high-temperature rotational transitions of water in ...journal of molecular spectroscopy 186,...

JOURNAL OF MOLECULAR SPECTROSCOPY 186, 422–447 (1997)ARTICLE NO. MS977449

High-Temperature Rotational Transitions of Waterin Sunspot and Laboratory Spectra

Oleg L. Polyansky,* ,1 Nikolai F. Zobov,* ,1 Serena Viti,* Jonathan Tennyson,*Peter F. Bernath,† ,2 and Lloyd Wallace‡

*Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom;†Departments of Chemistry and Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;

and ‡National Optical Observatories, P.O. Box 26732, Tucson, Arizona 85732

Received August 22, 1997

Assignments are presented for spectra of hot water obtained in absorption in sunspots (T Ç 30007C and 750 ° n °1010 cm01) and in emission in the laboratory (T Ç 15507C and 370 ° n ° 930 cm01) . These assignments are madeusing variational nuclear motion calculations based on a high-level ab initio electronic surface, with allowance for bothadiabatic and nonadiabatic corrections to the Born–Oppenheimer approximation. Some 3000 of the 4700 transitionsobserved in the laboratory spectrum are assigned as well as 1687 transitions observed in the sunspot spectrum. Allstrong lines are now assigned in the sunspot measurements. These transitions involve mostly high-lying rotational levelswithin the (0,0,0) , (0,1,0) , (0,2,0) , (1,0,0) , and (0,0,1) vibrational states. Transitions within the (0,3,0) , (0,4,0) ,(1,1,0) , (0,1,1) , (0,2,1) , (1,1,1) , (1,2,0) , and (1,0,1) states are also assigned. For most bands the range of Ka valuesobserved is significantly extended, usually doubled. New features observed include numerous cases where the closelydegenerate levels JKaKc

and JKaKc/1 with high Ka are split by Coriolis interactions. Comparisons are made with the recentline list of Partridge and Schwenke (1997, J. Chem. Phys. 106, 4618). q 1997 Academic Press

I. INTRODUCTION (12, 13) . The sunspot spectra were originally consideredunassignable and only small portions of the laboratory spec-

The infrared spectrum of water is arguably the most im- tra have been assigned on a case-by-case basis (12–14) .portant of all molecules because there are a multitude of However, in a recent paper (15) , henceforth I, we demon-applications. However, the spectrum of water is very compli- strated that by using a combination of high-level ab initiocated and the spectrum of hot water remains poorly under- calculation and careful spectral analysis it was possible tostood. Detailed, line-by-line data on hot water are required assign a large number of new transitions in both these spec-for radiative transport models of many hot systems. Such tra. This assignment procedure represents a significant shiftsystems include the spectra of oxygen-rich late-type stars away from traditional, perturbation theory-based, methods(1–3) for which water vapor is the most important source of spectral assignment. In this paper we present full resultsof infrared opacity and substellar objects, such as brown of this analysis.dwarfs, for which water is the most abundant molecule afterhydrogen (4, 5) . Hot water is also one of the primary prod- II. OBSERVED SPECTRAucts of the combustion of hydrocarbons and has been de-tected in emission from forest fires (6) and from flames, Both the spectra under analysis have been published else-for example, from an oxyacetylene torch (7) . There are where and here we confine ourselves to brief details.numerous military applications, including the simulation of The sunspot spectrum was published in an atlas by Wal-rocket plumes (8) and the identification of ships, aircraft, lace et al. (9–11) in the wavenumber range 420 ° n °helicopters, and tanks from their exhaust signatures. 1233 cm01 . It was recorded using the 1-m Fourier transform

Recently spectra of hot water have been observed in sun- spectrometer of the McMath–Pierce Solar Telescope of thespots (9–11) and at lower temperatures in the laboratory National Solar Observatory on Kitt Peak at a resolution of

about 0.005 cm01 . At both ends of this spectrum there aresignificant gaps due to telluric absorption and some portionsSupplementary data for this article may be found on the journal home

page (http: / /www.apnet.com/www/journal/ms.htm or http: / /www. show many strong absorptions due to other molecules, sucheurope.apnet.com/www/journal/ms.htm). as SiO. However, the region 750 ° n ° 1010 cm01 is

1 Permanent address: Institute of Applied Physics, Russian Academy ofdominated by absorption due to water and we concentratedScience, Uljanov Street 46, Nizhnii Novgorod, Russia 603024.on this region.2 Also: Department of Chemistry, University of Arizona, Tucson, AZ

85721. The observed sunspot spectrum is highly congested with

4220022-2852/97 $25.00Copyright q 1997 by Academic PressAll rights of reproduction in any form reserved.

