Complex Robert-Bonamy Calculations Research Articles

Modified Complex Robert-Bonamy calculations of line shape parameters for the CO2-H2O collision system

Modified Complex Robert-Bonamy calculations were made for the CO2-H2O collision system using an intermolecular potential comprised of quadrupole-dipole, quadrupole-quadrupole, Lennard-Jones atom-atom, induction, and London dispersion terms. The initial atom-atom parameters were obtained using combination rules and the other parameters from taken from the literature. The intermolecular potential was then adjusted to give results that agree with the measurements of Sung et al. [Can. J. Phys. 87,469-484, 2009]. The final potential results (pot 46) compared with the data of Sung et al. have an average percent difference of 0.07 and a standard deviation of 1.096 %. Calculations were then made for all transitions in the 00011-00001 band with J” from 0 to 120 at 13 temperatures from 200 to 3000 K. The speed dependence of the half-width and line shift were computed for use in more advanced line shape models. The temperature dependence of the half-widths and line shifts were determined using the double power-law (DPL) model of Gamache and Vispoel [JQSRT 217, 440-452, 2018].

Measurements of H2O-O2 line shape parameters and the determination of the intermolecular potential for modified complex Robert-Bonamy calculations

A series of spectra, one pure H2O and four H2O-O2 mixtures, were measured for the ν2 band in the 1200–1950 cm−1 region at room temperature using a single-pass copper cell housed in the Bruker 125HR high-resolution Fourier transform spectrometer (FTS) at Jet Propulsion Laboratory (JPL). All the five spectra were fit simultaneously using a multispectrum non-linear least-squares fitting software, Labfit programme suite, which adopts a speed-dependent Voigt line shape profile using full line mixing taken into account through a relaxation matrix operation. O2-broadened half-width and O2-induced frequency shift coefficients were determined for more than 350 transitions of H2 16O. These data were then checked using the smooth variation and paring rules [Brown et al. J Mol Spectrosc. 2007;246:1-21, Ma et al. Mol Phys. 2011;109:1925-41] and 186 transitions that obey the rules with less than 3% difference were chosen. Using these selected data, Modified Complex Robert-Bonamy calculations were made to determine the intermolecular potential for the H2O-O2 collision system. Some 93 potential were investigated resulting in a final potential (potential 74) that agrees with the selected half-width measurements having an average percent difference of 0.052 and a standard deviation of 5.108% between measurement and calculations.

Water vapor line profile at 183-GHz: Temperature dependence of broadening, shifting, and speed-dependent shape parameters

The water vapor line at 183 GHz was studied over the temperature range of 219–358 K using a spectrometer with radioacoustic detection of absorption, providing a signal-to-noise ratio of up to 8000. The study includes the first measurement of speed-dependent collisional broadening and shifting of this line for both self- and air-broadening, and their temperature dependences. The sign of self-shifting changes at about 280 K. Line-shape parameters are obtained for Voigt and quadratic speed-dependent Voigt shape factors. Temperature dependences of the line parameters are analyzed using empirical models from the literature. Theoretical Modified Complex Robert–Bonamy calculations of the line shape parameters, their temperature and speed-dependence are made over the temperature range of 200–3000 K. The measurements and calculations show very good agreement, although with some discrepancies for line shift parameters. The impact of the newly-measured line parameters on atmospheric water-vapor estimation from ground-based and satellite instruments is evaluated by simulation of downwelling and upwelling brightness temperatures and retrieved water-vapor mixing ratio, for atmospheric conditions typical of six climate zones. For the case of ground-based or limb-scanning radiometry with a background of cold space, the impact of speed-dependence is comparable to or exceeds that of measurement error and will introduce systematic errors if neglected. Therefore, consideration of speed-dependence is necessary for accurate estimation of water vapor with this line. The impact on upwelling brightness temperature is smaller.

Modified complex Robert-Bonamy calculations of line shape parameters and their temperature dependence for water vapor in collision with N2

Modified Complex Robert-Bonamy (MCRB) calculations of the half-width, line shift, and their temperature dependence were made for the H2O-N2 collision system. Several methods, intercomparison of the measured line shape data and the Group of Transitions methods, were tested to select a set of measured half-widths and line shifts with small uncertainty. The atom-atom parameters of the intermolecular potential were refined by matching the MCRB calculation results to those of the selected transitions. Transitions for the rotation and ν2 bands were selected from the HITRAN2016 database [Gordon et al. JQSRT 203, 3, 2017] and MCRB calculations employing the final intermolecular potential were made for these transitions. The calculations were made at 13 temperatures between 200 and 3000 K and the temperature dependence of the half-width and line shift determined. The MCRB data were compared with the measurement database. The comparison of the half-widths gives average percent differences of 4.71% and −2.74% and the comparison of the line shifts gives average deviations of −0.00166 and −0.000547 cm−1 atm−1 for the rotation and ν2 bands, respectively. A file of the final results is available as supplemental data and the corresponding author's website.

