAND AND M. A. H. SMITH
Atmospheric Sciences Division,NASA Langley Research Center, Hampton, Virginia23665-5225 Using0.005cm-’ resolution Fouriertransform spectra of 1603,generated by electric discharge from a >99.98% pure sample of 1602, an extensive analysis of the Y, + Yeand the Ye+ yj bands in the 5.7-pm region was performed. The rotational energy levels of the upper (110) and (011) vibrational states of 1603were reproduced within their experimental uncertainties using a Hamiltonian which takes explicitly into account the Coriolis-type interaction occurring between the rotational energy levels of both states. Improved vibrational energies and rotational and coupling constants were also derived for the (110) and (011) states. Precise transition moment constants for these two bands were deduced from analysis of 220 measured line intensities. Finally, a complete list of line positions, intensities, and lower state energies for both bands has been generated. 0 1987 AcademicPns, Inc. INTRODUCTION
Because of its atmospheric importance, the 1603 molecule and the isotopic species ‘60’80160 and 160’60LE0 have been the subject of numerous recent spectroscopic studies [(Z-6) and references therein]. Almost all of the recent works were concerned with the pure rotation spectrum and the lo-pm absorption region which are widely used for remote sensing measurements of this molecule in the terrestrial atmosphere. However, absorption by atmospheric ozone is clearly visible in many other spectral regions as well, and we present in this paper our work concerning the 5.7-pm region of 1603. The prominent bands appearing in this spectral region are the two combination bands zq + u2 and u2 + v3. These bands were analyzed in previous laboratory studies (7-9), but at a resolution lower than that achieved in the present work. This work also reports the first experimental measurements of individual line intensities in these bands.
0022-2852187 $3.00 wt 8 1987 by AcademicPress,Inc. Au rightsof nzpmduction in any form e-served.
174
Y, + v2 AND v2 + q BANDS EXPERIMENTAL
DETAILS
OF
I603
175
AND ANALYSIS
The ozone samples were prepared using >99.98% pure 1602. The technique of silent electric discharge was used in generating the ozone. The absorption cell used in these measurements was a 50-cm-long 5.08-cm-diameter Pyrex tube with Teflon valves. Potassium chloride windows were wedged 5- 10 mrad on the cell to prevent channeling arising from multiple reflections. The two spectra used in this analysis were recorded at room temperature with - 10.6 and -23.7 Torr of 1603 in the absorption cell. The sample pressures and temperatures were monitored continuously during the - l-hr scan time for each spectrum using a 0- to IOO-Tot-r Barocel pressure gauge and a thermocouple kept in contact with the cell body. Standards in the ~3band of ‘2C160~ reported by Guelachvili and Rao (IO) were multiplied by the factor 0.99999979 [average of the two factors reported by Brown and Toth (II)] and used to calibrate the wavelength scale of the spectra. Brown and Toth (12) have reported that their studies and two other studies using two different types of spectrometers, laser and FE, indicate directly or indirectly that the 1 - 0 and 2 - 0 positions of CO reported by Guelachvili are +0.0004 cm-’ higher compared with laser standards. Although we used the CO2 standards (10) to calibrate the present data, we have applied the correction factor indicated in Ref. (1 I) since the data used in this analysis were also recorded using the same Kitt Peak FTS as used in the work reported in Ref. (I I). For additional experimental details see Flaud et al. (4) and Rinsland et al. (5). Using the results reported in Ref. (9) it was rather easy to assign transitions with low and medium J and K, values (up to J N 45 and K, II 11). Following the initial assignments, a first calculation was performed using a Hamiltonian taking into account the Coriolis-type interaction between the rotational levels of the (110) and (011) vibrational states. In this way, an improved set of vibrational energies and rotational and coupling constants was obtained which allowed us to extend the assignments to new lines with higher J and K, values. The process was repeated until almost all of the yI f ~2 and v2 + u3 lines observable in the laboratory spectra were assigned. The rotational quantum numbers were extended up to J < 57, K, G 16 for V, + v2 and J i 55, K, G 15 for ~2+ ~3,thus greatly increasing the previous sets of observed quantum numbers (9). The experimental rotational energy levels of the (110) and (011) upper vibrational states were then obtained by adding the ground-state energy levels calculated from the ground-state rotational constants given in Ref. (3) to the measured line positions. THEORETICAL
CONSIDERATIONS
AND RESULTS
A. Line Positions According to the energy level scheme of ozone, the (I 10) and (011) vibrational states of this molecule can be treated as a diad of interacting states and the corresponding Hamiltonian matrix is given in Table I. The v-diagonal part consists of Watson-type Hamiltonians (one for each vibrational state) whereas the off-diagonal part contains operators which take into account the Coriolis-type interaction affecting the rotational levels of the two interacting states. The experimental energy levels were reproduced quite satifactorily with this Hamiltonian matrix since a standard deviation of 0.43
176
MALATHY
DEW
ET AL.
TABLE I Hamiltonian Matrices ”
=
(110)
Watson-type Hamiltonian
v’=
(0111
”
Coriolis ti= "'l
H
"Y
cooo,
Watson-type Hermitic conj.
