Robert Bonamy Formalism Research Articles

Branch dependence of halfwidths: Theoretical analysis of N2-broadened halfwidths of CH3Br in the v6 band

The N2-broadened halfwidths of CH3Br in the ν6 band have been calculated, along with the relaxation matrices W. These calculations employ our modified and refined versions of the Robert-Bonamy formalism. Extensive comparisons between the predicted halfwidths from the models and experimental measurements at T = 296 K are presented. Our latest model very closely matches the measurements. Meanwhile, we considered line mixing effects in the spectral profile of the RQ(j,0) sub-branch. Our method probably yields too large values of the off-diagonal elements of W. Finally, by comparing our calculated halfwidths with the data in HITRAN, we have observed generally good agreement, especially for lines with high values of j. However, the agreement becomes poor for lines with low values of j, deteriorating as j decreases. We identified a factor contributing to this poor agreement: the neglect of branch dependence in the development of HITRAN data. We believe that for lines with low values of j, this oversight undermines the reliability of the halfwidth values of CH3Br in HITRAN.

The influence of line mixing on the j and k dependencies of halfwidths and temperature exponents in N2-broadening coefficients of CH3F spectral lines

The N2-broadening halfwidths of CH3F in the ν5 and ν6 perpendicular bands have been calculated, along with their temperature exponents. These calculations utilize a modified and refined version of the Robert-Bonamy formalism, developed by the current authors within a semi-classical line shape framework. Extensive comparisons between the predicted halfwidths from the model and experimental measurements at 296 K and 183 K are presented. Our latest model accurately predicts the dependencies of the halfwidths on both the j and k quantum numbers. Furthermore, by extending our calculations to two additional temperatures, namely 240 K and 350 K, the temperature exponent N is determined for various sub-branches. The dependencies of N on j and k are analyzed, and theoretical explanations are provided to elucidate the predicted behaviors of N.

Line coupling and line mixing effects on calculated widths of symmetric-top molecules with the k-degeneracy: A theoretical study of N2-, O2-, and air-broadened lines of CH3I

Calculations of the N2-, O2-, and air-broadened widths, together with their temperature dependence exponents have been made for transitions of CH3I in the ν5 and ν6 bands. The calculations are based on a semi-classical line shape formalism developed by the current authors through modifying and refining the Robert-Bonamy formalism. In recent years, we have applied this formalism for linear molecules, symmetric-top molecules with inversion symmetry, and asymmetric-top molecules. For symmetric-top molecules with the k degeneracy such as CH3I, the formalism has a new feature. In this case, one should consider each of the CH3I transitions labeled by ki or f ≠ 0 as a doublet. Then, one needs to consider the effects of the line mixing process between these two components. Comparisons of our theoretical predictions with some data available demonstrate a very reasonable agreement. Finally we propose new experiments at higher perturber pressures that would enable one to check the theoretically calculated relaxation matrices and to extend the analysis to the inter-doublet mixing effects.

Vibrational dependence, temperature dependence, and prediction of line shape parameters for the H2O-N2 collision system

In a recent work [JQSRT 228,79(2019)], Vispoel et al. optimized the intermolecular potential used in the Modified Complex Robert-Bonamy (MCRB) formalism for the H2O-N2 collision system. Calculations were made for a number of transitions in the rotation and ν2 bands. The needs of the spectroscopic and astrophysics communities include data for water vapor transitions that have multiple vibrational quanta exchanged. In this work, MCRB calculations were made for 0–4 vibrational quanta exchanged in the ν1, ν2, and ν3 bands for 13 temperatures from 200–3000 K; 7272 transitions for each band. From these data, the vibrational and temperature dependence of the half-width and line shift were determined. The temperature dependence was determined using the Gamache-Vispoel model [JQSRT 217, 440(2018)]. The data allowed the development of a routine that can predict the half-width, line shift, and their temperature dependence for transitions not yet studied. The prediction algorithm is based on theory [JQSRT, 83, 119(2004)] and yields line shape parameters with much smaller uncertainty than obtained by fitting with ad hoc polynomials or J” averaged values. A line file based on the 2020 update to the HITRAN2016 water vapor line file was created with N2 as the broadening species. These data are useful for combustion studies and as a first step to determining air-broadening for the HITRAN and GEISA databases.

