The 2ν2Band of Water: Analysis of New FTS Measurements and High-KaTransitions and Energy Levels

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

184, 330–349 (1997)

MS977332

The 2n2 Band of Water: Analysis of New FTS Measurements and High-Ka Transitions and Energy Levels 1 S. N. Mikhailenko,* Vl. G. Tyuterev,* K. A. Keppler,† B. P. Winnewisser,‡ M. Winnewisser,‡ G. Mellau,‡ S. Klee,‡ and K. Narahari Rao§ *Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, Russia and LPMA Faculte des Sciences, Universite de Reims, Reims, France; †Department of Physics, Ohio Northern University, Ada, Ohio; ‡Justus-Liebig-Universitaet Giessen, Giessen, Germany; and §Department of Physics, The Ohio State University, Columbus, Ohio Received February 13, 1997; in revised form April 18, 1997

The spectrum of water has been recorded at high resolution in the range 2500–4560 cm01 . The spectrum was recorded at room temperature with a Fourier transform spectrometer using fully evacuated transfer optics and a White-type multireflection cell which made large pressure 1 pathlength products possible. Among 3385 lines assigned to transitions to the first triad of interacting states of H2 16O (bands 2n2 , n1 , and n3 ), 940 vibration–rotation transitions have been assigned to the 2n2 band, approximately 300 of them for the first time. According to our assignments some of these transitions, especially high-Ka transitions, show significant deviations from data available in various compilations and in previously published reports. Improved values of vibration–rotation energies of the (020) state up to J Å 17 and Ka Å 11 were determined. The anomalously strong centrifugal distortion of the (020) rotational levels and their resonance interactions with the (100) and (001) levels have been accounted for using the generating function model (1992, Vl. G. Tyuterev, J. Mol. Spectrosc. 151, 97–130; 1995, Vl. G. Tyuterev, V. I. Starikov, S. A. Tashkun, and S. N. Mikhailenko, J. Mol. Spectrosc. 170, 38–58), which allows a good agreement with observed data. The RMS standard deviation of the least-squares fit of vibration–rotational levels of the (020) state was 2.2 1 10 03 cm01 . q 1997 Academic Press INTRODUCTION

The infrared spectral range is important in the accurate modeling of radiative transfer phenomena, not only in the Earth’s atmosphere but also in other atmospheres as well. This explains the interest in experimental and theoretical studies of water vapor spectra in the 2–4 mm region in the past (1–10). High-resolution measurements of water bands in the region 2700–4500 cm01 and the detailed analysis of them performed by Flaud and Camy-Peyret and co-workers (3, 6–9) and by Pugh and Rao (4, 5) in the early 1970s have became spectrometric standards and a basis for several line parameter compilations for water (11–14) including HITRAN (12) and GEISA (13). The improvement of sensitivity and spectral resolution since that time has stimulated extensive new FTS measurements including those recently reported by Toth (15) and also measurements by Keppler et al., some results of which have been briefly reported elsewhere (16). Here the analysis of part of these infrared measurements using the Fourier transform spectrometer at the Justus Liebig University in Giessen is presented. Among a total of over 10 000 lines recorded in the 1

Reported in part at HighRus-93 11-th Symposium on High-Resolution Molecular Spectroscopy, Moscow, June–July 1993 and at the 14th Conference on High Resolution Spectroscopy, Prague, Czech Republic, paper J45, September 1996.

range 2500–4560 cm01 , 3385 lines have been assigned to transitions to the first triad of interacting states of H2 16O (bands 2n2 , n1 , and n3 ). In this paper we focus on the 2n2 band, which is doubly interesting for such a study. First, some high-Ka transitions and associated upper state energy levels, according to our assignment, show significant deviations from data available in various compilations and in previously published reports. This will be shown in the last section of this paper. Second, the experimental information on the high-Ka rotational levels of the bending states is particularly important in order to understand the effects of anomalously strong bending–rotational interactions in H2O (6, 17–28) and to validate relevant theoretical models. EXPERIMENTAL ASPECTS

The infrared spectrum of water was recorded at pressurebroadening-limited resolution using the combination of a 4m base length White-type multipass absorption cell (29, 30) and a Fourier transform infrared (FTIR) spectrometer, the Bruker IFS 120 HR (31). The experimental setup is shown in Fig. 1. The transfer optics were enclosed in a newly constructed vacuum system in a further development ( 32) of the system used in earlier D2O measurements performed by Ormsby (33).