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HOT ROTATIONAL TRANSITIONS OF H2O 423

up to 50 lines per wavenumber. Prior to I, there were no tionally convenient than, bond length–bond angle coordi-nates. We used a DVR grid of 40 points based on Gaussassigned water transitions in the spectrum but many transi-

tions could be attributed to water on the basis of a compari- (-associated) Legendre polynomials in the u coordinate. Forthe radial coordinates we used a DVR grid of 21 points withson with the laboratory spectrum described below. The as-

signed SiO vibration–rotation lines in the sunspot spectrum radial basis set parameters of re Å 2.06a0 , De Å 0.14Eh , andve Å 0.014Eh , where re is the equilibrium radius, De is thesuggest a temperature of TÇ 3200 K (9, 10) and this temper-

ature is assumed for the water lines. dissociation energy, and ve is the fundamental frequency ofthe Morse oscillator-like functions upon which the DVR isThe laboratory spectrum was obtained to confirm that the

sunspot features were indeed due to water (9). The emission based (24) . This number of grid points is sufficient to obtaingood convergence for low-lying vibrational levels (26) .spectrum, details of which can be found in Polyansky et al.

(12), was recorded using a Bruker Fourier transform spec- In the first ‘‘vibrational’’ step we diagonalized a seriesof final secular problems of dimension 1000 from whichtrometer located at the University of Waterloo (16). It covers

the wavenumber range 370° n° 930 cm01 and was recorded we retained the lowest 500 eigenvalues and eigenvectors.For given J , the full rovibrational problem was solvedat a temperature of 15507C. This spectrum has a similar reso-

lution (dnÇ 0.01 cm01) to the sunspot spectrum but is much using a basis of the 150 1 (J / 1) lowest solutions fromthe first step.less crowded because of the lower temperature. While many

of the water lines in the sunspot spectrum are blended, the The number of eigenvalues obtained varied with J withno fixed rule. We computed eigenvalues with energies oflines in the laboratory spectrum are nearly all resolved.up to at least 18 000 cm01 for J ° 25; for J Å 25 thiscorresponds to the lowest 500 eigenvalues for each symme-III. VARIATIONAL CALCULATIONStry block. For 25 ° J ° 33, eigenenergies up to 23 000

Assignments were made using synthetic spectra generated cm01 were computed corresponding to 320 eigenvalues perfrom an ab initio line list. Comparisons could also be made symmetry block for J Å 33. These criteria ensured that wewith recently published line lists (17–19) based on calcula- covered all the energy levels belonging to the (000), (100),tions made with effective, spectroscopically determined po- (010), (020), (001), and (030) vibrational states and oftential energy surfaces. We note that, in general, these fitted course, low Ka states of many higher vibrational bands arepotentials give line positions which have significantly smaller also included. Temperature-dependent spectra were gener-absolute errors than our ab initio line list, but that the errors ated using an adapted version of program SPECTRA (27)in the ab initio line list are much more systematic. This smooth which uses full nuclear spin statistics and only rigorous di-behavior of the errors proved to be crucial for making reliable pole transition selection rules.assignments. The use of more than one line list is helpfulfor checking assignments. Similar remarks were made in the IV. SPECTRAL ANALYSIScourse of the recent analysis of the spectrum of H/

3 (20);however, the spectroscopically determined H/

3 line list repro- IV.1. Procedureduced the experimental data to much higher accuracy (Ç0.015cm01) than any of the line lists available for water. A more For both laboratory and sunspot spectra, assignments were

made in a series of steps. First, all transitions between energydetailed comparison of the line lists derived from fitted andab initio potentials is given below. levels known from previous work (7, 12, 13, 28–32) were

assigned. Such assignments, which we will call trivial, formEnergy levels and wavefunctions were generated for ourline list using a very high-quality ab initio (Born–Oppenhei- only a minor part of both spectra. The next step was to use

our line list to generate synthetic spectra at an appropriatemer) potential energy surface due to Partridge and Schwenke(21) . Allowance for non-Born–Oppenheimer effects was temperature.