Vibrational dependence, temperature dependence, and prediction of line shape parameters for the H2O-H2 collision system

In a recent work on line shape parameters for the H2O-H2 [Renaud et al., Icarus, 306,275, 2018] it was shown that this far off-resonance collision system displays strong vibrational dependence. In Renaud et al., calculations were made for bands with one bend or stretch (symmetric or antisymmetric) vibrational quanta exchanged. Water is seen throughout the universe under a vast range of conditions. The needs of the spectroscopic and astrophysics communities include data for water vapor transitions with multiple quanta exchanged. In this work, calculations were made using the Modified Complex Robert-Bonamy (MCRB) formalism for 0–4 vibrational quanta exchanged in the ν1, ν2, and ν3 bands, and the 3ν1 + ν3 band at 13 temperatures from 200 to 3000 K: calculations for more than 100,000 transitions. From these data, the vibrational dependence of the half-width, line shift, and their temperature dependence are studied as a function of rotational transition. The results show a strong and unusual vibrational dependence. The data were used to develop a prediction routine, which is based on theory [Gamache and Hartmann, JQSRT, 83, 119, 2004] rather than ad hoc fitting to a polynomial or other forms. The resulting prediction algorithm gives line shape parameters with much lower uncertainty compared to those from J″ average values or polynomial methods. A line file, based on HITRAN2016, was created for remote sensing applications that study H2O in hydrogen-rich atmospheres.

First pressure shift measurement of ozone molecular lines at 9.54 μm using a tunable quantum cascade laser

Using a free-running distributed-feedback quantum cascade laser (QCL) emitting at 9.54 μm, the pressure shift parameters of four intense rovibrational transitions in the ν3 fundamental band of ozone induced by oxygen (O2), air and the noble gases helium (He), argon (Ar), and xenon (Xe) are obtained by employing second harmonic detection. The experimental analysis comprises a full uncertainty budget and provides line shift data which are traceable to SI. The high density of transitions in the ν3 spectral region of ozone make this region particularly difficult to study with more commonly used techniques such as Fourier transform spectroscopy. The comparatively high spectral resolution of the QCL in the MHz range, on the contrary, allows to measure molecular shifts at relatively low pressures (from 2 to 70 hPa), thus reducing the impact of spectral congestion due to pressure broadening of molecular lines. The comparison of our results with published data shows that presently recommended values for the pressure shift are too low in this region. This observation is corroborated by semi-classical calculations using the Robert-Bonamy formalism. A slight negative J dependence, already observed in other ozone vibrational bands, is predicted. Systematic use of our technique could be very useful to support this hypothesis and to make up for the lack of shift parameters for ozone ν3 transitions in molecular spectral databases. A subsequent stabilization of the QCL onto an optical frequency comb will open up possibilities to perform metrological measurements of Doppler-free molecular lines.