Hamiltonian H I"
H I"
interaction
=
Watson-type Hamiltonian HV’Y’
=E Y
+H:J:+H:,J:J2+H:xJ:(Jz)'+H; (5')' +h:~:.J:~)+h:~(J:,J:")J'+2h:J:~iJz1' +L;Jf+L;xlJ:Jz+L;,J: (J')2+L;I,J1 (J')'+L; (J'I' +1~~~,J~~)tl;,(J~,J~y)J1+1~~(J~,J~y}(Jz~2+2I;J~~(J*)3 +P;J:"+P:II,J:Jz+P:,,J~ (J')*+... +p~iJ:,J:,~~.,~:,J:.~+-.. HC ",V
IJx ,J* I )
= hC V," IJx,Jzl+h~~viJy+h~:C"(J? +h;: "“=IJ* .JzIJz+h;:;‘c (Jf-Jf)
with
IA
81
J=
XY
J+
= AB
+
81
= J' - Jz
=
Jx x
T i;
Y
X 1OV3cm-’ close to the measurement accuracy was obtained. The vibrational energies and rotational and coupling constants derived from the fit are gathered in Table II and, as noticed in previous works (2,3,9), it was not possible to determine simultaneously all the Coriolis coupling constants. Consequently, the h”(01,.I I0)coefficient of the operator iJy was fixed to the value previously used (3) for the (001) and (100) vibrational states of I60 From the diagonalization of the Hamiltonian matrix, it was easy to obtain the vibration-rotation wavefunctions which can be written as
Iwv~JKXc) =
2 C Cklv)lJK~) u=(llO),(Ol I) K
(1)
Y, + v2 AND
q +
177
BANDS OF 1603
~3
TABLE II Vibrational Energies and Rotational and Coupling Constants for the (I 10) and (011) Vibrational States of 1603 Vibrational
and Rotational
Constants
(110)
(011)
E”
1796.261870 t 0.000057
A"
3.610812134
B"
0.4414461608
f 0.00000050
0.4398971175
l 0.00000055
C"
o.3902987066
* 0.00000043
0.3885D33996
t 0.00000046
hV K
(o.23972792 l 0.000068)
by KJ
(-0.2075254 l 0.00091)
1726.522490 f 0.000075
f 0.0000035
3.552305711
x 10-3 x lo-$
f 0.0000053
(O.2286541 A 0.00012) (-o.159E22 t 0.001l)
x lO-3 x 10-5
Av J
(O.4668933 t 0.00025)
6" ii
(0.432119 I 0.0042)
x lO-s
(0.349531 * 0.0010)
x 10-5
6v
(0.647274 l 0.0020)
x lo_7
(0.7609g2 * 0.0023)
x 1O-7
(O.49965o i 0.0048)
x 1O-7
(O.46448 t 0.010)
iI
(-0.210352 f 0.0059)
c H"
JK
“Y hi “;;
x 10-6
I 10-8
(o.459857, b 0.00023)
x 10-~
(-0.187597 i 0.0027) (-o.31110 t 0.023)
(O.16922 f 0.079) x lo-'*
(o.1l362 * 0.059)
x 10-12
x 10-12
x lo-lo
(-0.~7~~ l 0.11) x 10-8 (-0.33ol f 0.16) x lo-lo (0.9160 l 0.53) X 10-13
(0.199gg * 0.059)
L" K
(-o.12635 t 0.010) x lo-10
(-o.10762 f 0.027)
0.2739 x 10-12
0.2739
-0.3251 x 10-15
-0.3251
0.2994 x 10-1~
0.2994
x lo-l7
P" K
0.1812 x 1O-12
0.1812
x IO-l2
P" K
0.333 x 10-14
0.333 x 10-14
P" KKKJ
0.1895 x lo-l5
0.1895
LYLE LY
x 10-8
(-O.83,6 * 0.13) x lo-lo
h" J
L"
x 10-6
Coupling
bTOl1)WO)
m (-0.1009976
* 0.00016)
- -Oe470
h&)~l,o)
- (0.85510 t 0.046)
b[AiE)cllO)
* (-0.106248 f 0.0063)
hi6iifciloj
x lo-l5
x IO-I5
Calstants
h" (011)(110)
-
x IO-lo
x 10-12
x 10-l
x 10-6 x 10-6
(-o.5931 t 0.23) x lo+
All the reaulta are in C.-I and the quoted errors are one standard deviation. The Constants without err~fs were held fixed during the calculation; they e,,me from Ref. (2).
178
MALATHY DEW ET AL.
where the (JKy)‘s are Wang functions:
IJK~)=+JK)+T~J-K))
K>O,
JJO+) = IJO).
y=fl
c-4
From the wavefunction of a given vibrational level it is possible to calculate the mixing coefficient, % (u) on the state IV) of this level, which is given by % (II) = c jcj$
(3)
K
This coefficient indicates whether the level is affected by a resonance or not. We have plotted in Fig. I the mixing coefficients of some (0 11) rotational levels and the following observations can be made: a. There is a smooth behavior of the mixing coefficients with J for the series of levels with K, = 12, 13, 14, 15, and 16. b. Contrary to the above series, the K, = 5 series is not regular. The large value of the mixing coefficient at J = 39 results from the accidental proximity of the resonating (110) [39 2 381 and the (011) [39 5 341 rovibrational levels.