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FIG. 1. Schematic diagram of the experiment.

The resolution for these measurements was not the maximum resolution of the spectrometer, but was instead chosen such that the full width at half maximum (FWHM) of the instrumental lineshape (ILS) of the FTIR spectrometer was one half as large as the narrowest Doppler width in the region covered by each measurement. The resolution is defined here as the reciprocal of the maximum optical path difference (MOPD). The measurements were performed with this resolution criterion because this choice provides the best compromise between S/N, lineshape fidelity, and measurement time (34). This resolution was maintained for higher pressure measurements in each region. The moving mirror in the interferometer travels at a velocity around 1.25 cm/sec, and a background scan taken at a resolution of 0.1 cm01 takes 8 sec to complete. The stability of the system (32) made it possible to measure for 12 hr and co-add all scans taken during this time, resulting in a large signal-to-noise ratio. This, together with the long path and the elimination of atmospheric absorption, made the detection and assignment of weak lines possible. The source for the 1950–2750 cm01 region was a globar. The source for all other regions was a tungsten lamp from Osram. The beamsplitter used was CaF2 , and the windows which separated the White-type cell from the evacuated optics and spectrometer were also CaF2 . The detector used was a photovoltaic InSb detector operating at 77 K. The Bruker software package OPUS, running under OS/2, was used for all measurements. The spectrum of water was recorded with pressures up to

30 mbar and pressure–pathlength products up to 8700 mbar m. The pathlength within the multi-reflection cell was varied from 288.5 m only once, to provide a comparison between two measurements with almost the same pressure–pathlength product. All recordings of the water spectrum were made at room temperature. The sample used for all of the spectra was doubly distilled water from the PhysikalischChemisches Institut, Justus-Liebig-Universitaet, Giessen. Care was taken to permit the pressure of sample in the cell to reach a fairly constant value before proceeding with the measurements. This was time consuming, due to the large surface area of the cell and the adsorbance of H2O on the cell walls. Pressure and temperature were recorded before and after the measurements were taken. The uncertainty of these readings is indicated in Table 1, which provides a summary of measurement conditions. The uncertainty varies due to adsorbance, desorbance, and leakage, checked by comparing spectra from successive blocks within each measurement. The typical block size was 75 scans per block. All data were evaluated as transmittance spectra, constructed from the ratio of several hundred high-resolution scans recorded with the sample in the cell and 60 low-resolution scans recorded with the cell evacuated. An overview of most of the spectrum is provided in Figs. 2 and 3. CALIBRATION OF THE H2O MEASUREMENT FILES

The line positions reported here are from 16 recordings obtained with four different optical filters. Each of the 16

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TABLE 1 Summary of Measurement Conditions

Note. The absorption pathlength was 288.5 m for all recordings except recordings g and ca for which the absorption pathlength was 64.5 m and cb for which the pathlength was 3 m.

recordings was calibrated separately using standard line positions of CO, CO2 , and OCS from frequency measurements. As discussed in Ref. (35), it is important to use the same peakfinding method to obtain the line positions for the sample molecule and the calibration species. All peak positions used in this work were determined using the lineshape fitting program INTBAT (36). Particular care had to be taken in selecting lines for calibration for two reasons. First, the large range of line intensities, due to the large pressure range and the long path, made some lines which were useful at low pressure too strong to be used at higher pressures. Second, initial calibration showed that the edge regions of each spectrum had to be calibrated carefully because the cutoff frequencies selected for the electrical filter settings were probably too close to the optical filter cutoffs, leading to a slight variation in calibration factor in the edge regions. The four spectra ( k, l, m, and n according to the notation of Table 1 ) recorded in the 1950 – 2750 cm01 spectral range were calibrated in three ranges with CO lines ( 2064 – 2199 cm01 ) and OCS lines ( 2042 – 2059 cm01 ) present in the spectra. To assure accurate calibration in

