The W2020 database of validated experimental transitions and accurate empirical energy levels of water isotopologues, introduced in the work of Furtenbacher et al. [J. Phys. Chem. Ref. Data 49, 033101 (2020)], is updated for H216O and newly populated with data for H217O and H218O. The H217O/H218O spectroscopic data utilized in this study are collected from 65/87 sources, with the sources arranged into 76/99 segments, and the data in these segments yield 27 045/66 166 (mostly measured) rovibrational transitions and 5278/6865 empirical energy levels with appropriate uncertainties. Treatment and validation of the collated transitions of H216O, H217O, and H218O utilized the latest, XML-based version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol and code, called xMARVEL. The empirical rovibrational energy levels of H217O and H218O form a complete set through 3204 cm−1 and 4031 cm−1, respectively. Vibrational band origins are reported for 37 and 52 states of H217O and H218O, respectively. The spectroscopic data of this study extend and improve the data collated by an International Union of Pure and Applied Chemistry Task Group in 2010 [J. Tennyson et al., J. Quant. Spectrosc. Radiat. Transfer 110, 2160 (2010)] as well as those reported in the HITRAN2016 information system. Following a minor but significant update to the W2020-H216O dataset, the joint analysis of the rovibrational levels for the series H216O, H217O, and H218O facilitated development of a consistent set of labels among these three water isotopologues and the provision of accurate predictions of yet to be observed energy levels for the minor isotopologues using the combination of xMARVEL results and accurate variational nuclear-motion calculations. To this end, 9925/8409 pseudo-experimental levels have been derived for H217O/H218O, significantly improving the coverage of accurate lines for these two minor water isotopologues up to the visible region. The W2020 database now contains almost all of the transitions, apart from those of HD16O, required for a successful spectroscopic modeling of atmospheric water vapor.

During the last century, one could witness outstanding research activity, yielding several hundred scientific papers, on the laboratory determination of rovibrational transitions of water isotopologues in the gas phase. This activity has been fueled largely by the considerable need for accurate line-by-line water data required by a number of scientific and engineering applications.1–4 The experimental studies have been aided by the appearance of new high-resolution and precision spectroscopic techniques5–12 as well as by the outstanding developments in the theory of (ultra)high-resolution spectroscopy.13–15 Most of the relevant spectroscopic data on water isotopologues available then were collected, cited, and analyzed in Refs. 16–20, detailing the work of a Task Group (TG) formed by the International Union of Pure and Applied Chemistry (IUPAC) on “A Database of Water Transitions from Experiment and Theory” (Project No. 2004-035-1-100). This TG carefully considered the measured transitions of water vapor and validated and recommended a large number of them, as well as came up with corresponding empirical energy levels. The studies of the IUPAC TG addressed nine water isotopologues, H2XO,16–18 HDXO,17 and D2XO19 (X = 16, 17, 18), and were based on the utilization of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) technique,21–26 a global spectrum analysis tool under steady development.27–31 These datasets will be referred to as TG-H216O, TG-H217O, and TG-H218O in the remainder of this paper.

No major modifications of the IUPAC TG water data20 have been made publicly available until 2020, when some of the authors of this study published31 an updated database, called W2020, of the parent water isotopologue, H216O. The present paper provides the second major extension of the IUPAC TG results, significantly enlarging and upgrading the TG-H217O and TG-H218O datasets. This extension relies on the most recent developments related to the MARVEL code,29–31 resulting in what is called the xMARVEL31 protocol, and takes advantage of all the H217O and H218O transitions detected during the last decade32–66 as well as before that.67–127 After assembling the W2020 datasets and verifying their entries, it becomes feasible to consider how the new experimental high-resolution results can be utilized to further improve our knowledge on water spectroscopy and to present new recommendations for old energy levels, occasionally including modifications to their labels. Through the use of the xMARVEL technique, a considerable number of new, reliable empirical energy levels, with dependable uncertainties, are derived from the observed transitions.

Joint consideration of the W2020 lines and levels for the series H216O, H217O, and H218O allows improvements to be made to the individual datasets as well as the prediction of new lines for a number of applications. To realize these achievements, it was deemed necessary to slightly modify the W2020-H216O dataset31 as part of the present work. The smooth change in the rovibrational energies upon isotopic substitution facilitates the provision of a consistent set of quantum labels for this set of water isotopologues. The empirical results obtained can be employed to yield accurate estimates for yet unobserved transitions; thus, they provide highly useful input to future experimental studies of these water isotopologues. The experimental and empirical data present in the W2020 database should be sufficient to improve the result of atmospheric modeling efforts based on line-by-line information on water vapor. Extension of the empirical W2020 data to the visible region with accurate lines should facilitate such efforts. This extension can be achieved, for example, by the use of lines derived from pseudo-experimental (PE) levels.128 

The concept of PE levels was introduced recently by Polyansky et al.,128 who showed that by combining the results of high-accuracy variational nuclear-motion calculations for one isotopologue of a molecule, say, H217O in our case, with empirical energy levels and variational results for a parent isotopologue, say, H216O, it becomes possible to predict the rovibrational levels of the daughter isotopologue with an accuracy as high as 0.01 cm−1–0.02 cm−1. A similar approach, albeit relying on perturbation theory rather than variational calculations, was proposed by Huang et al.129 The procedure of Polyansky et al.128 was used successfully by McKemmish et al.130 to derive accurate line positions for minor isotopologues of the heavy diatomic molecule 48Ti16O, contributing to the determination of Ti isotopic abundances in brown dwarfs based on high-resolution spectra.131 In order to complement the empirical energy levels deduced from the xMARVEL analyses for H217O and H218O, PE rovibrational energies are generated in this study for both minor water isotopologues. Carefully derived PE levels improve the coverage of water transitions up to and including the visible region.

The rest of this paper is organized as follows. In Sec. 2, the methodologies employed during this work are presented and the corresponding data-massaging treatments are sketched. Section 3 provides details about the construction of the W2020 datasets of the H216O, H217O, and H218O water isotopologues. Section 4 discusses the vibrational band origins (VBOs) covered by the W2020-H217O and W2020-H218O datasets. Section 5 describes how the validation of the transitions and especially of the empirical rovibrational energy levels of H217O and H218O was achieved. Section 6 presents the PE levels derived, as part of this study, for both H217O and H218O, expanding the coverage of the empirical energy-level lists. A comparison of the W2020 data with entries of the HITRAN2016 information system is given in Sec. 7. Section 8 discusses the accuracy of recently measured quadruple-allowed transitions in light of the complete spectroscopic network (SN) of H216O.24 As one stunning exercise of many similar possible ones, Sec. 9 reassesses the precision Lamb-dip spectroscopy data of one source, 10GaFaCaMa.32 Section 10 considers how the W2020 data presented may help atmospheric simulations. The paper ends with Sec. 11, where interesting and important conclusions are drawn as a summary of the present study.

To provide the best estimates for the empirical rovibrational energies of H216O, H217O, and H218O, all of the (mainly experimental) rovibrational lines, collated from the literature, were processed in a simultaneous way by including them in SNs.22,24,28,30 SNs are formed by nodes (energy levels) connected by edges (measured or computed lines); the latter are directed from their lower energy levels to the upper ones, regardless of whether they were observed in absorption, in emission, or through techniques of action spectroscopy. Often, there are multiple measurements of the same transition; these correspond to multiple edges in the SN. A special characteristic of SNs is that the nodes define a potential function.

SNs often contain several components, that is, sets of energy levels not linked by any transition. If a component of the SN contains the lowest-energy state of a nuclear-spin isomer of the molecule considered, this component is referred to as a principal component (PC); otherwise, it is called a floating component (FC). Excluded energy levels,30 whose determining transitions have all been removed for one reason or another, form special (single-node) FCs of the SN. For H216O, H217O, and H218O, transitions connecting states of their two nuclear-spin isomers (ortho and para) have not been detected;132 thus, the energy separation of the ortho and para PCs is not known from experiments. For further details about definitions and related notations concerning SNs and networks in general, see Sec. 2.1 of Ref. 30 and Ref. 133, respectively.

MARVEL started out21–26 as a protocol for inverting, in a weighted linear-least-squares sense, line positions taken from (ultra)high-resolution laboratory spectra to the best (optimal) set of consistent rovibrational (occasionally rovibronic) energy levels. The original MARVEL protocol is built heavily on spectroscopic data management schemes advanced by Flaud et al.134 and Tashkun et al.135 (note that probably one of the very first such line inversion studies was published by Aslund136). Over the years, there have been many developments27–31 improving how MARVEL treats and exploits experimental data. The different flavors of the MARVEL technique, including xMARVEL introduced in Refs. 30 and 31, have been used to treat nine isotopologues of water,16–20 three of which are the subject of the present investigation, as well as the laboratory spectroscopic data of a number of diatomics,137–141 triatomics,142–145 tetratomics,146–148 and beyond.149 

The xMARVEL procedure30,31 has been used extensively during the present study to treat experimental rovibrational data of H216O, H217O, and H218O. The corresponding xMARVEL input and output data files are provided in the supplementary material.

xMARVEL requires that the upper and lower states of each transition have unique labels with a set of quantum numbers and perhaps some other useful information (such as symmetry), characteristic of the rovibrational states considered. For water isotopologues, it is customary to identify their rovibrational states using approximate normal-mode (v1, v2, v3) and rigid-rotor (J, Ka, Kc) quantum numbers, often referred to as ( v 1 v 2 v 3 ) J K a , K c . In this list, J is the total rotational angular momentum quantum number, while Ka and Kc correspond to the projection of the rotational angular momentum on the molecular a and c axes, respectively. For H2XO (X = 16, 17, 18), v1, v2, and v3 are the number of vibrational quanta in the symmetric stretch, bend, and asymmetric stretch modes, respectively. Note that for symmetric water isotopologues, local-mode quantum numbers give a better representation of the physical nature of the higher-excited stretching states.150 One can map the vibrational quantum numbers from normal to local mode and vice versa,151 so either scheme can be used without loss of generality. For this reason, we retain the more conventional normal-mode labels when constructing the W2020 datasets.

Checking the correctness of the labels of the lower and upper states of the lines requires the understanding of symmetry characteristics. The symmetry characteristics and selection rules related to the approximate quantum numbers of H216O are listed in Ref. 20; the same set of rules applies to H 2 17 / 18 O .

In order to provide increased coverage of the accurately known rovibrational energy levels of H217O and H218O, and the related transitions, we decided to augment the W2020 dataset of these species with so-called PE128 energy levels. To justify this decision, we note that the accuracy of the PE energy levels is significantly better than that of their first-principles (FP) counterparts, upon which they are partially based (see below). The idea of the construction of PE energies for a daughter isotopologue from the knowledge of experimental (empirical) as well as FP energy levels of a major isotopologue was reported in Ref. 128. This approach is based on the approximate equality of the observed minus calculated (obs – calc) residuals of energy levels with the same vibrational and rotational assignment among the different isotopologues. In particular, in the present case of the water molecule, the obs – calc residuals for the rovibrational levels of H216O are very similar to those characterizing the related states of H217O and H218O.

To provide a formal definition for the PE states, let us consider the following trivial connection:

E v , r expt ( X ) = E v , r FP ( X ) + R v , r ( X ) ,
(1)

where E v , r expt ( X ) and E v , r FP ( X ) are the experimental (more precisely, empirical) and the FP energies of H2XO (X = 16, 17, 18), v = (v1v2v3) and r = J K a , K c denote the vibrational and rotational labels of the investigated level, respectively, and R v , r ( X ) = E v , r expt ( X ) E v , r FP ( X ) is the residual between the experimental and the FP energies. By employing the Rv,r(X) ≈ Rv,r(16) approximation for X = 17 and X = 18,

E v , r expt ( X ) E v , r FP ( X ) + R v , r ( 16 ) E v , r PE ( X )
(2)

is obtained, where E v , r PE ( X ) is the PE energy of the (v, r) state. In order to approach the accuracy of the empirical energy values derived in the present study, Eq. (2) needs to be modified to the form

E v , r PE ( X ) = E v , r FP ( X ) + R v , r ( 16 ) + Δ R 0 ( X ) ,
(3)

where

Δ R 0 ( X ) = 1 N i = 1 N [ R v [ i ] , r 0 ( X ) R v [ i ] , r 0 ( 16 ) ] ,
(4)

N is the total number of v[i] vibrational states considered in Eq. (4), and r0 = 00,0. Our preliminary calculations suggest that the simple ΔR0(17) and ΔR0(18) corrections (estimated to be 0.006 cm−1 and 0.012 cm−1, respectively) could be determined not only empirically, as suggested by Eq. (4), but also from vibrational non-adiabatic corrections.

The W2020 database can be considered as a significant update to and an extension of the datasets assembled by the IUPAC TG16–19 mentioned in the Introduction. Thus, the initial databases of this study were the experimental linelists of TG-H217O and TG-H218O.17 As to H216O, the W2020 dataset of Ref. 31 is enlarged here, the latter itself being a significant update of the TG-H216O list.18 

Although the W2020 dataset for H216O was published only recently,31 the dataset was further investigated as part of this study in order to improve our treatment of the data for H217O and H218O. In particular, the sources 01NaUbLePo,102 17CaMiVaRe,53 and 20MiBeOdTr,63 containing dipole-allowed transitions, were added to the W2020-H216O dataset.31 The sources 01NaUbLePo,102 17CaMiVaRe,53 and 20MiBeOdTr63 contain 1393, 183, and 604 assigned transitions, respectively, and what is especially important, inclusion of the transitions of 01NaUbLePo102 yields 71 new empirical energy levels for H216O. Due to the high quality of the assigned transitions in these three sources,53,63,102 it proved to be straightforward to expand the xMARVEL input with these new entries without any relabeling or significant uncertainty adjustments. Furthermore, in 2020, two studies reporting weak, quadrupole-allowed transitions152,153 of H216O appeared, containing 21 lines. In Ref. 31, only the data of Ref. 152 were considered, while all the quadrupole data form part of our extended W2020-H216O database. As a result of these changes, the original31/augmented W2020-H216O datasets contain 270 745/286 987 non-redundant rovibrational transitions with 19 204/19 225 empirical energy levels. The updated and enlarged W2020-H216O dataset can be found in the supplementary material.

To facilitate the construction and improve the consistent labeling of the W2020-H217O and W2020-H218O databases, the original W2020-H216O dataset was compared to the 20MiKaMoCa66 linelist as this list contains entries for H217O and H218O as well. This comparison yielded a number of important observations worth detailing here. To aid understanding of what follows, a few details about the 20MiKaMoCa66 linelist must be provided. Namely, the upper-state energies of the 20MiKaMoCa66 linelist were derived either from ground-state combination-difference (CD) relations or from published theoretical energy-level lists, while the lower-state energies were simply taken from TG-H2XO. The CDs also utilized the TG-H2XO lower-state energies when they were added to the wavenumbers extracted from intracavity laser absorption spectroscopy (ICLAS), Fourier-transform spectroscopy (FTS), cavity-ringdown spectroscopy (CRDS), comb-assisted CRDS (CA-CRDS), and Lamb-dip transitions.

Due to their significantly lower accuracy, all the 20MiKaMoCa66 transitions based on theoretical predictions or ICLAS measurements were neglected during the present analysis. After the comparison of the original W2020-H216O database to the 20MiKaMoCa66 lines, it was found that MARVEL reproduces 63 of the 77 Lamb-dip lines within 1 × 10−4 cm−1, 10 571 of the 11 775 CA-CRDS line positions within 1 × 10−3 cm−1, and 7427 of the 7607 CRDS/FTS lines within 1 × 10−2 cm−1. Although the 20MiKaMoCa lines are by and large in good agreement with their W2020 counterparts, some outliers, attributed to (at least) the following four factors, were revealed. First, compared to the TG-H216O database,18 the energy values of the W2020 dataset changed by a small but significant extent, on the order of 10−4 cm−1–10−3 cm−1, even within the ground vibrational state. If the 20MiKaMoCa database was reconstructed using the significantly more reliable W2020 entries instead of their TG counterparts, much better agreement between the 20MiKaMoCa and W2020 linelists could be achieved. Second, there were several cases where, instead of utilizing the lone (non-confirmed) CA-CRDS or CRDS/FTS transitions, the upper-state W2020 energies were close to values suggested by a handful of emission lines, confirming each other in the corresponding CD relations. After increasing the uncertainties of these emission transitions, xMARVEL was able to reproduce this subset of 20MiKaMoCa66 entries significantly better. Third, in a number of cases when the deviation between a xMARVEL and a 20MiKaMoCa line is larger than 0.01 cm−1, the empirical (xMARVEL) energies are determined solely by emission measurements. In other words, we could not find the sources of certain CRDS/FTS lines reported in 20MiKaMoCa.66 Without experimental information, nothing can be done within xMARVEL to improve this collection of empirical energies. Fourth, when two transitions have highly similar estimated accuracies, no individual uncertainties were reported for them in their literature sources, and the two transitions suggest two significantly different energies for the same state, the empirical energy of this state will be approximately the average of these different values with an appropriately increased uncertainty. This means that xMARVEL reproduces neither line perfectly, leading to considerable deviations from some of the 20MiKaMoCa predictions. This problem can be remedied once the experimental papers start reporting at least the correct order of magnitude of the individual uncertainties (e.g., 10−5 cm−1, 10−4 cm−1, 10−3 cm−1) for all the reported transitions. Based on all these observations, we decided to update the W2020-H216O dataset of Ref. 31, both by making the necessary adjustments indicated by comparisons with the 20MiKaMoCa66 linelist and by the availability of new sources.53,63,102,152,153 As is clear from Fig. 1, the updated W2020-H216O dataset is able to reproduce 10 939 CA-CRDS line positions (out of 11 775) and 7559 CRDS/FTS lines (out of 7607) within the above criteria, validating both linelists.

FIG. 1.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H216O counterparts.

FIG. 1.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H216O counterparts.

Close modal

As a next important step, the empirical W2020-H216O line positions derived during this study from the enlarged and updated dataset were compared to those of the lines of the SISAM database.154 The SISAM dataset contains 17 472 H216O lines in the range of 500.035 cm−1–7973.082 cm−1. All SISAM lines could be nicely matched with their W2020-H216O counterparts. In the 76 cases where probable labeling conflicts were found, due to the use of modified labels of the latest H216O publications included in W2020, they were excluded from the analysis. The list of the outlying SISAM lines can be found in the supplementary material.

As clearly shown in Fig. 2, the agreement is excellent between the SISAM dataset and the new version of the W2020-H216O database. Overall, 15 821 SISAM lines can be reproduced within 5 × 10−4 cm−1. It is also important to point out that all the lines in SISAM with absorption intensities larger than 1 × 10−26 cm molecule−1 have corresponding counterparts in the updated W2020-H216O dataset. This means that if the W2020-H216O entries of this study are used in building a future H216O linelist, then there appears to be no need to employ the transition wavenumbers present in SISAM.

FIG. 2.

Unsigned deviations of the SISAM154 lines from their updated W2020-H216O counterparts.

FIG. 2.

Unsigned deviations of the SISAM154 lines from their updated W2020-H216O counterparts.

Close modal

The W2020-H217O and W2020-H218O datasets were assembled based on the following five major tasks: (a) construct the most complete catalog of published experimental lines; (b) set the best possible (often unreported) initial uncertainties of the observed line positions to help the uncertainty refinement process; (c) certify the existence of the empirical energy levels by comparison with their FP (in the present case HotWat78128) counterparts; (d) create the best possible, consistent labels for the rovibrational states of the H2XO isotopologues, with X = 16, 17, and 18; and (e) expand the transition database with certain unmeasured, unreported, or even artificial transitions, inspired by well-founded spectroscopic information,155,156 and derive further empirical energy levels for these minor water isotopologues.

As to task (a), we added 35 and 37 new sources to the TG-H217O and TG-H218O databases, respectively.17 Note that most of the new sources appeared after the compilation of Ref. 17, though some of them had just been omitted accidentally during collection of experimental spectroscopic data performed more than a decade ago. As a result, the W2020-H217O database contains 65 sources of experimental data (divided into 76 segments), while the W2020-H218O database is built up from 87 sources (distributed into 99 segments).

During task (b), we tried to find the best possible initial uncertainties, called estimated segment uncertainties (ESUs), for segments of the measured line positions. First, we tried to use directly the uncertainties given in the sources. If individual uncertainties were not available in the source (this is more the rule than the exception), the median of the refined transition uncertainties within a given segment was calculated. If this value, called median segment uncertainty (MSU), is close to ESU, then the ESU value was accepted; otherwise, it was replaced with MSU. In contrast to the W2020-H216O database, the H217O and H218O databases include only a few sources where their typical uncertainties had to be modified, compared to the values established for TG-H217O and TG-H218O.17 For example, the ESU of 99CaFlMaBy99 was decreased from 1 × 10−3 cm−1 to 5 × 10−4 cm−1 for H217O and that of 05Tothb113 was decreased from 1 × 10−3 cm−1 to 5 × 10−4 cm−1 for H218O.