B. Line Intensities Using the equivalent width method, about 220 line intensities were measured with an average relative uncertainty of 10%. Although the two spectra described previously were used for the band analysis, only the higher pressure (-23.7 Torr) spectrum was used for intensity measurements. This is because many lines were too weak to be measured accurately in the lower abundance spectrum. Because the exact amount of ozone in the cell was not known, we decided to calibrate the intensities of the vI + u2 and u2 + v3 bands of ozone with respect to intensities measured in the IO-pm region which contains the v3 and vI bands (3). Consequently, we have measured from the same spectrum 95 v, line intensities which were calibrated using the results of Ref.
%(llO)
A 50-
10
20
40
30
50
60
J-+ FIG. I. Mixing coefficients in Z (110) for some rotational levels of the (01 I) state. For high K, values, the mixing coefficients vary smoothly with J; a crossing of levels occurs for K. = 14, 15, and 16. For K, = 5, the mixing is weak except for J = 39; the large mixing coefficient is caused by the accidental proximity of the (110) 139 2 381 and the (011) [39 5 341 rovibrational levels.
179
Y, + v> AND pz + vj BANDS OF l6O3
(3). In this way, the intensities in the 5.7-pm region (v, + u2 and uz + v3 bands) are consistent with the intensities in the lo-Frn region (v, and v3 bands). The vl + v2 and u2 + p3 experimental relative intensities were then reproduced using the following transformed transition moment operators [see Ref. (12) for detailed explanations]: v1 + v2 (B-type
band)
(OOO)(1 lo)&= (-0.5054,~0.0025)
X lo-‘&+(-O.1
132kO.021)
x 10-4{i~Y,Jz~ +(0.514,aO.OlO)X v2 + u3 (A-type
10-4{rb,,iJY) + f . .
(4)
band)
(o00)(0~1)~~=(-0.9081,-t0.0050)x
10-2~z+(0.93~~0.21)X
- ~i~~,J,}]+(0.933,0.43)X
lo-‘f@#+,iJ,)
10-5~[(~~,iJI,} + (i&,JJ]+
9- -
(5)
6
0 ;i & -2 u, LLJ -4 CC -6
0 90
1681.5
1682.0
WAVENUMBER
1682.5
(cm-‘)
FIG. 2. Laboratory (solid line) and best-fitcalculated (crosses) spectra in the region of the v2 + vj band around 1682 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Tom of 1603in a tiO_cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. The Y, + Yeline [39 2 381 + [40 5 351 located at 1681.838 cm-’ appears only because it IYXTOMits intensity from the v, + u, tine (39 5 341 + [40 5 351 at 1682.007 cm-‘. Although the A& = 3 Y, + v2 line is blended by a weaker hot band line, it can be seen that the intensities of the two resonating lines are almost equal because of a mixing coefficient of about 50% (see Fig. 1). Several high K,, lines of the vz + 4 band (marked with asterisks) are also observable in this region. Unassigned absorptions in this region are believed to be from the 2~2 + yj - ~2hot band and are indicated by solid triangles.
180
MALATHY DEVI ET AL.
with {A,B} =Ml+lL4
4, = L
(direction cosine)
J, = component of J along the molecular axis (Y. All of the results are given in Debye. The statistical analysis of the results is as follows:
o<+
10%
69.1% of the lines
ObS.
*0<+2or,
24.8% of the lines
ohs.
0.9c 18 1.3
I
1832.3
WAVENUMBER
(cm-‘)
FIG. 3. Laboratory (solid line) and best-fit calculated (crosses) spectra in the region of the Y, + Y*band around 1832 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Torr of “0, in a 50-cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. High J lines of the yI + Yeband (marked with asterisks) are observed in this spectral region. Their absorption is well reproduced by the calculations. Weak unassigned lines in this region are believed to be from the Y, + 2u2 - V~hot band and are indicated by solid triangles.
181
u, + v2 AND Ye + yp BANDS OF 160,
6.1% of the lines the calculated intensity. where 61 = IZOb.- Z,,C.j, lobs.is the observed and ZCalC. These results are very satisfactory since 69% of the intensities are reproduced within the experimental uncertainty of 10%. The following points of the analysis are of interest: 1. Since the line intensities are proportional to the square of the dipole moment matrix elements, only the relative signs of the transition moment constants are determined. A method to obtain their absolute signs (signs with respect to the permanent dipole moment of the molecule) would be to study the hot bands I, - v2 and v3 - v, as was done for the water molecule (13). 2. The constants, coefficients of & and &, are of the same order of magnitude which implies that the ul + u2 band is almost as intense as the v2 + v3 band, which is not very common. Usually, for ozone, in a given spectral region the A-type band is much stronger than the B-type band (see the lo-pm region for example).
-2 1
--I
1 .oo
2 0.95 z
u
cn J
29
1
I1
I
I
III~IILI11111
25
0.90
20
15
l
11
J
Ii20 1860.8
1858.7
WAVENUMBER
(cm-‘)
FIG. 4. Laboratory (solid line) and best-fit calculated (crosses) spectra in the region of the V, + v2 band around 1860 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Torr of 1603in a 50-cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. The RQK:= 9 line series (marked with asterisks) is clearly visible and is well reproduced by the calcuIations.
182
MALATHY DEVI ET AL.
