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Transformed dipole moment and line intensities for the H218O molecule first decade interacting vibrational states
JOURNAL
OF MOLECULAR
SPECTROSCOPY
l‘t‘t,
239-241 (1990)
NOTES Transformed Dipole Moment and Line Intensities for the Hz”0 Molecule First Decade Interacting Vibrational States In this note we continue our analysis of water vapor in the short-wave spectral region. The object of the present investigation is the spectrum of the Hz’*0 molecule in the region 9500- 11500 cm-‘. This region consists of transitions from the ground vibrational state (000) to the decade of interacting vibrational states (u > = (u,u~uJ) = (ZOI), (003), (121). (041). (300), (102). (220), (022). (140). (060). The high-precision experimental absorption spectra between 9500 and 11 500 cm-’ were analyzed by Chevillard et ul. in 1987 (I) (accuracies in line centers and absolute intensities are -10e3 cm-’ and 27%. respectively) We obtained the rotational, centrifugal, and resonance constants that reproduced the experimental line centers with accuracies near the experimental one (2). In this note the parameters of transformed dipole moment operator /.I:7= ClO)“k&(ul=
”
ClO)(C
”
(1)
‘“‘~;“A,)(ul
i
are considered. In Eq. ( 1) the “A, are the operators [we do not reproduce here the form of these operators. but they can be found in Refs. (3-5)] : and the (“‘*J are the parameters to be determined of the transformed dipole moment operator. The values of the “)pJ parameters have been obtained through a least-squares fit of the experimental intensities (1 j. In our calculation the 588 line intensities from Ref. (I) have been used as initial data. As emphasized in Ref. (2) some upper state energy levels seem to be incorrect in Ref. ( 1) [see Ref. (2) for details]. For this reason, the corresponding line intensities have not been used in our analysis. The (“)rJ parameters obtained are presented in Tables I and II. These parameters reproduce the experimental line intensities with a mean accuracy close to the experimental one. Among the 588 lines involved in the fit, the intensities of 403 lines (68.54% of all the lines) are reproduced within experimental accuracy (better than 7%); 74 ( 12.59%) lines are reproduced within lo-20% accuracy: and 3 I (5.27%) lines within 20-50%
TABLE 1 Parameters ‘“‘pi of the Transformed Dipole Moment Operator (in D) (u = u,uzuJ, uj Odd)’
!.I
P1104 +10'
(201)
18.022(22) -13.27
l22)
!+06
(1211
13.897(12)
-5.2597(99)
-4.55~15~
-4.82C1.5)
(041,
-1.ZSBl(35) -2.78(10)
2.385(43)
!+OL
2.59
(20,
!+Ob
1.002
(281
P610b
(003)
-2.107c57)
X5.38(12)
6.97(13)
28.83
(10)
12.770(87)
-3.80
23.44
(15,
lLlll13)
-6.57(19)
1.482(59,
c 10)
-1.58(12)
+ !+lO’
’
Values in parentheses in Tables 1 and 11are 1c confidence intervals. 239
0022-2852190 $3.00 Copyright D 1990 by Academc
Press. Inc.
All rights of reproduction in any form reserved.
TABLE II Parameters (“)pj of the Transformed Dipole Moment Operator (in D) (u = u,u2vj,u3Even) "l"Z"3 ,300)
w
p,105
54.393(54)
~102~
(220)
-8.112l45)
-2.63(18)
(022)
(140)
-7.03(32,
-4.07(99)
% -3.05(11)
v3106 P4105
-,.557(15>
+105
8.9219179)
P6106 lJ7107
-1.380(12>
0.126(25>
5.3421(69
-,.315(23)
-1.585(46) 0.735151)
,.515(22) -4.57(,7)
-5.25(,6)
'8
TABLE III Line Positions (in cm-‘) and Intensities ( 10e4 cm-* atm-‘) for the Decade of H2180 at 300K (Illustrative Portion)