Relying on the complete experimental linelist with the best possible initial uncertainties, one can determine dependable empirical rovibrational energies via executing the latest version of the xMARVEL protocol.31 After the determination of the empirical energies, as part of task (c), one needs to check whether these energies have counterparts in the FP energy list (HotWat78),128 within a tolerance of 10−4 × E (where E is the energy of the xMARVEL state examined) inside a given (J, symmetry) block with the natural restriction that each FP state should be utilized only once. The transitions of those empirical states that could not be matched within this criterion were excluded from the database.

While performing task (d), we attempted to find the best possible set of consistent labels for each rovibrational state. As is well known,31,157–159 there are no theoretical techniques yielding unambiguous labels for high-lying vibrational bands; thus, sometimes, it is very hard to find the best labeling scheme for the rovibrational states. During the first phase of the present study, the labels of the W2020-H216O database31 were utilized as a guide to create consistent labels for the rovibrational states of H217O and H218O. It is expected that the differences among the rovibrational energy levels of H216O and H2XO (X = 17 or 18) with the same labels follow, as a function of Ka, a simple trend within a given vibrational band. If the difference deviates significantly from a well-established trendline, we decided to relabel that particular state of H2XO. To illustrate this simple procedure, the differences of some H216O and H218O energy levels are plotted in Fig. 3 as a function of Ka at fixed J = 5 and P = 5, where P = 2v1 + v2 + 2v3 is the so-called polyad number. For high J values, say, those above J = 15, and higher vibrational excitations, there is not enough information to utilize such plots. Figure 3 shows that the differences decrease considerably faster in vibrational states with a high bending contribution compared to the stretching states. This is the reason why the bending trendline crosses that of the stretching one close to a particular Ka value (see Fig. 3). Unfortunately, near a crossing, the vibrational label becomes somewhat arbitrary. The correctness of the rovibrational labels is questioned when the calculated levels within the same symmetry block are closer to each other than 1 cm−1. In these cases, the trendlines were used for verifying the labels. At the end, more than 200 and 400 rovibrational states were relabeled for H217O and H218O, respectively. Compared to the overall number of empirical energy levels known for these two minor water isotopologues, these changes are not drastic but significant for a number of applications, such as seeking PE energy levels (vide infra) or estimating pressure-broadening parameters. As a result, we believe that, whenever possible, the labels of the rovibrational states within the W2020 database of H216O, H217O, and H218O are consistent with each other.

FIG. 3.

Differences between the H216O and H218O rovibrational energies for the vibrational bands of the P = 5 polyad at J = 5.

FIG. 3.

Differences between the H216O and H218O rovibrational energies for the vibrational bands of the P = 5 polyad at J = 5.

Close modal

During task (e), several transitions that cannot be (or have not been) measured were introduced into the W2020 datasets. For example, the disconnected ortho and para states were linked by so-called magic numbers, which correspond to the energy difference of the (0 0 0)10,1 and (0 0 0)00,0 states. In the case of H217O, the value93 of 23.773 51(2) cm−1 is adopted as the magic number, while for H218O, the value93 of 23.754 902(5) cm−1 is employed. Nearby ortho and para states (as confirmed by accurate FP calculations) were searched for in the FP databases.128 Using these nearly degenerate states, virtual lines were introduced in order to maximize the number of empirically known energy levels for both H217O and H218O. 154 and 226 such virtual lines, collected into a source “20virt” and distributed in segments having different accuracy, are used for H217O and H218O, respectively. If the HotWat78 energy-level set indicated that the complementary (usually para) transition (separated by no more than 5 × 10−3 cm−1 based on FP information) is not reported in the data source of an experimental (mainly ortho) line with a σ wavenumber, then this complementary transition was added to the source “20compl” with the same σ wavenumber. Altogether, 66 and 319 complementary lines are included in the 20compl source for H217O and H218O, respectively. Finally, it is important to note that the W2020-H218O database contains calculated lines from the source 16CoCh.50 This source was added to the W2020-H218O database because the accuracy of its records is comparable to that of the typical experimental uncertainty, allowing us to connect high-lying FCs to the PCs.

Tables 1 and 2 provide a summary of all the data sources treated during this work for H217O and H218O, respectively. These tables contain the wavenumber ranges and the number of assigned (A) and validated (V) transitions, as well as the number of non-redundant lines (N), with distinct tags for each segment. Tags set boldface in these tables signify the new sources, compared to Ref. 17, employed in the present study.

TABLE 1.

Data source segments and their characteristics for the H217O moleculea

Segment tag Range A/N/V ESU MSU LSU Recalib. factor
09PuCaHaVa127   6.471 2–18.413  5/5/5  2.00 × 10−8  2.00 × 10−8  3.00 × 10−8   
10GaFaCaMa32   7 084.0–7 222.3  2/2/2  3.34 × 10−7  3.34 × 10−7  3.34 × 10−7   
99MaNaNaOd100   15.671–177.15  125/125/125  1.40 × 10−6  1.53 × 10−6  2.72 × 10−5   
11Koshelev35   24.966–24.966  1/1/1  2.17 × 10−6  2.17 × 10−6  2.17 × 10−6   
71StBe70   0.451 50–6.471 2  2/2/2  3.34 × 10−6  3.34 × 10−6  3.34 × 10−6   
75LuHe74   18.413–24.966  2/2/2  3.34 × 10−6  9.97 × 10−6  1.51 × 10−5   
20virt  0.000 000–0.000 000  24/24/24  5.00 × 10−6  5.00 × 10−6  5.00 × 10−6   
20virt_S2  0.000 140–0.000 977  17/17/17  5.00 × 10−4  5.00 × 10−4  5.00 × 10−4   
20virt_S3  0.001 117–0.009 973  113/113/113  5.00 × 10−3  4.65 × 10−3  4.32 × 10−2   
92Toth93   23.774–23.774  1/1/1  2.00 × 10−5  2.00 × 10−5  2.00 × 10−5   
92Toth_S293   1 063.8–2 155.1  443/440/440  5.00 × 10−5  3.78 × 10−5  5.77 × 10−4   
92Toth_S393   1 011.9–2 224.2  258/258/255  5.00 × 10−4  1.86 × 10−4  3.22 × 10−3   
92Toth_S493   1 120.7–1 724.8  4/4/4  5.00 × 10−3  1.00 × 10−3  1.63 × 10−3   
93Toth94   1 314.1–3 938.9  84/84/84  5.00 × 10−5  5.00 × 10−5  4.39 × 10−4   
93Toth_S294   1 314.7–3 944.8  221/220/220  5.00 × 10−4  2.01 × 10−4  1.65 × 10−3   
93Toth_S394   1 898.6–3 679.7  33/33/33  5.00 × 10−3  1.03 × 10−3  5.59 × 10−3   
94Tothc95   3 254.1–4 080.4  350/350/350  5.00 × 10−5  4.96 × 10−5  7.44 × 10−4   
94Tothc_S295   3 223.7–4 242.7  407/406/406  5.00 × 10−4  2.59 × 10−4  2.21 × 10−3   
94Tothc_S395   3 223.2–4 216.0  68/68/68  5.00 × 10−3  1.35 × 10−3  3.14 × 10−2   
94Tothd96   6 752.6–7 301.0  11/11/11  5.00 × 10−5  5.00 × 10−5  2.60 × 10−4   
94Tothd_S296   6 619.9–7 639.2  580/579/578  5.00 × 10−4  4.21 × 10−4  3.76 × 10−2   
94Tothd_S396   6 616.8–7 540.1  264/263/261  5.00 × 10−3  1.29 × 10−3  3.01 × 10−2   
20MiBeOdTr63   48.030–665.56  619/618/618  5.00 × 10−5  4.32 × 10−5  6.69 × 10−3   
83Guelachv84   1 315.6–1 986.0  200/200/198  9.80 × 10−5  3.61 × 10−5  1.03 × 10−2  0.999 999 762 9 
17CaMiVaRe53   4 249.9–4 533.7  20/19/19  1.00 × 10−4  1.00 × 10−4  5.78 × 10−3   
17MoMiKaBe55   7 443.3–7 921.0  1596/1595/1593  1.00 × 10−4  2.27 × 10−4  1.71 × 10−2   
18MiMoKaKa56   6 667.7–7 449.2  3544/3530/3528  1.00 × 10−4  2.61 × 10−4  1.48 × 10−2   
73CaFlGuAm73   3 581.5–3 909.4  58/58/56  5.00 × 10−4  4.50 × 10−4  4.97 × 10−3   
98Toth98   599.00–797.32  31/31/31  5.00 × 10−4  2.63 × 10−4  8.06 × 10−3   
99CaFlMaBy99   9 711.8–11 335  1063/1063/1062  5.00 × 10−4  5.00 × 10−4  1.37 × 10−2   
02MiTyStAl103   4 206.7–4 999.1  8/8/8  5.00 × 10−4  2.68 × 10−4  4.36 × 10−3   
05Tothb113   5 018.3–5 684.7  312/312/312  5.00 × 10−4  2.15 × 10−4  4.19 × 10−3   
07JeDaReTy121   4 206.7–6 599.5  574/567/563  5.00 × 10−4  5.59 × 10−4  2.47 × 10−2   
09LiNaKaCa126   5 907.8–6 725.2  212/211/211  5.00 × 10−4  6.54 × 10−4  1.71 × 10−2   
11LeNaCa36   13 541–14 107  391/391/388  5.00 × 10−4  1.00 × 10−3  3.46 × 10−2   
11LeNaCab37   12 585–13 555  126/125/124  5.00 × 10−4  5.00 × 10−4  2.54 × 10−2   
11MiKaWaCa38   7 408.2–7 902.2  346/344/341  5.00 × 10−4  6.07 × 10−4  4.14 × 10−2   
12LeMiMoKa40   6 886.9–7 404.9  696/672/669  5.00 × 10−4  4.53 × 10−4  1.34 × 10−2   
16MiLeKaMo51   5 850.9–6 670.8  2512/2492/2487  5.00 × 10−4  4.89 × 10−4  3.64 × 10−2   
19MiKaVaMo60   5 693.5–5 988.4  188/185/185  5.00 × 10−4  3.79 × 10−4  4.11 × 10−2   
19MiMoKaKa61   5 693.0–5 849.9  502/502/502  5.00 × 10−4  4.31 × 10−4  1.41 × 10−2   
19ReThReMi62   6 531.3–7 801.3  1136/1128/1128  5.00 × 10−4  7.32 × 10−4  1.82 × 10−2   
07MiLeKaCa123   5 988.1–7 015.5  236/235/234  6.00 × 10−4  8.15 × 10−4  2.27 × 10−2   
17LoBiWa54   1 853.7–3 988.3  620/620/620  6.00 × 10−4  1.52 × 10−4  4.95 × 10−3   
78KaKaKy80   100.37–301.14  20/20/19  1.00 × 10−3  1.13 × 10−3  1.48 × 10−2   
80KaKy82   53.510–727.83  371/371/371  1.00 × 10−3  1.00 × 10−3  3.34 × 10−2   
81Partridg83   16.081–46.917  17/17/17  1.00 × 10−3  1.02 × 10−3  3.01 × 10−3   
05TaNaBrTe110   11 365–14 472  873/873/859  1.00 × 10−3  2.25 × 10−3  3.92 × 10−2   
08ToTe125   10 140–13 910  326/251/246  1.00 × 10−3  1.46 × 10−3  3.10 × 10−2   
12MiNaNiVa41   6 691.3–8 883.6  130/128/128  1.00 × 10−3  1.89 × 10−3  1.60 × 10−2   
14ReOuMiWa47   6 619.2–9 187.3  616/584/583  1.00 × 10−3  1.22 × 10−3  3.32 × 10−2   
15CaMiLoKa48   7 915.6–8 332.8  232/229/229  1.00 × 10−3  1.00 × 10−3  3.28 × 10−2   
18MiSeSi57   16 640–17 003  106/106/105  1.00 × 10−3  5.17 × 10−3  4.52 × 10−2   
18TaMiWaLi58   12 278–12 893  1283/1280/1272  1.00 × 10−3  1.24 × 10−3  2.36 × 10−2   
19LiLiZhWa59   12 057–12 260  441/437/424  1.00 × 10−3  1.00 × 10−3  2.17 × 10−2   
20VaNaSeSi65   14 912–15 598  661/661/661  1.00 × 10−3  1.67 × 10−3  1.92 × 10−2   
04MaRoMiNa108   6 170.8–6 746.9  232/231/228  2.00 × 10−3  1.39 × 10−3  3.82 × 10−2   
13LeMiMoKa44   5 855.5–6 604.9  266/264/264  2.00 × 10−3  1.18 × 10−3  3.45 × 10−2   
20SiSePoBy64   5 201.7–6 195.8  1071/1071/1070  2.00 × 10−3  1.11 × 10−3  4.05 × 10−2   
20compl  176.60–15 436  66/66/64  2.00 × 10−3  7.08 × 10−3  3.80 × 10−2   
05ToNaZoSh111   10 140–13 718  244/242/240  3.00 × 10−3  4.26 × 10−3  3.25 × 10−2   
07MaToCa122   11 547–12 728  326/323/312  3.00 × 10−3  2.82 × 10−3  4.52 × 10−2   
15MiSeSi49   15 127–15 941  106/106/106  3.00 × 10−3  3.00 × 10−3  2.03 × 10−2   
69FrNaJo68   3 444.5–3 942.4  103/102/99  5.00 × 10−3  4.97 × 10−3  3.96 × 10−2   
71WiNaJo71   1 338.3–1 912.6  133/132/116  5.00 × 10−3  6.87 × 10−3  4.46 × 10−2   
77ToFlCa76   5 174.2–5 524.9  84/81/78  5.00 × 10−3  1.89 × 10−3  4.50 × 10−2   
77ToFlCab77   7 093.7–7 333.3  20/20/17  5.00 × 10−3  7.23 × 10−3  3.93 × 10−2   
77Winther78   61.437–391.87  48/48/46  5.00 × 10−3  7.83 × 10−3  3.15 × 10−2   
80CaFlPa81   1 591.3–1 839.9  11/11/11  5.00 × 10−3  2.29 × 10−3  1.80 × 10−2   
83PiCoCaFl85   3 648.9–3 830.1  2/2/2  5.00 × 10−3  5.54 × 10−3  9.70 × 10−3   
05ToTe112   7 424.1–9 051.8  178/178/175  5.00 × 10−3  1.49 × 10−3  2.94 × 10−2   
06LiHuCaMa117   8 563.1–9 331.9  466/466/465  5.00 × 10−3  1.92 × 10−3  3.04 × 10−2   
06MaNaKaBy119   12 406–12 641  12/12/12  5.00 × 10−3  6.46 × 10−3  1.72 × 10−2   
06NaSnTaSh120   16 666–17 125  513/513/490  5.00 × 10−3  5.00 × 10−3  4.40 × 10−2   
12VaMiSeSi43   13 545–13 923  81/78/78  5.00 × 10−3  3.59 × 10−3  2.36 × 10−2   
78JoMc79   1 613.1–1 643.6  2/2/2  1.00 × 10−2  2.78 × 10−2  4.43 × 10−2   
Segment tag Range A/N/V ESU MSU LSU Recalib. factor
09PuCaHaVa127   6.471 2–18.413  5/5/5  2.00 × 10−8  2.00 × 10−8  3.00 × 10−8   
10GaFaCaMa32   7 084.0–7 222.3  2/2/2  3.34 × 10−7  3.34 × 10−7  3.34 × 10−7   
99MaNaNaOd100   15.671–177.15  125/125/125  1.40 × 10−6  1.53 × 10−6  2.72 × 10−5   
11Koshelev35   24.966–24.966  1/1/1  2.17 × 10−6  2.17 × 10−6  2.17 × 10−6   
71StBe70   0.451 50–6.471 2  2/2/2  3.34 × 10−6  3.34 × 10−6  3.34 × 10−6   
75LuHe74   18.413–24.966  2/2/2  3.34 × 10−6  9.97 × 10−6  1.51 × 10−5   
20virt  0.000 000–0.000 000  24/24/24  5.00 × 10−6  5.00 × 10−6  5.00 × 10−6   
20virt_S2  0.000 140–0.000 977  17/17/17  5.00 × 10−4  5.00 × 10−4  5.00 × 10−4   
20virt_S3  0.001 117–0.009 973  113/113/113  5.00 × 10−3  4.65 × 10−3  4.32 × 10−2   
92Toth93   23.774–23.774  1/1/1  2.00 × 10−5  2.00 × 10−5  2.00 × 10−5   
92Toth_S293   1 063.8–2 155.1  443/440/440  5.00 × 10−5  3.78 × 10−5  5.77 × 10−4   
92Toth_S393   1 011.9–2 224.2  258/258/255  5.00 × 10−4  1.86 × 10−4  3.22 × 10−3   
92Toth_S493   1 120.7–1 724.8  4/4/4  5.00 × 10−3  1.00 × 10−3  1.63 × 10−3   
93Toth94   1 314.1–3 938.9  84/84/84  5.00 × 10−5  5.00 × 10−5  4.39 × 10−4   
93Toth_S294   1 314.7–3 944.8  221/220/220  5.00 × 10−4  2.01 × 10−4  1.65 × 10−3   
93Toth_S394   1 898.6–3 679.7  33/33/33  5.00 × 10−3  1.03 × 10−3  5.59 × 10−3   
94Tothc95   3 254.1–4 080.4  350/350/350  5.00 × 10−5  4.96 × 10−5  7.44 × 10−4   
94Tothc_S295   3 223.7–4 242.7  407/406/406  5.00 × 10−4  2.59 × 10−4  2.21 × 10−3   
94Tothc_S395   3 223.2–4 216.0  68/68/68  5.00 × 10−3  1.35 × 10−3  3.14 × 10−2   
94Tothd96   6 752.6–7 301.0  11/11/11  5.00 × 10−5  5.00 × 10−5  2.60 × 10−4   
94Tothd_S296   6 619.9–7 639.2  580/579/578  5.00 × 10−4  4.21 × 10−4  3.76 × 10−2   
94Tothd_S396   6 616.8–7 540.1  264/263/261  5.00 × 10−3  1.29 × 10−3  3.01 × 10−2   
20MiBeOdTr63   48.030–665.56  619/618/618  5.00 × 10−5  4.32 × 10−5  6.69 × 10−3   
83Guelachv84   1 315.6–1 986.0  200/200/198  9.80 × 10−5  3.61 × 10−5  1.03 × 10−2  0.999 999 762 9 
17CaMiVaRe53   4 249.9–4 533.7  20/19/19  1.00 × 10−4  1.00 × 10−4  5.78 × 10−3   
17MoMiKaBe55   7 443.3–7 921.0  1596/1595/1593  1.00 × 10−4  2.27 × 10−4  1.71 × 10−2   
18MiMoKaKa56   6 667.7–7 449.2  3544/3530/3528  1.00 × 10−4  2.61 × 10−4  1.48 × 10−2   
73CaFlGuAm73   3 581.5–3 909.4  58/58/56  5.00 × 10−4  4.50 × 10−4  4.97 × 10−3   
98Toth98   599.00–797.32  31/31/31  5.00 × 10−4  2.63 × 10−4  8.06 × 10−3   
99CaFlMaBy99   9 711.8–11 335  1063/1063/1062  5.00 × 10−4  5.00 × 10−4  1.37 × 10−2   
02MiTyStAl103   4 206.7–4 999.1  8/8/8  5.00 × 10−4  2.68 × 10−4  4.36 × 10−3   
05Tothb113   5 018.3–5 684.7  312/312/312  5.00 × 10−4  2.15 × 10−4  4.19 × 10−3   
07JeDaReTy121   4 206.7–6 599.5  574/567/563  5.00 × 10−4  5.59 × 10−4  2.47 × 10−2   
09LiNaKaCa126   5 907.8–6 725.2  212/211/211  5.00 × 10−4  6.54 × 10−4  1.71 × 10−2   
11LeNaCa36   13 541–14 107  391/391/388  5.00 × 10−4  1.00 × 10−3  3.46 × 10−2   
11LeNaCab37   12 585–13 555  126/125/124  5.00 × 10−4  5.00 × 10−4  2.54 × 10−2   
11MiKaWaCa38   7 408.2–7 902.2  346/344/341  5.00 × 10−4  6.07 × 10−4  4.14 × 10−2   
12LeMiMoKa40   6 886.9–7 404.9  696/672/669  5.00 × 10−4  4.53 × 10−4  1.34 × 10−2   
16MiLeKaMo51   5 850.9–6 670.8  2512/2492/2487  5.00 × 10−4  4.89 × 10−4  3.64 × 10−2   
19MiKaVaMo60   5 693.5–5 988.4  188/185/185  5.00 × 10−4  3.79 × 10−4  4.11 × 10−2   
19MiMoKaKa61   5 693.0–5 849.9  502/502/502  5.00 × 10−4  4.31 × 10−4  1.41 × 10−2   
19ReThReMi62   6 531.3–7 801.3  1136/1128/1128  5.00 × 10−4  7.32 × 10−4  1.82 × 10−2   
07MiLeKaCa123   5 988.1–7 015.5  236/235/234  6.00 × 10−4  8.15 × 10−4  2.27 × 10−2   
17LoBiWa54   1 853.7–3 988.3  620/620/620  6.00 × 10−4  1.52 × 10−4  4.95 × 10−3   
78KaKaKy80   100.37–301.14  20/20/19  1.00 × 10−3  1.13 × 10−3  1.48 × 10−2   
80KaKy82   53.510–727.83  371/371/371  1.00 × 10−3  1.00 × 10−3  3.34 × 10−2   
81Partridg83   16.081–46.917  17/17/17  1.00 × 10−3  1.02 × 10−3  3.01 × 10−3   
05TaNaBrTe110   11 365–14 472  873/873/859  1.00 × 10−3  2.25 × 10−3  3.92 × 10−2   
08ToTe125   10 140–13 910  326/251/246  1.00 × 10−3  1.46 × 10−3  3.10 × 10−2   
12MiNaNiVa41   6 691.3–8 883.6  130/128/128  1.00 × 10−3  1.89 × 10−3  1.60 × 10−2   
14ReOuMiWa47   6 619.2–9 187.3  616/584/583  1.00 × 10−3  1.22 × 10−3  3.32 × 10−2   
15CaMiLoKa48   7 915.6–8 332.8  232/229/229  1.00 × 10−3  1.00 × 10−3  3.28 × 10−2   
18MiSeSi57   16 640–17 003  106/106/105  1.00 × 10−3  5.17 × 10−3  4.52 × 10−2   
18TaMiWaLi58   12 278–12 893  1283/1280/1272  1.00 × 10−3  1.24 × 10−3  2.36 × 10−2   
19LiLiZhWa59   12 057–12 260  441/437/424  1.00 × 10−3  1.00 × 10−3  2.17 × 10−2   
20VaNaSeSi65   14 912–15 598  661/661/661  1.00 × 10−3  1.67 × 10−3  1.92 × 10−2   
04MaRoMiNa108   6 170.8–6 746.9  232/231/228  2.00 × 10−3  1.39 × 10−3  3.82 × 10−2   
13LeMiMoKa44   5 855.5–6 604.9  266/264/264  2.00 × 10−3  1.18 × 10−3  3.45 × 10−2   
20SiSePoBy64   5 201.7–6 195.8  1071/1071/1070  2.00 × 10−3  1.11 × 10−3  4.05 × 10−2   
20compl  176.60–15 436  66/66/64  2.00 × 10−3  7.08 × 10−3  3.80 × 10−2   
05ToNaZoSh111   10 140–13 718  244/242/240  3.00 × 10−3  4.26 × 10−3  3.25 × 10−2   
07MaToCa122   11 547–12 728  326/323/312  3.00 × 10−3  2.82 × 10−3  4.52 × 10−2   
15MiSeSi49   15 127–15 941  106/106/106  3.00 × 10−3  3.00 × 10−3  2.03 × 10−2   
69FrNaJo68   3 444.5–3 942.4  103/102/99  5.00 × 10−3  4.97 × 10−3  3.96 × 10−2   
71WiNaJo71   1 338.3–1 912.6  133/132/116  5.00 × 10−3  6.87 × 10−3  4.46 × 10−2   
77ToFlCa76   5 174.2–5 524.9  84/81/78  5.00 × 10−3  1.89 × 10−3  4.50 × 10−2   
77ToFlCab77   7 093.7–7 333.3  20/20/17  5.00 × 10−3  7.23 × 10−3  3.93 × 10−2   
77Winther78   61.437–391.87  48/48/46  5.00 × 10−3  7.83 × 10−3  3.15 × 10−2   
80CaFlPa81   1 591.3–1 839.9  11/11/11  5.00 × 10−3  2.29 × 10−3  1.80 × 10−2   
83PiCoCaFl85   3 648.9–3 830.1  2/2/2  5.00 × 10−3  5.54 × 10−3  9.70 × 10−3   
05ToTe112   7 424.1–9 051.8  178/178/175  5.00 × 10−3  1.49 × 10−3  2.94 × 10−2   
06LiHuCaMa117   8 563.1–9 331.9  466/466/465  5.00 × 10−3  1.92 × 10−3  3.04 × 10−2   
06MaNaKaBy119   12 406–12 641  12/12/12  5.00 × 10−3  6.46 × 10−3  1.72 × 10−2   
06NaSnTaSh120   16 666–17 125  513/513/490  5.00 × 10−3  5.00 × 10−3  4.40 × 10−2   
12VaMiSeSi43   13 545–13 923  81/78/78  5.00 × 10−3  3.59 × 10−3  2.36 × 10−2   
78JoMc79   1 613.1–1 643.6  2/2/2  1.00 × 10−2  2.78 × 10−2  4.43 × 10−2   
a