the wavenumber region near the upper edge of the band pass, a separate spectrum of H2O, D 2O, OCS, and N2O, labeled ca in Table 1, was recorded with the same filter as that used for spectra h, i, and j, providing an overlap with spectra k, l, m, and n. The H2O lines in spectrum ca were calibrated using more than 200 OCS lines in the ranges 2690 – 2790, 2850 – 2950, and 3050 – 3130 cm01 . The H2O lines at the upper edge, above 2700 cm01 in the spectra k, l, m, and n, were then calibrated using the H2O lines from spectrum ca. A set of these calibrated H2O lines, in each case selected to have a useful intensity, was then used to calibrate spectra h, i, and j. The initial calibration of spectra b, c, e, and f was made using nine CO2 lines present in the spectrum in the region 3697–3733 cm01 . Another separate calibration spectrum, cb, containing lines of H2O, D2O, and CO, was recorded in the range 3950–4750 cm01 in order to calibrate the upper end of the range of spectra b, c, e, and f, and also to calibrate spectra o, p, and q. The intensities of some of the lines of the d-enriched sample of the calibration cb, recorded in a 3m cell, turned out to be equivalent to the intensities of H2O or D2O lines in natural abundance in the high-pressure, long path spectra, and were thus important for this calibration. Again, sets of H2O lines present in the spectrum cb and in the sample spectra with comparable intensities were used for the final calibration. The two calibration spectra ca and cb were recorded later under filter conditions that guaranteed a consistent calibration over the entire range of the spectra. With the procedure outlined here, the edge effects mentioned for the H2O spectra could be compensated, so that the contribution to the accuracy of the line positions reported here due to the calibration errors should not be more than 0.00001 cm01 . SPECTRUM ASSIGNMENT: ANALYSIS OF LINE POSITIONS OF THE 2n2 BAND

A total of 3385 transitions have been assigned to the transitions to the first triad of interacting states (020)/(100)/ (001), including transitions up to J Å 20 and Ka max Å 11. A summary concerning the data for each of the bands 2n2 , n1 , and n3 is given in Table 2. These lines are among the 10 000 lines observed in the range 2500–4560 cm01 . The remaining lines were identified as belonging to hot bands, higher polyad-transitions, HDO, D2O, H2 18O, and H2 17O isotopic species and also to the impurities CO2 , N2O, H2CO, CH4 , and OCS, the latter group being partly used for calibration purposes. The majority of strong and medium lines show good agreement with previously published measurements and analyses by Flaud and Camy-Peyret (6, 7), Pugh and Rao (4, 5), and Toth (15) and with the last available releases of the HITRAN-96 (12) and GEISA-92 (13) database com-

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FIG. 2. Infrared spectrum of H2O in natural abundance (2500–3500 cm01 ). The recording from which the spectrum was obtained is indicated in the upper right-hand corner (see Table 1).

pilations. This was not always the case, however. We were able to observe and assign numerous weak and medium intensity transitions for the first time. Furthermore, in some regions, deviations from published line positions, especially for weak transitions, amount to as much as 2 cm01 . Examples of such deviations are given in Fig. 4. For reasons explained in the Introduction we focus on line positions of the 2n2 band in the present paper. We were able to observe and assign 940 vibration–rotational transitions of the 2n2 band, as compared to the 642 transitions recently reported by Toth (15). Low-J transitions could be readily assigned using available database compilations (12, 13), and associated line positions are in excellent agreement with the recent Toth measurements (15). An assignment of higher J, Ka transitions requires extrapolations based on theoretical calculations. Because the standard polynomial model of the effective Hamiltonian in the case of water-type nonrigid molecules has poor convergence and extrapolation properties, as was discussed in (18, 20–26), we have used the generating

function model (20–23) taking into account resonance interactions as described in the next section. The assignment of upper state energy levels has been performed using step-bystep iterative extrapolations. Finally, in most cases, except for a few very weak lines, the assignment could be confirmed from combination differences involving two or more observed transitions. Observed line positions, together with their rotational assignments, are given in Table 3. Spectral line parameters have been determined by fitting transmittance data points to a Voigt profile convoluted with the FTS instrumental function using the program INTBAT (36). The standard errors of the line positions obtained from this procedure are presented in the second column of Table 3. The value D given in the third column represents the deviation between the observed position and the transition wavenumber calculated from the refined upper energy levels. Though we do not analyze self-pressure shifts in detail in this paper, the pressure values indicated in the last column of Table 3, together with the D value of the third column,