Line parameters for CO2- and self-broadening in the ν3 band of HD16O

Pressure-broadened line shape parameters of transitions in the ν3 band of HDO (ν0=3707.4cm-1) were measured from spectra of HDO and mixtures of HDO and CO2 for application to accurate retrievals of HDO abundances and D/H ratios for CO2-rich planetary atmospheres of Mars and Venus. A few calculated line lists have recently been published on HDO-CO2 line shapes and their temperature dependences, but the present study represents the first laboratory measurements of those parameters in the ν3 band; Measurements for nearly 100 transitions in the ν3 band have been made. Room temperature measurements of self-broadened width and shift coefficients for all of these transitions, line mixing via off-diagonal relaxation matrix element coefficients and quadratic speed dependence parameter were measured for the majority of these transitions. All these measurements were made by simultaneously fitting eleven high-resolution spectra of HDO and HDO-CO2 mixtures at various temperatures and pressures recorded with the Bruker Fourier transform spectrometer at the Jet Propulsion Laboratory. Two specially built coolable absorption cells with path lengths of 20.38cm and 20.941m were used to contain the sample mixtures. Multispectrum nonlinear least squares fitting algorithm was employed in the analysis.Calculations using the Modified Complex Robert-Bonamy formalism (MCRB) were made for the half-width coefficients, their temperature dependences and pressure shift coefficients for the HDO–CO2 and HDO–HDO collision systems. The calculations were made for all ν3 band transitions in the 1100–4100cm-1 region on the HITRAN2012 database. Present measurements are compared with the MCRB calculations and other literature values.

Modified Complex Robert-Bonamy (MCRB) calculations of H2O transitions broadened by H2 for applications to planetary and exoplanet atmospheres

Line shape parameters for hydrogen broadening of water vapor are needed to understand remote sensing measurements of planetary and exoplanet atmospheres. In order to address these needs, semiclassical calculations based on the Modified Complex Robert-Bonamy (MCRB) formalism were made. The intermolecular potential for the calculation is comprised of electrostatic, atom-atom (expanded to order 16 and rank 4), induction, and London dispersion terms. The trajectories were determined by numerical integration of the Hamilton’s equations. The average over the Maxwell–Boltzmann distribution of velocities was performed by integration over 35 velocities corresponding to the temperature range 75K – 27000K. The formalism is complex valued yielding the half-width and line shift from a single calculation. The calculations are reported at 7 temperatures from 200 to 700 K. The half-width temperature dependence coefficient n was determined using the relation γ(T) = γ(T)[T0/T]n with T0=296K. The calculations are compared with the measurements of Brown and Plymate [JQSRT 56, 263, 1996]. Future plans for further refinement of the intermolecular potential are discussed.

Line parameters for CO2- and self-broadening in the ν1 band of HD16O

Lorentz half-width coefficients and their temperature dependence exponents for CO2 broadening in the fundamental bands of HDO are important for reliable and accurate interpretation of Mars and Venus atmospheric data and to determine D/H. Uncertainties in the temperature dependences of the CO2-broadened half-width coefficients lead to large errors in the retrieved mixing ratios and hence in HDO column abundances. In this high-resolution FTIR laboratory study, we report first measurements of the temperature dependences of half-width coefficients for HDO transitions in the ν1 and 2ν2 bands broadened by CO2. Accurate line positions, intensities, CO2-broadened width and pressure shift coefficients, their temperature dependences, collisional line mixing coefficients for HDO-CO2 system and quadratic speed dependence parameters have been retrieved for a large number of transitions in the ν1 band. Room-temperature self-broadened half-width coefficients, self-shift coefficients, and collisional line-mixing coefficients for HDO-HDO system were also measured for the same number of ν1 transitions. Positions and intensities were measured for nearly 60 transitions in the weaker 2ν2 band along with a few room-temperature measurements of CO2- and self-broadening and pressure-shift coefficients. These results were obtained from simultaneous nonlinear least squares fittings of ten high-resolution absorption spectra recorded with the Bruker IFS-125HR FTS at JPL and two coolable sample cells. Modified Complex Robert-Bonamy (MCRB) formalism was applied to compute both types of broadening and pressure shift coefficients, and the temperature dependences of the CO2- and self-broadening parameters. Present measurements are compared with the MCRB calculations and other theoretical values reported in the literature.