Tags denote the segments used in this study. Bold entries are new segments compared to TG-H217O.17 The column “Range” indicates the range (in cm−1) corresponding to validated wavenumbers within the transition list. A is the number of assigned transitions, N is the number of non-redundant lines (with distinct wavenumbers or labels), and V is the number of validated transitions obtained at the end of the xMARVEL analysis. In the heading of this table, ESU, MSU, and LSU denote the estimated, the median, and the largest segment uncertainties in cm−1, respectively. Rows are arranged in the order of the ESUs with the restriction that the segments of the same data source should be listed consecutively.

TABLE 2.

Data source segments and their characteristics for the H218O moleculea

Segment tag Range A/N/V ESU MSU LSU Recalib. factor
06GoMaGuKn114   6.784 9–18.269  6/6/6  1.33 × 10−7  1.33 × 10−7  5.00 × 10−7   
11GaGaFaCa34   7 222.3–7 222.3  1/1/1  4.34 × 10−7  4.34 × 10−7  4.34 × 10−7   
87BeKoPoTr91   0.187 63–24.861  21/9/9  6.67 × 10−7  6.67 × 10−7  2.74 × 10−5   
10GaFaCaMa32   7 084.0–7 241.6  18/18/18  1.00 × 10−6  1.00 × 10−6  1.03 × 10−6   
99MaNaNaOd100   18.508–174.81  118/118/118  1.28 × 10−6  1.40 × 10−6  2.27 × 10−5   
70PoJo69   0.187 63–0.187 63  1/1/1  3.34 × 10−6  3.34 × 10−6  3.34 × 10−6   
71StBe70   0.187 63–6.784 9  2/2/2  3.34 × 10−6  5.13 × 10−6  6.93 × 10−6   
72LuHeCoGob72   6.784 9–24.861  11/11/11  3.34 × 10−6  3.34 × 10−6  8.39 × 10−6   
20virt  0.000 000–0.000 001  6/6/6  5.00 × 10−6  5.00 × 10−6  5.00 × 10−6   
20virt_S2  0.000 016–0.000 093  10/10/10  5.00 × 10−5  5.00 × 10−5  5.00 × 10−5   
20virt_S3  0.000 123–0.000 981  39/39/38  5.00 × 10−4  5.00 × 10−4  7.74 × 10−3   
20virt_S4  0.001 028–0.009 990  171/171/171  5.00 × 10−3  4.24 × 10−3  4.78 × 10−2   
92Toth93   23.755–23.755  1/1/1  1.00 × 10−5  1.00 × 10−5  1.00 × 10−5   
92Toth_S293   1 061.7–2 219.2  503/503/500  5.00 × 10−5  3.27 × 10−5  7.11 × 10−4   
92Toth_S393   1 009.6–2 198.8  247/247/245  5.00 × 10−4  1.54 × 10−4  1.17 × 10−2   
92Toth_S493   1 055.9–2 192.4  29/29/29  5.00 × 10−3  1.00 × 10−3  1.06 × 10−3   
93Toth94   1 341.9–3 874.1  186/186/186  5.00 × 10−5  5.21 × 10−5  8.54 × 10−4   
93Toth_S294   1 312.2–3 879.5  265/265/262  5.00 × 10−4  2.00 × 10−4  1.55 × 10−2   
93Toth_S394   2 969.9–3 622.9  10/10/10  5.00 × 10−3  1.08 × 10−3  4.80 × 10−3   
94Tothc95   3 227.6–4 236.4  321/321/320  5.00 × 10−5  4.64 × 10−5  1.84 × 10−3   
94Tothc_S295   3 117.1–4 290.8  590/589/582  5.00 × 10−4  2.13 × 10−4  8.13 × 10−3   
94Tothc_S395   3 212.5–4 340.2  127/126/126  5.00 × 10−3  1.00 × 10−3  7.65 × 10−3   
94Tothd96   7 114.4–7 360.1  22/22/22  5.00 × 10−5  9.41 × 10−5  4.44 × 10−4   
94Tothd_S296   6 608.1–7 607.7  503/481/480  5.00 × 10−4  3.29 × 10−4  2.03 × 10−2   
94Tothd_S396   6 608.0–7 639.3  440/430/426  5.00 × 10−3  1.00 × 10−3  4.82 × 10−2   
06JoPaZeCo115   1 483.9–1 485.0  2/2/2  5.00 × 10−5  1.94 × 10−5  2.88 × 10−5   
17LoBiWa54   1 853.3–3 994.7  1036/1036/1036  5.00 × 10−5  5.58 × 10−5  6.24 × 10−3   
20MiBeOdTr63   48.581–670.75  733/732/731  5.00 × 10−5  4.34 × 10−5  1.75 × 10−2   
83Guelachv84   1 253.9–2 053.0  306/306/305  7.20 × 10−5  3.08 × 10−5  1.37 × 10−2  0.999 999 773 1 
17CaMiVaRe53   4 249.8–4 533.3  32/32/32  1.00 × 10−4  5.72 × 10−4  3.54 × 10−3   
17MoMiKaBe55   7 443.8–7 919.0  639/637/636  1.00 × 10−4  4.91 × 10−4  1.94 × 10−2   
18MiMoKaKa56   6 667.7–7 442.6  1840/1808/1808  1.00 × 10−4  4.55 × 10−4  1.66 × 10−2   
85Johns88   33.179–280.32  145/145/145  2.00 × 10−4  1.24 × 10−4  1.05 × 10−2   
73CaFlGuAm73   3 533.5–3 935.6  128/126/126  5.00 × 10−4  2.65 × 10−4  2.49 × 10−2   
83PiCoCaFl85   3 512.4–3 889.6  35/33/33  5.00 × 10−4  7.32 × 10−4  2.43 × 10−3   
83ToBr86   3 717.8–3 738.0  3/3/3  5.00 × 10−4  1.68 × 10−4  2.20 × 10−4   
85ChMaFlCa87   4 433.7–6 086.9  1367/1363/1354  5.00 × 10−4  2.66 × 10−4  2.79 × 10−2   
86ChMaCaFlb89   5 924.2–7 862.2  2137/2137/2118  5.00 × 10−4  5.56 × 10−4  2.88 × 10−2   
86ChMaFlCa90   4 897.4–5 918.1  186/186/186  5.00 × 10−4  4.33 × 10−4  1.91 × 10−2   
87ChMaFlCa92   9 639.6–11 374  2093/2093/2078  5.00 × 10−4  4.59 × 10−4  2.52 × 10−2   
98Toth98   595.53–943.98  75/74/74  5.00 × 10−4  1.92 × 10−4  2.37 × 10−2   
01MoSaGiCi101   7 182.1–7 184.5  3/1/1  5.00 × 10−4  1.31 × 10−4  1.31 × 10−4   
03MiTyMe106   399.30–806.26  167/151/151  5.00 × 10−4  5.00 × 10−4  3.04 × 10−2   
06LiDuSoWa116   1 082.9–5 997.3  5233/5025/4990  5.00 × 10−4  3.74 × 10−4  4.10 × 10−2   
06LiNaSoVo118   6 000.7–8 003.0  3168/3055/3050  5.00 × 10−4  4.66 × 10−4  4.60 × 10−2   
07JeDaReTy121   4 201.0–6 599.2  1054/967/967  5.00 × 10−4  6.50 × 10−4  3.65 × 10−2   
08ToTe125   9 880.9–14 362  864/713/703  5.00 × 10−4  3.58 × 10−4  2.77 × 10−2   
09LiNaKaCa126   5 905.8–6 725.3  2015/1959/1959  5.00 × 10−4  5.00 × 10−4  2.84 × 10−2   
11MiKaWaCa38   7 410.5–7 917.1  537/512/508  5.00 × 10−4  4.43 × 10−4  4.13 × 10−2   
12LeMiMoKa40   6 886.7–7 405.8  1014/880/880  5.00 × 10−4  4.70 × 10−4  1.05 × 10−2   
12OuReMiTh42   1 005.7–2 331.9  1645/1508/1507  5.00 × 10−4  2.43 × 10−4  1.50 × 10−2   
16MiLeKaMo51   5 850.8–6 670.6  1170/999/999  5.00 × 10−4  5.90 × 10−4  2.32 × 10−2   
19MiKaVaMo60   5 693.0–5 990.5  204/200/200  5.00 × 10−4  4.21 × 10−4  2.55 × 10−2   
19MiMoKaKa61   5 693.0–5 848.8  178/177/177  5.00 × 10−4  5.00 × 10−4  2.32 × 10−2   
07MiLeKaCa123   5 918.1–7 015.0  454/453/453  6.00 × 10−4  7.35 × 10−4  1.62 × 10−2   
78KaKaKy80   55.233–370.51  62/61/60  1.00 × 10−3  1.44 × 10−3  1.56 × 10−2   
80KaKy82   53.571–725.11  369/369/369  1.00 × 10−3  1.00 × 10−3  2.38 × 10−2   
81Partridg83   21.588–46.800  16/14/14  1.00 × 10−3  1.00 × 10−3  2.36 × 10−3   
95ByNaPeSc97   11 600–12 696  736/736/731  1.00 × 10−3  1.56 × 10−3  3.17 × 10−2   
02MiTyStAl103   4 201.0–4 997.4  70/69/69  1.00 × 10−3  1.29 × 10−3  1.81 × 10−2   
02ScLeCaBr104   13 485–14 384  42/42/28  1.00 × 10−3  5.51 × 10−3  2.71 × 10−2   
05TaNaBrTe110   12 405–14 518  1087/1078/1065  1.00 × 10−3  1.69 × 10−3  3.32 × 10−2   
06MaNaKaBy119   11 741–12 664  66/66/65  1.00 × 10−3  3.36 × 10−3  2.58 × 10−2   
08NaVoMaTe124   12 209–12 607  4/4/3  1.00 × 10−3  6.64 × 10−3  1.14 × 10−2   
11LeNaCa36   13 541–14 112  1788/1707/1699  1.00 × 10−3  2.17 × 10−3  3.09 × 10−2   
11LeNaCab37   12 585–13 557  1214/1212/1203  1.00 × 10−3  2.07 × 10−3  3.95 × 10−2   
12MiNaNiVa41   6 522.5–9 136.7  1261/1170/1170  1.00 × 10−3  1.10 × 10−3  1.67 × 10−2   
13MiSeSiVa45   15 002–15 779  466/466/465  1.00 × 10−3  1.62 × 10−3  4.71 × 10−2   
14LiNaKaCa46   5 855.7–6 802.2  235/205/205  1.00 × 10−3  1.08 × 10−3  1.31 × 10−2   
14ReOuMiWa47   6 519.2–9 222.4  1429/1343/1343  1.00 × 10−3  1.35 × 10−3  3.36 × 10−2   
15CaMiLoKa48   7 917.1–8 337.1  425/412/412  1.00 × 10−3  1.00 × 10−3  4.15 × 10−2   
16CoCh50   10.756–4 983.9  7385/7379/7353  1.00 × 10−3  1.00 × 10−3  4.31 × 10−2   
18MiSeSi57   16 463–17 192  987/987/967  1.00 × 10−3  2.45 × 10−3  4.38 × 10−2   
18TaMiWaLi58   12 278–12 794  411/389/389  1.00 × 10−3  1.70 × 10−3  2.52 × 10−2   
19LiLiZhWa59   12 055–12 260  161/156/156  1.00 × 10−3  2.03 × 10−3  4.65 × 10−2   
19ReThReMi62   6 527.0–8 010.9  4236/4191/4189  1.00 × 10−3  1.00 × 10−3  4.57 × 10−2   
20VaNaSeSi65   15 057–15 495  94/92/90  1.00 × 10−3  1.98 × 10−3  1.82 × 10−2   
03ToTeShZo107   9 980.8–12 517  580/580/574  2.00 × 10−3  1.26 × 10−3  3.62 × 10−2   
04MaRoMiNa108   6 134.5–6 748.5  490/472/458  2.00 × 10−3  1.40 × 10−3  4.73 × 10−2   
04TaSnUbTe109   16 577–17 121  375/375/312  2.00 × 10−3  5.38 × 10−3  4.85 × 10−2   
13LeMiMoKa44   5 852.2–6 606.3  598/550/550  2.00 × 10−3  1.03 × 10−3  1.42 × 10−2   
20compl  33.197–16 957  319/319/289  2.00 × 10−3  4.95 × 10−3  4.72 × 10−2   
05ToNaZoSh111   9 251.5–14 384  736/729/724  3.00 × 10−3  3.70 × 10−3  4.16 × 10−2   
07MaToCa122   11 520–12 810  1833/1693/1670  3.00 × 10−3  2.33 × 10−3  4.89 × 10−2   
12DoTeOrCh39   6 508.3–6 959.8  343/343/343  3.00 × 10−3  1.21 × 10−3  1.61 × 10−2  1.000 002 863 4 
15MiSeSi49   15 002–16 014  816/444/444  3.00 × 10−3  3.00 × 10−3  4.72 × 10−2   
69FrNaJo68   3 347.7–4 028.6  618/616/578  5.00 × 10−3  6.38 × 10−3  4.92 × 10−2   
71WiNaJo71   1 334.3–1 955.0  234/234/214  5.00 × 10−3  5.26 × 10−3  4.74 × 10−2   
76FlGi75   13.030–39.995  11/11/11  5.00 × 10−3  1.09 × 10−3  4.46 × 10−3   
77ToFlCa76   5 036.9–5 638.0  527/527/511  5.00 × 10−3  2.56 × 10−3  4.68 × 10−2   
77ToFlCab77   6 974.6–7 386.8  372/372/351  5.00 × 10−3  5.09 × 10−3  4.63 × 10−2   
77Winther78   54.496–524.06  122/122/117  5.00 × 10−3  5.78 × 10−3  4.89 × 10−2   
02TaBrTe105   12 403–14 494  747/747/683  5.00 × 10−3  1.36 × 10−3  4.81 × 10−2   
05ToTe112   7 428.4–9 270.6  502/502/491  5.00 × 10−3  1.20 × 10−3  4.60 × 10−2   
06LiHuCaMa117   8 012.1–9 336.8  1533/1533/1532  5.00 × 10−3  1.64 × 10−3  3.74 × 10−2   
11BeMiCa33   13 563–14 039  19/19/19  5.00 × 10−3  7.30 × 10−3  2.55 × 10−2   
12VaMiSeSi43   13 397–14 442  724/709/707  5.00 × 10−3  3.15 × 10−3  3.37 × 10−2   
69BePoTo67   178.18–397.46  10/10/8  1.00 × 10−2  1.00 × 10−2  2.31 × 10−2  1.000 088 431 0 
78JoMc79   1 640.2–1 693.7  2/2/2  1.00 × 10−2  3.94 × 10−2  4.57 × 10−2   
Segment tag Range A/N/V ESU MSU LSU Recalib. factor
06GoMaGuKn114   6.784 9–18.269  6/6/6  1.33 × 10−7  1.33 × 10−7  5.00 × 10−7   
11GaGaFaCa34   7 222.3–7 222.3  1/1/1  4.34 × 10−7  4.34 × 10−7  4.34 × 10−7   
87BeKoPoTr91   0.187 63–24.861  21/9/9  6.67 × 10−7  6.67 × 10−7  2.74 × 10−5   
10GaFaCaMa32   7 084.0–7 241.6  18/18/18  1.00 × 10−6  1.00 × 10−6  1.03 × 10−6   
99MaNaNaOd100   18.508–174.81  118/118/118  1.28 × 10−6  1.40 × 10−6  2.27 × 10−5   
70PoJo69   0.187 63–0.187 63  1/1/1  3.34 × 10−6  3.34 × 10−6  3.34 × 10−6   
71StBe70   0.187 63–6.784 9  2/2/2  3.34 × 10−6  5.13 × 10−6  6.93 × 10−6   
72LuHeCoGob72   6.784 9–24.861  11/11/11  3.34 × 10−6  3.34 × 10−6  8.39 × 10−6   
20virt  0.000 000–0.000 001  6/6/6  5.00 × 10−6  5.00 × 10−6  5.00 × 10−6   
20virt_S2  0.000 016–0.000 093  10/10/10  5.00 × 10−5  5.00 × 10−5  5.00 × 10−5   
20virt_S3  0.000 123–0.000 981  39/39/38  5.00 × 10−4  5.00 × 10−4  7.74 × 10−3   
20virt_S4  0.001 028–0.009 990  171/171/171  5.00 × 10−3  4.24 × 10−3  4.78 × 10−2   
92Toth93   23.755–23.755  1/1/1  1.00 × 10−5  1.00 × 10−5  1.00 × 10−5   
92Toth_S293   1 061.7–2 219.2  503/503/500  5.00 × 10−5  3.27 × 10−5  7.11 × 10−4   
92Toth_S393   1 009.6–2 198.8  247/247/245  5.00 × 10−4  1.54 × 10−4  1.17 × 10−2   
92Toth_S493   1 055.9–2 192.4  29/29/29  5.00 × 10−3  1.00 × 10−3  1.06 × 10−3   
93Toth94   1 341.9–3 874.1  186/186/186  5.00 × 10−5  5.21 × 10−5  8.54 × 10−4   
93Toth_S294   1 312.2–3 879.5  265/265/262  5.00 × 10−4  2.00 × 10−4  1.55 × 10−2   
93Toth_S394   2 969.9–3 622.9  10/10/10  5.00 × 10−3  1.08 × 10−3  4.80 × 10−3   
94Tothc95   3 227.6–4 236.4  321/321/320  5.00 × 10−5  4.64 × 10−5  1.84 × 10−3   
94Tothc_S295   3 117.1–4 290.8  590/589/582  5.00 × 10−4  2.13 × 10−4  8.13 × 10−3   
94Tothc_S395   3 212.5–4 340.2  127/126/126  5.00 × 10−3  1.00 × 10−3  7.65 × 10−3   
94Tothd96   7 114.4–7 360.1  22/22/22  5.00 × 10−5  9.41 × 10−5  4.44 × 10−4   
94Tothd_S296   6 608.1–7 607.7  503/481/480  5.00 × 10−4  3.29 × 10−4  2.03 × 10−2   
94Tothd_S396   6 608.0–7 639.3  440/430/426  5.00 × 10−3  1.00 × 10−3  4.82 × 10−2   
06JoPaZeCo115   1 483.9–1 485.0  2/2/2  5.00 × 10−5  1.94 × 10−5  2.88 × 10−5   
17LoBiWa54   1 853.3–3 994.7  1036/1036/1036  5.00 × 10−5  5.58 × 10−5  6.24 × 10−3   
20MiBeOdTr63   48.581–670.75  733/732/731  5.00 × 10−5  4.34 × 10−5  1.75 × 10−2   
83Guelachv84   1 253.9–2 053.0  306/306/305  7.20 × 10−5  3.08 × 10−5  1.37 × 10−2  0.999 999 773 1 
17CaMiVaRe53   4 249.8–4 533.3  32/32/32  1.00 × 10−4  5.72 × 10−4  3.54 × 10−3   
17MoMiKaBe55   7 443.8–7 919.0  639/637/636  1.00 × 10−4  4.91 × 10−4  1.94 × 10−2   
18MiMoKaKa56   6 667.7–7 442.6  1840/1808/1808  1.00 × 10−4  4.55 × 10−4  1.66 × 10−2   
85Johns88   33.179–280.32  145/145/145  2.00 × 10−4  1.24 × 10−4  1.05 × 10−2   
73CaFlGuAm73   3 533.5–3 935.6  128/126/126  5.00 × 10−4  2.65 × 10−4  2.49 × 10−2   
83PiCoCaFl85   3 512.4–3 889.6  35/33/33  5.00 × 10−4  7.32 × 10−4  2.43 × 10−3   
83ToBr86   3 717.8–3 738.0  3/3/3  5.00 × 10−4  1.68 × 10−4  2.20 × 10−4   
85ChMaFlCa87   4 433.7–6 086.9  1367/1363/1354  5.00 × 10−4  2.66 × 10−4  2.79 × 10−2   
86ChMaCaFlb89   5 924.2–7 862.2  2137/2137/2118  5.00 × 10−4  5.56 × 10−4  2.88 × 10−2   
86ChMaFlCa90   4 897.4–5 918.1  186/186/186  5.00 × 10−4  4.33 × 10−4  1.91 × 10−2   
87ChMaFlCa92   9 639.6–11 374  2093/2093/2078  5.00 × 10−4  4.59 × 10−4  2.52 × 10−2   
98Toth98   595.53–943.98  75/74/74  5.00 × 10−4  1.92 × 10−4  2.37 × 10−2   
01MoSaGiCi101   7 182.1–7 184.5  3/1/1  5.00 × 10−4  1.31 × 10−4  1.31 × 10−4   
03MiTyMe106   399.30–806.26  167/151/151  5.00 × 10−4  5.00 × 10−4  3.04 × 10−2   
06LiDuSoWa116   1 082.9–5 997.3  5233/5025/4990  5.00 × 10−4  3.74 × 10−4  4.10 × 10−2   
06LiNaSoVo118   6 000.7–8 003.0  3168/3055/3050  5.00 × 10−4  4.66 × 10−4  4.60 × 10−2   
07JeDaReTy121   4 201.0–6 599.2  1054/967/967  5.00 × 10−4  6.50 × 10−4  3.65 × 10−2   
08ToTe125   9 880.9–14 362  864/713/703  5.00 × 10−4  3.58 × 10−4  2.77 × 10−2   
09LiNaKaCa126   5 905.8–6 725.3  2015/1959/1959  5.00 × 10−4  5.00 × 10−4  2.84 × 10−2   
11MiKaWaCa38   7 410.5–7 917.1  537/512/508  5.00 × 10−4  4.43 × 10−4  4.13 × 10−2   
12LeMiMoKa40   6 886.7–7 405.8  1014/880/880  5.00 × 10−4  4.70 × 10−4  1.05 × 10−2   
12OuReMiTh42   1 005.7–2 331.9  1645/1508/1507  5.00 × 10−4  2.43 × 10−4  1.50 × 10−2   
16MiLeKaMo51   5 850.8–6 670.6  1170/999/999  5.00 × 10−4  5.90 × 10−4  2.32 × 10−2   
19MiKaVaMo60   5 693.0–5 990.5  204/200/200  5.00 × 10−4  4.21 × 10−4  2.55 × 10−2   
19MiMoKaKa61   5 693.0–5 848.8  178/177/177  5.00 × 10−4  5.00 × 10−4  2.32 × 10−2   
07MiLeKaCa123   5 918.1–7 015.0  454/453/453  6.00 × 10−4  7.35 × 10−4  1.62 × 10−2   
78KaKaKy80   55.233–370.51  62/61/60  1.00 × 10−3  1.44 × 10−3  1.56 × 10−2   
80KaKy82   53.571–725.11  369/369/369  1.00 × 10−3  1.00 × 10−3  2.38 × 10−2   
81Partridg83   21.588–46.800  16/14/14  1.00 × 10−3  1.00 × 10−3  2.36 × 10−3   
95ByNaPeSc97   11 600–12 696  736/736/731  1.00 × 10−3  1.56 × 10−3  3.17 × 10−2   
02MiTyStAl103   4 201.0–4 997.4  70/69/69  1.00 × 10−3  1.29 × 10−3  1.81 × 10−2   
02ScLeCaBr104   13 485–14 384  42/42/28  1.00 × 10−3  5.51 × 10−3  2.71 × 10−2   
05TaNaBrTe110   12 405–14 518  1087/1078/1065  1.00 × 10−3  1.69 × 10−3  3.32 × 10−2   
06MaNaKaBy119   11 741–12 664  66/66/65  1.00 × 10−3  3.36 × 10−3  2.58 × 10−2   
08NaVoMaTe124   12 209–12 607  4/4/3  1.00 × 10−3  6.64 × 10−3  1.14 × 10−2   
11LeNaCa36   13 541–14 112  1788/1707/1699  1.00 × 10−3  2.17 × 10−3  3.09 × 10−2   
11LeNaCab37   12 585–13 557  1214/1212/1203  1.00 × 10−3  2.07 × 10−3  3.95 × 10−2   
12MiNaNiVa41   6 522.5–9 136.7  1261/1170/1170  1.00 × 10−3  1.10 × 10−3  1.67 × 10−2   
13MiSeSiVa45   15 002–15 779  466/466/465  1.00 × 10−3  1.62 × 10−3  4.71 × 10−2   
14LiNaKaCa46   5 855.7–6 802.2  235/205/205  1.00 × 10−3  1.08 × 10−3  1.31 × 10−2   
14ReOuMiWa47   6 519.2–9 222.4  1429/1343/1343  1.00 × 10−3  1.35 × 10−3  3.36 × 10−2   
15CaMiLoKa48   7 917.1–8 337.1  425/412/412  1.00 × 10−3  1.00 × 10−3  4.15 × 10−2   
16CoCh50   10.756–4 983.9  7385/7379/7353  1.00 × 10−3  1.00 × 10−3  4.31 × 10−2   
18MiSeSi57   16 463–17 192  987/987/967  1.00 × 10−3  2.45 × 10−3  4.38 × 10−2   
18TaMiWaLi58   12 278–12 794  411/389/389  1.00 × 10−3  1.70 × 10−3  2.52 × 10−2   
19LiLiZhWa59   12 055–12 260  161/156/156  1.00 × 10−3  2.03 × 10−3  4.65 × 10−2   
19ReThReMi62   6 527.0–8 010.9  4236/4191/4189  1.00 × 10−3  1.00 × 10−3  4.57 × 10−2   
20VaNaSeSi65   15 057–15 495  94/92/90  1.00 × 10−3  1.98 × 10−3  1.82 × 10−2   
03ToTeShZo107   9 980.8–12 517  580/580/574  2.00 × 10−3  1.26 × 10−3  3.62 × 10−2   
04MaRoMiNa108   6 134.5–6 748.5  490/472/458  2.00 × 10−3  1.40 × 10−3  4.73 × 10−2   
04TaSnUbTe109   16 577–17 121  375/375/312  2.00 × 10−3  5.38 × 10−3  4.85 × 10−2   
13LeMiMoKa44   5 852.2–6 606.3  598/550/550  2.00 × 10−3  1.03 × 10−3  1.42 × 10−2   
20compl  33.197–16 957  319/319/289  2.00 × 10−3  4.95 × 10−3  4.72 × 10−2   
05ToNaZoSh111   9 251.5–14 384  736/729/724  3.00 × 10−3  3.70 × 10−3  4.16 × 10−2   
07MaToCa122   11 520–12 810  1833/1693/1670  3.00 × 10−3  2.33 × 10−3  4.89 × 10−2   
12DoTeOrCh39   6 508.3–6 959.8  343/343/343  3.00 × 10−3  1.21 × 10−3  1.61 × 10−2  1.000 002 863 4 
15MiSeSi49   15 002–16 014  816/444/444  3.00 × 10−3  3.00 × 10−3  4.72 × 10−2   
69FrNaJo68   3 347.7–4 028.6  618/616/578  5.00 × 10−3  6.38 × 10−3  4.92 × 10−2   
71WiNaJo71   1 334.3–1 955.0  234/234/214  5.00 × 10−3  5.26 × 10−3  4.74 × 10−2   
76FlGi75   13.030–39.995  11/11/11  5.00 × 10−3  1.09 × 10−3  4.46 × 10−3   
77ToFlCa76   5 036.9–5 638.0  527/527/511  5.00 × 10−3  2.56 × 10−3  4.68 × 10−2   
77ToFlCab77   6 974.6–7 386.8  372/372/351  5.00 × 10−3  5.09 × 10−3  4.63 × 10−2   
77Winther78   54.496–524.06  122/122/117  5.00 × 10−3  5.78 × 10−3  4.89 × 10−2   
02TaBrTe105   12 403–14 494  747/747/683  5.00 × 10−3  1.36 × 10−3  4.81 × 10−2   
05ToTe112   7 428.4–9 270.6  502/502/491  5.00 × 10−3  1.20 × 10−3  4.60 × 10−2   
06LiHuCaMa117   8 012.1–9 336.8  1533/1533/1532  5.00 × 10−3  1.64 × 10−3  3.74 × 10−2   
11BeMiCa33   13 563–14 039  19/19/19  5.00 × 10−3  7.30 × 10−3  2.55 × 10−2   
12VaMiSeSi43   13 397–14 442  724/709/707  5.00 × 10−3  3.15 × 10−3  3.37 × 10−2   
69BePoTo67   178.18–397.46  10/10/8  1.00 × 10−2  1.00 × 10−2  2.31 × 10−2  1.000 088 431 0 
78JoMc79   1 640.2–1 693.7  2/2/2  1.00 × 10−2  3.94 × 10−2  4.57 × 10−2   
a