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FIG. 3. Infrared spectrum of H2O in natural abundance (3500–4250 cm01 ). The recording from which the spectrum was obtained is indicated in the upper right-hand corner (see Table 1).

could in certain cases be helpful for an estimation of this effect. Note that because of the pressure shift contribution, a true accuracy of line positions should not always be identified with D and is expected to be better than D in those cases in which some high-pressure lines have been used for an upper state energy determination.

TABLE 2 Summary of Assignments in the 2n2 , n1 , and n3 Bands of H2 16O in the Range 2500–4560 cm01

Though line intensity values have also been determined from the recorded spectra and have also been calculated, their uncertainties are large due to experimental limitations. These data were not originally collected for the purpose of accurate intensity determinations. A proper consideration of the intensity data and sources of error will be published separately. However, for the purpose of assignment the intensities are helpful. In this paper we limit ourselves to a qualitative stick-diagram of 2n2 observed transitions given in Fig. 5. Since the range of linestrengths exhibited by the recorded spectra was 2 1 10 5 , a logarithmic scale is chosen for this diagram. THEORETICAL MODELING OF THE FIRST TRIAD OF INTERACTING STATES (020)/(100)/(001)

Although we focus on the study of the 2n2 band, an adequate theoretical analysis requires a simultaneous modeling of all three vibrational states belonging to the first triad. It is well known that there are two major effects which complicate an accurate calculation of excited vibration–rotational states of the water molecule and related analysis of highresolution spectra: (a) extremely strong centrifugal distortion resulting from bending–rotational coupling which is especially pronounced for (0n0) states (17–24, 37, 38);

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FIG. 4. Example of the comparison of line positions predicted in the HITRAN-96 and GEISA databases (origin of arrows) with line positions determined in this work (head of arrows) for two lines, (a) 1165 R 1276 and (b) 1166 R 1275 transitions of the 2n2 band. The hot band transition at 2892.318 cm01 was assigned to 523 R 634 of (030) R (010). The transition at 2892.450 cm01 was assigned to H2CO, present as an impurity (recording i).

(b) resonance interactions of both anharmonic and Coriolis type (8, 9). Because of (a) the standard power series expansion of the effective rotational Hamiltonian Hrot used in many previous papers pertaining to the assignment of the water spectrum (5–9, 15) has a limited domain of validity, depending on rotational quantum numbers and on the excitation of the ‘‘floppy’’ bending vibration. This is already understood and is discussed in the early papers by Camy-Peyret and Flaud (6, 18, 37) devoted to the analysis of the first triad. According to estimations (20, 21, 39) of the convergence radius of this expansion, the domain of its applicability is limited by a maximal value Ka max which depends on £2 . Thus for Ka ú Ka max the power series expansion of Hrot diverges and its extrapolation possibilities degrade dramatically even within a ‘‘one-step’’ extrapolation Ka r Ka / 1. In the case of the (020) state of the water molecule Ka max Å 7, but we have observed transitions with upper state values of Ka up to 11. To account for the anomalous centrifugal distortion

at high rotational energies, we use the generating function model (20–23) which was shown to possess better extrapolation properties, especially above the domain of convergence of the power series expansion (22). In the case of the (020) state an explicit comparison of the two models has been performed within the isolated state approximation (23) showing that the generating function approach provides more accurate calculations even within the domain of applicability of the traditional model, Ka £ Ka max . In the present paper the effective Hamiltonian for the first triad of interacting (020)/(100)/(001) states is written in the form

H

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Å

F

H020 H anh H100 h.c.

H cor 2 H cor 1 H001

G

,

[1]

where h.c. means hermitian conjugate and the diagonal vibrational blocks H£1£2£3 are expanded in the generating function G according to Refs. (20, 22),

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TABLE 3 Observed Line Positions of the 2n2 Water Band of H2 16O

Note. nobs , observed line positions in cm01 . s, the standard error of the line position fit using the program INTBAT ( 36), in units 10 05 cm01 . D, the deviation between the observed line position and the calculated value E upper –E lower (using upper levels reported here), in units 10 05 cm01 . P, spectrum label as given in Table 1 in which water vapor pressure is listed.

