oleg l. polyansky et al- hot bands of water in the nu2 manifold up to 5nu2-4nu2

8/3/2019 Oleg L. Polyansky et al- Hot Bands of Water in the nu2 Manifold up to 5nu2-4nu2

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OURNAL OF MOLECULAR SPECTROSCOPY 184, 3550 ( 1997)

RTICLE NO. MS977307

Hot Bands of Water in the n2 Manifold up to 5n2-4n2

Oleg L. Polyansky,* ,1 Nick F. Zobov,* ,1 Jonathan Tennyson,* John A. Lotoski, and Peter F. Bernath ,2

*Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom;

and Departments of Chemistry and Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received October 10, 1996; revised March 21, 1997

A spectrum of the hot water molecule has been recorded in emission at a temperature of 1000C in the region 900cm01 to 2000 cm01 . A total of 4381 lines were observed; 1750 are assigned, mostly to the n2 , 2n2 0 n2 , 3n2 0 2n2 ,4n2 0 3n2 , and 5n2 0 4n2 bands. The 5n2 0 4n2 band has been seen for the first time and the rotational analysis of theother hot bands has been extended to high Jand Ka values. The assignment of transitions involving previously unobservedlevels was achieved using high accuracy ab initio electronic structure calculations, an ab initio adiabatic correction tothis potential, and variational nuclear motion calculations of the spectra. The band origin of 5n2 is determined to be7542.39 cm01 { 0.05 cm01 , significantly different from the value obtained from the dark state perturbative treatment. 1997 Academic Press

I. INTRODUCTION vibrational state ( 18 ) and Ka 10 for the (010) state ( 19 ).

This trend continues, so divergence can be expected for Kavalues near unity for the (040) and (050) states. One way ofThe scientific literature on the vibrationrotation bands ofsolving this problem is to substitute variational calculationswater is vast and the spectra are used in many applications,using a fitted potential energy surface (e.g., ( 20 )) for theuch as the identification of water vapor in sunspots (1 ).conventional effective Hamiltonian approach. The stretchinghe subject of this paper is the hot bands of the 2 sequence.energy levels of water are known up to 25 000 cm01 (21 )n classic works by Flaud, Camy-Peyret, and co-authors ( 2 and have been used for the fitting the effective potential), rotational energy levels in the n2 0, 1, 2, 3, and 4energy surface (PES) ( 22 ). In contrast, the highest bendingibrational states were determined from hot water emissionlevels known experimentally lie at 7000 cm01 (5 ). The addi-pectra from flames and overtone absorption spectra for thetion of higher Ka rotational levels of 2 4 and any levelsn2 and 4n2 bands. Most of these levels were used in the

of2 5 would be of great value in any attempt to improveomprehensive water vapor atlas ( 6). Subsequently im-the bending part of the water PES.roved room temperature spectra of n2 (7), (8), 2n2 0 n2

The only source of experimental information on the (050)9 ), and 4n2 bands (10 ) (among many other bands) havevibrational state until now has been the so-called darkeen observed and assigned. More recently, Dana et al. (11,state analysis (23 ). The strong resonance between the2 ) have measured new flame spectra. They concentrated on(130) and (050) states leads to a shift of the (130) levelsmeasuring collisional linewidths, rather than the determina-because of interactions with (050) levels. Thus informationon of new energy levels, but they did assign some newon the value of the (050) energy levels could be indirectlyotational lines, particularly for the 4n2 0 3n2 band. A newobtained from the known (130) values. The band origin ofendingrotation effective Hamiltonian analysis of the pub-the (050) state was determined to be 7552 cm01 (23 ). How-shed 2 0 and 1 rotational energy levels, based on theever, recent theoretical analysis ( 22 ), based on the use ofmodified model due to Makarewizc ( 13 ), was carried out

variational calculations and spectroscopically determinedy Coudert ( 14 ) as well as very recent n2 band analysis (15 ).potential energy surfaces, has suggested that this value isFurther expansion of the n2 manifold of levels up to 5n2too high by between 10 and 15 cm01 .as been hampered by the extreme weakness of this band

The hot band spectra associated with the n2 mode of watersee for example ( 16, 17).were recorded a few years ago in an attempt to identify linesAnother reason there are problems in assigning the higherin the Kitt Peak sunspot spectra ( 1 ), ( 27), (28 ). Since theseKa rotational levels of highly excited bending vibrationallaboratory spectra had a temperature of only 1000C, theytates is that the conventional power series effective rota-were not useful for this purpose. It was not until spectraonal Hamiltonian diverges at about Ka 15 for the groundwere recorded at 1550C (1 ), (27) that we obtained a line

density in the pure rotational region (400900 cm01 ) that1 Permanent address: Institute of Applied Physics, Russian Academy of

was comparable to the line density in the sunspot. The identi-cience, Uljanov Street 46, Nizhnii Novgorod, Russia 603024.

fication of water vapor in the sunspot ( 1 ) was followed by2Also: Department of Chemistry, University of Arizona, Tucson, AZ5721. a partial assignment ( 27) of the 1550C laboratory spectrum.

