Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

Ar-Broadening of isotropic Raman lines in the ν2 band of acetylene

Using a high resolution Raman spectrometer, we have measured Ar-broadening coefficients in the ν₂Q branch of C₂H₂ for 22 lines at 295 K, 20 lines at 174 K, and 16 lines at 134 K. These lines with J values ranging from 1 to 23 are located in the spectral range 1970.9-1974.3 cm⁻¹. The collisional widths are obtained by fitting each spectral line with a Rautian profile. The resulting broadening coefficients are compared with theoretical values arising from close coupling and coupled states calculations. A satisfactory agreement is obtained at room as well as at low temperatures, especially for odd J lines. By comparing broadening coefficients at 295, 174, and 134 K from a simple power law, the temperature dependence of these broadenings has been determined both experimentally, and theoretically.     

Comparison of classical, semiclassical and quantum methods in hydrogen broadening of acetylene lines

Quantum close coupling (CC) calculations of H₂-broadening coefficients of infrared and isotropic Raman lines of acetylene (C₂H₂) are performed for temperatures between 77 and 2000 K. They are used to test three more approximate methods, the quantum coupled states (CS) theory, the semiclassical Robert-Bonamy (RB) formalism and the full classical (FC) model of Gordon. In order to allow a clear and well founded comparison, all the dynamical calculations were performed employing the same ab initio potential energy surface free of any adjustable parameters. It is shown that below room temperature both the coupled states method and full classical method fail at reproducing the close coupling pressure broadening coefficients while above room temperature they are correct and predict comparable accurate values for temperatures greater than about 1000 K. The values provided by the RB method are clearly not satisfactory even at the highest temperature examined. However, the temperature dependence of the RB results follows the functional form used for interpolating and extrapolating CC, CS and FC pressure broadening coefficients.     

Ar- and air-broadening coefficients in the ν3 band of CS2 at room and low temperatures

Using a diode-laser spectrometer, Ar-broadening coefficients for 16 spectral lines in the fundamental ν₃ band of CS₂ have been measured at five temperatures: 298.0, 273.2, 248.2, 223.2 and 198.2 K. These lines with J values ranging from 2 to 64 are located in the spectral range 1519-1547 cm⁻¹. The broadening coefficients are also calculated from a semiclassical impact model performed by using a simple empirical intermolecular potential. From the theoretical and experimental results obtained at the different temperatures, we have determined the n exponent values governing the temperature dependence of the broadening coefficients. The air-broadening coefficients for four spectral lines in the ν₃ band of CS₂ have also been measured experimentally at the same temperatures. They are compared to the values derived from those obtained previously for the perturbers N₂, O₂ and also Ar.     

Measurements and theoretical calculations of N2-broadening and N2-shift coefficients in the ν2 band of CH3D

In this paper, we report measured Lorentz N₂-broadening and N₂-induced pressure-shift coefficients of CH₃D in the ν₂ fundamental band using a multispectrum fitting technique. These measurements were made by analyzing 11 laboratory absorption spectra recorded at 0.0056 cm⁻¹ resolution using the McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak, Arizona. The spectra were obtained using two absorption cells with path lengths of 10.2 and 25 cm. The total sample pressures ranged from 0.98 to 402.25 Torr with CH₃D volume mixing ratios of 0.01 in nitrogen. We have been able to determine the N₂ pressure-broadening coefficients of 368 ν₂ transitions with quantum numbers as high as J″ = 20 and K = 16, where K″ = K′ ≡ K (for a parallel band). The measured N₂-broadening coefficients range from 0.0248 to 0.0742 cm⁻¹ atm⁻¹ at 296 K. All the measured pressure-shifts are negative. The reported N₂-induced pressure-shift coefficients vary from about −0.0003 to −0.0094 cm⁻¹ atm⁻¹. We have examined the dependence of the measured broadening and shift parameters on the J″, and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = −J″, J″, and J″ + 1 in the ^QP-, ^QQ-, and ^QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.7%. The N₂-broadening and pressure-shift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results of the broadening coefficients are in good overall agreement with the experimental data (8.7%). The N₂-pressure shifts whose vibrational contribution is derived from parameters fitted in the ^QQ-branch of self-induced shifts of CH₃D, are also in reasonable agreement with the scattered experimental data (20% in most cases).     