3. The rotational correcting terms are not negligible, particularly for the B-type band. In fact, these terms allow the calculation to reproduce quite satisfactorily the intensity peculiarities which were noted in Ref. (9). Finally, using the vibrational energies and the rotational and coupling constants given in Table II as well as the transition moment constants given in Eqs. (4) and (5), we have generated a list of 7 110 line positions and intensities for the vI + ZQand v2 + ~3 bands of ozone. The calculations were performed’ using an intensity cutoff of 0.1 X 1O-24cm-‘/molecule cme2 at 296 K, maximum values of 70 for J and 2 1 for K,, and a maximum lower state energy of 3000 cm-‘. Total band intensities of 0.237 X lo-l9 and 0.536 X IO-l9 cm-‘/molecule cmV2 at 296 K were obtained respectively for the v1 + u2 and u2 + u3bands of 1603. These results agree within 10% with the lowresolution integrated band intensities reported in Ref. (7), which is quite satisfactory. Figures 2 to 4 show comparisons of the measured and calculated spectra in three different spectral regions. In all cases the observed features of the vI + v2 and the v2 + y3 bands are reproduced very well by the calculations. The weak unassigned lines in Fig. 2, marked by solid triangles, are believed to be transitions of the 2~2 + ~3 - u2 hot band. Similarly, the few unassigned absorptions marked by solid triangles in Fig. 3 are probably lines of the v1 + 2~2 - u2 hot band. These hot band lines are about 5% as strong as the strongest lines of the vl + v2 and the ~2 + u3 bands. Because of the weakness of the hot band lines in the present spectra and the absence of assignments for the 2u2 + y3 and the V, + 2u2 bands, analysis of these features has not been attempted at this time. It should be emphasized that the absolute values of the intensities calculated here for the ZJ~+ u2 and v2 + v3 bands have been calibrated against intensities from the lo-pm spectral region which have been obtained assuming the value (a~Jeq3), = -0.2662 D [see Ref. (3) for more details]. ACKNOWLEDGMENTS The authors thank Charles T. Solomon of NASA Langley and Rob Hubbard and Jeremy Wagner of the National Solar Observatory (NSO) for their help with the laboratory experiment, Gregg Ladd for the computer processing of the data at NSO, and D. Chris Benner of William and Mary and Carolyn H. Sutton of SASC Technologies for their assistance in the processing of the spectra at NASA Langley. Research at the College of William and Mary was supported under Cooperative Agreement NCC I-80 with NASA. C. Camy-Peyret and J.-M. Flaud acknowledge partial support of their research work under USAF Agreement RES D5-674. 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 Regional de Calcul Electronique, CNRS, 9 1405 Orsay, France. RECEIVED:
February 5, 1987 REFERENCES
I. M. CARLOTTI, G. DI LONARDO, L. FUSINA, A. TROMBETTI,A. B~NE’ITI, B. CARLI, AND F. MENCARAGLIA,J. Mol. Spectrosc. 107, 89-93 (1984). 2. H. M. PICKETT, E. A. COHEN, AND J. S. MARGOLIS,J. Mol. Spectrosc. 110, 186-214 (1985). 3. J.-M. FLAUD, C. CAMY-PEYRET,V. MALATHY DEW, C. P. RINSLAND,AND M. A. H. SMITH,accepted for publication.
’ A partition function Z(296) = 3473 was used in the intensity calculations.
vI + u2 AND v2 + v, BANDS OF I603
183
4. J.-M. FLAUD, C. CAMY-PEYRET, V. MALATHY DEVI, C. P. RINSLAND, AND M. A. H. SMITH,J. Mol. Spectrosc. 118, 334-344 (1986). 5. C. P. RINSLAND, V. MALATHY DEVI, J.-M. FLAUD, C. CAMY-PEYRET, M. A. H. SMITH, AND G. M. STOKES,J. Geophys. Rex 90, 10719-10725 (1985). 6. C. CAMY-J?EYRET,J.-M. FLAUD, A. PERRIN, V. MALATHY DEVI, C. P. RINSLAND, AND M. A. H. SMITH, J. Mol. Spectrosc. 118, 345-354 (1986). 7. D. J. MCCAA AND J. H. SHAW, J. Mol. Spectrosc. 25, 374-397 (1968). 8. C. JONES AND J. H. SHAW, J. Mol. Specfrosc. 68,48-55 (1977). 9. A. BARBE,C. SECROUN,P. JOUVE,C. CAMY-PEYRET, AND J.-M. FLAUD, J. Mol. Spectrosc. 75, 103110 (1979). 10. G. GUELACHV~LIAND K. NARAHARI RAO, “Handbook of Infrared Standards,” Academic Press,Orlando. FL, 1986. 1 I. L. R. BROWN AND R. A. TOTH, J. Opt. Sot. Amer. B 2,842-856 (1985). 12. J.-M. FLAUD, C. CAMY-PEYRET, AND R. A. TOTH, “Water Vapor Line Parameters from Microwave to Medium Infrared,” Pergamon, Oxford, 1981. 13. C. CAMY-PEYRET AND J.-M. FLAUD, in “Molecular Spectroscopy: Modern Research” (K. Namhari Rao, Ed.). Vol. III. Academic Press, Orlando, FL, 1985.
125, 174-183 ( 1987)
Line Positions and Intensities for the v1 + v2 and v2 + u3 Bands of 1603 V. MALATHY DEW Department of Physics, College of Williamand Mary, Williamsburg,Virginia23185 J.-M. FLAUD AND C. CAMY-PEYRET Laboratoire de Physique Molkculaireet Atmosphkrique,Tour 13. 3’ &age, UniversitkPierre et Marie Curie et CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France AND C.