350022-2852/97 $25.00

Copyright 1997 by Academic Press

All rights of reproduction in any form reserved.


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POLYANSKY ET AL.6

TABLE 1

List of H162 O Transitions Assigned to 020010 Hot Band (Wavenumbers in cm01 , Intensities (Int) in Arbitrary Relative Units)



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BENDING HOT BANDS OF H2O 37

TABLE 1 Continued



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POLYANSKY ET AL.8

TABLE 1 Continued



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TABLE 1 Continued



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POLYANSKY ET AL.0

TABLE 1 Continued



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TABLE 1 Continued with a KCl beamsplitter, Si:As detectors, and an InAs

filter. The 550 2800 cm01 region was covered at a resolu-

tion of 0.005 cm01 .

The center of a 1 m long by 5 cm diameter alumina tube

was heated to about 1000C. The spectrum was recorded as

the temperature changed from 904 to 1008C. The tube was

evacuated and the ends were sealed with cooled KBr win-

dows. A steady flow of water vapor passed through the cell

at a pressure of 0.9 Torr. The thermal emission ( 29 ) fromthe hot water vapor was sent into the entrance aperture of

the spectrometer. Twelve scans were co-added in 61 min of

integration.

The H2O emission lines from 920 cm01 to 2000 cm01

were measured with the data reduction program DECOMP.

Each of 4381 lines was fitted with a Voigt lineshape func-

tion. A typical linewidth of 0.008 cm01 was measured and

the maximum signal-to-noise ratio was about 300. The lines

were calibrated by multiplication by the factor 0.999999397

obtained using the measurements of Toth ( 9 ). Strong un-

blended lines should have an absolute accuracy of about

0.0001 cm01 .

III. ANALYSIS

We found that the sequence bands with D2 1 were

much stronger than other hot bands such as n3 / n2 0 n3 .

For example, the 3n2 0 2n2 band is about 10 times stronger

than the n3 / n2 0 n3 band although the upper levels have

comparable energies and populations. This is due to the well

known increase in transition dipole moment for sequence

bands as the vibrational quantum number increases. For ex-

ample, for a harmonic oscillator the matrix element ( /1 x ) 2 (/2mv)( / 1) increases linearly with

. Since this matrix element is directly proportional to the

intensity, it tends to offset the decreasing population (Boltz-

mann factor) as increases.The bulk of the strong lines observed belong to the n2

and 2n20 n2 bands reported in ( 7 9 ). Our 1000C spectrum

of the n2 band has some higher J, Ka transitions than reported

for the room temperature spectra ( 7, 8 ) and they were as-

signed using energy levels determined from the flame spectra

(2, 3 ). A few lines of the n2 band involved higher J, Ka

levels than listed in the references ( 2, 3 ). In this case theTo our surprise, the 1000C spectrum in the 1000 to 2200 rotational energy levels of the ground and (010) vibrationalm01 showed many previously unobserved transitions. We states obtained in our previous work were used ( 27), thusave been able to identify the new 5n2 0 4n2 band and confirming the correctness of these levels. These assign-onsiderably extend the rotational assignments in other hot ments (which we call trivial) were simple to make and weands. will not discuss them further.

For the 3n2 0 2n2 and 4n2 0 3n2 bands, only a small

proportion of the lines could be assigned using the publishedII. EXPERIMENTAL DETAILSenergy levels (4 9 ). For the 5n2 0 4n2 bands there were

no known energy levels, since no spectra involving the (050)The hot water spectra were recorded on April 9, 1993

with the Fourier transform spectrometer associated with state had been obtained experimentally. The nontrivial as-

signment of these new lines with higher J, Ka than given inhe McMathPierce Telescope of the National Solar Ob-

ervatory on Kitt Peak. The spectrometer was operated the literature requires highly accurate calculations.



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TABLE 2 Continued



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POLYANSKY ET AL.4

TABLE 2 Continued and ( 010) exited vibrational state. Variational calcula-

tions, however, have been demonstrated to have better

extrapolation properties than an effective Hamiltonian ap-

proach ( 20 ). Variational calculations also calculate en-

ergy levels involving all the vibrational states at one time,

automatically solving the problem of the accidental reso-

nances between various vibrational states, which have to

be included explicitly for every resonance in an effective

Hamiltonian matrix approach. These two properties makevariational calculations invaluable for assigning highly

excited rovibrational levels of water.