Self-, N2- and O2-broadening coefficients for the CO2 transitions near-IR measured by a diode laser photoacoustic spectrometer

Using a high-resolution tunable diode laser photoacoustic spectrometer, self-, N₂ and O₂ pressure broadening coefficients for the first 11 transitions of ¹²C¹⁶O₂ in the R branch of the (30012) ← (00001) overtone band at the 6348 cm⁻¹ have been revisited at room temperature (∼298 K). Air-broadening parameters have also been calculated from the N₂ and O₂ measurements. The dependence of the broadening on rotational quantum number m is discussed. The recorded lineshapes are fitted with standard Voigt line profiles in order to determine the collisional broadening coefficients of carbon dioxide transitions. The results are compared to our previous measurements and to the values reported in the HITRAN04 database and by other research group with a different spectroscopic technique.     

N2-broadening coefficients in the ν3 band of CS2 at room and low temperatures

Using a tunable diode-laser spectrometer, N₂-broadening coefficients have been measured for 15 lines in the ν₃ band of C³²S₂ at room and low temperatures (298, 273.2, 248.2, 223.2, and 198.2 K). These lines with J values ranging from 2 to 62 are located in the spectral range 1519-1545 cm⁻¹. The collisional widths are obtained by fitting each measured spectral line with a Voigt and a Rautian lineshape model and for a few lines we also used a Galatry model. From these results, we have determined the n parameter of the temperature dependence of each broadening coefficient. A semiclassical calculation of these broadenings has been performed by considering in addition to the main electrostatic quadrupole-quadrupole interaction an anisotropic dispersion contribution leading to satisfactory results at all temperatures and providing the n temperature dependence parameter in good agreement with the experimental determination.     

Pressure shift and broadening of 110-101 water vapor lines by atmosphere gases

This paper is devoted to the measurement of pressure shift and broadening parameters of water-vapor lines of the pure rotational transition 1₁₀-1₀₁ in the ground vibrational state of H₂¹⁶O at 556.936 GHz, H₂¹⁷O at 552.02 GHz, H₂¹⁸O at 547.676 GHz, and the vibrationally excited state v₂=1 line of H₂¹⁶O at 658.003 GHz. The broadening coefficients of the line at 556.936 GHz (for N₂ and O₂ as perturbing gases) coincide within the errors with the values obtained recently by Seta et al. [Pressure broadening coefficients of the water vapor lines at 556.936 and 752.033 GHz. JQSRT 2008;109:144-50] by means of a very different technique (THz-TDS). Pressure shift and broadening for other lines were measured for the first time. Comparison of our results with previous measurements and theoretical calculations is presented.     

CO2-broadening coefficients in the ν4 + ν5 band of acetylene

The CO₂-broadening coefficients of 24 P- and R-branch transitions in the ν₄ + ν₅ band of acetylene were measured at room temperature using a diode-laser spectrometer. These lines with J values up to 26, were located in the spectral range 1270 to 1400 cm⁻¹. The collisional broadening coefficients were retrieved by fitting the experimental profiles to the Voigt, Rautian, and Galatry lineshape models. Two experimental values for the narrowing coefficient were determined from the spectra and compared with the theoretical narrowing coefficient. The calculations of these broadenings were also performed in the frame of a semiclassical formalism involving a simple intermolecular potential with an adjustable parameter. The theoretical results are in good agreement with the experimental results and reproduce well the J dependence of the broadening coefficients.     