For the laboratory spectra, intensities were observed tomade by adding an ab initio mass-dependent adiabatic sur-face (22) and by adjusting the effective atomic masses to vary from 0.7 to 0.003 in relative units (12) . Synthetic spec-

tra gave excellent line-by-line agreement in intensity overallow, in part, for nonadiabatic effects. Following Zobov etal. (22) we used an H atom mass of 1.007551 amu, midway the entire dynamic range. This meant that intensities as well

as line positions could be used as guides for assignment.between that of H and a proton, and an O atom of 15.990526amu. Dipole transitions were calculated using the ab initio For the sunspot the situation is more complicated. With-

out implementing a detailed radiative transport model it isdipole surfaces of Gabriel et al. (23) .Calculations were performed using the DVR3D program not possible to use the measured absorptions directly to

give line intensities. Instead the sunspot spectrum was di-suite (24) which was modified somewhat to improve perfor-mance for large calculations such as these. The calculations vided into four echelons on the basis of the strength of

these absorptions. Strong transitions show 6–8% absorp-were performed using symmetrized Radau coordinates (r1 ,r2 , u) (25) , which for water are close to, but more computa- tion, medium transitions show 4–6% absorption, weak ab-

Copyright q 1997 by Academic Press

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POLYANSKY ET AL.424

TABLE 1Assigned Line Frequencies ( in cm01 ) of the Hot Water Spectrum Observed in Sunspots

(Laboratory Frequencies Are Also Given where Observed)


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TABLE 1—Continued


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POLYANSKY ET AL.426

TABLE 1—Continued


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TABLE 1—Continued


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POLYANSKY ET AL.428

TABLE 1—Continued


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TABLE 1—Continued


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POLYANSKY ET AL.430

TABLE 1—Continued


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TABLE 1—Continued


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POLYANSKY ET AL.432

TABLE 1—Continued


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TABLE 1—Continued


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POLYANSKY ET AL.434

TABLE 1—Continued


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TABLE 1—Continued


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POLYANSKY ET AL.436

TABLE 1—Continued


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TABLE 1—Continued

Sunspot frequencies are from (11) and have an estimated absolute accuracy of 0.002 cm01. Laboratory frequencies given to 5 decimal places are from(12) and have an estimated absolute accuracy of 0.001 cm01. Laboratory frequencies given to 4 decimal places are derived from experimental termvalues.

sorptions show 2–4% absorption, and there is a great deal work we present assignments to all of the strong transitions,nearly all of the medium transitions, and some of the weakof poorly resolved structure at the less than 2% absorption

level. Comparison with our synthetic spectra suggest that lines. We are confident that the extension of our calcula-tions to higher vibrational states will lead to the assignmentgoing from the strong to medium echelons represents a

drop in transition intensity by a factor of about 5. In this of the remaining weaker transitions.


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POLYANSKY ET AL.438

A crucial step in our assignment procedure was the use which two high Ka transitions which should appear as a singleline are split by (presumably) Coriolis interactions with levelsof branches. For the purposes of this analysis, a branch was

defined as a series of transitions with Ka Å J 0 na , where of a different vibrational state. It is not possible to plot theentire spectrum here. In paper I, we presented the regionna is constant for each branch. In the laboratory spectrum,

which contains a significant number of transitions involving 870.0–875.4 cm01 , in which many water transitions wereobserved in the laboratory, and the region 924.0–925.6 cm01 ,states of low Ka , we also followed branches defined by Kc