To assign the hotter transitions observed here, we used a

variational calculation based on the exact kinetic energy

(EKE) approach. These calculations use a high accuracy ab

initio BornOppenheimer potential energy surface due to

Partridge and Schwenke ( 30 ). This potential was then modi-

fied by the addition of an ab initio mass-dependent surface

representing the adiabatic correction to the BornOppenhei-

mer approximation (31 ). Nonadiabatic effects have also

been shown to be important for rotationally excited water

(22 ); these were introduced phenomenologically by using

a hydrogenic mass intermediate between atomic H and the

proton (see (31 )). A full treatment of the effects of Born

Oppenheimer breakdown in water will be the subject of

future work (32 ).

Nuclear motion calculations were performed using the

DVR3D program suite ( 33 ) using basis sets developed for

previous studies ( 22 ). To bring the ab initio estimates of

the transition frequencies into line with the observations,

each rovibrational energy level was adjusted by the differ-

ence between the observed and calculated band origin for

the vibrational level in question.In a table which is available from the author or editor on

request, we present the observed n2 , 2n2 0 n2 , 3n2 0 2n2 ,

4n2 0 3n2 , and 5n2 0 4n2 hot band lines. More than 1700

lines of the total 4381 lines were assigned. Some of them

are identical to the room temperature water spectrum ofn2and 2n2 0 n2 , presented in ( 8 ), (9 ).

Lines with lower J belonging to n2 , which are strong

in room temperature spectra, suffered from self absorption

caused by cooler water at the ends of the cell, atmospheric

water, and trace amounts of water in the spectrometer. Be-

cause of the Doppler effect, the high temperature emissionlines are broader than the cooler absorption lines. The cooler

water thus removes the line center from the emission lines,

resulting in doublet line artifacts (see Ref. ( 1 ) for an exam-

ple). As a rule, the line centers of these doublets were foundFor example, the water in the sunspot spectrum has an to be shifted to the right and to the left by approximately

ffective temperature of about 2800C and has an average 0.005 cm01 from the line center of the room temperaturene density of nearly 50 lines/cm01 . The present spectrum transition.as a line density of 510 lines/cm01 , which makes the Transitions assigned to 2n2 0 n2 , 3n2 0 2n2 , 4n2 0 3n2 ,ew assignments easier than for the sunspot spectrum. and 5n2 0 4n2 bands are given in Tables 1, 2, 3, and 4,n our previous paper ( 27) we have used an effective respectively. More than half of the measured lines remain

Hamiltonian in a Pade Borel form ( 18 ) for the calcula- unassigned and they belong to the other hot bands and to

higher Js and Kas of the n2 manifold of hot bands. Theon of the high J, Ka energy levels of water in the ground



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TABLE 3

List of H162 O Transitions Assigned to 040030 Hot Band (Wavenumbers in cm01 ,

Intensities (Int) in Arbitrary Relative Units)



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POLYANSKY ET AL.6

TABLE 4 those obtained in this work (Tables 57) shows that signifi-List of H 162 O Transitions Assigned to 050040 Hot Band cantly higher J and Ka levels are derived in this study. The

Wavenumbers in cm01 , Intensities ( Int) in Arbitrary Rela- energy levels for (030) ( 4 ) and (040) (5 ) are confirmed inve Units) this study, whereas some levels in the (020) state ( 9 ) are

derived from misassigned transitions. The levels presented

in Tables 57 are involved as a rule in two and often three

transitions (P , Q , and R branches) , which confirms our

assignments.

We decided not to present the energy levels of the (050)state, since at this stage only a few of them could be

derived from the list of 5n2 0 4n2 transitions (Table 4).

From the lines in Table 4 one can see that only three levels

( 505 , 303 , and 312 ) are involved in more than one transition.

These three levels should be considered as definitely es-

tablished, since combination difference confirm the as-

signment. The assignment of the other lines are not so

reliable and their assignment should be considered as ten-

tative. Among these lines is the 000 111 transition which

gives a value of the (050) band origin equal to 7542.39

cm

01

. A more reliable source of information on the bandorigin is the levels confirmed by combination differences.

The difference between the calculated and experimentally

derived energies for these levels is constant to within 0.05

cm01 . In this spirit we consider our value of the 5n2 band

origin as 7542.39 { 0.05 cm01 .