Helium- and argon-broadening coefficients of phosphine lines in the ν2 and ν4 bands

Pressure broadening of phosphine lines by helium and argon at room temperature has been experimentally investigated by high-resolution diode-laser spectroscopy. The broadening coefficients are measured for 38 transitions of PH₃ in the ^QR branch of the ν₂ band and in the ^PP and ^RP branches of the ν₄ band. The recorded lines with J values ranging from 3 to 14 and K from 0 to 10 are located between 1062 and 1094 cm⁻¹. The retrieval of the collisional widths is carried out by fitting each spectral line with a Voigt profile, a Rautian profile and a speed-dependent Rautian profile. The latter model provides larger broadening coefficients than the Voigt model. They are also calculated on the basis of a semiclassical model involving the atom-atom Lennard-Jones potential. The theoretical results are in reasonable agreement with the experimental data and reproduce the J and K dependencies of the broadenings.     

Pressure broadening coefficients of ν5 fundamental band lines of CH3I at 7 μm measured by diode laser absorption spectroscopy

We have measured the room temperature pressure broadening coefficients, γ, of over 100 lines in five Q-branches of the ν₅ perpendicular band of methyl iodide (¹²CH₃I) using tuneable diode laser absorption spectroscopy. The profiles of individual lines in the ^PQ₂, ^PQ₄, ^PQ₅, ^PQ₆ and ^RQ₃ branches were recorded in a 1 m long White cell and at nitrogen or oxygen pressures up to 15 Torr. The lines were fitted to the Voigt profile to obtain the collision broadened line widths. Within individual Q-branches the broadening coefficients decreased monotonically with increasing J and for nitrogen broadening varied between 0.19 cm⁻¹ atm⁻¹ at low J and 0.12 cm⁻¹ atm⁻¹ at high J. The corresponding oxygen broadening coefficients were approximately 20% smaller. Self broadening coefficients were also measured for several of the Q-branches and found to be up to ∼4 times higher than the corresponding nitrogen broadening values.     

Hydrogen line broadening in the ν2 and ν4 bands of phosphine at low temperature

Using a tunable diode-laser spectrometer, we have measured H₂-broadening coefficients of PH₃ at low temperature (173.2 K) for 27 lines in the ^QR branch of the ν₂ band and in the ^PP and ^RP branches of the ν₄ band. The recorded lines with J values ranging from 2 to 11 and K from 0 to 9 are located between 1016 and 1093 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile and a speed-dependent Rautian profile which provides slightly larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the weak electrostatic contributions. Except for three ^QR(J,K) lines, where K = J, the calculated broadening coefficients are in good agreement with the experimental data. By comparing the results obtained at room and low temperatures, the temperature dependence of linewidths has been determined both theoretically and experimentally.     

Self- and foreign-gas-broadened lineshapes in the ν1 band of NH3

Precise N₂, O₂, H₂, Ar, He, and self-broadenings and shifts have been obtained for Q- and R-branch transitions in the ν₁ fundamental band of ammonia from simultaneous fits of low-noise, high-resolution difference-frequency laser spectra at pressures from 0.07 to 27 kPa (0.5-200 Torr). Observed lineshapes exhibit significant deviations from the conventional Voigt profile, which may be attributed to Dicke narrowing and/or speed-dependent broadening. At the higher pressures, line mixing is evident and must be included in the fits. For self-broadening, line mixing is dominated by collisional tunneling transitions, whereas for the non-polar buffers, rotational relaxation among selected K states is the primary mixing mechanism.     

Experimental line broadening and line shift coefficients of the acetylene ν1 + ν3 band pressurized by hydrogen and deuterium and comparison with calculations

Theoretical and experimental values have been determined for the pressure broadening of the ν₁ + ν₃ band of acetylene by hydrogen and deuterium at 195 K, and experimental values of the pressure shifts have been determined. Theoretical values have been calculated on the basis of a recent potential energy surface using the close coupling scheme. We discuss the detailed contribution of the various rotational angular momenta of the perturbing gas and the ortho and para contribution to the total pressure broadening cross-sections. We give routes to circumvent the computational cost of such calculations. Experimental values have been measured using a tunable diode laser spectrometer assuming a Voigt line shape. These pressure broadening parameters are compared with measurements performed recently at room temperature and with present measurements performed at 195 K in the ν₁ + ν₃ band of acetylene. A satisfactory agreement is obtained with the present results and available ones at 295 K.     