Tags denote the segments used in this study. Bold entries are new segments compared to TG-H218O. The column “Range” indicates the range (in cm−1) corresponding to the validated wavenumbers within the transition list. A is the number of assigned transitions, N is the number of non-redundant lines (with distinct wavenumbers or labels), and V is the number of validated transitions obtained at the end of the xMARVEL analysis. In the heading of this table, ESU, MSU, and LSU denote the estimated, the median, and the largest segment uncertainties in cm−1, respectively. Rows are arranged in the order of the ESUs with the restriction that the segments of the same data source should be listed consecutively.

The W2020-H217O dataset is composed of 27 045 assigned and 26 819 non-redundant transitions (the latter having distinct wavenumbers or labels), a threefold increase when compared to the TG-H217O database,17 which contains only 9034 lines. As seen in Table 1, the source 18MiMoKaKa56 reports the largest set of experimentally determined lines (3530). The W2020 database of H218O lines and levels, comprising 66 166 assigned and 63 972 non-redundant transitions, became more than twice as large as the one in Ref. 17, which contained 31 730 lines.

The W2020-H217O database contains 5278 rovibrational energy levels related to the PCs, which means that there are twice as many energy levels in the W2020 database than in TG-H217O.17 In the case of W2020-H218O, the increase in the number of empirical energy levels is not nearly as significant: the W2020-H218O compilation provides 6865 rovibrational energy levels, while the TG-H218O dataset is built up from 5133.17 The empirical rovibrational energy levels of H217O and H218O form a complete set through 3204 cm−1 and 4031 cm−1, respectively. All the W2020-H217O and W2020-H218O empirical energy levels are presented in the supplementary material.

The VBOs defined by the W2020-H217O and W2020-H218O experimental linelists are displayed in Tables 3 and 4, respectively. The number of experimentally known VBOs is 37 and 52 for H217O and H218O, respectively (due to the smaller number of measurements, the number of known VBOs is considerably less than for H216O, where this number is 133). All the VBOs are below 17 000 cm−1, and the highest ones [(3 2 1), (4 0 1), and (0 4 3)] belong to the P = 10 polyad for both isotopologues.

TABLE 3.

VBOs within the W2020-H217O dataseta

(v1v2v3) VBO/cm−1 (v1v2v3) VBO/cm−1
(0 0 0)  0.0  (2 0 1)  10 598.475 61(50) 
(0 1 0)  1591.325 696(61)  (1 0 2)  10 853.505 32(50) 
(0 2 0)  3144.980 73(13)  (0 0 3)  11 011.882 91(50) 
(1 0 0)  3653.142 265(50)  (1 3 1)  11 792.824 6(25) 
(0 0 1)  3748.318 070(54)  (3 1 0)  12 122.203 6(10) 
(1 1 0)  5227.705 62(50)  (2 1 1)  12 132.992 8(10) 
(0 1 1)  5320.251 07(14)  (1 1 2)  12 389.097 8(10) 
(0 4 0)  6121.547 92(50)  (0 1 3)  12 541.226 8(13) 
(1 2 0)  6764.725 64(79)  (2 2 1)  13 631.501 51(50) 
(0 2 1)  6857.272 54(10)  (3 0 1)  13 812.158 31(50) 
(2 0 0)  7193.244 79(10)  (1 0 3)  14 296.277 5(20) 
(1 0 1)  7238.713 84(17)  (0 7 1)  13 808.301 31(50) 
(0 0 2)  7431.076 86(25)  (2 3 1)  15 095.165 8(10) 
(1 3 0)  8260.775 60(50)  (4 1 0)  15 322.533 2(10) 
(0 3 1)  8356.527 88(10)  (3 1 1)  15 325.615 5(12) 
(2 1 0)  8749.903 61(10)  (1 1 3)  15 807.053 1(30) 
(1 1 1)  8792.550 69(10)  (3 2 1)  16 797.164 2(34) 
(0 1 2)  8982.869 2(50)  (4 0 1)  16 875.619 6(10) 
(1 2 1)  10 311.202 51(50)     
(v1v2v3) VBO/cm−1 (v1v2v3) VBO/cm−1
(0 0 0)  0.0  (2 0 1)  10 598.475 61(50) 
(0 1 0)  1591.325 696(61)  (1 0 2)  10 853.505 32(50) 
(0 2 0)  3144.980 73(13)  (0 0 3)  11 011.882 91(50) 
(1 0 0)  3653.142 265(50)  (1 3 1)  11 792.824 6(25) 
(0 0 1)  3748.318 070(54)  (3 1 0)  12 122.203 6(10) 
(1 1 0)  5227.705 62(50)  (2 1 1)  12 132.992 8(10) 
(0 1 1)  5320.251 07(14)  (1 1 2)  12 389.097 8(10) 
(0 4 0)  6121.547 92(50)  (0 1 3)  12 541.226 8(13) 
(1 2 0)  6764.725 64(79)  (2 2 1)  13 631.501 51(50) 
(0 2 1)  6857.272 54(10)  (3 0 1)  13 812.158 31(50) 
(2 0 0)  7193.244 79(10)  (1 0 3)  14 296.277 5(20) 
(1 0 1)  7238.713 84(17)  (0 7 1)  13 808.301 31(50) 
(0 0 2)  7431.076 86(25)  (2 3 1)  15 095.165 8(10) 
(1 3 0)  8260.775 60(50)  (4 1 0)  15 322.533 2(10) 
(0 3 1)  8356.527 88(10)  (3 1 1)  15 325.615 5(12) 
(2 1 0)  8749.903 61(10)  (1 1 3)  15 807.053 1(30) 
(1 1 1)  8792.550 69(10)  (3 2 1)  16 797.164 2(34) 
(0 1 2)  8982.869 2(50)  (4 0 1)  16 875.619 6(10) 
(1 2 1)  10 311.202 51(50)     
a

The label (v1v2v3) denotes a specific VBO, where v1, v2, and v3 are the standard normal-mode quantum numbers describing the symmetric stretch, bend, and asymmetric stretch vibrational excitations, respectively. The uncertainties related to the last two digits of the VBOs are provided in parentheses.

TABLE 4.

VBOs within the W2020-H218O dataseta

(v1v2v3) VBO (cm−1) (v1v2v3) VBO (cm−1) (v1v2v3) VBO (cm−1)
(0 0 0)  0.0  (0 1 2)  8 967.562 9(22)  (2 2 1)  13 612.710 7(10) 
(0 1 0)  1588.275 697(20)  (0 4 1)  9 795.331 50(50)  (4 0 0)  13 793.260 7(10) 
(0 2 0)  3139.050 022(14)  (2 2 0)  10 256.584 86(50)  (3 0 1)  13 795.401 00(50) 
(1 0 0)  3649.685 347(61)  (1 2 1)  10 295.634 00(40)  (1 2 2)  13 870.485 5(10) 
(0 0 1)  3741.566 834(52)  (0 2 2)  10 483.221 46(50)  (0 2 3)  14 015.510 7(10) 
(0 3 0)  4648.477 21(15)  (3 0 0)  10 573.916 86(50)  (2 0 2)  14 187.987 4(50) 
(1 1 0)  5221.243 96(50)  (2 0 1)  10 585.285 00(10)  (1 0 3)  14 276.337 8(10) 
(0 1 1)  5310.462 005(51)  (1 0 2)  10 839.955 96(50)  (0 7 1)  13 784.246 1(10) 
(0 4 0)  6110.423 71(15)  (0 0 3)  10 993.680 65(25)  (2 3 1)  15 073.955(20) 
(1 2 0)  6755.510 76(20)  (2 3 0)  11 734.525 1(30)  (4 1 0)  15 303.032 1(10) 
(0 2 1)  6844.598 59(10)  (1 3 1)  11 774.707 6(10)  (3 1 1)  15 305.804 6(10) 
(2 0 0)  7185.877 68(10)  (0 3 2)  11 963.537 2(30)  (2 1 2)  15 703.506 2(30) 
(1 0 1)  7228.877 76(10)  (3 1 0)  12 106.977 7(30)  (1 1 3)  15 784.299 0(14) 
(0 0 2)  7418.723 44(68)  (2 1 1)  12 116.797 6(10)  (3 2 1)  16 775.383 7(28) 
(1 3 0)  8249.038 37(50)  (1 1 2)  12 372.704 9(10)  (4 0 1)  16 854.990 9(20) 
(0 3 1)  8341.104 45(10)  (0 1 3)  12 520.122 0(10)  (0 4 3)  16 906.206 5(10) 
(2 1 0)  8739.528 6(28)  (2 4 0)  13 167.718 4(10)     
(1 1 1)  8779.718 98(21)  (1 4 1)  13 212.678 2(10)     
(v1v2v3) VBO (cm−1) (v1v2v3) VBO (cm−1) (v1v2v3) VBO (cm−1)
(0 0 0)  0.0  (0 1 2)  8 967.562 9(22)  (2 2 1)  13 612.710 7(10) 
(0 1 0)  1588.275 697(20)  (0 4 1)  9 795.331 50(50)  (4 0 0)  13 793.260 7(10) 
(0 2 0)  3139.050 022(14)  (2 2 0)  10 256.584 86(50)  (3 0 1)  13 795.401 00(50) 
(1 0 0)  3649.685 347(61)  (1 2 1)  10 295.634 00(40)  (1 2 2)  13 870.485 5(10) 
(0 0 1)  3741.566 834(52)  (0 2 2)  10 483.221 46(50)  (0 2 3)  14 015.510 7(10) 
(0 3 0)  4648.477 21(15)  (3 0 0)  10 573.916 86(50)  (2 0 2)  14 187.987 4(50) 
(1 1 0)  5221.243 96(50)  (2 0 1)  10 585.285 00(10)  (1 0 3)  14 276.337 8(10) 
(0 1 1)  5310.462 005(51)  (1 0 2)  10 839.955 96(50)  (0 7 1)  13 784.246 1(10) 
(0 4 0)  6110.423 71(15)  (0 0 3)  10 993.680 65(25)  (2 3 1)  15 073.955(20) 
(1 2 0)  6755.510 76(20)  (2 3 0)  11 734.525 1(30)  (4 1 0)  15 303.032 1(10) 
(0 2 1)  6844.598 59(10)  (1 3 1)  11 774.707 6(10)  (3 1 1)  15 305.804 6(10) 
(2 0 0)  7185.877 68(10)  (0 3 2)  11 963.537 2(30)  (2 1 2)  15 703.506 2(30) 
(1 0 1)  7228.877 76(10)  (3 1 0)  12 106.977 7(30)  (1 1 3)  15 784.299 0(14) 
(0 0 2)  7418.723 44(68)  (2 1 1)  12 116.797 6(10)  (3 2 1)  16 775.383 7(28) 
(1 3 0)  8249.038 37(50)  (1 1 2)  12 372.704 9(10)  (4 0 1)  16 854.990 9(20) 
(0 3 1)  8341.104 45(10)  (0 1 3)  12 520.122 0(10)  (0 4 3)  16 906.206 5(10) 
(2 1 0)  8739.528 6(28)  (2 4 0)  13 167.718 4(10)     
(1 1 1)  8779.718 98(21)  (1 4 1)  13 212.678 2(10)     
a

See footnote a to Table 3.