10832.123 ,0833.46,8 10833.790 10834.057 10834.782 10837.302 10839.083 10840.283 10840.283 10840.283 10850.277 10851.244 10855.153 10857.034 10857.819 10858.96, 10859.121 10859.723 10860.986 10862.615 10863.632 10864.362 10864.547 10864.90, 10865.186 ,0865.,86 10865.186 10865.613 10865.830 10866.687 iO868.227 10868.953 10868.953 1086B.953 10869.642 10869.981 10870.733 10871.088 10873.663 10875.466 10877.513 10878.030 10878.693 10880.675 10880.936
201 003 003 003 003 003 201 20, 003
5 0 7 0 615 6 2 7 17 532 6 15 5 2 5 3
003 20, 102 003 003 003 003 102 102 102 102 102 003 102 003 201
5 7
6 2 6 0 514 5 2 6 16 431 734 6 4 4 3
4 6
3 2 1 6 2 4 1 0,110 6 0 6 6 16 514 5 2 4 202 6 2 4 4 13 606 3 12 634 5 14 9 3 6 5 I5
2 7
2 3
5 0 5 L 413 4 2 211 6 3 4 2 533 3 21 615 5 2 9 3 6 2
5 5
003 201 003 LO2 102 102
4 7 432 303 2 5
3 8 33, 312 2 5
3 4
0 4
2 3
0 2
201 iO2 102 to2
5 2 11 6 I5 2 2 000 4 2 7 16 432 422 404 505
6 4 2 0 6 2 3,2 111 3 2 B 3 413 43, 413 404
3 2 4
102
003 201 003 102 102 003
3 2
5
3 3
1 5
I, 2 3 4 1 1 2
0 4
4
1.29 3.69 1.37 3.45 1.04 2.70 0.587
2 2
3 3 2
3 7 4
1 5
1.83 0.302 0.355 3.81 1.91 6.01 6.49 1.69 1.45 0.359 1.09 0.183 3.58 0.40, 2.1,
0.209 0.921 0.732 2.67 3.43
2.82 0.203 0.467 0.510 0.309 0.866 2.17 0.690 0.34, 0.638 0.776 8.69
1.233 3.754 1.330 3.605 1.028 2.849 0.6050 0.959 0.950 I.909 0.2836 0.3477 4.342 1.904 6.161 6.54, I.809 1.615 0.298, 1.094 0.1761 3.880 0.3760 2.065 0.0086 0.2073 0.2159 0.9232 0.7975 2.764 3.776 0.9605 1.429 2.390 0.1735 0.4759 0.4372 0.3143 0.9350 2.187 0.7687 0.3417 0.5879 0.8085 9.079
0.057 -0.064 0.040 -0.155 0.012 -0.149 -0.018 I* *t -0.079 0.018 0.007 -0.532 0.006 -0.15, -0.05, -0.119 -0.165 0.060 -0.004 0.007 -0.300 0.025 0.105 tt tt -0.007 -0.002 -0.066 -0.094 -0.346 *t t* 0.430 0.029 -0.009 0.073 -0.005 -0.069 -0.017 -0.049 -0.00, 0.050 -0.033 -0.389
4.39 -1.74 2.93 -4.50 1.14 -5.52 -3.06
-4.33 6.10 2.06 -13.96 0.34 -2.5, -0.79 -7.05 -11.39 16.81 -0.33 3.78 -8.37 6.24 4.82
-3.28 -0.23 -8.95 -3.52 -10.08
15.26 14.55 -1.90 14.28 -,.71 -7.97 -0.78 -7.06 -0.2, 7.85 -4.19 -4.47
“The complete version of Table III is on deposit in the Editorial Office of the Journal ofMolecular Spectroscopy.
241
NOTES
FIG. 1.
Wavenumber dependence of lg( k) [k = k{ (cm -* atm-‘)/ IO-“’ cm -’ atm-‘1
accuracy. In Table III, an illustrative portion of the list of line positions and intensities is presented (asterisks indicate blended lines). For many practical problems, knowledge of integrated band intensities is needed. However, in the case considered here, both regular and accidental resonance interactions are so strong that it is difficult to separate the contribution of one given vibrational band from that of another. For this reason, we have not calculated integrated band intensities, but have determined only the absorption coefficient kf( cm-’ atm-‘). This has been done by dividing the 9000- 12 500 cm -I region into 20.cm _’-wide intervals and by summing in each interval the intensities of all the lines appearing in it. The final results are presented in Fig. 1. REFERENCES 1. J.-P. CHEVILLARD, J.-Y. MANDIN, C. CAMY-PEYRET, AND J.-M. FLAW, Canad. J. PhJJs. 65.777-189
(1987). 2. Yu. S. MAKUSHKIN, 0. N. ULENIKOV, AND I. V. LEVASHKIN, J. Mol. Spectrosc. 144, l-17 ( I 990 1. 3. J.-M. FLAUD AND C. CAMY-PEYRET, J. Mol. Spectrosc. 55, 278-310 ( 1975). 4. J.-M. FLAUD, C. CAMY-PEYRET, AND R. A. TOTH. “Water Vapor Line Parameters from Microwave to Medium Infrared,” Pergamon, Elmsford. NY, 198 I. 5. 0. N. ULENIKOV AND A. S. ZHILYAKOV, J. Mol. Spectrosc. 133. 239-243 ( 1989). Yu. S.
MAKUSHKIN
0. N. ULENIKOV’ A. S. ZHILYAK~V
Laboratory ofAppIiedSpectroscopy Physics Department Tomsk State Universily Tomsk 634010, USSR Received November 13. 1989
’ Author to whom correspondence should be addressed.