Structure and broadening coefficients (He, Ar and N2) of the ν4 band of CF4

Spectra of CF₄ in the ν₄ fundamental band region have been recorded in pure gas and in mixtures with He, Ar and N₂ at resolution up to . Obtained data allowed us to evaluate the integrated band intensity, line intensity distribution and effective broadening coefficients for J-multiplets. The broadening coefficient behavior is similar to that previously registered for linear molecules: they coincide for P and R branches; the J-dependence in the case of argon is more pronounced than that for helium. The broadening coefficients for nitrogen and helium are practically the same but the values for nitrogen are scattered around the general trend.Q-branch broadening is different from that for J-manifolds. The coefficients of branch broadening are noticeably smaller. Nitrogen broadening is very close to result for the case of argon though there is a marked difference between them for J-manifolds. Collisions with argon and nitrogen broaden the Q-branch almost 3 times more effectively than collisions with helium.     

Semiclassical line broadening calculations,using an ab initio potential energy surface,in Q‐branch and S‐branch of N2 perturbed by H2

In order to improve the accuracy of Raman combustion diagnostics, the broadening coefficients of N₂ perturbed by H₂ for Q‐branch and S‐branch have been calculated by the semiclassical Robert–Bonamy model using an ab initio potential energy surface. The calculations have been performed for a large range of temperatures (from 77 to 800 K) and J rotational quantum numbers (from 0 to 60). This paper shows that our results and their temperature dependence are in good agreement with earlier published experimental and theoretical data. Moreover, our results improve the semiclassical calculations made earlier with an adapted analytical potential. The results, obtained at high temperatures and for a large range of rotational quantum numbers, are presented in order to be implemented for optical diagnostics in combustion media. Copyright © 2012 John Wiley & Sons, Ltd.     

Room-temperature broadening and pressure-shift coefficients in the ν2 band of CH3D-O2: Measurements and semi-classical calculations

We report measured Lorentz O₂-broadening and O₂-induced pressure-shift coefficients of CH₃D in the ν₂ fundamental band. Using a multispectrum fitting technique we have analyzed 11 laboratory absorption spectra recorded at 0.011 cm⁻¹ resolution using the McMath-Pierce Fourier transform spectrometer, Kitt Peak, Arizona. Two absorption cells with path lengths of 10.2 and 25 cm were used to record the spectra. The total sample pressures ranged from 0.98 to 339.85 Torr with CH₃D volume mixing ratios of 0.012 in oxygen. We report measurements for O₂ pressure-broadening coefficients of 320 ν₂ transitions with quantum numbers as high as J″ = 17 and K = 14, where K″ = K′ ≡ K (for a parallel band). The measured O₂-broadening coefficients range from 0.0153 to 0.0645 cm⁻¹ atm⁻¹ at 296 K. All the measured pressure-shifts are negative. The reported O₂-induced pressure-shift coefficients vary from about −0.0017 to −0.0068 cm⁻¹ atm⁻¹. We have examined the dependence of the measured broadening and shift parameters on the J″, and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = −J″, J″, and J″ + 1 in the ^QP-, ^QQ-, and ^QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.4%. The O₂-broadening and pressure shift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results of the broadening coefficients are generally larger than the experimental data. Using for the trajectory model an isotropic Lennard-Jones potential derived from molecular parameters instead of the spherical average of the atom-atom model, a better agreement is obtained with these data, especially for |m| ? 12 values (11.3% for the first calculation and 8.1% for the second calculation). The O₂-pressure shifts whose vibrational contribution are either derived from parameters fitted in the ^QQ-branch of self-induced shifts of CH₃D or those obtained from pressure shifts induced by Xe in the ν₃ band of CH₃D are in reasonable agreement with the scattered experimental data (17.0% for the first calculation and 18.7% for the second calculation).     