For H217O, already the (0 3 0) bending overtone, at about 4660 cm−1, is missing. Similarly, the (0 5 0) bending overtone is not present among the P = 5 VBOs. The coverage becomes much less complete above 11 000 cm−1, which is about the height of the barrier to linearity of water.160–162 For H218O, the situation is similar: the first missing VBO is the (0 5 0) bending overtone. Beyond P = 5, the high bending excitations are systematically missing. It would be of interest to design high-resolution spectroscopic experiments aiming at the determination of the missing VBOs of these two minor water isotopologues.

The accuracy of the VBOs appears to be outstanding for both H217O and H218O. Even the least accurately known fundamental of H217O, the (0 1 0) bending fundamental, has an uncertainty of 6.1 × 10−5 cm−1. For H218O, the least accurate fundamental, (1 0 0), is derived with a remarkable uncertainty of 6.1 × 10−5 cm−1.

As an independent validation of the transition wavenumbers, the derived empirical rovibrational energies and the labels of the W2020-H217O and W2020-H218O datasets were compared in a systematic and mostly automated way with the results of variational nuclear-motion calculations128 and the energies of the so-called SISAM database.154 The SISAM dataset154 was probably the largest and most accurate energy-level set for both H217O and H218O available prior to this study. These comparisons were executed in order to identify and exclude from the W2020 database those transitions that would lead to energy levels with large deviations from well-established FP or empirical/experimental values.

Figures 4 and 5 show the unsigned deviations (UDs) corresponding to the comparison of the W2020 and SISAM energy levels for H217O and H218O, respectively. As can be seen there, the average UD is about 5 × 10−4 cm−1 for both molecules. These figures also reveal that occasionally the differences are quite large (UD > 0.1 cm−1). These large deviations may be attributed to those energy values of the SISAM dataset that were deduced from only very few (one or two) observed (but unreported) transitions via CD relations. As an example, one of the largest deviations is for the H217O level (0 1 1)141,14, with an UD of 0.94 cm−1. The W2020-H217O estimate, 7341.595 03(50) cm−1, relies on two experimental lines, of 07JeDaReTy121 and 20SiSePoBy,64 while the SISAM value, 7342.538 51(300) cm−1, can be found in Table 2 of 05Tothb,113 and according to this table, it was calculated from one line not listed in 05Tothb. In addition, one can extract 7341.60 cm−1 from the HotWat78 energy list, which corroborates the W2020 energy. Based on these findings, we feel that the SISAM datum should be incorrect, and, therefore, we decided to retain our estimate, confirmed by two independent data sources, in the W2020-H217O dataset. A detailed, one-by-one analysis of the outliers of Figs. 4 and 5 is beyond the scope of this paper. The list of the incorrect SISAM lines can be found in the supplementary material.

FIG. 4.

Unsigned deviations of the SISAM154 states from their W2020-H217O counterparts.

FIG. 4.

Unsigned deviations of the SISAM154 states from their W2020-H217O counterparts.

Close modal
FIG. 5.

Unsigned deviations of the SISAM154 states from their W2020-H218O counterparts.

FIG. 5.

Unsigned deviations of the SISAM154 states from their W2020-H218O counterparts.

Close modal

The empirical energy levels of this study were also matched with their FP counterparts listed in the HotWat78128 state list. The UDs for H217O and H218O are plotted in Figs. 6 and 7, respectively. Figures 6 and 7 show that for both molecules, the average UD is about 0.01 cm−1, a very pleasing agreement from the point of view of the underlying fourth-age14 quantum-chemical computations. This means that the FP energy levels are of considerable accuracy, significantly better than what could have been achieved even just a decade ago, mostly due to our improved understanding of how potential energy hypersurfaces can be refined based on available empirical energy values. Thus, the line positions calculated from FP energies and augmented with high-accuracy FP intensities are of considerable utility for the design of new experiments aimed at the observation of experimentally unknown rovibrational states.

FIG. 6.

Unsigned deviations of the HotWat78128 energies from their W2020-H217O counterparts.

FIG. 6.

Unsigned deviations of the HotWat78128 energies from their W2020-H217O counterparts.

Close modal
FIG. 7.

Unsigned deviations of the HotWat78128 energies from their W2020-H218O counterparts.

FIG. 7.

Unsigned deviations of the HotWat78128 energies from their W2020-H218O counterparts.

Close modal

Our H217O and H218O xMARVEL linelists were also compared with the 20MiKaMoCa66 lines (see Figs. 8 and 9, respectively). Figure 8 shows that all H217O CRDS/FTS lines could be reproduced within 8 × 10−3 cm−1. In the case of the H217O CA-CRDS lines, 4399 lines out of 5329 could be reproduced within 5 × 10−4 cm−1, and only 74 labeling conflicts were found. As to H218O, 43 and 83 discrepancies were identified between the 20MiKaMoCa and W2020 labels for the CA-CRDS and CRDS/FTS lines, respectively. Figure 9 shows that for H218O, all the CRDS/FTS lines could be reproduced within 9 × 10−3 cm−1 and 3367 out of 4570 CA-CRDS lines could be matched within 5 × 10−5 cm−1.

FIG. 8.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H217O counterparts.

FIG. 8.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H217O counterparts.

Close modal
FIG. 9.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H218O counterparts.

FIG. 9.

Unsigned deviations of the 20MiKaMoCa66 lines from their W2020-H218O counterparts.

Close modal

In Sec. 2.4, a procedure was described for obtaining PE energy levels for H217O and H218O with an accuracy approaching that of Fourier-transform infrared (FT-IR) measurements, based on the available empirical and FP energies of H216O. The first set of PE levels for H217O and H218O, relying on empirical energy values for H216O available at that time, was reported in Ref. 128. When these levels were tested against empirical levels of H216O of this study, it turned out that only about 95% of the PE levels were within the standard deviation of 0.02 cm−1. The outliers helped us to derive criteria, detailed below, to remove insufficiently accurate PE levels, yielding the final set reported in this study. For cleansing the PE energy-level set, we adopted what we call the F and G criteria.

Criterion F is based on the quantity

F v , r = 2 E v , r PE ( 17 ) E v , r PE ( 16 ) E v , r PE ( 18 ) ,
(5)

reflecting the empirical connection

E v , r PE ( 17 ) [ E v , r PE ( 16 ) + E v , r PE ( 18 ) ] / 2 .
(6)

Through the analysis of the Fv,r residuals, one can monitor the smoothness of the changes within the H216O–H217O–H218O series. If the Fv,r values are in the [Fmin, Fmax] interval, where Fmin and Fmax are selected to be 0 cm−1 and 7 cm−1, respectively, and the related Ka dependence is adequately smooth, then we say that the underlying PE levels satisfy criterion F. In the opposite case, the anomalous PE levels, not following a rigorous trend, have been excluded from further consideration.

Criterion G involves the use of the residuals

G v , r ( X ) = E v , r PE ( X ) E v , r ref ( X ) ,
(7)

where E v , r ref ( X ) (X = 17, 18) denotes the accurate reference energy values taken from 08ShZoOvPo.163 If Gv,r(X) ∈ [Gmin, Gmax] for a given (v, r) state, where Gmin and Gmax are set to −0.07 and +0.07 cm−1, respectively, then it is said that the underlying PE level obeys criterion G. Otherwise, this PE state is deemed to be unreliable.

The parameters of the F and G criteria, that is, Fmin, Fmax, Gmin, and Gmax, were chosen so that about 99% of the newly derived levels of Refs. 55, 57, and 58 coincided with our PE levels within 0.0045 cm−1 for H217O and 0.0090 cm−1 for H218O. The PE levels obtained were then compared with the much more extensive xMARVEL states of this study. This comparison also helped to deduce a consistent set of labels for the H216O–H217O–H218O series.

In particular, from the about 19 200 H216O levels of this study, about 14 950 and 14 650 PE energy levels were obtained for H217O and H218O, respectively, without the use of the F and G criteria. The loss of more than 4000 levels is due to issues with the unique identification of the FP states beyond the W2020 list. The joint use of the F and G criteria reduces the number of PE levels to 10 600 and 10 060 for H217O and H218O, respectively. These constitute the final PE energy collections of this study, which have average absolute deviations of 0.004 cm−1 and 0.008 cm−1 against the W2020-H217O and W2020-H218O datasets, respectively. Ignoring those states whose empirical energies are available in the W2020-H2XO datasets, 9925/6270 and 8409/4602 PE levels were obtained for H217O and H218O, respectively, without/with the use of the F and G criteria. These four datasets are reported in the supplementary material. Table 5 shows statistics related to the comparison of the PE energies with their xMARVEL counterparts.

TABLE 5.

Comparison of the PE energies with their xMARVEL counterparts

Absolute residual (cm−1) H217O H218O Comment
<0.005  2777  2025  Perfect 
0.005–0.05  1475  3288  Good 
>0.05  61  105  Inaccurate 
All  4313  5428   
Absolute residual (cm−1) H217O H218O Comment
<0.005  2777  2025  Perfect 
0.005–0.05  1475  3288  Good 
>0.05  61  105  Inaccurate 
All  4313  5428   

The HITRAN2016 information system4 embraces a considerable number of transitions for H217O and H218O, as they are needed in a number of engineering and scientific applications, including atmospheric modeling (see Sec. 10, as well). For H217O, there are 27 543 transitions going up to 19 945.257 cm−1, while for H218O 39 901 transitions can be found in HITRAN2016, covering the range of 0.052 cm−1–19 917.617 cm−1. Since xMARVEL works with the measured line positions and the labels of the experimental transitions and it results in empirical energy levels, only three types of spectroscopic information, i.e., the lower state energy values, the transition wavenumbers, and their assignments, were examined within HITRAN2016. After a detailed comparison of the W2020-H217O and W2020-H218O databases with their HITRAN2016 analogs, issues falling into three main categories could be diagnosed.

  • Forbidden transitions. Employing the rovibrational symmetry of the lower and upper states, 159 and 10 forbidden transitions were discovered in HITRAN2016 for H217O and H218O, respectively. There is no such trouble with the W2020 datasets. The problems observed are collated in the supplementary material. The cause of these incorrect lines is not completely clear, but these issues can be remedied straightforwardly during the construction of the next version of HITRAN.

  • Missing upper labels. Both HITRAN2016 datasets exhibit a significant number of transitions, namely, 8258 (H217O) and 5588 (H218O), where the labels of the upper states are missing. For many of these unassigned upper states (697 and 402, respectively), feasible W2020 recommendations were found. The other unknown upper levels within HITRAN2016 are derived from theoretical computations164 and not from measurements; thus, new experiments need to be performed to properly characterize the remaining unassigned lines. The list of the HITRAN2016 lines with missing labels and the corresponding W2020 recommendations is presented in the supplementary material. Experimental high-resolution spectroscopists are encouraged to utilize this list, as well as the collection of the unlabeled transitions, to ensure an even more complete coverage of H217O and H218O spectra for future HITRAN editions. At the same time, it is important to point out that the intensities of the unassigned lines, where available, are quite low; therefore, these HITRAN entries may not be overly important for most applications where line-by-line databases of water isotopologues are needed.

  • Inaccurate line positions and labeling conflicts. Matching HITRAN2016 lines with their xMARVEL-predicted counterparts was guided by the HITRAN2016 labels, adopting a reasonable matching condition,

| σ HITRAN σ xMARVEL | max 1 0 6 × E HITRAN up , δ xMARVEL ,
(8)

where σHITRAN and σxMARVEL are the HITRAN and xMARVEL predictions of a particular line, respectively, E HITRAN up is the upper energy of the given transition in HITRAN2016, and δxMARVEL is the estimated uncertainty of σxMARVEL. In total, 949 and 1057 lines not satisfying Eq. (8) were found and explored for H217O and H218O, respectively. There are at least three feasible reasons that help explain the mismatches. First, some line positions are different due to a labeling conflict between W2020 and HITRAN2016. In this case, assuming that the label of the lower state is the same, the HITRAN2016 line was attempted to be relabeled to its xMARVEL counterpart. Second, certain HITRAN2016 transitions come only from theoretical sources, without having publicly available experimental counterparts. In this case, obviously, W2020 cannot be utilized to improve the HITRAN2016 dataset. Third, xMARVEL predictions may be considerably more accurate than their HITRAN2016 siblings. In these cases, the line positions should be replaced with the xMARVEL wavenumbers during the next update of HITRAN. Overall, 44 and 329 entries of the H217O and H218O datasets should be reassigned, respectively, while for the rest of the problems found, the third reason applies, and thus, these HITRAN2016 entries should be replaced by their xMARVEL counterparts.

The inclusion of quadrupole-allowed lines in the W2020-H216O dataset, taken from 20CaKaYaKy152 and 20CaSoSoYa,153 strongly affects the structure of the underlying SN. This structural change is manifested in the violation of the bipartite character27,28,165 of the original SN formed only by dipole-allowed transitions, making the presence of odd-numbered cycles allowed (note that in bipartite SNs, only even-membered cycles are permitted). This effect should be taken into account during the validation of the rovibrational labels.

Recording extremely weak quadrupole-allowed lines of water vapor is a truly significant success from an experimental (and from a technical) point of view. Nevertheless, the accuracy of the line positions determined in Refs. 152 and 153 is significantly less than either that of recent (CA-)CRDS measurements or our xMARVEL predictions (see Table 6). It can be seen from Table 6 that the uncertainties of the xMARVEL estimates are around 1 × 10−4 cm−1–2 × 10−4 cm−1, except for one wavenumber derived from NICE-OHMS transitions,15 which has an accuracy of 6 × 10−7 cm−1, while the deviations between the xMARVEL and the observed values are on the order of 1 × 10−4 cm−1–7 × 10−3 cm−1. On the one hand, this means that, to date, the quadrupole-allowed line positions of H216O can be determined more precisely in an empirical way than by direct observation, though this situation may change in the near future. On the other hand, the data show that the xMARVEL energy levels are accurate enough to serve as a basis to search for further quadrupole-allowed transitions (the search should be helped with accurate FP quadrupole intensities).

TABLE 6.

Comparison of quadrupole-allowed transitions of H216O reported in 20CaKaYaKy152 and 20CaSoSoYa153 with their xMARVEL counterparts. The residuals are relative to the xMARVEL predictions

σobs (cm−1) σxMARVEL (cm−1) Residual (cm−1) Upper state Lower state
1819.727  1819.727 66(3)  −0.000 7  (0 1 0)60,6  (0 0 0)40,4 
1926.040  1926.039 33(3)  0.000 7  (0 1 0)90,9  (0 0 0)70,7 
4032.147  4032.148 23(9)  −0.001 2  (0 0 1)53,3  (0 0 0)32,1 
4040.838  4040.838 14(1)  −0.000 1  (0 0 1)80,8  (0 0 0)61,6 
4041.450  4041.449 03(5)  0.001 0  (0 0 1)81,8  (0 0 0)60,6 
4052.893  4052.895 17(9)  −0.002 2  (0 0 1)72,6  (0 0 0)51,4 
4071.454  4071.455 24(1)  −0.001 2  (0 0 1)63,4  (0 0 0)42,2 
4083.035  4083.031 18(1)  0.003 8  (0 0 1)82,7  (0 0 0)61,5 
4100.719  4100.718 42(9)  0.000 6  (1 0 0)72,5  (0 0 0)50,5 
4106.763  4106.762 74(9)  0.000 3  (0 0 1)73,5  (0 0 0)52,3 
4108.852  4108.852 77(9)  −0.000 8  (0 0 1)64,2  (0 0 0)43,2 
4150.162  4150.162 70(3)  −0.000 7  (0 0 1)74,4  (0 0 0)53,2 
7474.6325  7474.635 0(1)  −0.002 5  (1 0 1)61,5  (0 0 0)42,3 
7475.4020  7475.400 7(1)  0.001 3  (1 0 1)52,4  (0 0 0)31,2 
7488.5747  7488.577 769 9(6)  −0.003 1  (1 0 1)66,0  (0 0 0)55,0 
7488.9183  7488.922 4(1)  −0.004 1  (1 0 1)70,7  (0 0 0)51,5 
7490.3117  7490.312 1(1)  −0.000 4  (1 0 1)71,7  (0 0 0)50,5 
7533.4649  7533.464 4(1)  0.000 5  (1 0 1)72,6  (0 0 0)51,4 
7551.7653  7551.764 7(1)  0.000 6  (1 0 1)91,9  (0 0 0)70,7 
7581.1247  7581.117 3(2)  0.007 4  (1 0 1)100,10  (0 0 0)81,8 
7613.8512  7613.848 8(1)  0.002 4  (1 0 1)102,9  (0 0 0)81,7 
σobs (cm−1) σxMARVEL (cm−1) Residual (cm−1) Upper state Lower state
1819.727  1819.727 66(3)  −0.000 7  (0 1 0)60,6  (0 0 0)40,4 
1926.040  1926.039 33(3)  0.000 7  (0 1 0)90,9  (0 0 0)70,7 
4032.147  4032.148 23(9)  −0.001 2  (0 0 1)53,3  (0 0 0)32,1 
4040.838  4040.838 14(1)  −0.000 1  (0 0 1)80,8  (0 0 0)61,6 
4041.450  4041.449 03(5)  0.001 0  (0 0 1)81,8  (0 0 0)60,6 
4052.893  4052.895 17(9)  −0.002 2  (0 0 1)72,6  (0 0 0)51,4 
4071.454  4071.455 24(1)  −0.001 2  (0 0 1)63,4  (0 0 0)42,2 
4083.035  4083.031 18(1)  0.003 8  (0 0 1)82,7  (0 0 0)61,5 
4100.719  4100.718 42(9)  0.000 6  (1 0 0)72,5  (0 0 0)50,5 
4106.763  4106.762 74(9)  0.000 3  (0 0 1)73,5  (0 0 0)52,3 
4108.852  4108.852 77(9)  −0.000 8  (0 0 1)64,2  (0 0 0)43,2 
4150.162  4150.162 70(3)  −0.000 7  (0 0 1)74,4  (0 0 0)53,2 
7474.6325  7474.635 0(1)  −0.002 5  (1 0 1)61,5  (0 0 0)42,3 
7475.4020  7475.400 7(1)  0.001 3  (1 0 1)52,4  (0 0 0)31,2 
7488.5747  7488.577 769 9(6)  −0.003 1  (1 0 1)66,0  (0 0 0)55,0 
7488.9183  7488.922 4(1)  −0.004 1  (1 0 1)70,7  (0 0 0)51,5 
7490.3117  7490.312 1(1)  −0.000 4  (1 0 1)71,7  (0 0 0)50,5 
7533.4649  7533.464 4(1)  0.000 5  (1 0 1)72,6  (0 0 0)51,4 
7551.7653  7551.764 7(1)  0.000 6  (1 0 1)91,9  (0 0 0)70,7 
7581.1247  7581.117 3(2)  0.007 4  (1 0 1)100,10  (0 0 0)81,8 
7613.8512  7613.848 8(1)  0.002 4  (1 0 1)102,9  (0 0 0)81,7 

With the appearance of 10GaFaCaMa,32 one of the earliest sets of rovibrational Lamb-dip spectroscopy results became available for water isotopologues. While this study listed only two ultraprecise transitions for H217O, it provided 18 lines for H218O. All these transitions were characterized with an accuracy of 30 kHz,32 in stark contrast to traditional high-resolution spectroscopy measurements, which have uncertainties of 3 MHz–300 MHz, mainly limited by Doppler broadening. It is worth discussing these ground-breaking results for H218O in view of developments in precision spectroscopy15 and the spectroscopic-network approach.