OF MOLECULAR
SPECTROSCOPY
l‘t‘t,
239-241 (1990)
NOTES Transformed Dipole Moment and Line Intensities for the Hz”0 Molecule First Decade Interacting Vibrational States In this note we continue our analysis of water vapor in the short-wave spectral region. The object of the present investigation is the spectrum of the Hz’*0 molecule in the region 9500- 11500 cm-‘. This region consists of transitions from the ground vibrational state (000) to the decade of interacting vibrational states (u > = (u,u~uJ) = (ZOI), (003), (121). (041). (300), (102). (220), (022). (140). (060). The high-precision experimental absorption spectra between 9500 and 11 500 cm-’ were analyzed by Chevillard et ul. in 1987 (I) (accuracies in line centers and absolute intensities are -10e3 cm-’ and 27%. respectively) We obtained the rotational, centrifugal, and resonance constants that reproduced the experimental line centers with accuracies near the experimental one (2). In this note the parameters of transformed dipole moment operator /.I:7= ClO)“k&(ul=
”
ClO)(C
”
(1)
‘“‘~;“A,)(ul
i
are considered. In Eq. ( 1) the “A, are the operators [we do not reproduce here the form of these operators. but they can be found in Refs. (3-5)] : and the (“‘*J are the parameters to be determined of the transformed dipole moment operator. The values of the “)pJ parameters have been obtained through a least-squares fit of the experimental intensities (1 j. In our calculation the 588 line intensities from Ref. (I) have been used as initial data. As emphasized in Ref. (2) some upper state energy levels seem to be incorrect in Ref. ( 1) [see Ref. (2) for details]. For this reason, the corresponding line intensities have not been used in our analysis. The (“)rJ parameters obtained are presented in Tables I and II. These parameters reproduce the experimental line intensities with a mean accuracy close to the experimental one. Among the 588 lines involved in the fit, the intensities of 403 lines (68.54% of all the lines) are reproduced within experimental accuracy (better than 7%); 74 ( 12.59%) lines are reproduced within lo-20% accuracy: and 3 I (5.27%) lines within 20-50%
TABLE 1 Parameters ‘“‘pi of the Transformed Dipole Moment Operator (in D) (u = u,uzuJ, uj Odd)’
!.I
P1104 +10'
(201)
18.022(22) -13.27
l22)
!+06
(1211
13.897(12)
-5.2597(99)
-4.55~15~
-4.82C1.5)
(041,
-1.ZSBl(35) -2.78(10)
2.385(43)
!+OL
2.59
(20,
!+Ob
1.002
(281
P610b
(003)
-2.107c57)
X5.38(12)
6.97(13)
28.83
(10)
12.770(87)
-3.80
23.44
(15,
lLlll13)
-6.57(19)
1.482(59,
c 10)
-1.58(12)
+ !+lO’
’
Values in parentheses in Tables 1 and 11are 1c confidence intervals. 239
0022-2852190 $3.00 Copyright D 1990 by Academc
Press. Inc.
All rights of reproduction in any form reserved.
TABLE II Parameters (“)pj of the Transformed Dipole Moment Operator (in D) (u = u,u2vj,u3Even) "l"Z"3 ,300)
w
p,105
54.393(54)
~102~
(220)
-8.112l45)
-2.63(18)
(022)
(140)
-7.03(32,
-4.07(99)
% -3.05(11)
v3106 P4105
-,.557(15>
+105
8.9219179)
P6106 lJ7107
-1.380(12>
0.126(25>
5.3421(69
-,.315(23)
-1.585(46) 0.735151)
,.515(22) -4.57(,7)
-5.25(,6)
'8
TABLE III Line Positions (in cm-‘) and Intensities ( 10e4 cm-* atm-‘) for the Decade of H2180 at 300K (Illustrative Portion)
10832.123 ,0833.46,8 10833.790 10834.057 10834.782 10837.302 10839.083 10840.283 10840.283 10840.283 10850.277 10851.244 10855.153 10857.034 10857.819 10858.96, 10859.121 10859.723 10860.986 10862.615 10863.632 10864.362 10864.547 10864.90, 10865.186 ,0865.,86 10865.186 10865.613 10865.830 10866.687 iO868.227 10868.953 10868.953 1086B.953 10869.642 10869.981 10870.733 10871.088 10873.663 10875.466 10877.513 10878.030 10878.693 10880.675 10880.936