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TABLE 3 —Continued

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TABLE 3 —Continued

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TABLE 3 —Continued

H£1£2£3 Å d H£1£2£3 / d nd

nd

H£1£2£3

[2]

r,l ,m

H£1£2£3 Å SgnmJ 2 n {G( a ( J ) )} m 2n

2 /

H anh Å ∑ FLmR (J 2 ) l {J 2/r (Jz / r) m

[3]

2 0

H£1£2£3 Å SunmJ [(J / J ), {G( b

(J)

/ ( 01) m (Jz / r) m J 20r },

m

)} ]/ , [4]

where the definition of the generating function is q

G å G( a ( J ) ) Å (2/ a ( J ) ){ 1 / a ( J ) J 2z 0 1}

[5]

and all related definitions are as given in Refs. (20, 22). cor The interaction blocks H anh , H cor 1 , and H 2 , accounting explicitly for anharmonic and Coriolis interactions (8, 9), are written in cylindrical components of the angular momentum operator using the rotational operator ordering of Refs. (40– 42). In this paper we report calculations using a power series expansion of interaction operators.2 In this case for Coriolis interaction blocks (41)

where the index R Å 2r corresponds to powers of the ladder operators and r Å 0, 1, 2, 3, . . . . The operator H anh has nonvanishing matrix elements with even DK. In Eqs. [6] and [7] one has l, m Å 0, 1, 2, 3, rrr with L å 2l. We have included in the fit those 189 rotational energy levels (including pairs of nearly degenerate levels) of the (020) state which have been deduced from two or more

TABLE 4 Statistics of the Fitting of the Vibration–Rotation Levels of the (020) State of H2 16O

H cor Å ∑ ∑ CLmr (J 2 ) l {J r/ (Jz / r/2) m r l ,m odd

[6] 0 ( 01) m (Jz / r/2) m J r0 }.

For the C2£ point group, the allowed powers of the ladder operators J are r Å 1, 3, 5, rrr which correspond to the nonvanishing matrix elements with DK Å 1, 3, 5, rrr in the É J, K … basis. The expansion coefficients are simply related to d coefficients of Ref. (41): CLmr Å drml . For the anharmonic interaction blocks (42), 2

Calculations using an expansion of the interaction operators in the Gfunction will be reported elsewhere.

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FIG. 5. Stick diagram of 2n2 observed transitions using a logarithmic representation of intensity (in cm01 /mol cm02 at 296 K), showing in the top trace all transitions and in the lower trace transitions observed here for the first time.

observed transitions.3 The rotational energy levels of the (100) and (001) states recovered from our spectra were determined at this stage of the analysis with less accuracy and were given, on average, one third of the weight of (020) transitions. To stabilize higher order parameters of (100) and (001) states we have also included less accurate higher energy levels from Ref. (44) deduced from flame spectra up to 10 000 cm01 for (001) energies and up to 12 000 cm01 for (100) energies with low weights varying from 10 01 to 10 02 compared to the (020) data. The statistics of the fitting of the (020) energy levels is given in Table 4 and the parameter values in Table 5. The RMS standard deviation of the fit for the (020) state energy levels was 2.2 1 10 03 cm01 . Calculation of the energy levels of the (100) and (001) states and associated transitions will be presented separately. Here we just note that the anharmonic resonance interactions with the (100) state appear to be extremely important

for high rotational states of (020) state. The mixing coefficients of the wavefunctions reach nearly ‘‘fifty-fifty’’ for Ka Å 10, as can be seen in Tables 6A and 6B. Columns 7, 8, and 9 of this table represent resonance mixing coefficients %(v) versus rotational quantum numbers. The mixing coefficients are defined according to Refs. (8, 9) as %(v) Å S(C vK ) 2 ,

[8]

where C vK represent contributions of isolated state Wangtype functions to the eigenfunction of the interacting state Hamiltonian (1), É£1£2£3 JKa Kc … Å

∑ ∑ C vK É JKvG… v

K

with v Å {(020), (100), and (001)}. ENERGY LEVELS OF THE (020) STATE

3

Except for the level with J Å 0. Pairs of nearly degenerate levels were also included in the fit if we were able to observe at least two transitions involving one or the other component.