Semiclassical calculations of half-widths and line shifts for transitions in the 30012←00001 and 30013←00001 bands of CO2 II: Collisions with O2 and air

The complex Robert–Bonamy (CRB) formalism was used to calculate the half-width, its temperature dependence, and the line shift for CO2 for transitions in the 30012←00001 and 30013←00001 bands with O2 as the perturbing gas. The calculations were done for rotational quantum numbers from J=0 to J=120 with no ad hoc scaling of the line shape equations. The intermolecular potential parameters are adjusted on accurate experimental measurements of the half-widths, its temperature dependence, and the pressure-induced line shifts so that a single intermolecular potential reproduces all three parameters. Using the results of this work and previous results for N2-broadening, air-broadening line shape parameters were also determined. The comparison of the CRB calculations with the experimental data available in the literature for the three line shape coefficients demonstrates the quality of the present calculations for the both bands under study.

Comparison of trajectory models in calculations of N2-broadened half-widths and N2-induced line shifts for the rotational band of H216O and comparison with measurements

In this work, Complex Robert–Bonamy calculations of half-widths and line shifts were done for N2-broadening of water for 1639 transitions in the rotational band using two models for the trajectories. The first is a model correct to second order in time, the Robert–Bonamy parabolic approximation. The second is the solution of Hamilton's equations. Both models use the isotropic part of the atom–atom potential to determine the trajectories. The present calculations used an intermolecular potential expanded to 20th order to assure the convergence of the half-widths and line shifts. The aim of the study is to assess if the difference in the half-widths and line shifts determined from the two trajectory models is greater than the accuracy requirements of the spectroscopic and remote sensing communities. The results of the calculations are compared with measurements of the half-widths and line shifts. It is shown that the effects of the trajectory model greatly exceed the needs of current remote sensing measurements and that line shape parameters calculated using trajectories determined by solving Hamilton's equations agree better with measurement.

Theoretical calculations of N 2-broadened half-widths of ν5 transitions of HNO 3

A number of satellite instruments are measuring nitric acid, HNO 3, in the Earth's atmosphere. In order to do retrievals of temperature and concentration profiles, the spectral parameters for many thousands of HNO 3 transitions must be known. Currently the HITRAN database uses a constant estimated value for the air-broadened half-width of HNO 3. To help improve the line shape parameters, complex Robert–Bonamy calculations were made to determine N 2-broadened half-widths for some 5000 transitions of HNO 3 in the ν 5 band. The intermolecular potential is a sum of electrostatic terms (dipole–quadrupole and quadrupole–quadrupole) and the atom–atom potential expanded to eighth order. The trajectory parameters were adjusted to yield better agreement with measurement. Velocity integrated calculations were made at seven temperatures in order to determine the temperature dependence of the half-widths. The half-width data are compared with available rotation band measurements. The average percent difference between the measured and calculated half-widths is −2.38 for N 2-broadening and −0.65 for air-broadening. The temperature, vibrational, and rotational state dependence of the half-width are investigated.

N 2-, O 2- and air-broadened half-widths and line shifts for transitions in the ν3 band of methane in the 2726- to 3200-cm −1 spectral region

Complex Robert–Bonamy calculations of the pressure-broadened half-width and the pressure-induced line shift are made for some 4000 transitions in the ν 3 band of methane with N 2, O 2, and air as the perturbing gases. This work focuses on A and F symmetry transitions in the spectral range 2726 to 3200 cm −1. More work is needed on the intermolecular potential before calculations can be made for the E-symmetry transitions. The calculations are made at 225 and 296 K in order to determine the temperature dependence of the half-width. The calculations are compared with measurements. These data are to support remote sensing of the Earth and Titan atmospheres.