P. RINSLAND AND M. A. H. SMITH
Atmospheric Sciences Division,NASA Langley Research Center, Hampton, Virginia23665-5225 Using0.005cm-’ resolution Fouriertransform spectra of 1603,generated by electric discharge from a >99.98% pure sample of 1602, an extensive analysis of the Y, + Yeand the Ye+ yj bands in the 5.7-pm region was performed. The rotational energy levels of the upper (110) and (011) vibrational states of 1603were reproduced within their experimental uncertainties using a Hamiltonian which takes explicitly into account the Coriolis-type interaction occurring between the rotational energy levels of both states. Improved vibrational energies and rotational and coupling constants were also derived for the (110) and (011) states. Precise transition moment constants for these two bands were deduced from analysis of 220 measured line intensities. Finally, a complete list of line positions, intensities, and lower state energies for both bands has been generated. 0 1987 AcademicPns, Inc. INTRODUCTION
Because of its atmospheric importance, the 1603 molecule and the isotopic species ‘60’80160 and 160’60LE0 have been the subject of numerous recent spectroscopic studies [(Z-6) and references therein]. Almost all of the recent works were concerned with the pure rotation spectrum and the lo-pm absorption region which are widely used for remote sensing measurements of this molecule in the terrestrial atmosphere. However, absorption by atmospheric ozone is clearly visible in many other spectral regions as well, and we present in this paper our work concerning the 5.7-pm region of 1603. The prominent bands appearing in this spectral region are the two combination bands zq + u2 and u2 + v3. These bands were analyzed in previous laboratory studies (7-9), but at a resolution lower than that achieved in the present work. This work also reports the first experimental measurements of individual line intensities in these bands.
0022-2852187 $3.00 wt 8 1987 by AcademicPress,Inc. Au rightsof nzpmduction in any form e-served.
174
Y, + v2 AND v2 + q BANDS EXPERIMENTAL
DETAILS
OF
I603
175
AND ANALYSIS
The ozone samples were prepared using >99.98% pure 1602. The technique of silent electric discharge was used in generating the ozone. The absorption cell used in these measurements was a 50-cm-long 5.08-cm-diameter Pyrex tube with Teflon valves. Potassium chloride windows were wedged 5- 10 mrad on the cell to prevent channeling arising from multiple reflections. The two spectra used in this analysis were recorded at room temperature with - 10.6 and -23.7 Torr of 1603 in the absorption cell. The sample pressures and temperatures were monitored continuously during the - l-hr scan time for each spectrum using a 0- to IOO-Tot-r Barocel pressure gauge and a thermocouple kept in contact with the cell body. Standards in the ~3band of ‘2C160~ reported by Guelachvili and Rao (IO) were multiplied by the factor 0.99999979 [average of the two factors reported by Brown and Toth (II)] and used to calibrate the wavelength scale of the spectra. Brown and Toth (12) have reported that their studies and two other studies using two different types of spectrometers, laser and FE, indicate directly or indirectly that the 1 - 0 and 2 - 0 positions of CO reported by Guelachvili are +0.0004 cm-’ higher compared with laser standards. Although we used the CO2 standards (10) to calibrate the present data, we have applied the correction factor indicated in Ref. (1 I) since the data used in this analysis were also recorded using the same Kitt Peak FTS as used in the work reported in Ref. (I I). For additional experimental details see Flaud et al. (4) and Rinsland et al. (5). Using the results reported in Ref. (9) it was rather easy to assign transitions with low and medium J and K, values (up to J N 45 and K, II 11). Following the initial assignments, a first calculation was performed using a Hamiltonian taking into account the Coriolis-type interaction between the rotational levels of the (110) and (011) vibrational states. In this way, an improved set of vibrational energies and rotational and coupling constants was obtained which allowed us to extend the assignments to new lines with higher J and K, values. The process was repeated until almost all of the yI f ~2 and v2 + u3 lines observable in the laboratory spectra were assigned. The rotational quantum numbers were extended up to J < 57, K, G 16 for V, + v2 and J i 55, K, G 15 for ~2+ ~3,thus greatly increasing the previous sets of observed quantum numbers (9). The experimental rotational energy levels of the (110) and (011) upper vibrational states were then obtained by adding the ground-state energy levels calculated from the ground-state rotational constants given in Ref. (3) to the measured line positions. THEORETICAL
CONSIDERATIONS
AND RESULTS
A. Line Positions According to the energy level scheme of ozone, the (I 10) and (011) vibrational states of this molecule can be treated as a diad of interacting states and the corresponding Hamiltonian matrix is given in Table I. The v-diagonal part consists of Watson-type Hamiltonians (one for each vibrational state) whereas the off-diagonal part contains operators which take into account the Coriolis-type interaction affecting the rotational levels of the two interacting states. The experimental energy levels were reproduced quite satifactorily with this Hamiltonian matrix since a standard deviation of 0.43
176
MALATHY
DEW
ET AL.
TABLE I Hamiltonian Matrices ”
=
(110)
Watson-type Hamiltonian
v’=
(0111
”
Coriolis ti= "'l
H
"Y
cooo,
Watson-type Hermitic conj.