Å J 0 nc for a constant nc . in which only one laboratory transition is observed.With a definitive and complete set of assignments it isOur variational calculations are not completely accurate,

largely due to residual errors in the Born–Oppenheimer po- possible to build up stacks of observed energy levels forwater. Such tabulations are particularly useful for makingtential, but they give errors which vary slowly and systemati-

cally with J for a given branch. Typically, using our ab initio trivial assignments in other spectral regions (see Ref. 33,for example) . Table 3 presents the observed energy levelsline list, the next member of a branch could be predicted with

an accuracy of Ç0.02 cm01 . It is thus possible to step along for the ground vibrational state. A full tabulation (Table 4)for the (000), (010), (020), (100), and (001) vibrationalmembers of the branch starting from low J transitions, which

are generally well characterized, to the previously unas- states has been placed in the electronic archive. These tabula-tions greatly extend the previous ones (7, 12, 29, 32) , thesigned higher J lines. For transitions observed both in the

laboratory and in sunspots, a crude confirmation of each results of which have been incorporated for completeness.These tabulations are provided only for the convenience ofassignment was obtained by comparing the ratio of line in-

tensities with that estimated from Boltzmann distributions the reader and it should be stressed that the fundamental dataare the assigned transitions not these derived energy levels.at the appropriate temperature.

After assigning all strong and many medium lines in the In particular nearly all of our newly derived energy levels arebased on a single transition, which means that one misassign-sunspot spectrum by analyzing branches with high Ka , we

were left with a set of approximately 50 unassigned medium- ment leads to a large number of erroneous energy levels. Inaddition, the propagation of experimental errors degrades thestrength lines. These transitions were assigned to states with

intermediate values of Ka and the assignments were checked accuracy of the derived energy levels. Our data are not com-plete enough to build similar energy level ladders for theby comparison with the line lists generated using spectro-

scopically determined potentials (17–19) . We found the higher vibrational states. Table 3 shows that we have approxi-mately doubled the energy range of the rotational levels andline list of Partridge and Schwenke (19) , which became

available after the bulk of the assignments reported here had obtained a large increase in the range of observed Ka levels.been made, particularly useful for this purpose.

V. DISCUSSION

IV.2. ResultsThe newly assigned transitions show two phenomena

which are not observed in low-temperature spectra. The firstTable 1 presents the lines assigned in the sunspot spec-trum. There are 1687 transitions, all of which, with the ex- of these is a family of so-called rotational difference bands

that we have discussed previously (14, 15) . These transi-ception of the rotational difference transitions (13) discussedbelow, are pure rotational transitions which arise mainly tions are caused by the mixing of rotational manifolds of

neighboring vibrational states via Fermi interactions. Thefrom excited vibrational states. Transitions are assigned tothe (000), (010), (020), (100), (001), (030), (110), mixing results in intensity sharing between pure rotational

transitions and what are nominally vibration–rotation transi-(011), and (021) vibrational states.Table 2 which can be obtained from the electronic archive, tions. The perturbations cause a doubling of the number of

rotational transitions from 2 to 4 (see Fig. 3 in Ref. 15) .contains the 4700 lines observed in the laboratory spectrumof Polyansky et al. (12) , for which we have been able to Differences between any three of these transitions give an

exact prediction for the fourth transition, so that these quar-make some 3000 assignments. Nearly all of these are rota-tional transitions involving the (000), (010), (020), (100), tets can be securely identified.

Isolated interactions between two individual rovibrational(001), (030), (040), (110), (011), (021), (111), (120),and (101) vibrational states; there are also a few P-branch levels are to be expected. However, the interesting feature

of the difference transitions is that they are not caused bytransitions from the (0,1,0) bending fundamental.To illustrate both the success of our assignment procedure such a single interaction but by a whole series of perturba-

tions, which give rise to a series, or bands of transitions. Thusand some of the interesting features of the spectra, we haveplotted two portions of both spectra labeled with assignments. the (100) – (020) rotational difference band is strongest for

rotational levels involving Ka Å 9 but is also observable forFigure 1 shows the region 771.5–775.5 cm01 in which transi-tions belonging to three distinct difference band transitions Ka Å 8, 10, and 11. In the course of the assignments reported

here we also found rotational difference bands caused bycan be seen. Figure 2 shows the region 841.5–849.5 cm01 in


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FIG. 1. Sunspot absorption spectrum (upper, Wallace et al. (9, 11) and laboratory emission spectrum (lower, Wallace et al. (9) , Polyansky et al.(12)) in the wavenumber region 771.5–775.5 cm01 . Newly assigned water transitions are labeled using standard notation JKaKc

for rotational levels and

(n1n2n3) for vibrational levels.