Line parameters for CO2 broadening in the ν2 band of HD16O

CO2-rich planetary atmospheres such as those of Mars and Venus require accurate knowledge of CO2 broadened HDO half-width coefficients and their temperature dependence exponents for reliable abundance determination. Although a few calculated line lists have recently been published on HDO–CO2 line shapes and their temperature dependences, laboratory measurements of those parameters are thus far non-existent. In this work, we report the first measurements of CO2-broadened half-width and pressure-shift coefficients and their temperature dependences for over 220 transitions in the ν2 band. First measurements of self-broadened half-width and self-shift coefficients at room temperature are also obtained for majority of these transitions. In addition, the first experimental determination of collisional line mixing has been reported for 11 transition pairs for HDO–CO2 and HDO–HDO systems. These results were obtained by analyzing ten high-resolution spectra of HDO and HDO–CO2 mixtures at various sample temperatures and pressures recorded with the Bruker IFS-125HR Fourier transform spectrometer at the Jet Propulsion Laboratory (JPL). Two coolable absorption cells with path lengths of 20.38cm and 20.941m were used to record the spectra. The various line parameters were retrieved by fitting all ten spectra simultaneously using a multispectrum nonlinear least squares fitting algorithm.The HDO transitions in the 1100–4100cm−1 range were extracted from the HITRAN2012 database. For the ν2 and 2ν2 -ν2 bands there were 2245 and 435 transitions, respectively. Modified Complex Robert–Bonamy formalism (MCRB) calculations were made for the half-width coefficients, their temperature dependence and the pressure shift coefficients for the HDO–CO2 and HDO–HDO collision systems. MCRB calculations are compared with the measured values.

Pressure broadening of the electric dipole and Raman lines of CO2 by argon: Stringent test of the classical impact theory at different temperatures on a benchmark system

A classical approach is applied to calculate pressure broadening coefficients of CO2 vibration–rotational spectral lines perturbed by Ar. Three types of spectra are examined: electric dipole (infrared) absorption; isotropic and anisotropic Raman Q branches. Simple and explicit formulae of the classical impact theory are used along with exact 3D Hamilton equations for CO2–Ar molecular motion. The calculations utilize vibrationally independent most accurate ab initio potential energy surface (PES) of Hutson et al. expanded in Legendre polynomial series up to lmax = 24. New improved algorithm of classical rotational frequency selection is applied. The dependences of CO2 half-widths on rotational quantum number J up to J=100 are computed for the temperatures between 77 and 765K and compared with available experimental data as well as with the results of fully quantum dynamical calculations performed on the same PES. To make the picture complete, the predictions of two independent variants of the semi-classical Robert-Bonamy formalism for dipole absorption lines are included. This method. however, has demonstrated poor accuracy almost for all temperatures. On the contrary, classical broadening coefficients are in excellent agreement both with measurements and with quantum results at all temperatures. The classical impact theory in its present variant is capable to produce quickly and accurately the pressure broadening coefficients of spectral lines of linear molecules for any J value (including high Js) using full-dimensional ab initio - based PES in the cases where other computational methods are either extremely time consuming (like the quantum close coupling method) or give erroneous results (like semi-classical methods).

The relaxation matrix for symmetric tops with inversion symmetry. I. Effects of line coupling on self-broadened ν1 and pure rotational bands of NH3.

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Line mixing in parallel and perpendicular bands of CO2: A further test of the refined Robert-Bonamy formalism.

Starting from the refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)], we propose here an extension of line mixing studies to infrared absorptions of linear polyatomic molecules having stretching and bending modes. The present formalism does not neglect the internal degrees of freedom of the perturbing molecules, contrary to the energy corrected sudden (ECS) modelling, and enables one to calculate the whole relaxation matrix starting from the potential energy surface. Meanwhile, similar to the ECS modelling, the present formalism properly accounts for roles played by all the internal angular momenta in the coupling process, including the vibrational angular momentum. The formalism has been applied to the important case of CO2 broadened by N2. Applications to two kinds of vibrational bands (Σ → Σ and Σ → Π) have shown that the present results are in good agreement with both experimental data and results derived from the ECS model.

Effects on calculated half-widths and shifts from the line coupling for asymmetric-top molecules.