Hamiltonian H I"
H I"
interaction
=
Watson-type Hamiltonian HV’Y’
=E Y
+H:J:+H:,J:J2+H:xJ:(Jz)'+H; (5')' +h:~:.J:~)+h:~(J:,J:")J'+2h:J:~iJz1' +L;Jf+L;xlJ:Jz+L;,J: (J')2+L;I,J1 (J')'+L; (J'I' +1~~~,J~~)tl;,(J~,J~y)J1+1~~(J~,J~y}(Jz~2+2I;J~~(J*)3 +P;J:"+P:II,J:Jz+P:,,J~ (J')*+... +p~iJ:,J:,~~.,~:,J:.~+-.. HC ",V
IJx ,J* I )
= hC V," IJx,Jzl+h~~viJy+h~:C"(J? +h;: "“=IJ* .JzIJz+h;:;‘c (Jf-Jf)
with
IA
81
J=
XY
J+
= AB
+
81
= J' - Jz
=
Jx x
T i;
Y
X 1OV3cm-’ close to the measurement accuracy was obtained. The vibrational energies and rotational and coupling constants derived from the fit are gathered in Table II and, as noticed in previous works (2,3,9), it was not possible to determine simultaneously all the Coriolis coupling constants. Consequently, the h”(01,.I I0)coefficient of the operator iJy was fixed to the value previously used (3) for the (001) and (100) vibrational states of I60 From the diagonalization of the Hamiltonian matrix, it was easy to obtain the vibration-rotation wavefunctions which can be written as
Iwv~JKXc) =
2 C Cklv)lJK~) u=(llO),(Ol I) K
(1)
Y, + v2 AND
q +
177
BANDS OF 1603
~3
TABLE II Vibrational Energies and Rotational and Coupling Constants for the (I 10) and (011) Vibrational States of 1603 Vibrational
and Rotational
Constants
(110)
(011)
E”
1796.261870 t 0.000057
A"
3.610812134
B"
0.4414461608
f 0.00000050
0.4398971175
l 0.00000055
C"
o.3902987066
* 0.00000043
0.3885D33996
t 0.00000046
hV K
(o.23972792 l 0.000068)
by KJ
(-0.2075254 l 0.00091)
1726.522490 f 0.000075
f 0.0000035
3.552305711
x 10-3 x lo-$
f 0.0000053
(O.2286541 A 0.00012) (-o.159E22 t 0.001l)
x lO-3 x 10-5
Av J
(O.4668933 t 0.00025)
6" ii
(0.432119 I 0.0042)
x lO-s
(0.349531 * 0.0010)
x 10-5
6v
(0.647274 l 0.0020)
x lo_7
(0.7609g2 * 0.0023)
x 1O-7
(O.49965o i 0.0048)
x 1O-7
(O.46448 t 0.010)
iI
(-0.210352 f 0.0059)
c H"
JK
“Y hi “;;
x 10-6
I 10-8
(o.459857, b 0.00023)
x 10-~
(-0.187597 i 0.0027) (-o.31110 t 0.023)
(O.16922 f 0.079) x lo-'*
(o.1l362 * 0.059)
x 10-12
x 10-12
x lo-lo
(-0.~7~~ l 0.11) x 10-8 (-0.33ol f 0.16) x lo-lo (0.9160 l 0.53) X 10-13
(0.199gg * 0.059)
L" K
(-o.12635 t 0.010) x lo-10
(-o.10762 f 0.027)
0.2739 x 10-12
0.2739
-0.3251 x 10-15
-0.3251
0.2994 x 10-1~
0.2994
x lo-l7
P" K
0.1812 x 1O-12
0.1812
x IO-l2
P" K
0.333 x 10-14
0.333 x 10-14
P" KKKJ
0.1895 x lo-l5
0.1895
LYLE LY
x 10-8
(-O.83,6 * 0.13) x lo-lo
h" J
L"
x 10-6
Coupling
bTOl1)WO)
m (-0.1009976
* 0.00016)
- -Oe470
h&)~l,o)
- (0.85510 t 0.046)
b[AiE)cllO)
* (-0.106248 f 0.0063)
hi6iifciloj
x lo-l5
x IO-I5
Calstants
h" (011)(110)
-
x IO-lo
x 10-12
x 10-l
x 10-6 x 10-6
(-o.5931 t 0.23) x lo+
All the reaulta are in C.-I and the quoted errors are one standard deviation. The Constants without err~fs were held fixed during the calculation; they e,,me from Ref. (2).
178
MALATHY DEW ET AL.
where the (JKy)‘s are Wang functions:
IJK~)=+JK)+T~J-K))
K>O,
JJO+) = IJO).
y=fl
c-4
From the wavefunction of a given vibrational level it is possible to calculate the mixing coefficient, % (u) on the state IV) of this level, which is given by % (II) = c jcj$
(3)
K
This coefficient indicates whether the level is affected by a resonance or not. We have plotted in Fig. I the mixing coefficients of some (0 11) rotational levels and the following observations can be made: a. There is a smooth behavior of the mixing coefficients with J for the series of levels with K, = 12, 13, 14, 15, and 16. b. Contrary to the above series, the K, = 5 series is not regular. The large value of the mixing coefficient at J = 39 results from the accidental proximity of the resonating (110) [39 2 381 and the (011) [39 5 341 rovibrational levels.