Experimental values of rotational energy levels of the (020) state have been determined using the conventional

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TABLE 5 Fitted Values of Hamiltonian Parameters for the First Triad of Interacting States of H2 16O

Note. Total number of vibration–rotational levels of (020)/(100)/(001) states included in the fit was 900. All values of parameters and their standard errors are given in cm01 . Asterisks indicate parameter values held fixed in the least-squares fit.

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TABLE 6A Experimental Vibration–Rotation Energies of the (020) State, Uncertainties, and Resonance Mixing Coefficients in the First Triad of H2 16O: Energy Levels Included in the Fit

Note. dobs , experimental st. error of energy level determination from observed transitions, in units of 10 05 cm01 . O–C, Observed-calculated energy, in units of 10 03 cm01 ; calculations performed with the Hamiltonian parameters of Table 5. Nt , Number of observed transitions (Table 3) to a given upper state level. Transitions to those levels indicated by ∗ in this column were not resolved. The energy for such levels were fixed to those of observed coincident partners. *Uncertainty values for levels marked by asterisk account for estimated energy splitting.

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TABLE 6B Experimental Vibration–Rotation Energies of the (020) State of H2 16O: Energy Levels Corresponding to Only One Observed Transition (Not Included in the Fit)

Note. dobs , 2 1 Standard error of energy level determination from observed transitions, in units of 10 04 cm01 .

two-step procedure. First, from known ground state rotational energies and each assigned observed transition we have obtained upper state energies. Then, the values given in Tables 6A and 6B have been obtained as a weighted average over all energies derived from transitions to a given upper state. As the ground state rotational levels we have used a combination of low J, Ka energy values of Toth (43) and higher J, Ka energy values of Camy-Peyret and Flaud (44) with a few rotational level values corrected according to the conclusions of a paper by Tyuterev et al. (22). The experimentally determined (020) term values are listed in Table 6. The uncertainty ( dobs ) given in parentheses for each experimental energy listed in Table 6A represents one standard deviation, taking into account an error propagation in the two-step procedure mentioned above. Note that self-pressure line shifts have not been analyzed in this paper and therefore may contribute to the true uncertainties of the energy levels obtained. The Obs. 0 Calc. values in the third column (O 0 C) of Table 6A show that the generating function model 4 described in the previous section provides a good agreement for observed 2n2 data: the maximum discrepancy for fitted (020) levels was 5.3 1 10 03 cm01 . Those energy levels which have been deduced from only one observed transition were not included in the fit. Their values are given in Table 6B. The RMS standard deviation of the calculation of such energy levels was 1.75 1 10 02 cm01 . Wavefunction mixing coefficients given in Table 6A for each observed vibration– rotation level indicate that the majority of the strong resonance perturbations in the 2n2 band are due to the anharmonic interactions with n1 (which confirms previous conclusions by Flaud and Camy-Peyret (8)) and that the effects of the interactions are extremely irregular. DISCUSSION

Nine hundred forty transitions of the 2n2 band of water have been reported here, around 300 of these for the first 4

Fits of the first triad data performed with the generating function model using a part of preliminary energy levels values obtained in the present analysis (before the final calibration of the data was achieved) were reported in (16, 45).