Figure 10 shows the network formed by the 18 observations for H218O provided by 10GaFaCaMa, all referring to the (0 0 0) and (1 0 1) vibrational states. It is obvious from Fig. 10 that the lines of 10GaFaCaMa form five components without any cycles, making the checking of their internal consistency and precision impossible. Furthermore, these ultraprecise measurements are not connected to the (0 0 0)00,0 or (0 0 0)10,1 states, limiting their utility for the extremely precise determination of the underlying energy levels. Fortunately, there are highly accurate transitions from 06GoMaGuKn114 that help connect the states involved in the lines of 10GaFaCaMa. As also clearly shown in Fig. 10, these additional experimental results allow the formation of connected paths with the quite fragmented set of 10GaFaCaMa transitions, allowing the accurate derivation of the ortho energy levels [panel (a)] via the extended Ritz principle.15 As to the para path [panel (b) of Fig. 10], further precision-spectroscopy measurements should be designed and performed to connect its starting node [(0 0 0)21,1] to the rovibrational ground state.

FIG. 10.

Pictorial representation of all the non-isolated precision measurements performed for ortho- [panel (a)] and para-H218O [panel (b)]. The J K a , K c rotational labels within the squares/circles for the para/ortho nuclear-spin isomers of H218O represent rovibrational states, whose (v1v2v3) vibrational labels are indicated in the left-hand-side legend with different colors. Transitions denoted with brown, blue, and cyan arrows are results from 06GoMaGuKn,114 10GaFaCaMa,32 and 11GaGaFaCa,34 respectively. Lines are associated with their experimental frequencies (in kHz) and the uncertainties of the last few frequency digits (in parentheses).

FIG. 10.

Pictorial representation of all the non-isolated precision measurements performed for ortho- [panel (a)] and para-H218O [panel (b)]. The J K a , K c rotational labels within the squares/circles for the para/ortho nuclear-spin isomers of H218O represent rovibrational states, whose (v1v2v3) vibrational labels are indicated in the left-hand-side legend with different colors. Transitions denoted with brown, blue, and cyan arrows are results from 06GoMaGuKn,114 10GaFaCaMa,32 and 11GaGaFaCa,34 respectively. Lines are associated with their experimental frequencies (in kHz) and the uncertainties of the last few frequency digits (in parentheses).

Close modal

As the data of Tables 7 and 8 demonstrate, the agreement of the present xMARVEL results is almost perfect not only with the transitions but also with the energy-level separations of 10GaFaCaMa (see Tables 1 and 2 of Ref. 32). It is important to emphasize that in 2011, the (1 0 1)22,0 ← (0 0 0)22,1 transition was remeasured and extrapolated to zero pressure, as reported in another paper by the Gianfrani group.34 This newly observed frequency differs from the result of 10GaFaCaMa by 35 kHz, exemplifying how substantial the pressure shift is at this level of precision. The present xMARVEL value agrees with the improved experimental datum34 within 6 kHz.

TABLE 7.

Comparison of the 10GaFaCaMa32 lines to their xMARVEL counterparts for H218O

Assignment f(10GaFaCaMa) (kHz) f(xMARVEL) (kHz) Residual (kHz)
(1 0 1)43,1 ← (0 0 0)53,2  212 372 948 620  212 372 948 629  −9 
(1 0 1)43,1 ← (0 0 0)43,2  216 163 440 240  216 163 440 231 
(1 0 1)33,1 ← (0 0 0)43,2  213 284 147 000  213 284 146 983  17 
(1 0 1)33,1 ← (0 0 0)33,0  216 191 670 190  216 191 670 207  −17 
(1 0 1)32,2 ← (0 0 0)42,3  213 593 222 590  213 593 222 621  −31 
(1 0 1)32,2 ← (0 0 0)32,1  216 226 026 160  216 226 026 129  31 
(1 0 1)22,0 ← (0 0 0)32,1  214 200 946 980  214 200 946 980 
(1 0 1)22,0 ← (0 0 0)22,1  216 519 045 920  216 519 045 950  −30 
(1 0 1)31,3 ← (0 0 0)41,4  214 079 703 410  214 079 703 428  −18 
(1 0 1)31,3 ← (0 0 0)31,2  215 607 014 210  215 607 014 192  18 
(1 0 1)21,1 ← (0 0 0)31,2  214 282 880 600  214 282 880 599 
(1 0 1)21,1 ← (0 0 0)21,2  217 097 759 250  217 097 759 251  −1 
(1 0 1)22,1 ← (0 0 0)32,2  214 338 783 640  214 338 783 628  12 
(1 0 1)22,1 ← (0 0 0)22,0  216 436 513 940  216 436 513 952  −12 
(1 0 1)21,2 ← (0 0 0)31,3  214 727 582 030  214 727 582 001  29 
(1 0 1)21,2 ← (0 0 0)21,1  216 129 993 490  216 129 993 519  −29 
(1 0 1)11,1 ← (0 0 0)21,2  215 384 571 430  215 384 571 426 
(1 0 1)11,1 ← (0 0 0)11,0  216 492 761 020  216 492 761 024  −4 
Assignment f(10GaFaCaMa) (kHz) f(xMARVEL) (kHz) Residual (kHz)
(1 0 1)43,1 ← (0 0 0)53,2  212 372 948 620  212 372 948 629  −9 
(1 0 1)43,1 ← (0 0 0)43,2  216 163 440 240  216 163 440 231 
(1 0 1)33,1 ← (0 0 0)43,2  213 284 147 000  213 284 146 983  17 
(1 0 1)33,1 ← (0 0 0)33,0  216 191 670 190  216 191 670 207  −17 
(1 0 1)32,2 ← (0 0 0)42,3  213 593 222 590  213 593 222 621  −31 
(1 0 1)32,2 ← (0 0 0)32,1  216 226 026 160  216 226 026 129  31 
(1 0 1)22,0 ← (0 0 0)32,1  214 200 946 980  214 200 946 980 
(1 0 1)22,0 ← (0 0 0)22,1  216 519 045 920  216 519 045 950  −30 
(1 0 1)31,3 ← (0 0 0)41,4  214 079 703 410  214 079 703 428  −18 
(1 0 1)31,3 ← (0 0 0)31,2  215 607 014 210  215 607 014 192  18 
(1 0 1)21,1 ← (0 0 0)31,2  214 282 880 600  214 282 880 599 
(1 0 1)21,1 ← (0 0 0)21,2  217 097 759 250  217 097 759 251  −1 
(1 0 1)22,1 ← (0 0 0)32,2  214 338 783 640  214 338 783 628  12 
(1 0 1)22,1 ← (0 0 0)22,0  216 436 513 940  216 436 513 952  −12 
(1 0 1)21,2 ← (0 0 0)31,3  214 727 582 030  214 727 582 001  29 
(1 0 1)21,2 ← (0 0 0)21,1  216 129 993 490  216 129 993 519  −29 
(1 0 1)11,1 ← (0 0 0)21,2  215 384 571 430  215 384 571 426 
(1 0 1)11,1 ← (0 0 0)11,0  216 492 761 020  216 492 761 024  −4 
TABLE 8.

Energy separation between selected pairs of pure rotational levels of H218O

State pair ΔE(10GaFaCaMa32) (kHz) ΔE(xMARVEL) (kHz) Residual (kHz)
(0 0 0)21,2 − (0 0 0)11,0  1 108 189 590  1 108 189 597  −7 
(0 0 0)31,3 − (0 0 0)21,1  1 402 411 460  1 402 411 517  −57 
(0 0 0)41,4 − (0 0 0)31,2  1 527 310 800  1 527 310 764  36 
(0 0 0)32,2 − (0 0 0)22,0  2 097 730 300  2 097 730 325  −25 
(0 0 0)32,1 − (0 0 0)22,1  2 318 098 940  2 318 098 970  −30 
(0 0 0)42,3 − (0 0 0)32,1  2 632 803 570  2 632 803 509  61 
(0 0 0)31,2 − (0 0 0)21,2  2 814 878 650  2 814 878 651  −1 
(0 0 0)43,2 − (0 0 0)33,0  2 907 523 190  2 907 523 223  −33 
(0 0 0)53,2 − (0 0 0)43,2  3 790 491 620  3 790 491 602  18 
State pair ΔE(10GaFaCaMa32) (kHz) ΔE(xMARVEL) (kHz) Residual (kHz)
(0 0 0)21,2 − (0 0 0)11,0  1 108 189 590  1 108 189 597  −7 
(0 0 0)31,3 − (0 0 0)21,1  1 402 411 460  1 402 411 517  −57 
(0 0 0)41,4 − (0 0 0)31,2  1 527 310 800  1 527 310 764  36 
(0 0 0)32,2 − (0 0 0)22,0  2 097 730 300  2 097 730 325  −25 
(0 0 0)32,1 − (0 0 0)22,1  2 318 098 940  2 318 098 970  −30 
(0 0 0)42,3 − (0 0 0)32,1  2 632 803 570  2 632 803 509  61 
(0 0 0)31,2 − (0 0 0)21,2  2 814 878 650  2 814 878 651  −1 
(0 0 0)43,2 − (0 0 0)33,0  2 907 523 190  2 907 523 223  −33 
(0 0 0)53,2 − (0 0 0)43,2  3 790 491 620  3 790 491 602  18 

Linelists of water isotopologues are often employed to simulate laboratory as well as “solar” spectra of interest to atmospheric scientists. These simulations require accurate line positions, intensities, widths (broadening, self, and foreign), and shifts (self and foreign). The W2020 database in itself contributes only to the simulation of transition wavenumbers, though it can be straightforwardly complemented with FP computed intensities. Absorption features due to water vapor are notoriously ubiquitous throughout the extended (far- and near-) infrared region, making knowledge of water lines important on their own right. At the same time, water is the major interferent during the retrieval of other gases in atmospheres.166–168 Thus, the spectroscopy of water vapor must be nearly perfect in its own windows, as well as in those windows where gases other than water are retrieved.166,168,169 As to our own planet, the amount of water varies several orders of magnitude in the Earth’s atmosphere.167,170 Therefore, detailed coverage and outstanding line-to-line and window-to-window consistency is needed in water vapor spectroscopy. As seen in Table 9, which provides details about the line position coverage with different absorption intensity cutoff values for H216O, H217O, and H218O, as well as in Figs. 11–15, providing details about spectrum coverage, this is indeed achieved by entries of the W2020 dataset. The linelists of H216O, H217O, and H218O produced during this study are presented in the supplementary material.

TABLE 9.

Number of FP (Ref. 156 for H216O and HotWat78128 for H217O and H218O), xMARVEL, and PE transitions of three water isotopologues, with different intensity cutoff values in cm molecule−1. The intensities correspond to room temperature (T = 296 K), and those of the minor isotopologues are corrected with their natural terrestrial isotopic abundances. The PE data (also including those levels with existing xMARVEL counterparts) are obtained both with (FG) and without (noFG) the use of the F and G criteria, which are explained in the text

Species Cutoff No. of FP No. of xMARVEL No. of PE(FG) No. of PE(noFG)
H216 10−26  35 394  35 349  …  … 
10−27  60 535  58 876  …  … 
10−28  101 646  88 925  …  … 
10−29  168 007  125 882  …  … 
10−30  273 614  171 283  …  … 
H217 10−26  4 341  4 322  4 339  4 339 
10−27  8 383  8 085  8 358  8 368 
10−28  15 535  14 054  15 331  15 426 
10−29  27 782  22 181  26 548  27 143 
10−30  48 103  32 407  43 070  45 026 
H218 10−26  7 025  7 027  7 025  7 025 
10−27  13 145  13 117  13 133  13 135 
10−28  23 674  22 949  23 413  23 505 
10−29  41 550  36 313  39 410  40 151 
10−30  70 765  52 501  60 673  63 218 
Species Cutoff No. of FP No. of xMARVEL No. of PE(FG) No. of PE(noFG)
H216 10−26  35 394  35 349  …  … 
10−27  60 535  58 876  …  … 
10−28  101 646  88 925  …  … 
10−29  168 007  125 882  …  … 
10−30  273 614  171 283  …  … 
H217 10−26  4 341  4 322  4 339  4 339 
10−27  8 383  8 085  8 358  8 368 
10−28  15 535  14 054  15 331  15 426 
10−29  27 782  22 181  26 548  27 143 
10−30  48 103  32 407  43 070  45 026 
H218 10−26  7 025  7 027  7 025  7 025 
10−27  13 145  13 117  13 133  13 135 
10−28  23 674  22 949  23 413  23 505 
10−29  41 550  36 313  39 410  40 151 
10−30  70 765  52 501  60 673  63 218 
FIG. 11.

Room-temperature (T = 296 K), one-photon, dipole-allowed H216O linelist up to 30 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL line positions and PoKaZaTeL156 line positions. In the cases where both datasets provide estimates for the same transition wavenumber, only the xMARVEL value is retained in the figure. The intensities are taken from Ref. 156. Completeness of the xMARVEL data is clearly visible.

FIG. 11.

Room-temperature (T = 296 K), one-photon, dipole-allowed H216O linelist up to 30 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL line positions and PoKaZaTeL156 line positions. In the cases where both datasets provide estimates for the same transition wavenumber, only the xMARVEL value is retained in the figure. The intensities are taken from Ref. 156. Completeness of the xMARVEL data is clearly visible.

Close modal
FIG. 12.

Room-temperature one-photon, dipole-allowed H217O linelist up to 14 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL and the HotWat78128 line positions. In the cases where both datasets provide estimates for the same transition wavenumber, only the xMARVEL value is retained in the figure. The intensities are taken from Ref. 128.

FIG. 12.

Room-temperature one-photon, dipole-allowed H217O linelist up to 14 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL and the HotWat78128 line positions. In the cases where both datasets provide estimates for the same transition wavenumber, only the xMARVEL value is retained in the figure. The intensities are taken from Ref. 128.

Close modal
FIG. 13.

Room-temperature one-photon, dipole-allowed H217O linelist up to 30 000 cm−1, with an intensity cutoff of 10−30 cm molecule−1, based on xMARVEL, HotWat78,128 and PE line positions. In the cases where a wavenumber is provided by more than one dataset, only the most accurate value is retained in the figure, following the xMARVEL > HotWat78 > PE accuracy relations. The intensities are taken from Ref. 128.

FIG. 13.

Room-temperature one-photon, dipole-allowed H217O linelist up to 30 000 cm−1, with an intensity cutoff of 10−30 cm molecule−1, based on xMARVEL, HotWat78,128 and PE line positions. In the cases where a wavenumber is provided by more than one dataset, only the most accurate value is retained in the figure, following the xMARVEL > HotWat78 > PE accuracy relations. The intensities are taken from Ref. 128.

Close modal
FIG. 14.

Room-temperature one-photon, dipole-allowed H218O linelist up to 30 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL line positions. The intensities are taken from Ref. 128.

FIG. 14.

Room-temperature one-photon, dipole-allowed H218O linelist up to 30 000 cm−1, with an intensity cutoff of 10−26 cm molecule−1, based on xMARVEL line positions. The intensities are taken from Ref. 128.

Close modal
FIG. 15.

Room-temperature one-photon, dipole-allowed H218O linelist up to 30 000 cm−1, with an intensity cutoff of 10−30 cm molecule−1, based on xMARVEL, HotWat78,128 and PE line positions. In the cases where a wavenumber is provided by more than one dataset, only the most accurate value is retained in the figure, following the xMARVEL > HotWat78 > PE accuracy relations. The intensities are taken from Ref. 128.

FIG. 15.

Room-temperature one-photon, dipole-allowed H218O linelist up to 30 000 cm−1, with an intensity cutoff of 10−30 cm molecule−1, based on xMARVEL, HotWat78,128 and PE line positions. In the cases where a wavenumber is provided by more than one dataset, only the most accurate value is retained in the figure, following the xMARVEL > HotWat78 > PE accuracy relations. The intensities are taken from Ref. 128.

Close modal

The structure and the data of Table 9 need a brief explanation. Taking into account all factors influencing water vapor measurements in the Earth’s atmosphere, it is safe to assume that room-temperature absorption intensities smaller than 5 × 10−28 cm molecule−1 are unlikely to be of concern for line-by-line database developers. Then, it is valid to question how complete the W2020 dataset is with respect to different intensity cutoffs for H216O. Of course, minor isotopologues contributing to water spectra should also be considered. The natural abundances of 16O, 17O, and 18O are ∼0.9976, 0.0004, and 0.0020, respectively. Of course, enrichment should also be considered if the focus were on laboratory spectra. It is necessary to emphasize that in Table 9, the intensities are corrected for the natural terrestrial isotopic abundances. Then, the data of Table 9 show the total number of transitions with different intensity cutoff values computed via accurate FP techniques and the number of transitions known after the present xMARVEL analyses, with and without PE lines augmenting the xMARVEL data. As seen there, almost all of the lines above 10−26 cm molecule−1 are known as a result of the present xMARVEL analyses (more than 99% of the lines are known based on the W2020 data) and more than 60% are empirically available using the cutoff value of 10−30 cm molecule−1 for each isotopologue. Thus, W2020 provides truly remarkable coverage with an outstanding accuracy, as discussed above.

Figures 11–15 display the coverage of water lines based on the W2020 datasets at 296 K. Clearly, with an intensity cutoff of 10−26 cm molecule−1, the W2020 dataset can be considered complete for all three water isotopologues. Inclusion of PE lines, based on PE rovibrational energy levels, makes our predictions much more complete in between 10−26 and 10−30 cm molecule−1. Thus, new experimental results guided by the PE predictions would be highly beneficial for further improving the simulations of water vapor applicable to atmospheric modeling.

The principal results of the present study are the W2020 datasets for three H2XO isotopologues (X = 16, 17, 18). The W2020 databases contain all rovibrational transitions of these isotopologues collated from the literature, with appropriate labels and uncertainties, as well as empirical energy levels, with well-defined uncertainties, obtained from the measured line positions. The xMARVEL protocol30,31 was employed to perform the analysis of the experimental rovibrational transitions of these water isotopologues. xMARVEL was able to validate the great majority of the measurements and yielded a consistent set of uncertainties for the observed transitions and the derived energy values.

The improvements compared to previous extensive compilations17,18 available in the literature for these water isotopologues were achieved in several steps. The most important aspects and the consequences of these steps are summarized below.

First, the W2020-H216O dataset31 was updated with three relevant sources53,63,102 to facilitate the subsequent analysis of the high-resolution spectroscopic data of H217O and H218O. As part of this step, some of the labels in the original W2020-H216O dataset31 were changed so that the dataset now mimics considerably better than before (and even supersedes) the limited SISAM154 and 20MiKaMoCa66 linelists. The most important advantages of the updated W2020-H216O dataset are that (a) it comprises essentially all the transitions accessible within the SISAM dataset, providing the base of the HITRAN2016 linelists, but occasionally with considerably higher accuracy, and (b) it shows full agreement with the lines of Ref. 66 with significant absorption intensities.

Second, all sources published after 2010 on high-resolution spectra of H217O and H218O were gathered and added to the W2020 dataset together with the results of those studies missed during the compilation of the TG-H217O and TG-H218O databases.16,17 Due to this comprehensive search, 35 and 37 new experimental sources were appended to the TG-H217O and TG-H218O line catalogs, respectively. The W2020-H217O list consists of 27 045 transitions, yielding 5278 empirical energies with statistically dependable uncertainties. Although the W2020-H217O database became three times larger than the original TG-H217O collection, the number of empirical energy values determined by these transitions increased only twofold, while the number of newly derived energy levels is even less favorable for H218O. The W2020-H218O dataset contains 66 166 transitions; thus, it is about twice as large as its parent TG database.17 Nevertheless, the number of accurately deduced empirical energy levels increased from 5133 to only 6865. These statistics are not only important in themselves, but they also provide a warning to spectroscopists that there is considerable room to improve the design of high-resolution experiments if the goal is to extend our knowledge about the rovibrational energy levels of water isotopologues (needless to say, the same holds for all molecules).

The empirical energies of the W2020 datasets allowed the creation of accurate linelists with well-defined uncertainties for all three H2XO isotopologues, which represent one of the most significant results of the present study. It must also be mentioned that the overwhelming majority of the theoretical lines are associated with xMARVEL predictions for all three species considered, providing a much improved coverage compared to the empirical information extracted from the previous TG-H2XO databases.16–20 The rovibrational states unknown from experiments but necessary to obtain full coverage are listed, together with their approximate energies, in the supplementary material.