This is significantly different, 10 cm01 , from the value

predicted by the dark state perturbative analysis of Uleni-

kov and Ushakova ( 23 ). This value has been used ( 24 ) for

the fitting of the water PES to the set of 70 experimental

band origins (levels with J 0) present in HITRAN data

base (25 ). As has been commented on ( 26), the use of thevalue of 7552 cm01 for (050) band origin might be one

reason this potential (24 ) performs so badly for excited Jssignment of these lines will the next step in our analysiscalculations. Even for the moderately excited J 10 thisf the higher temperature spectrum (1550C) spectrum,potential gives a discrepancy of about 100 cm01 for (000)which is now in progress.and (010) states ( 26), while the standard deviation for theA very effective means of compressing the informationfitted band origins is very good, 1 cm01 .n thousands of lines is to derive energy levels from the

Indeed, our newly determined 5n2 band origin is veryansitions reported in the unpublished table previously re-much in line with values predicted by Polyansky et al. (22 )erred to. The energy levels of the (020), (030) and (040)from a variational fit to the available data on H2O with Jibrational states are presented in Tables 57. We do not 14. These workers found that they could not reproduceresent here the energy levels of the ground and (010) states,the high value for the 5n

2band origin obtained from the

ince all the transitions observed here are of lower J and Ka dark state analysis and predicted that the actual value washan in our previous work ( 27). There is one important pointsignificantly lower.oncerning these states which should be mentioned. One

After submission of our paper, we obtained two additionalmotivation for this study was to check the energy levels ofpapers on the bending levels of water. Starikov ( 35 ) hashe (000 ) and ( 010) states obtained in (27). Indeed we haveapplied a new Hamiltonian model for the energy levels ofound that the assignment of two lines in the 2 1 statethe (020), (001) and (100) states and his calculations arehould be interchanged. In particular, the 1717 0 1616 1 transi-in accord with our measurements. Mikhailenko et al. (36)on of (010) is now at 722.9167 cm01 , and 1716 1 1615 2 ishave analyzed the 2n2 overtone band and extended thet 722.3721 cm

01 . This leads to the corresponding change

known energy levels in the (020) state. They cover a similarf energy levels in ( 27). A more complete discussion of the

range of J and Ka levels for this particular vibrational stateorrections to Ref. ( 27) will appear in another paper ( 34 ).

as reported here based on the 2n2 0 n2 hot band and theirThe comparison of the energy levels of the (020), (030),

nd ( 040) vibrational states taken from the literature with work is also in agreement with our measurements.



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TABLE 5

Energy Levels in cm01 of (020) Vibrational State of H 162 O Derived from the

Experimental Line Frequencies of Table 1

Note. For J 14, only levels which differ from those in Toth ( 9 ) are presented. For J 14, all

available experimental energy levels are given.



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POLYANSKY ET AL.8

TABLE 6

Energy Levels in cm01 of (030) Vibrational State of H162 O Derived from the Experi-

mental Line Frequencies of Table 2 (The Results of Flaud et al. (4 ) Are Given for

Comparison)



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TABLE 7 IV. CONCLUSION

Energy Levels in cm01 of (040) Vibra-

tional State of H162 O Derived from the Ex- We have observed hot bands of water in the n2 manifoldperimental Line Frequencies of Table 4 in a spectrum recorded at 1000C. A total of 4381 lines have

been measured, belonging mainly to the n2 , 2n2 0 n2 , 3n20 2n2 , 4n2 0 3n2 , and 5n2 0 4n2 bands. The rotational

analysis of the n2 2, 3, and 4 vibrational levels has been

extended to higher quantum numbers. The experimental deri-

vation of the energy levels of

2

5 has been made fromthe lines of the 5n2 0 4n2 hot band.

ACKNOWLEDGMENTS

We thank R. S. Ram, J. Wagner, and C. Plymate for assistance in

recording the spectra and H. Partridge and D. W. Schwenke for supply-

ing their potential energy surface prior to publication. We thank Dr. L.

Sinitsa for drawing our attention to Ref. ( 10 ). O.L.P. is grateful to

Pina Colarusso for assistance in providing access to the University of

Waterloo computer facilities. The National Solar Observatory is oper-

ated by the Association of Universities for Research in Astronomy,

Inc., under contract to the National Science Foundation. The authors

acknowledge NATO Grant 5-2-05/ CRG951293 for making the experi-mentaltheoretical collaboration possible. N.F.Z. thanks the Royal So-

ciety for funding his visit to University College London. The work of

O.L.P. was supported in part by the Russian Fund for Fundamental

Studies. This work was supported by the Natural Sciences and Engi-

neering Research Council of Canada ( NSERC) . Acknowledgment is

made to the Petroleum Research Fund for partial support of this work.

Some support was also provided by the NASA Laboratory Astrophysics

Program, the UK Engineering and Science Research Council, and the

UK Particle Physics and Astronomy Research Council.

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oleg l. polyansky et al- hot bands of water in the nu2 manifold up to 5nu2-4nu2

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