B. Line Intensities Using the equivalent width method, about 220 line intensities were measured with an average relative uncertainty of 10%. Although the two spectra described previously were used for the band analysis, only the higher pressure (-23.7 Torr) spectrum was used for intensity measurements. This is because many lines were too weak to be measured accurately in the lower abundance spectrum. Because the exact amount of ozone in the cell was not known, we decided to calibrate the intensities of the vI + u2 and u2 + v3 bands of ozone with respect to intensities measured in the IO-pm region which contains the v3 and vI bands (3). Consequently, we have measured from the same spectrum 95 v, line intensities which were calibrated using the results of Ref.
%(llO)
A 50-
10
20
40
30
50
60
J-+ FIG. I. Mixing coefficients in Z (110) for some rotational levels of the (01 I) state. For high K, values, the mixing coefficients vary smoothly with J; a crossing of levels occurs for K. = 14, 15, and 16. For K, = 5, the mixing is weak except for J = 39; the large mixing coefficient is caused by the accidental proximity of the (110) 139 2 381 and the (011) [39 5 341 rovibrational levels.
179
Y, + v> AND pz + vj BANDS OF l6O3
(3). In this way, the intensities in the 5.7-pm region (v, + u2 and uz + v3 bands) are consistent with the intensities in the lo-Frn region (v, and v3 bands). The vl + v2 and u2 + p3 experimental relative intensities were then reproduced using the following transformed transition moment operators [see Ref. (12) for detailed explanations]: v1 + v2 (B-type
band)
(OOO)(1 lo)&= (-0.5054,~0.0025)
X lo-‘&+(-O.1
132kO.021)
x 10-4{i~Y,Jz~ +(0.514,aO.OlO)X v2 + u3 (A-type
10-4{rb,,iJY) + f . .
(4)
band)
(o00)(0~1)~~=(-0.9081,-t0.0050)x
10-2~z+(0.93~~0.21)X
- ~i~~,J,}]+(0.933,0.43)X
lo-‘f@#+,iJ,)
10-5~[(~~,iJI,} + (i&,JJ]+
9- -
(5)
6
0 ;i & -2 u, LLJ -4 CC -6
0 90
1681.5
1682.0
WAVENUMBER
1682.5
(cm-‘)
FIG. 2. Laboratory (solid line) and best-fitcalculated (crosses) spectra in the region of the v2 + vj band around 1682 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Tom of 1603in a tiO_cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. The Y, + Yeline [39 2 381 + [40 5 351 located at 1681.838 cm-’ appears only because it IYXTOMits intensity from the v, + u, tine (39 5 341 + [40 5 351 at 1682.007 cm-‘. Although the A& = 3 Y, + v2 line is blended by a weaker hot band line, it can be seen that the intensities of the two resonating lines are almost equal because of a mixing coefficient of about 50% (see Fig. 1). Several high K,, lines of the vz + 4 band (marked with asterisks) are also observable in this region. Unassigned absorptions in this region are believed to be from the 2~2 + yj - ~2hot band and are indicated by solid triangles.
180
MALATHY DEVI ET AL.
with {A,B} =Ml+lL4
4, = L
(direction cosine)
J, = component of J along the molecular axis (Y. All of the results are given in Debye. The statistical analysis of the results is as follows:
o<+
10%
69.1% of the lines
ObS.
*0<+2or,
24.8% of the lines
ohs.
0.9c 18 1.3
I
1832.3
WAVENUMBER
(cm-‘)
FIG. 3. Laboratory (solid line) and best-fit calculated (crosses) spectra in the region of the Y, + Y*band around 1832 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Torr of “0, in a 50-cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. High J lines of the yI + Yeband (marked with asterisks) are observed in this spectral region. Their absorption is well reproduced by the calculations. Weak unassigned lines in this region are believed to be from the Y, + 2u2 - V~hot band and are indicated by solid triangles.
181
u, + v2 AND Ye + yp BANDS OF 160,
6.1% of the lines the calculated intensity. where 61 = IZOb.- Z,,C.j, lobs.is the observed and ZCalC. These results are very satisfactory since 69% of the intensities are reproduced within the experimental uncertainty of 10%. The following points of the analysis are of interest: 1. Since the line intensities are proportional to the square of the dipole moment matrix elements, only the relative signs of the transition moment constants are determined. A method to obtain their absolute signs (signs with respect to the permanent dipole moment of the molecule) would be to study the hot bands I, - v2 and v3 - v, as was done for the water molecule (13). 2. The constants, coefficients of & and &, are of the same order of magnitude which implies that the ul + u2 band is almost as intense as the v2 + v3 band, which is not very common. Usually, for ozone, in a given spectral region the A-type band is much stronger than the B-type band (see the lo-pm region for example).
-2 1
--I
1 .oo
2 0.95 z
u
cn J
29
1
I1
I
I
III~IILI11111
25
0.90
20
15
l
11
J
Ii20 1860.8
1858.7
WAVENUMBER
(cm-‘)
FIG. 4. Laboratory (solid line) and best-fit calculated (crosses) spectra in the region of the V, + v2 band around 1860 cm-’ (lower panel). The laboratory spectrum was recorded with about 23.7 Torr of 1603in a 50-cm-long absorption path at room temperature. Residuals (observed minus calculated) are shown in the upper panel. The RQK:= 9 line series (marked with asterisks) is clearly visible and is well reproduced by the calcuIations.