Third, a concerted effort was made to “optimize” the uncertainties attached to the observed lines entering the xMARVEL analysis. This means that the uncertainties were decreased as much as feasible within certain experimental limitations. The upgraded uncertainties are utilized to classify the transitions of a particular source into segments,30 as required by the xMARVEL protocol. Note that xMARVEL is capable of retaining the accuracy of the most precise experimental lines during the xMARVEL analysis and transferring that to the empirical energy values to the maximal extent allowed by the deviations of the line positions.

Fourth, the best set of consistent labels was created for the rovibrational states of the H2XO isotopologues, synchronizing the H217O and H218O labels with their W2020-H216O counterparts. Therefore, we believe that, whenever possible, the labels of the rovibrational states included in the three W2020-H2XO databases are consistent with each other.

Fifth, based on trends characterizing the differences (residuals) of FP and empirical energies for the various H2XO isotopologues, so-called PE energy values128 were derived, which provide enhanced accuracy for yet-to-be-observed rovibrational states of H217O and H218O. These PE levels, whose accuracy should be close to that of standard FT-IR measurements, can be employed to supplement the empirical energies coming from the xMARVEL procedure. When PE levels are involved in the generation of spectra based on W2020 energies, a considerably improved coverage can be obtained, especially for the visible part of the water spectra, where whole new bands appear (with intensities below 10−28 cm molecule−1). It must be noted that during the course of this work, a small number of so far unobserved H216O levels were identified, which could also be determined using the PE scheme, by inverting the parent–daughter roles of the water species. These H216O energy levels will be presented elsewhere, alongside an analysis of what matching these levels for different isotopologues tells us about limits of the Born–Oppenheimer approximation.

As to the final conclusion of this study, we recommend that both the validated rovibrational transitions and the accurate empirical energy levels of this study should be included in the next generation of line-by-line spectroscopic information systems, such as HITRAN.4 

See the supplementary material for lists of transitions and energy levels characterizing the W2020 dataset of H216O, H217O, and H218O, as well as for PE levels of H217O and H218O and the problematic transitions of the SISAM dataset and the HITRAN2016 information system. A room-temperature linelist based principally on empirical (xMARVEL) energy levels is also provided, employing an intensity cutoff of 10−30 cm molecule−1.

The work performed in Budapest received support from NKFIH (Grant No. K119658), from the ELTE Institutional Excellence Program (Grant No. TKP2020-IKA-05) financed by the Hungarian Ministry of Human Capacities, and from the grant VEKOP-2.3.2-16-2017-000. The work performed in the United Kingdom received support from the UK Natural Environment Research Council (NERC) through Grant No. NE/T000767/1 and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme through Advance Grant No. 883830. The joint work between the Budapest and London groups received support from the COST Action MOLIM (Molecules in Motion, CM1405), also in the form of a Short Term Scientific Mission (STSM) awarded to A.G.C. The work performed by A.A.K. and R.I.O. was supported by State Project IAP RAS No. 0035-2019-0016. O.L.P. and N.F.Z. were funded by RFBR under Project No. 18-02-00577. Dr. Eamon Conway is thanked for fruitful discussions concerning the HITRAN datasets of H216O, H217O, and H218O.

The data that support the findings of this study are available within the article and its supplementary material and on the ReSpecTh website at http://ReSpecTh.hu.