Modified complex Robert–Bonamy formalism calculations for strong to weak interacting systems

In 1979 Robert and Bonamy published a complex formalism (CRB) for the calculations of the pressure broadened half-width and collision-induced line shifts [J. Phys. Paris 40, 923 (1979)]. Application of the linked cluster theorem produced expressions that no longer needed the cut-off procedure that plagued earlier line shape theories. Recently, Ma, Tipping and Boulet (MTB) suggested that the application of the linked cluster theorem in their derivation of Robert and Bonamy was based on an invalid assumption. In their work MTB gave the modified expressions and state that the effect of the modification is more important for strong interaction systems. Here the effect of the MTB modification on the formalism of Robert and Bonamy is studied for systems which range in interaction strength from strong to weak. In particular, complex Robert–Bonamy calculations and calculations based on the modified formalism are made in the mean-relative thermal velocity approximation for the systems H2O–H2O, H2O–N2, H2O–O2, O3–N2, O3–O2, and CH4–N2 and the results from the formalisms compared for both the pressure-broadened half-width and pressure-induced line shift. The results of the two methods of computation are compared with the measurement database. It is shown that the difference between the two methods of computation is proportional to the strength of the radiator–perturber interaction and for some systems is larger than the uncertainty desired by the spectroscopy and remote sensing communities. Comparison with the measurement database shows better agreement with the CRB calculations.

Lineshape parameters for water vapor in the 3.2–17.76 μm region for atmospheric applications

Several NASA EOS instruments, the atmospheric infrared sounder (AIRS) on Aqua, and the tropospheric emission spectrometer (TES) and the high-resolution dynamics limb sounder (HIRDLS) on AURA, will be measuring water vapor in the Earth’s atmosphere in the 3.2–17.76 μm spectral region. In order to do retrievals of temperature and concentration profiles, the spectral parameters for many thousands of water vapor transitions must be known. Currently the largest uncertainty in these data is associated with the pressure-broadened half-width. To help ameliorate this situation, complex Robert–Bonamy calculations were made to determine N 2-, O 2-, and air-broadened half-widths and line shifts for 5442 transitions of the principal isotopologue of water vapor for the 11 vibrational bands in this region. The intermolecular potential is a sum of electrostatic terms (dipole–quadrupole and quadrupole–quadrupole), isotropic induction and London dispersion terms, and the atom–atom potential expanded to eighth order. The parameters are adjusted as described in Gamache and Hartmann [J. Quant. Spectrosc. Radiat. Transfer 83 (2004) 119]. Calculations were made at 225 and 296 K in order to determine the temperature dependence of the half-widths. When possible the data are compared with measurements. The average percent difference between the measured and calculated half-widths is −1.97, 2.6, and −1.55 for N 2-, O 2-, and air-broadening of water vapor, respectively. The agreement for the line shifts is less satisfactory. It is clear from this work that the calculations will benefit from a comprehensive adjustment of the intermolecular potential.

Analytical Evaluation of the Maxwell–Boltzmann Velocity Average in Pressure-Broadened Half-Width Calculations

For the first time the half-width within the complex Robert–Bonamy (CRB) formalism is calculated without making the mean relative thermal velocity approximation. The application is to the nitrogen-broadened half-width of the 500.4-GHz transition (342 32←341 33) of the ground vibrational state of ozone. For each state of the perturber, the optical cross sections are determined at a number of velocities with the intermolecular potential taken as a sum of electrostatic contributions and Lennard–Jones (6–12) atom–atom components. The dynamics of the collision process are correct to second order in time. Using a nonlinear least-squares fitting method, the optical cross sections are fit to a double power law, which allows the velocity integral for the half-width to be done analytically. The results are compared with the mean relative thermal velocity complex Robert–Bonamy calculations and with measurement. The temperature dependence of the half-width, which is necessary for reduction of remotely sensed data, is determined from both methods and compared with experiment.

Argon-induced halfwidths and line shifts of water vapor transitions

Pressure-broadened halfwidths and pressure-induced line shifts are determined for water vapor transitions with argon as the perturbing gas. Calculations based on the complex Robert–Bonamy (CRB) formalism are made for a number of vibrational bands, for which there are experimental data to compare with. The intermolecular potential is taken as a sum of Lennard–Jones (6–12) atom–atom, isotropic induction, and dispersion components. The dynamics of the collision process are correct to second order in time. The calculations demonstrate that the atom–atom potential for this system should be expanded to 12th order. A new feature in the CRB approach is that the real and imaginary components of the Liouville S matrix affect both the halfwidth and the line shift. It is shown here that the imaginary parts of the S matrix strongly affect the calculated H 2O–Ar halfwidths. The calculated values are compared with those obtained in a number of experimental studies. In general, good agreement is observed between the CRB calculations and the measured values for both halfwidths and line shifts. It is also clear that some parameters describing the intermolecular potential need to be better determined.