(110) – (030) and (120) – (040) interactions with the same of their full line list PS truncated the basis set used for thevariational calculations for J ú 4 at the level of their J Åvalues of Ka as found in the (100) – (020) case.4 calculations. Note that one would expect more uniformThe second unusual feature we observe is the localizedconvergence if they had used a final basis whose size wasdoubling of a number of pure rotational transitions with highproportional to J / p , where the rotational or Wang parityKa . It is a standard result of rotational spectroscopy thatis given by (01) J/p .levels with JKaKc

and JKa/1Kcfor high Kc and JKaKc

andFor low J energy levels PS’s calculations give superbJKaKc/1 for high Ka are degenerate. For water this leads to

results, reproducing experiment with a much higher accuracytransitions for JÇ 25 which can be separated only at resolu- than either the ab initio line list used here or Viti et al.’stions much higher than 0.001 cm01 . In the course of this (VTP1) previous line list, which was generated using anwork we found many isolated examples where these transi- empirical potential derived from spectroscopic data (35) .tions are split, presumably by Coriolis interactions with rota- However, for higher rotational states, particularly those withtional levels belonging to other nearby vibrational states. J ú 20, we find that a very high proportion of rotational

In the course of our variational calculations we have un- states which one expects to be degenerate in fact show signif-dertaken a number of comparisons with the line list and icant splittings in the PS line list. This phenomenon is notenergy levels obtained by Partridge and Schwenke (PS) the same as the isolated splittings discussed above but seems(19) . PS optimized their ab initio potential using experimen- to be a uniform property of the higher levels. Neither ourtal line positions for low-lying rotational levels (J ° 5) analysis of the experimental levels, the present calculations,

or the VTP1 line list shows any evidence for such splittings.taken from the HITRAN data base (34) . In the calculation


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POLYANSKY ET AL.440

FIG

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FIG

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POLYANSKY ET AL.442

FIG

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To illustrate this point, Table 5 gives a comparison for the The conventional vibrational quantum numbers (n1 , n2 ,observed J Å 24 rotational levels of the manifold of the n3 ) and the rotational labels (Ka , Kc ) are only approximate(001) vibrational state. quantum numbers, although their values are constrained

It is clear from Table 5 that PS’s line list systematically by J , p , and q .gives splittings which appear to be artificial. In particular, for Variational calculations are usually performed using thethe high Ka levels, the p Å 1 parity rotational levels (those full symmetry of the system in question and therefore thewith Kc odd for this band) all lie below the p Å 0 parity (Kc calculated energy levels are automatically labeled with theeven) levels with which they should be quasi-degenerate. exact quantum numbers. In this work, the other quantumSince PS truncated their variational rotation–vibration calcu- numbers were determined as part of the procedure of follow-lations at 7500 energy-selected basis functions independent ing the branches in the spectrum. Although we have notof the parity, p , this means that the p Å 1 calculations will implemented such an algorithm, it is attractive to have acontain states of higher cutoff energy that the p Å 0 calcula- method of automatically assigning approximate quantumtion. Because of the variational principle, the p Å 1 states numbers to the calculated energy levels. Indeed both PS andwill be better converged and hence lower in energy. the recent HITEMP database (18) have implemented such

To test the hypothesis that the splitting found in PS’s procedures. A comparison with our manual assignments isrotational levels is an artifact of a lack of variational con- interesting.vergence, we performed calculations using the spectroscop- In both cases we find that the reliability of these auto-ically optimized potential that PS used for their line lists. matic assignments shows a strong dependence on energy,Our calculations were performed with the same basis set particularly of the vibrational level involved. The approxi-parameters that were used to construct our ab initio line mate quantum numbers given by HITEMP become untrust-list, as specified in Section III, and masses as specified by

worthy for states above about 10 000 cm01 . PS’s assign-PS. For J Å 0, our calculations agree to within 0.01 cm01

ments are more reliable but they still give many wrongwith PS’s up to Ç25 000 cm01 . However, for J Å 24 our

labels above about 15 000 cm01 . In both cases, where acalculations gave energy levels which were systematically

level is mislabeled, the labeling given usually appears tolower than those of PS (by up to 1 cm01) . Furthermore