1.
R. P.
Wayne
,
Chemistry of Atmospheres
, 3rd ed. (
Oxford University Press
,
New York
,
2000
).
2.
P. F.
Bernath
,
Phys. Chem. Chem. Phys.
4
,
1501
(
2002
).
3.
C. D.
Boone
,
K. A.
Walker
, and
P. F.
Bernath
,
J. Quant. Spectrosc. Radiat. Transfer
105
,
525
(
2007
).
4.
I. E.
Gordon
,
L. S.
Rothman
,
C.
Hill
,
R. V.
Kochanov
,
Y.
Tan
,
P. F.
Bernath
,
M.
Birk
,
V.
Boudon
,
A.
Campargue
,
K. V.
Chance
,
B. J.
Drouin
,
J.-M.
Flaud
,
R. R.
Gamache
,
J. T.
Hodges
,
D.
Jacquemart
,
V. I.
Perevalov
,
A.
Perrin
,
K. P.
Shine
,
M.-A. H.
Smith
,
J.
Tennyson
,
G. C.
Toon
,
H.
Tran
,
V. G.
Tyuterev
,
A.
Barbe
,
A. G.
Császár
,
V. M.
Devi
,
T.
Furtenbacher
,
J. J.
Harrison
,
J.-M.
Hartmann
,
A.
Jolly
,
T. J.
Johnson
,
T.
Karman
,
I.
Kleiner
,
A. A.
Kyuberis
,
J.
Loos
,
O. M.
Lyulin
,
S. T.
Massie
,
S. N.
Mikhailenko
,
N.
Moazzen-Ahmadi
,
H. S. P.
Müller
,
O. V.
Naumenko
,
A. V.
Nikitin
,
O. L.
Polyansky
,
M.
Rey
,
M.
Rotger
,
S. W.
Sharpe
,
K.
Sung
,
E.
Starikova
,
S. A.
Tashkun
,
J.
Vander Auwera
,
G.
Wagner
,
J.
Wilzewski
,
P.
Wcisło
,
S.
Yu
, and
E. J.
Zak
,
J. Quant. Spectrosc. Radiat. Transfer
203
,
3
(
2017
).
5.
J. L.
Hall
,
Rev. Mod. Phys.
78
,
1279
(
2006
).
6.
T. W.
Hänsch
,
Rev. Mod. Phys.
78
,
1297
(
2006
).
7.
Handbook of High-Resolution Spectroscopy
, edited by
M.
Quack
and
F.
Merkt
(
Wiley
,
New York
,
2014
).
8.
S.
Twagirayezu
,
M. J.
Cich
,
T. J.
Sears
,
C. P.
McRaven
, and
G. E.
Hall
,
J. Mol. Spectrosc.
316
,
64
(
2015
).
9.
L.
Santamaria
,
V.
Di Sarno
,
P.
De Natale
,
M.
De Rosa
,
M.
Inguscio
,
S.
Mosca
,
I.
Ricciardi
,
D.
Calonico
,
F.
Levi
, and
P.
Maddaloni
,
Phys. Chem. Chem. Phys.
18
,
16715
(
2016
).
10.
D.
Gatti
,
R.
Gotti
,
A.
Gambetta
,
M.
Belmonte
,
G.
Galzerano
,
P.
Laporta
, and
M.
Marangoni
,
Sci. Rep.
6
,
27183
(
2016
).
11.
J.
Wang
,
Y. R.
Sun
,
L.-G.
Tao
,
A.-W.
Liu
,
T.-P.
Hua
,
F.
Meng
, and
S.-M.
Hu
,
Rev. Sci. Instrum.
88
,
043108
(
2017
).
12.
Z. D.
Reed
,
D. A.
Long
,
H.
Fleurbaey
, and
J. T.
Hodges
,
Optica
7
,
1209
(
2020
).
13.
K.
Pachucki
and
J.
Komasa
,
Phys. Chem. Chem. Phys.
12
,
9188
(
2010
).
14.
A. G.
Császár
,
C.
Fábri
,
T.
Szidarovszky
,
E.
Mátyus
,
T.
Furtenbacher
, and
G.
Czakó
,
Phys. Chem. Chem. Phys.
14
,
1085
(
2012
).
15.
R.
Tóbiás
,
T.
Furtenbacher
,
I.
Simkó
,
A. G.
Császár
,
M. L.
Diouf
,
F. M. J.
Cozijn
,
J. M. A.
Staa
,
E. J.
Salumbides
, and
W.
Ubachs
,
Nat. Commun.
11
,
1708
(
2020
).
16.
J.
Tennyson
,
P. F.
Bernath
,
L. R.
Brown
,
A.
Campargue
,
M. R.
Carleer
,
A. G.
Császár
,
R. R.
Gamache
,
J. T.
Hodges
,
A.
Jenouvrier
,
O. V.
Naumenko
,
O. L.
Polyansky
,
L. S.
Rothman
,
R. A.
Toth
,
A. C.
Vandaele
,
N. F.
Zobov
,
L.
Daumont
,
A. Z.
Fazliev
,
T.
Furtenbacher
,
I. E.
Gordon
,
S. N.
Mikhailenko
, and
S. V.
Shirin
,
J. Quant. Spectrosc. Radiat. Transfer
110
,
573
(
2009
).
17.
J.
Tennyson
,
P. F.
Bernath
,
L. R.
Brown
,
A.
Campargue
,
A. G.
Császár
,
L.
Daumont
,
R. R.
Gamache
,
J. T.
Hodges
,
O. V.
Naumenko
,
O. L.
Polyansky
,
L. S.
Rothman
,
R. A.
Toth
,
A. C.
Vandaele
,
N. F.
Zobov
,
S.
Fally
,
A. Z.
Fazliev
,
T.
Furtenbacher
,
I. E.
Gordon
,
S.-M.
Hu
,
S. N.
Mikhailenko
, and
B. A.
Voronin
,
J. Quant. Spectrosc. Radiat. Transfer
111
,
2160
(
2010
).
18.
J.
Tennyson
,
P. F.
Bernath
,
L. R.
Brown
,
A.
Campargue
,
A. G.
Császár
,
L.
Daumont
,
R. R.
Gamache
,
J. T.
Hodges
,
O. V.
Naumenko
,
O. L.
Polyansky
,
L. S.
Rothman
,
A. C.
Vandaele
,
N. F.
Zobov
,
A. R.
Al Derzi
,
C.
Fábri
,
A. Z.
Fazliev
,
T.
Furtenbacher
,
I. E.
Gordon
,
L.
Lodi
, and
I. I.
Mizus
,
J. Quant. Spectrosc. Radiat. Transfer
117
,
29
(
2013
).
19.
J.
Tennyson
,
P. F.
Bernath
,
L. R.
Brown
,
A.
Campargue
,
A. G.
Császár
,
L.
Daumont
,
R. R.
Gamache
,
J. T.
Hodges
,
O. V.
Naumenko
,
O. L.
Polyansky
,
L. S.
Rothman
,
A. C.
Vandaele
,
N. F.
Zobov
,
N.
Dénes
,
A. Z.
Fazliev
,
T.
Furtenbacher
,
I. E.
Gordon
,
S.-M.
Hu
,
T.
Szidarovszky
, and
I. A.
Vasilenko
,
J. Quant. Spectrosc. Radiat. Transfer
142
,
93
(
2014
).
20.
J.
Tennyson
,
P. F.
Bernath
,
L. R.
Brown
,
A.
Campargue
,
A. G.
Császár
,
L.
Daumont
,
R. R.
Gamache
,
J. T.
Hodges
,
O. V.
Naumenko
,
O. L.
Polyansky
,
L. S.
Rothman
,
A. C.
Vandaele
, and
N. F.
Zobov
,
Pure Appl. Chem.
86
,
71
(
2014
).
21.
A. G.
Császár
,
G.
Czakó
,
T.
Furtenbacher
, and
E.
Mátyus
,
Annu. Rep. Comput. Chem.
3
,
155
(
2007
).
22.
T.
Furtenbacher
,
A. G.
Császár
, and
J.
Tennyson
,
J. Mol. Spectrosc.
245
,
115
(
2007
).
23.
T.
Furtenbacher
and
A. G.
Császár
,
J. Quant. Spectrosc. Radiat. Transfer
109
,
1234
(
2008
).
24.
A. G.
Császár
and
T.
Furtenbacher
,
J. Mol. Spectrosc.
266
,
99
(
2011
).
25.
T.
Furtenbacher
and
A. G.
Császár
,
J. Quant. Spectrosc. Radiat. Transfer
113
,
929
(
2012
).
26.
T.
Furtenbacher
and
A. G.
Császár
, “
The role of intensities in determining characteristics of spectroscopic networks
,”
J. Mol. Spectrosc.
1009
,
123
(
2012
).
27.
T.
Furtenbacher
,
P.
Árendás
,
G.
Mellau
, and
A. G.
Császár
,
Sci. Rep.
4
,
4654
(
2014
).
28.
A. G.
Császár
,
T.
Furtenbacher
, and
P.
Árendás
,
J. Phys. Chem. A
120
,
8949
(
2016
).
29.
R.
Tóbiás
,
T.
Furtenbacher
, and
A. G.
Császár
,
J. Quant. Spectrosc. Radiat. Transfer
203
,
557
(
2017
).
30.
R.
Tóbiás
,
T.
Furtenbacher
,
J.
Tennyson
, and
A. G.
Császár
,
Phys. Chem. Chem. Phys.
21
,
3473
(
2019
).
31.
T.
Furtenbacher
,
R.
Tóbiás
,
J.
Tennyson
,
O. L.
Polyansky
, and
A. G.
Császár
,
J. Phys. Chem. Ref. Data
49
,
033101
(
2020
).
32.
A.
Gambetta
,
E.
Fasci
,
A.
Castrillo
,
M.
Marangoni
,
G.
Galzerano
,
G.
Casa
,
P.
Laporta
, and
L.
Gianfrani
,
New J. Phys.
12
,
103006
(
2010
).
33.
S.
Béguier
,
S.
Mikhailenko
, and
A.
Campargue
,
J. Mol. Spectrosc.
265
,
106
(
2011
).
34.
G.
Galzerano
,
A.
Gambetta
,
E.
Fasci
,
A.
Castrillo
,
M.
Marangoni
,
P.
Laporta
, and
L.
Gianfrani
,
Appl. Phys. B
102
,
725
(
2011
).
35.
M. A.
Koshelev
,
J. Quant. Spectrosc. Radiat. Transfer
112
,
550
(
2011
).
36.
O. M.
Leshchishina
,
O. V.
Naumenko
, and
A.
Campargue
,
J. Mol. Spectrosc.
268
,
28
(
2011
).
37.
O. M.
Leshchishina
,
O. V.
Naumenko
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
112
,
913
(
2011
).
38.
S.
Mikhailenko
,
S.
Kassi
,
L.
Wang
, and
A.
Campargue
,
J. Mol. Spectrosc.
269
,
92
(
2011
).
39.
M. J.
Down
,
J.
Tennyson
,
J.
Orphal
,
P.
Chelin
, and
A. A.
Ruth
,
J. Mol. Spectrosc.
282
,
1
(
2012
).
40.
O.
Leshchishina
,
S.
Mikhailenko
,
D.
Mondelain
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
113
,
2155
(
2012
).
41.
S. N.
Mikhailenko
,
O. V.
Naumenko
,
A. V.
Nikitin
,
I. A.
Vasilenko
,
A.-W.
Liu
,
K.-F.
Song
,
H.-Y.
Ni
, and
S.-M.
Hu
,
J. Quant. Spectrosc. Radiat. Transfer
113
,
653
(
2012
).
42.
C.
Oudot
,
L.
Régalia
,
S.
Mikhailenko
,
X.
Thomas
,
P.
Von Der Heyden
, and
D.
Décatoire
,
J. Quant. Spectrosc. Radiat. Transfer
113
,
859
(
2012
).
43.
S. S.
Vasilchenko
,
S. N.
Mikhailenko
,
V. I.
Serdyukov
, and
L. N.
Sinitsa
,
Opt. Spectrosc.
113
,
499
(
2012
).
44.
O.
Leshchishina
,
S. N.
Mikhailenko
,
D.
Mondelain
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
130
,
69
(
2013
).
45.
S. N.
Mikhailenko
,
V. I.
Serdyukov
,
L. N.
Sinitsa
, and
S. S.
Vasilchenko
,
Opt. Spectrosc.
115
,
912
(
2013
).
46.
A.-W.
Liu
,
O. V.
Naumenko
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
138
,
97
(
2014
).
47.
L.
Regalia
,
C.
Oudot
,
S.
Mikhailenko
,
L.
Wang
,
X.
Thomas
,
A.
Jenouvrier
, and
P.
Von der Heyden
,
J. Quant. Spectrosc. Radiat. Transfer
136
,
119
(
2014
).
48.
A.
Campargue
,
S. N.
Mikhailenko
,
B. G.
Lohan
,
E. V.
Karlovets
,
D.
Mondelain
, and
S.
Kassi
,
J. Quant. Spectrosc. Radiat. Transfer
157
,
135
(
2015
).
49.
S. N.
Mikhailenko
,
V. I.
Serdyukov
, and
L. N.
Sinitsa
,
J. Quant. Spectrosc. Radiat. Transfer
156
,
36
(
2015
).
50.
L. H.
Coudert
and
P.
Chelin
,
J. Mol. Spectrosc.
326
,
130
(
2016
).
51.
S. N.
Mikhailenko
,
O.
Leshchishina
,
E. V.
Karlovets
,
D.
Mondelain
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
177
,
108
(
2016
).
52.
M.
Birk
,
G.
Wagner
,
J.
Loos
,
L.
Lodi
,
O. L.
Polyansky
,
A. A.
Kyuberis
,
N. F.
Zobov
, and
J.
Tennyson
,
J. Quant. Spectrosc. Radiat. Transfer
203
,
88
(
2017
).
53.
A.
Campargue
,
S. N.
Mikhailenko
,
S.
Vasilchenko
,
C.
Reynaud
,
S.
Béguier
,
P.
Čermák
,
D.
Mondelain
,
S.
Kassi
, and
D.
Romanini
,
J. Quant. Spectrosc. Radiat. Transfer
189
,
407
(
2017
).
54.
J.
Loos
,
M.
Birk
, and
G.
Wagner
,
J. Quant. Spectrosc. Radiat. Transfer
203
,
103
(
2017
).
55.
D.
Mondelain
,
S. N.
Mikhailenko
,
E. V.
Karlovets
,
S.
Béguier
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
203
,
206
(
2017
).
56.
S. N.
Mikhailenko
,
D.
Mondelain
,
E. V.
Karlovets
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
206
,
163
(
2018
).
57.
S. N.
Mikhailenko
,
V. I.
Serdyukov
, and
L. N.
Sinitsa
,
J. Quant. Spectrosc. Radiat. Transfer
217
,
170
(
2018
).
58.
Y.
Tan
,
S. N.
Mikhailenko
,
J.
Wang
,
A.-W.
Liu
,
X.-Q.
Zhao
,
G.-L.
Liu
, and
S.-M.
Hu
,
J. Quant. Spectrosc. Radiat. Transfer
221
,
233
(
2018
).
59.
A.-W.
Liu
,
G.-L.
Liu
,
X.-Q.
Zhao
,
J.
Wang
,
Y.
Tan
, and
S.-M.
Hu
,
J. Quant. Spectrosc. Radiat. Transfer
239
,
106651
(
2019
).
60.
S. N.
Mikhailenko
,
E. V.
Karlovets
,
S.
Vasilchenko
,
D.
Mondelain
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
236
,
106574
(
2019
).
61.
S. N.
Mikhailenko
,
D.
Mondelain
,
E. V.
Karlovets
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
222-223
,
229
(
2019
).
62.
L.
Régalia
,
X.
Thomas
,
T.
Rennesson
, and
S.
Mikhailenko
,
J. Quant. Spectrosc. Radiat. Transfer
235
,
257
(
2019
).
63.
S. N.
Mikhailenko
,
S.
Béguier
,
T. A.
Odintsova
,
M. Yu.
Tretyakov
,
O.
Pirali
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
253
,
107105
(
2020
).
64.
L. N.
Sinitsa
,
V. I.
Serdyukov
,
E. R.
Polovtseva
,
A. D.
Bykov
, and
A. P.
Scherbakov
,
J. Quant. Spectrosc. Radiat. Transfer
246
,
106916
(
2020
).
65.
I. A.
Vasilenko
,
O. V.
Naumenko
,
V. I.
Serdyukov
, and
L. N.
Sinitsa
,
J. Quant. Spectrosc. Radiat. Transfer
253
,
107101
(
2020
).
66.
S. N.
Mikhailenko
,
S.
Kassi
,
D.
Mondelain
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
245
,
106840
(
2020
).
67.
W. S.
Benedict
,
M. A.
Pollack
, and
W. J.
Tomlinson
 III
,
IEEE J. Quantum Electron.
5
,
108
(
1969
).
68.
P. E.
Fraley
,
K.
Narahari Rao
, and
L. H.
Jones
,
J. Mol. Spectrosc.
29
,
312
(
1969
).
69.
F. X.
Powell
and
D. R.
Johnson
,
Phys. Rev. Lett.
24
,
637
(
1970
).
70.
G.
Steenbeckeliers
and
J.
Bellet
,
C. R. Acad. Sci. Paris
273
,
471
(
1971
).
71.
J. G.
Williamson
,
K.
Narahari Rao
, and
L. H.
Jones
,
J. Mol. Spectrosc.
40
,
372
(
1971
).
72.
F. C. D.
Lucia
,
P.
Helminger
,
R. L.
Cook
, and
W.
Gordy
,
Phys. Rev. A
6
,
1324
(
1972
).
73.
C.
Camy-Peyret
,
J. M.
Flaud
,
G.
Guelachvili
, and
C.
Amiot
,
Mol. Phys.
26
,
825
(
1973
).
74.
F. C. D.
Lucia
and
P.
Helminger
,
J. Mol. Spectrosc.
56
,
138
(
1975
).
75.
J. W.
Fleming
and
M. J.
Gibson
,
J. Mol. Spectrosc.
62
,
326
(
1976
).
76.
R. A.
Toth
,
J. M.
Flaud
, and
C.
Camy-Peyret
,
J. Mol. Spectrosc.
67
,
185
(
1977
).
77.
R. A.
Toth
,
J.-M.
Flaud
, and
C.
Camy-Peyret
,
J. Mol. Spectrosc.
67
,
206
(
1977
).
78.
F.
Winther
,
J. Mol. Spectrosc.
65
,
405
(
1977
).
79.
J. W. C.
Johns
and
A. R. W.
McKellar
,
Can. J. Phys.
56
,
737
(
1978
).
80.
J.
Kauppinen
,
T.
Kärkkäinen
, and
E.
Kyrö
,
J. Mol. Spectrosc.
71
,
15
(
1978
).
81.
C.
Camy-Peyret
,
J.-M.
Flaud
, and
N.
Papineau
,
C. R. Acad. Sci. Paris
290B
,
537
(
1980
).
82.
J.
Kauppinen
and
E.
Kyrö
,
J. Mol. Spectrosc.
84
,
405
(
1980
).
83.
R. H.
Partridge
,
J. Mol. Spectrosc.
87
,
429
(
1981
).
84.
G.
Guelachvili
,
J. Opt. Soc. Am.
73
,
137
(
1983
).
85.
A. S.
Pine
,
M. J.
Coulombe
,
C.
Camy-Peyret
, and
J.-M.
Flaud
,
J. Phys. Chem. Ref. Data
12
,
413
(
1983
).
86.
R. A.
Toth
and
J. W.
Brault
,
Appl. Opt.
22
,
908
(
1983
).
87.
J.-P.
Chevillard
,
J.-Y.
Mandin
,
J.-M.
Flaud
, and
C.
Camy-Peyret
,
Can. J. Phys.
63
,
1112
(
1985
).
88.
J. W. C.
Johns
,
J. Opt. Soc. Am. B
2
,
1340
(
1985
).
89.
J.-P.
Chevillard
,
J.-Y.
Mandin
,
C.
Camy-Peyret
, and
J.-M.
Flaud
,
Can. J. Phys.
64
,
746
(
1986
).
90.
J.-P.
Chevillard
,
J.-Y.
Mandin
,
J.-M.
Flaud
, and
C.
Camy-Peyret
,
J. Quant. Spectrosc. Radiat. Transfer
36
,
395
(
1986
).
91.
S. P.
Belov
,
I. N.
Kozin
,
O. L.
Polyansky
,
M. Y.
Tret’yakov
, and
N. F.
Zobov
,
J. Mol. Spectrosc.
126
,
113
(
1987
).
92.
J.-P.
Chevillard
,
J.-Y.
Mandin
,
J.-M.
Flaud
, and
C.
Camy-Peyret
,
Can. J. Phys.
65
,
777
(
1987
).
93.
R. A.
Toth
,
J. Opt. Soc. Am. B
9
,
462
(
1992
).
94.
R. A.
Toth
,
J. Opt. Soc. Am. B
10
,
1526
(
1993
).
95.
R. A.
Toth
,
J. Mol. Spectrosc.
166
,
184
(
1994
).
96.
R. A.
Toth
,
Appl. Opt.
33
,
4868
(
1994
).
97.
A.
Bykov
,
O.
Naumenko
,
T.
Petrova
,
A.
Scherbakov
,
L.
Sinitsa
,
J. Y.
Mandin
,
C.
Camy-Peyret
, and
J.-M.
Flaud
,
J. Mol. Spectrosc.
172
,
243
(
1995
).
98.
R. A.
Toth
,
J. Mol. Spectrosc.
190
,
379
(
1998
).
99.
C.
Camy-Peyret
,
J.-M.
Flaud
,
J.-Y.
Mandin
,
A.
Bykov
,
O.
Naumenko
,
L.
Sinitsa
, and
B.
Voronin
,
J. Quant. Spectrosc. Radiat. Transfer
61
,
795
(
1999
).
100.
F.
Matsushima
,
H.
Nagase
,
T.
Nakauchi
,
H.
Odashima
, and
K.
Takagi
,
J. Mol. Spectrosc.
193
,
217
(
1999
).
101.
L.
Moretti
,
A.
Sasso
,
L.
Gianfrani
, and
R.
Ciurylo
,
J. Mol. Spectrosc.
205
,
20
(
2001
).
102.
H.
Naus
,
W.
Ubachs
,
P. F.
Levelt
,
O. L.
Polyansky
,
N. F.
Zobov
, and
J.
Tennyson
,
J. Mol. Spectrosc.
205
,
117
(
2001
).
103.
S. N.
Mikhailenko
,
V. G.
Tyuterev
,
V. I.
Starikov
,
K. K.
Albert
,
B. P.
Winnewisser
,
M.
Winnewisser
,
G.
Mellau
,
C.
Camy-Peyret
,
R.
Lanquetin
,
J.-M.
Flaud
, and
J. W.
Brault
,
J. Mol. Spectrosc.
213
,
91
(
2002
).
104.
R.
Schermaul
,
R. C. M.
Learner
,
A. A. D.
Canas
,
J. W.
Brault
,
O. L.
Polyansky
,
D.
Belmiloud
,
N. F.
Zobov
, and
J.
Tennyson
,
J. Mol. Spectrosc.
211
,
169
(
2002
).
105.
M.
Tanaka
,
J. W.
Brault
, and
J.
Tennyson
,
J. Mol. Spectrosc.
216
,
77
(
2002
).
106.
S. N.
Mikhailenko
,
V. G.
Tyuterev
, and
G.
Mellau
,
J. Mol. Spectrosc.
217
,
195
(
2003
).
107.
R. N.
Tolchenov
,
J.
Tennyson
,
S. V.
Shirin
,
N. F.
Zobov
,
O. L.
Polyansky
, and
A. N.
Maurellis
,
J. Mol. Spectrosc.
221
,
99
(
2003
).
108.
P.
Macko
,
D.
Romanini
,
S. N.
Mikhailenko
,
O. V.
Naumenko
,
S.
Kassi
,
A.
Jenouvrier
,
V. G.
Tyuterev
, and
A.
Campargue
,
J. Mol. Spectrosc.
227
,
90
(
2004
).
109.
M.
Tanaka
,
M.
Sneep
,
W.
Ubachs
, and
J.
Tennyson
,
J. Mol. Spectrosc.
226
,
1
(
2004
).
110.
M.
Tanaka
,
O.
Naumenko
,
J. W.
Brault
, and
J.
Tennyson
,
J. Mol. Spectrosc.
234
,
1
(
2005
).
111.
R. N.
Tolchenov
,
O.
Naumenko
,
N. F.
Zobov
,
S. V.
Shirin
,
O. L.
Polyansky
,
J.
Tennyson
,
M.
Carleer
,
P.-F.
Coheur
,
S.
Fally
,
A.
Jenouvrier
, and
A. C.
Vandaele
,
J. Mol. Spectrosc.
233
,
68
(
2005
).
112.
R. N.
Tolchenov
and
J.
Tennyson
,
J. Mol. Spectrosc.
231
,
23
(
2005
).
113.
R. A.
Toth
,
J. Quant. Spectrosc. Radiat. Transfer
94
,
51
(
2005
).
114.
G. Y.
Golubiatnikov
,
V. N.
Markov
,
A.
Guarnieri
, and
R.
Knochel
,
J. Mol. Spectrosc.
240
,
191
(
2006
).
115.
L.
Joly
,
B.
Parvitte
,
V.
Zéninari
,
D.
Courtois
, and
G.
Durry
,
J. Quant. Spectrosc. Radiat. Transfer
102
,
129
(
2006
).
116.
A.-W.
Liu
,
J.-H.
Du
,
K.-F.
Song
,
L.
Wang
,
L.
Wan
, and
S.-M.
Hu
,
J. Mol. Spectrosc.
237
,
149
(
2006
).
117.
A.-W.
Liu
,
S.-M.
Hu
,
C.
Camy-Peyret
,
J.-Y.
Mandin
,
O.
Naumenko
, and
B.
Voronin
,
J. Mol. Spectrosc.
237
,
53
(
2006
).
118.
A.-W.
Liu
,
O.
Naumenko
,
K.-F.
Song
,
B.
Voronin
, and
S.-M.
Hu
,
J. Mol. Spectrosc.
236
,
127
(
2006
).
119.
F.
Mazzotti
,
O. V.
Naumenko
,
S.
Kassi
,
A. D.
Bykov
, and
A.
Campargue
,
J. Mol. Spectrosc.
239
,
174
(
2006
).
120.
O.
Naumenko
,
M.
Sneep
,
M.
Tanaka
,
S. V.
Shirin
,
W.
Ubachs
, and
J.
Tennyson
,
J. Mol. Spectrosc.
237
,
63
(
2006
).
121.
A.
Jenouvrier
,
L.
Daumont
,
L.
Régalia-Jarlot
,
V. G.
Tyuterev
,
M.
Carleer
,
A. C.
Vandaele
,
S.
Mikhailenko
, and
S.
Fally
,
J. Quant. Spectrosc. Radiat. Transfer
105
,
326
(
2007
).
122.
F.
Mazzotti
,
R. N.
Tolchenov
, and
A.
Campargue
,
J. Mol. Spectrosc.
243
,
78
(
2007
).
123.
S. N.
Mikhailenko
,
W.
Le
,
S.
Kassi
, and
A.
Campargue
,
J. Mol. Spectrosc.
244
,
170
(
2007
).
124.
O. V.
Naumenko
,
B. A.
Voronin
,
F.
Mazzotti
,
J.
Tennyson
, and
A.
Campargue
,
J. Mol. Spectrosc.
248
,
122
(
2008
).
125.
R.
Tolchenov
and
J.
Tennyson
,
J. Quant. Spectrosc. Radiat. Transfer
109
,
559
(
2008
).
126.
A.
Liu
,
O.
Naumenko
,
S.
Kassi
, and
A.
Campargue
,
J. Quant. Spectrosc. Radiat. Transfer
110
,
1781
(
2009
).
127.
C.
Puzzarini
,
G.
Cazzoli
,
M. E.
Harding
,
J.
Vázquez
, and
J.
Gauss
,
J. Chem. Phys.
131
,
234304
(
2009
).
128.
O. L.
Polyansky
,
A. A.
Kyuberis
,
L.
Lodi
,
J.
Tennyson
,
S. N.
Yurchenko
,
R. I.
Ovsyannikov
, and
N. F.
Zobov
,
Mon. Not. R. Astron. Soc.
466
,
1363
(
2017
).
129.
X.
Huang
,
D. W.
Schwenke
, and
T. J.
Lee
,
J. Quant. Spectrosc. Radiat. Transfer
230
,
222
(
2019
).
130.
L. K.
McKemmish
,
T.
Masseron
,
H. J.
Hoeijmakers
,
V.
Pérez-Mesa
,
S. L.
Grimm
,
S. N.
Yurchenko
, and
J.
Tennyson
,
Mon. Not. R. Astron. Soc.
488
,
2836
(
2019
).
131.
Ya. V.
Pavlenko
,
S. N.
Yurchenko
,
L. K.
McKemmish
, and
J.
Tennyson
,
Astron. Astrophys.
642
,
A77
(
2020
).
132.
A.
Miani
and
J.
Tennyson
,
J. Chem. Phys.
120
,
2732
(
2004
).
133.
M. E. J.
Newman
,
Networks
(
Oxford University Press
,
Oxford
,
2000
).
134.
J.-M.
Flaud
,
C.
Camy-Peyret
, and
J. P.
Maillard
,
Mol. Phys.
32
,
499
(
1976
).
135.
S. A.
Tashkun
,
V. I.
Perevalov
,
J.-L.
Teffo
,
A. D.
Bykov
, and
N. N.
Lavrentieva
,
J. Quant. Spectrosc. Radiat. Transfer
82
,
165
(
2003
).
136.
N.
Åslund
,
J. Mol. Spectrosc.
50
,
424
(
1974
).
137.
T.
Furtenbacher
,
I.
Szabó
,
A. G.
Császár
,
P. F.
Bernath
,
S. N.
Yurchenko
, and
J.
Tennyson
,
Astrophys. J. Suppl. Ser.
224
,
44
(
2016
).
138.
L. K.
McKemmish
,
T.
Masseron
,
S.
Sheppard
,
E.
Sandeman
,
Z.
Schofield
,
T.
Furtenbacher
,
A. G.
Császár
,
J.
Tennyson
, and
C.
Sousa-Silva
,
Astrophys. J. Suppl. Ser.
228
,
15
(
2017
).
139.
L. K.
McKemmish
,
J.
Borsovszky
,
K. L.
Goodhew
,
S.
Sheppard
,
A. F. V.
Bennett
,
A. D. J.
Martin
,
A.
Singh
,
C. A. J.
Sturgeon
,
T.
Furtenbacher
,
A. G.
Császár
, and
J.
Tennyson
,
Astrophys. J.
867
,
33
(
2018
).
140.
D.
Darby-Lewis
,
H.
Shah
,
D.
Joshi
,
F.
Khan
,
M.
Kauwo
,
N.
Sethi
,
P. F.
Bernath
,
T.
Furtenbacher
,
R.
Tóbiás
,
A. G.
Császár
 et al,
J. Mol. Spectrosc.
362
,
69
(
2019
).
141.
L. K.
McKemmish
,
A.-M.
Syme
,
J.
Borsovszky
,
S. N.
Yurchenko
,
J.
Tennyson
,
T.
Furtenbacher
, and
A. G.
Császár
,
Mon. Not. R. Astron. Soc.
497
,
1081
(
2020
).
142.
T.
Furtenbacher
,
T.
Szidarovszky
,
C.
Fábri
, and
A. G.
Császár
,
Phys. Chem. Chem. Phys.
15
,
10181
(
2013
).
143.
T.
Furtenbacher
,
T.
Szidarovszky
,
E.
Mátyus
,
C.
Fábri
, and
A. G.
Császár
,
J. Chem. Theor. Comput.
9
,
5471
(
2013
).
144.
K. L.
Chubb
,
O.
Naumenko
,
S.
Keely
,
S.
Bartolotto
,
S.
MacDonald
,
M.
Mukhtar
,
A.
Grachov
,
J.
White
,
E.
Coleman
,
A.
Liu
,
A. Z.
Fazliev
,
E. R.
Polovtseva
,
V.-M.
Horneman
,
A.
Campargue
,
T.
Furtenbacher
,
A. G.
Császár
,
S. N.
Yurchenko
, and
J.
Tennyson
,
J. Quant. Spectrosc. Radiat. Transfer
218
,
178
(
2018
).
145.
R.
Tóbiás
,
T.
Furtenbacher
,
A. G.
Császár
,
O. V.
Naumenko
,
J.
Tennyson
,
J.-M.
Flaud
,
P.
Kumar
, and
B.
Poirier
,
J. Quant. Spectrosc. Radiat. Transfer
208
,
152
(
2018
).
146.
A. R.
Al Derzi
,
T.
Furtenbacher
,
J.
Tennyson
,
S. N.
Yurchenko
, and
A. G.
Császár
,
J. Quant. Spectrosc. Radiat. Transfer
161
,
117
(
2015
).
147.
K. L.
Chubb
,
M.
Joseph
,
J.
Franklin
,
N.
Choudhury
,
T.
Furtenbacher
,
A. G.
Császár
,
G.
Gaspard
,
P.
Oguoko
,
A.
Kelly
,
S. N.
Yurchenko
,
J.
Tennyson
, and
C.
Sousa-Silva
,
J. Quant. Spectrosc. Radiat. Transfer
204
,
42
(
2018
).
148.
T.
Furtenbacher
,
P. A.
Coles
,
J.
Tennyson
,
S. N.
Yurchenko
,
S.
Yu
,
B.
Drouin
,
R.
Tóbiás
, and
A. G.
Császár
,
J. Quant. Spectrosc. Radiat. Transfer
251
,
107027
(
2020
).
149.
C.
Fábri
,
E.
Mátyus
,
T.
Furtenbacher
,
L.
Nemes
,
B.
Mihály
,
T.
Zoltáni
, and
A. G.
Császár
,
J. Chem. Phys.
135
,
094307
(
2011
).
150.
M. S.
Child
and
L.
Halonen
,
Adv. Chem. Phys.
57
,
1
(
1984
).
151.
M.
Carleer
,
A.
Jenouvrier
,
A.-C.
Vandaele
,
P. F.
Bernath
,
M. F.
Mérienne
,
R.
Colin
,
N. F.
Zobov
,
O. L.
Polyansky
,
J.
Tennyson
, and
V. A.
Savin
,
J. Chem. Phys.
111
,
2444
(
1999
).
152.
A.
Campargue
,
S.
Kassi
,
A.
Yachmenev
,
A. A.
Kyuberis
,
J.
Küpper
, and
S. N.
Yurchenko
,
Phys. Rev. Res.
2
,
023091
(
2020
).
153.
A.
Campargue
,
A. M.
Solodov
,
A. A.
Solodov
,
A.
Yachmenev
, and
S. N.
Yurchenko
,
Phys. Chem. Chem. Phys.
22
,
12476
(
2020
).
154.
R. A.
Toth
, SISAM database, https://mark4sun.jpl.nasa.gov/h2o.html,
2005
.
155.
R. J.
Barber
,
J.
Tennyson
,
G. J.
Harris
, and
R. N.
Tolchenov
,
Mon. Not. R. Astron. Soc.
368
,
1087
(
2006
).
156.
O. L.
Polyansky
,
A. A.
Kyuberis
,
N. F.
Zobov
,
J.
Tennyson
,
S. N.
Yurchenko
, and
L.
Lodi
,
Mon. Not. R. Astron. Soc.
480
,
2597
(
2018
).
157.
E.
Mátyus
,
C.
Fábri
,
T.
Szidarovszky
,
G.
Czakó
,
W. D.
Allen
, and
A. G.
Császár
,
J. Chem. Phys.
133
,
034113
(
2010
).
158.
J.
Smydke
and
A. G.
Császár
,
Mol. Phys.
117
,
1682
(
2019
).
159.
M. S.
Child
,
T.
Weston
, and
J.
Tennyson
,
Mol. Phys.
96
,
371
(
1999
).
160.
A. G.
Császár
,
W. D.
Allen
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
110
,
11971
(
1999
).
161.
G.
Tarczay
,
A. G.
Császár
,
W.
Klopper
,
V.
Szalay
,
W. D.
Allen
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
110
,
11971
(
1999
).
162.
E. F.
Valeev
,
W. D.
Allen
,
H. F.
Schaefer
 III
, and
A. G.
Császár
,
J. Chem. Phys.
114
,
2875
(
2001
).
163.
S. V.
Shirin
,
N. F.
Zobov
,
R. I.
Ovsyannikov
,
O. L.
Polyansky
, and
J.
Tennyson
,
J. Chem. Phys.
128
,
224306
(
2008
).
164.
L.
Lodi
and
J.
Tennyson
,
J. Quant. Spectrosc. Radiat. Transfer
113
,
850
(
2012
).
165.
P.
Árendás
,
T.
Furtenbacher
, and
A. G.
Császár
,
J. Math. Chem.
54
,
806
(
2016
).
166.
D.
Wunch
,
G. C.
Toon
,
J.-F. L.
Blavier
,
R. A.
Washenfelder
,
J.
Notholt
,
B. J.
Connor
,
D. W. T.
Griffith
,
V.
Sherlock
, and
P. O.
Wennberg
,
Philos. Trans. R. Soc. A
369
,
2087
(
2011
).
167.
H.
Vogelmann
,
R.
Sussmann
,
T.
Trickl
, and
A.
Reichert
,
Atmos. Chem. Phys.
15
,
3135
(
2015
).
168.
E.
Dupuy
,
I.
Morino
,
N. M.
Deutscher
,
Y.
Yoshida
,
O.
Uchino
,
B. J.
Connor
,
M.
De Mazière
,
D. W. T.
Griffith
,
F.
Hase
,
P.
Heikkinen
,
P. W.
Hillyard
,
L. T.
Iraci
,
S.
Kawakami
,
R.
Kivi
,
T.
Matsunaga
,
J.
Notholt
,
C. M.
Petri
,
J. R.
Podolske
,
D. F.
Pollard
,
M.
Rettinger
,
C.
Roehl
,
V. A.
Sherlock
,
R.
Sussmann
,
G. C.
Toon
,
V. A.
Velazco
,
T.
Warneke
,
P. O.
Wennberg
,
D.
Wunch
, and
T.
Yokota
,
Remote Sensing
8
,
414
(
2016
).
169.
C.
Clerbaux
,
J.
Hadji-Lazaro
,
S.
Turquety
,
G.
Mégie
, and
P.-F.
Coheur
,
Atmos. Chem. Phys.
3
,
1495
(
2003
).
170.
G. E.
Nedoluha
,
R.
Michael Gomez
,
D. R.
Allen
,
A.
Lambert
,
C.
Boone
, and
G.
Stiller
,
J. Geophys. Res.: Atmos.
118
,
11285
(
2013
).

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