182
MALATHY DEVI ET AL.
3. The rotational correcting terms are not negligible, particularly for the B-type band. In fact, these terms allow the calculation to reproduce quite satisfactorily the intensity peculiarities which were noted in Ref. (9). Finally, using the vibrational energies and the rotational and coupling constants given in Table II as well as the transition moment constants given in Eqs. (4) and (5), we have generated a list of 7 110 line positions and intensities for the vI + ZQand v2 + ~3 bands of ozone. The calculations were performed’ using an intensity cutoff of 0.1 X 1O-24cm-‘/molecule cme2 at 296 K, maximum values of 70 for J and 2 1 for K,, and a maximum lower state energy of 3000 cm-‘. Total band intensities of 0.237 X lo-l9 and 0.536 X IO-l9 cm-‘/molecule cmV2 at 296 K were obtained respectively for the v1 + u2 and u2 + u3bands of 1603. These results agree within 10% with the lowresolution integrated band intensities reported in Ref. (7), which is quite satisfactory. Figures 2 to 4 show comparisons of the measured and calculated spectra in three different spectral regions. In all cases the observed features of the vI + v2 and the v2 + y3 bands are reproduced very well by the calculations. The weak unassigned lines in Fig. 2, marked by solid triangles, are believed to be transitions of the 2~2 + ~3 - u2 hot band. Similarly, the few unassigned absorptions marked by solid triangles in Fig. 3 are probably lines of the v1 + 2~2 - u2 hot band. These hot band lines are about 5% as strong as the strongest lines of the vl + v2 and the ~2 + u3 bands. Because of the weakness of the hot band lines in the present spectra and the absence of assignments for the 2u2 + y3 and the V, + 2u2 bands, analysis of these features has not been attempted at this time. It should be emphasized that the absolute values of the intensities calculated here for the ZJ~+ u2 and v2 + v3 bands have been calibrated against intensities from the lo-pm spectral region which have been obtained assuming the value (a~Jeq3), = -0.2662 D [see Ref. (3) for more details]. ACKNOWLEDGMENTS The authors thank Charles T. Solomon of NASA Langley and Rob Hubbard and Jeremy Wagner of the National Solar Observatory (NSO) for their help with the laboratory experiment, Gregg Ladd for the computer processing of the data at NSO, and D. Chris Benner of William and Mary and Carolyn H. Sutton of SASC Technologies for their assistance in the processing of the spectra at NASA Langley. Research at the College of William and Mary was supported under Cooperative Agreement NCC I-80 with NASA. C. Camy-Peyret and J.-M. Flaud acknowledge partial support of their research work under USAF Agreement RES D5-674. 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 Regional de Calcul Electronique, CNRS, 9 1405 Orsay, France. RECEIVED:
February 5, 1987 REFERENCES
I. M. CARLOTTI, G. DI LONARDO, L. FUSINA, A. TROMBETTI,A. B~NE’ITI, B. CARLI, AND F. MENCARAGLIA,J. Mol. Spectrosc. 107, 89-93 (1984). 2. H. M. PICKETT, E. A. COHEN, AND J. S. MARGOLIS,J. Mol. Spectrosc. 110, 186-214 (1985). 3. J.-M. FLAUD, C. CAMY-PEYRET,V. MALATHY DEW, C. P. RINSLAND,AND M. A. H. SMITH,accepted for publication.
’ A partition function Z(296) = 3473 was used in the intensity calculations.
vI + u2 AND v2 + v, BANDS OF I603
183
4. J.-M. FLAUD, C. CAMY-PEYRET, V. MALATHY DEVI, C. P. RINSLAND, AND M. A. H. SMITH,J. Mol. Spectrosc. 118, 334-344 (1986). 5. C. P. RINSLAND, V. MALATHY DEVI, J.-M. FLAUD, C. CAMY-PEYRET, M. A. H. SMITH, AND G. M. STOKES,J. Geophys. Rex 90, 10719-10725 (1985). 6. C. CAMY-J?EYRET,J.-M. FLAUD, A. PERRIN, V. MALATHY DEVI, C. P. RINSLAND, AND M. A. H. SMITH, J. Mol. Spectrosc. 118, 345-354 (1986). 7. D. J. MCCAA AND J. H. SHAW, J. Mol. Spectrosc. 25, 374-397 (1968). 8. C. JONES AND J. H. SHAW, J. Mol. Specfrosc. 68,48-55 (1977). 9. A. BARBE,C. SECROUN,P. JOUVE,C. CAMY-PEYRET, AND J.-M. FLAUD, J. Mol. Spectrosc. 75, 103110 (1979). 10. G. GUELACHV~LIAND K. NARAHARI RAO, “Handbook of Infrared Standards,” Academic Press,Orlando. FL, 1986. 1 I. L. R. BROWN AND R. A. TOTH, J. Opt. Sot. Amer. B 2,842-856 (1985). 12. J.-M. FLAUD, C. CAMY-PEYRET, AND R. A. TOTH, “Water Vapor Line Parameters from Microwave to Medium Infrared,” Pergamon, Oxford, 1981. 13. C. CAMY-PEYRET AND J.-M. FLAUD, in “Molecular Spectroscopy: Modern Research” (K. Namhari Rao, Ed.). Vol. III. Academic Press, Orlando, FL, 1985.