201 003 003 003 003 003 201 20, 003
5 0 7 0 615 6 2 7 17 532 6 15 5 2 5 3
003 20, 102 003 003 003 003 102 102 102 102 102 003 102 003 201
5 7
6 2 6 0 514 5 2 6 16 431 734 6 4 4 3
4 6
3 2 1 6 2 4 1 0,110 6 0 6 6 16 514 5 2 4 202 6 2 4 4 13 606 3 12 634 5 14 9 3 6 5 I5
2 7
2 3
5 0 5 L 413 4 2 211 6 3 4 2 533 3 21 615 5 2 9 3 6 2
5 5
003 201 003 LO2 102 102
4 7 432 303 2 5
3 8 33, 312 2 5
3 4
0 4
2 3
0 2
201 iO2 102 to2
5 2 11 6 I5 2 2 000 4 2 7 16 432 422 404 505
6 4 2 0 6 2 3,2 111 3 2 B 3 413 43, 413 404
3 2 4
102
003 201 003 102 102 003
3 2
5
3 3
1 5
I, 2 3 4 1 1 2
0 4
4
1.29 3.69 1.37 3.45 1.04 2.70 0.587
2 2
3 3 2
3 7 4
1 5
1.83 0.302 0.355 3.81 1.91 6.01 6.49 1.69 1.45 0.359 1.09 0.183 3.58 0.40, 2.1,
0.209 0.921 0.732 2.67 3.43
2.82 0.203 0.467 0.510 0.309 0.866 2.17 0.690 0.34, 0.638 0.776 8.69
1.233 3.754 1.330 3.605 1.028 2.849 0.6050 0.959 0.950 I.909 0.2836 0.3477 4.342 1.904 6.161 6.54, I.809 1.615 0.298, 1.094 0.1761 3.880 0.3760 2.065 0.0086 0.2073 0.2159 0.9232 0.7975 2.764 3.776 0.9605 1.429 2.390 0.1735 0.4759 0.4372 0.3143 0.9350 2.187 0.7687 0.3417 0.5879 0.8085 9.079
0.057 -0.064 0.040 -0.155 0.012 -0.149 -0.018 I* *t -0.079 0.018 0.007 -0.532 0.006 -0.15, -0.05, -0.119 -0.165 0.060 -0.004 0.007 -0.300 0.025 0.105 tt tt -0.007 -0.002 -0.066 -0.094 -0.346 *t t* 0.430 0.029 -0.009 0.073 -0.005 -0.069 -0.017 -0.049 -0.00, 0.050 -0.033 -0.389
4.39 -1.74 2.93 -4.50 1.14 -5.52 -3.06
-4.33 6.10 2.06 -13.96 0.34 -2.5, -0.79 -7.05 -11.39 16.81 -0.33 3.78 -8.37 6.24 4.82
-3.28 -0.23 -8.95 -3.52 -10.08
15.26 14.55 -1.90 14.28 -,.71 -7.97 -0.78 -7.06 -0.2, 7.85 -4.19 -4.47
“The complete version of Table III is on deposit in the Editorial Office of the Journal ofMolecular Spectroscopy.
241
NOTES
FIG. 1.
Wavenumber dependence of lg( k) [k = k{ (cm -* atm-‘)/ IO-“’ cm -’ atm-‘1
accuracy. In Table III, an illustrative portion of the list of line positions and intensities is presented (asterisks indicate blended lines). For many practical problems, knowledge of integrated band intensities is needed. However, in the case considered here, both regular and accidental resonance interactions are so strong that it is difficult to separate the contribution of one given vibrational band from that of another. For this reason, we have not calculated integrated band intensities, but have determined only the absorption coefficient kf( cm-’ atm-‘). This has been done by dividing the 9000- 12 500 cm -I region into 20.cm _’-wide intervals and by summing in each interval the intensities of all the lines appearing in it. The final results are presented in Fig. 1. REFERENCES 1. J.-P. CHEVILLARD, J.-Y. MANDIN, C. CAMY-PEYRET, AND J.-M. FLAW, Canad. J. PhJJs. 65.777-189
(1987). 2. Yu. S. MAKUSHKIN, 0. N. ULENIKOV, AND I. V. LEVASHKIN, J. Mol. Spectrosc. 144, l-17 ( I 990 1. 3. J.-M. FLAUD AND C. CAMY-PEYRET, J. Mol. Spectrosc. 55, 278-310 ( 1975). 4. J.-M. FLAUD, C. CAMY-PEYRET, AND R. A. TOTH. “Water Vapor Line Parameters from Microwave to Medium Infrared,” Pergamon, Elmsford. NY, 198 I. 5. 0. N. ULENIKOV AND A. S. ZHILYAKOV, J. Mol. Spectrosc. 133. 239-243 ( 1989). Yu. S.
MAKUSHKIN
0. N. ULENIKOV’ A. S. ZHILYAK~V
Laboratory ofAppIiedSpectroscopy Physics Department Tomsk State Universily Tomsk 634010, USSR Received November 13. 1989
’ Author to whom correspondence should be addressed.