be very wild; that is, it belongs to a level which is distantnone of the ‘‘artificial’’ splittings are present in these newin energy to the one being considered. Furthermore neitherlevels (see Table 5) .dataset gives a well-constructed set of energy labels in theThis artificial splitting of lines has two possible conse-sense that there are occasional energy levels with the samequences. The first is that it is more difficult to use the linelabels and certain sets of labels which are completely ab-list for assignments. The second consequence is perhapssent. This results in a number of distinct transitions withmore subtle. A major objective of PS was to construct a listidentical labels. It should be stressed that we found noof over 300 million water transitions in order to model theevidence for chaotic behavior in the states of water weatmospheres of cool (T Ç 2000–4000 K) stars. An im-analyze here. As far as we can tell, our assignments haveportant consideration in these radiative transport models isyet to reach parts of the water spectrum where the energyhow the line absorptions fill in the gaps in the spectrum.level labels become ambiguous, except possibly in the caseTwo transitions which, to within their linewidth, are coinci-of some of the accidental degeneracies discussed above.dent will have a rather different effect than two well-sepa-This is not the case for H/

3 where the recorded high-resolu-rated transitions. In the latter case the overall stellar opacitytion spectra already probe the region where such labelingwill be overestimated. For T Ç 2000–4000 K, Boltzmannbecomes rather arbitrary (20 ) .considerations suggest that transitions involving states with

Finally it should be noted that the sunspot spectrum isJ Å 20–30 are the dominant sources of opacity. Artificiallyavailable at other wavelengths (10, 11, 36 ) . We have re-doubling the number of lines for these J values could havecently undertaken a detailed analysis of transitions lyingserious consequences for the opacity prediction.in the so-called K band (33 ) with a particular focus on theAlthough we have not discussed our assignment proce-region 4860–4930 cm01 where the water transitions aredure in great detail, there are, in fact, two aspects to makingdensest. This analysis commenced by using the energycorrect line assignments. One step is associating a particu-levels determined here to make trivial assignments butlar transition with a particular combination of upper andresulted in assigning transitions between many states in-lower energy levels; the other step is assigning quantumvolving higher vibrational levels, not observed previously.number labels to these two energy levels. These labels takeThese vibrational states are higher in energy than thosetwo forms: rigorously exact quantum numbers or symmet-probed here and a comparison with the energy levels ofries and approximate labels. For water the only exact quan-PS showed significant deviations between predictions andtum numbers are the total rotational angular momentum,observations. Full results of this study will be presentedJ , the rotational parity, p , and the vibrational parity or

ortho /para designation which we normally denote q (24 ) . elsewhere (33 ) .


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TABLE 3Energy Levels of Water ( in cm01 ) Obtained from the Wavenumbers of the Hot Water Spectra for the Vibrational Ground States


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TABLE 3—Continued


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POLYANSKY ET AL.446

TABLE 3—Continued bound H/3 molecule (20) , which up until now has been

something of a special case. This change will represent amajor shift away from the traditional perturbation theory-based analysis of high-resolution spectra.

This new method of analysis is computationally muchmore expensive but is not without its benefits. Here, whenconfronted with a vast quantity of unanalyzed and seem-ingly unassignable data, we have based our calculations onab initio potentials, occasionally reinforced by the use ofcalculations based on spectroscopically determined poten-

TABLE 5Energy Levels for J Å 24 Rotational Levels

of the (001) State in cm01

VI. CONCLUSIONS

In this work we present detailed assignments for hot waterspectra obtained in a sunspot and in the laboratory. Althoughthe work presented here concerns hot water, many of thecharacteristics of the spectrum will be common to the spectraof other light polyatomic molecules at high temperatures.It would seem, therefore, that a full quantum mechanicaltreatment based on variational calculations and high-qualitypotential energy surfaces, possibly with allowance for thefailure of the Born–Oppenheimer approximation, will benecessary for spectral analysis and modeling of such sys-

Note. Experimental levels with Ka ° 3 are from Flaud et al. (7) ;tems. Indeed this is already the norm for much simpler di-levels with Ka ¢ 11 are from this work. Calculated energy levels

atomic systems, which display none of the spectral features are from Partridge and Schwenke (19) (PS), from this work usingdescribed above, and for van der Waals complexes (37) . PS’s spectroscopically refined potential, and from this work, ab

initio.This procedure has also been applied to the chemically


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9. L. Wallace, P. F. Bernath, W. Livingston, K. Hinkle, J. Busler, B. Guo,tials. However, spectroscopically determined potentials,and K. Zhang, Science 268, 1155–1158 (1995).derived from iterative variational calculations and fits to