The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H2O immersed in N2 bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator -iS1 - S2, quantitative tools are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H2O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H2O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.

Two dimensional symmetric correlation functions of the ${\rm \hat S}$Ŝ operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the Ŝ operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Refinement of the Robert-Bonamy formalism: Considering effects from the line coupling

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS1 - S2) can be replaced by the exponential of the matrix elements of -iS1 - S2. With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS1 - S2) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N2-N2 pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the "true" values.

Speed dependence of collisional relaxation in ground vibrational state of OCS: Rotational behaviour

Accurate experimental data on pressure broadened profiles of (16)O(12)C(32)S pure rotational lines in a broad range of quantum number J have been analyzed taking into account the speed dependence of collisional relaxation. Refined values of collisional self-broadening coefficients are determined and compared to previously known data. New quantitative information on departures of observed line shapes from the traditional Voigt profile is obtained. It is shown that these departures result mainly from the speed dependence of collisional relaxation. Theoretical calculations of self-broadening parameters are performed in the framework of the semiclassical impact Robert-Bonamy formalism where the mean relative molecular speed as well as the Maxwell-Boltzmann distribution of relative speeds is considered. The necessity of allowance for the speed dependence in line shape models is confirmed and satisfactory results have been obtained by arbitrarily limiting the integration of the differential cross section to a finite value of the impact parameter. It is shown for the first time for the whole rotational spectrum that speed dependent models not only improve accuracy of modeling the observed line profiles but also give physically grounded values of collisional relaxation parameters.

Theoretical studies of N2-broadened half-widths of H2O lines involving high j states

Based on the properties of the energy levels and wave functions of H2O states, one can categorize H2O lines into individually defined groups such that within the same group, the energy levels and the wave functions associated with two paired lines have an identity property while those associated with different pairs have a similarity property. Meanwhile, by thoroughly analyzing processes used to calculate N2-broadened half-widths, it was found that the ‘Fourier series’ of and and a factor P 222(jf τf jiτi ) are the key items in the Robert-Bonamy formalism to distinguish contributions to ReS 2(rc ) among different transitions of jf τf ← ji τi . However, these items are completely determined by the energy levels and the wave functions associated with their initial and final states and they must bear the latter's features as well. Thus, it becomes obvious that for two paired lines in the same group, their calculated half-widths must be almost identical and the values associated with different pairs must vary smoothly as their ji values vary. Thus, the pair identity and the smooth variation rules are established within individual groups of lines. One can use these rules to screen half-width data listed in HITRAN and to improve the data accuracies.

Water in planetary and cometary atmospheres: H 2O/HDO transmittance and fluorescence models

We developed a modern methodology to retrieve water (H 2O) and deuterated water (HDO) in planetary and cometary atmospheres, and constructed an accurate spectral database that combines theoretical and empirical results. On the basis of a greatly expanded set of spectroscopic parameters, we built a full non-resonance cascade fluorescence model and computed fluorescence efficiencies for H 2O (500 million lines) and HDO (700 million lines). The new line list was also integrated into an advanced terrestrial radiative transfer code (LBLRTM) and adapted to the CO 2 rich atmosphere of Mars, for which we adopted the complex Robert–Bonamy formalism for line shapes. We retrieved water and D/ H in the atmospheres of Mars, comet C/2007 W1 (Boattini), and Earth by applying the new formalism to spectra obtained with the high-resolution spectrograph NIRSPEC/Keck II atop Mauna Kea (Hawaii). The new model accurately describes the complex morphology of the water bands and greatly increases the accuracy of the retrieved abundances (and the D/ H ratio in water) with respect to previously available models. The new model provides improved agreement of predicted and measured intensities for many H 2O lines already identified in comets, and it identifies several unassigned cometary emission lines as new emission lines of H 2O. The improved spectral accuracy permits retrieval of more accurate rotational temperatures and production rates for cometary water.