time. The uncertainty of the line position determinations is estimated as 3 1 10 05 to 1 1 10 04 cm01 for good isolated lines and is on the average one order of magnitude higher for weaker and overlapping lines. Comparison of the 2n2 line positions from this study (Table 3) with those reported by Toth (15) shows, in general, excellent agreement for low and medium Ka transitions. Among transitions measured and assigned in the present work, 30% of the line position differences Dn Å Én Toth 0 n ourÉ are less than 1 1 10 04 cm01 , and 35% of the line position differences are between 1 1 10 04 and 1 1 10 03 cm01 . For high-Ka transitions and/or corresponding upper energy levels, however, there are some pronounced disagreements with Ref. (15). These are illustrated in Table 7. Columns 3 and 4 of Table 7 present line positions for transitions involving high J, Ka states given in the observed line list of Ref. (15) and in Table 3. Column 5 shows their differences Dn (in cm01 ). Columns 6 and 7 give the wavenumbers of transitions to the same upper states, calculated from the experimental energies of Toth (15) and of Table 6, and column 8 shows the corresponding differences in upper state energy levels DE. In all cases where pronounced disagreements in the experimental values of (020) rotational energies exist, we have observed several transitions to the same upper level confirming the assignment, whereas in Ref. (15), only one transition (or no transitions) has been reported in the observed line list. The portions of the H2O spectra shown in Figs. 6–8 illustrate these assignments. Figures 6 through 8 also illustrate that predicted lines (Column 6, Table 7) which would unambiguously confirm that the assignments reported in Ref. (15) could not be assigned in our spectra, although the signal-to-noise ratio of the spectra made it possible to assign even weaker transitions. The differences in assignment are probably due to the difference in the theoretical models used for stepwise extrapolations. The standard power series expansion of the effective rotational Hamiltonian diverges (20) for the higher rotational quantum numbers in question (Ka ú 7) and does not provide reliable extrapolations whereas the generating function model proves to be applicable over a wider range of J and Ka values. It should be noted that the new corrected

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TABLE 7 Comparison of Observed High- Ka Transition Wavenumbers and Upper State Energy Levels with Previously Published Data for H2 16O

Note. All line positions and energy differences are given in cm01 . Dn Å n (this work) 0 n (Ref. 15); DE Å E (this work) 0 E (Ref. 15) for upper state levels corresponding to quantum numbers given in the column 1; Column 9 represents line positions calculated from generating-function Hamiltonian (1–7) (with parameters of Table 5) and ground state energies. All values are rounded off to a precision of 10 03 cm01 .

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TABLE 7 —Continued

energy level values reported here for high J and Ka should be important in the determination from experimental data of the bending behavior of the molecular potential function (see for example (46–48)). In conclusion, the present study has used data with a large pressure–pathlength product obtained with a FTIR spectrometer at pressure-broadening-limited resolution to significantly extend the range of reliable experimental and calculated transitions and energy levels for the (020) state of H2O. ACKNOWLEDGMENTS Vl.G.T. thanks the Alexander von Humboldt Stiftung for support. K.A.K. gratefully acknowledges the assistance of the Fulbright Kommission and

the DAAD. This work was supported in part by the Deutsche Forschungsgemeinshaft and the Fonds der Chemischen Industrie, with additional funding provided by NATO for travel between the USA and Germany and computing facilities partially funded by NASA. S.N.M. acknowledges support from the ISF and RFFI foundations. The authors are grateful to Markus Mengel for assistance and valuable advice.

REFERENCES 1. W. S. Benedict and E. K. Plyler, J. Res. Natl. Bur. Std. 46, 256 (1951). 2. P. E. Fraley and K. Narahari Rao, J. Mol. Spectrosc. 29, 348–364 (1969). 3. J.-M. Flaud, C. Camy-Peyret, and A. Valentin, J. Physique 33, 741 (1972).

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FIG. 6. Example of assignments of transitions to the 990 level of the (020) state. The lower traces are expanded plots of the upper spectrum in each case. (a) Transition 990 R 1010 1 . Arrows denote the positions given for this transition by O: this work (recording j); H: HITRAN-96/GEISA predictions; T: Ref. (15). (We assign the absorption feature at 3046.62 cm01 to 1073 R 962 of n3 in HDO.) (b) Transition 990 R 981 . O: this work (recording e); Tc : derived from the upper state energy given in Ref. ( 15).

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FIG. 7. Example of assignments of transitions to the 109,2 level of the (020) state. (a) Transition 1092 R 1110 1 . O: this work (recording j); T: assignment of Ref. (15). (b) Transition 1092 R 981 . O: this work (recording f). Tc : transition wavenumber derived from upper state energy given in Ref. (15).

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FIG. 8. Example of assignments of the transition 1010 1 R 990 of the 2n2 band. O: this work (recording e). Tc : transition wavenumber derived from the upper state energy given in Ref. ( 15).

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