10. L. Wallace, W. Livingston, K. Hinkle, and P. F. Bernath, Astrophys.known spectroscopic data, are already widely used for mol- J. Suppl. Ser. 106, 165–169 (1996).ecules such as water (18, 19, 35, 38 ) . The effective poten- 11. L. Wallace, W. Livingston, and P. F. Bernath, ‘‘An Atlas of the Sunspot

Spectrum from 470 to 1233 cm01 (8.1 to 21 mm) and the Photospherictials derived from such calculations give a much more com-Spectrum from 460 to 630 cm01 (16 to 22 mm),’’ NSO Technicalpact representation of the data than the traditional, vibra-Report 1994-01, Tucson, AZ, 1994.tional-state by vibrational-state, perturbation theory-based

12. O. L. Polyansky, J. R. Busler, B. Guo, K. Zhang, and P. Bernath, J.approaches. They also have vastly superior extrapolation Mol. Spectrosc. 176, 305–315 (1996).properties (35 ) . 13. O. L. Polyansky, N. F. Zobov, J. Tennyson, J. A. Lotoski, and P. F.

Bernath, J. Mol. Spectrosc. 184, 35–50 (1997).By the use of a full quantum mechanical treatment of the14. O. L. Polyansky, J. Tennyson, and P. Bernath, J. Mol. Spectrosc., inwater nuclear motion problem we have managed to assign

press.the seemingly unassignable high-temperature spectrum of 15. O. L. Polyansky, N. F. Zobov, J. Tennyson, S. Viti, P. F. Bernath, andwater. Perturbation theory-based methods have proved to be L. Wallace, Science 277, 346–348 (1997).

16. P. F. Bernath, Chem. Soc. Rev. 25, 111–115 (1996).excellent for interpreting the spectra of cool molecules. We17. S. Viti, J. Tennyson, and O. L. Polyansky, Mon. Not. R. Astron. Soc.suggest that a new spectroscopic paradigm is required for

287, 79–86 (1997).hot molecules based on variational calculations. This leaves 18. L. S. Rothman, R. Gamache, J. W. Schroeder, A. McCann, and R. B.superexcited molecules in the dissociation region as the final Wattson, SPIE Proc. 2471, 105 (1995); L. S. Rothman, private commu-

nication (1996).frontier for the theory of small-molecule rotation–vibration19. H. Partridge and D. W. Schwenke, J. Chem. Phys. 106, 4618–4639spectroscopy.

(1997).20. B. M. Dinelli, L. Neale, O. L. Polyansky, and J. Tennyson, J. Mol.

Spectrosc. 181, 142–150 (1997).ACKNOWLEDGMENTS21. D. W. Schwenke, private communication (1996). [Preliminary fit to

the ab initio data of Ref. (19)]We thank H. Partridge and D. W. Schwenke for supplying their poten-22. N. F. Zobov, O. L. Polyansky, C. R. Le Sueur, and J. Tennyson, Chem.tial energy surface prior to publication. The authors acknowledge NATO

Phys. Lett. 260, 381–385 (1996).Grant 5-2-05 /CRG951293 for making the experimental– theoretical col-23. W. Gabriel, E.-A. Reinsch, P. Rosmus, S. Carter, and N. C. Handy, J.laboration possible. N.F.Z. thanks the Royal Society for funding his visit

Chem. Phys. 99, 897–900 (1993).to the University College London. The work of O.L.P. was supported in24. J. Tennyson, J. R. Henderson, and N. G. Fulton, Comput. Phys. Com-part by the Russian Fund for Fundamental Studies. This work was sup-

mun. 86, 175–198 (1995).ported by the Natural Sciences and Engineering Research Council of25. J. Tennyson and B. T. Sutcliffe, Int. J. Quantum Chem. 42, 941–952Canada (NSERC). Acknowledgment is made to the Petroleum Research

(1992).Fund for partial support of this work. Support was also provided by the

26. N. G. Fulton, Ph.D. thesis, Chap. 4, University of London (1994).NASA Laboratory Astrophysics Program, the UK Engineering and Sci-

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