Broadening, shifting, and line mixing in the 030 ← 010 parallel Q branch of N2O

The 03¹0 ← 01¹0 parallel Q branch of N₂O has been studied at 297 K and over the pressure range 1-130 torr. Absorption spectra were recorded using a high resolution (1.5 MHz or 5 × 10⁻⁵ cm⁻¹) and high signal-to-noise (>3500:1) mid-infrared spectrometer based on difference-frequency infrared generation in AgGaS₂. In the low-pressure range (1-11 torr) we obtained accurate values for the line strengths, the broadening coefficients, the weak mixing coefficients, and the overall shifting of the branch. The medium pressure results, ranging from 23 to 130 torr, were analyzed by treating the band as a whole, using a relaxation matrix formalism, based on an energy gap scaling law. We find, effectively, that only 36% of the rotationally inelastic collisions are associated with Q branch mixing, the rest presumably being associated with Q-P and Q-R mixing in the same vibrational band. The pressure shifting coefficient of the 03¹0 ← 01¹0 Q branch as a whole was also determined and found to be 5.8 × 10⁻³ cm⁻¹/atm towards lower frequencies.     

Pressure broadening coefficients of transitions in the ν5 band of methyl bromide from fitting to Voigt and Galatry line profiles

Tuneable diode laser absorption spectroscopy has been used to measure the room temperature pressure broadening coefficients (γ) of rotational transitions in the v₅ fundamental band of methyl bromide (¹²CH₃⁷⁹Br and ¹²CH₃⁸¹Br) around 6.9 μm. Nitrogen, oxygen and self-broadening coefficients have been determined for 125 lines in the ^RQ₁, ^PQ₃, ^PQ₅, ^PQ₇ and ^PQ₈ branches and 49 P and R branch transitions. Line profiles within Q branches were recorded at incremental pressures of nitrogen and oxygen up to 15 Torr and fitted to a Voigt profile to yield the broadening coefficients. The nitrogen broadened data for 14 lines, chosen from the five Q branches, were also fitted with Galatry profiles. The line profiles of the P and R branch transitions were recorded for total nitrogen and oxygen pressures of up to 300 Torr and fitted to both Voigt and Galatry profiles. Within individual Q branches, nitrogen broadening coefficients were found to decrease monotonically with increasing J from 0.14 cm⁻¹ atm⁻¹ at low J to 0.09 cm⁻¹ atm⁻¹ at high J. The corresponding values for oxygen were approximately 25% smaller. Self-broadening coefficients were found to vary between 0.48 and 0.16 cm⁻¹ atm⁻¹ with a similar J dependence to the foreign gas broadening for J > 20. However, between J = 2 and J ≈ 20 the broadening coefficient was found to increase with J. The magnitude of the pressure broadening coefficient for P and R branch transitions was found to closely follow the J dependence measured for the Q branch lines.     

Measurements and theoretical calculations of self-broadening and self-shift coefficients in the ν2 band of CH3D

In this paper, we report measured Lorentz self-broadening and self-induced pressure-shift coefficients of ¹²CH₃D in the ν₂ fundamental band (ν₀ ≈ 2200 cm⁻¹). The multispectrum fitting technique allowed us to analyze simultaneously seven self-broadened absorption spectra. All spectra were recorded at the McMath-Pierce Fourier transform spectrometer of the National Solar Observatory (NSO) on Kitt Peak, AZ with an unapodized resolution of 0.0056 cm⁻¹. Low-pressure (0.98-2.95 Torr) as well as high-pressure (17.5-303 Torr) spectra of ¹²C-enriched CH₃D were recorded at room temperature to determine the pressure-broadening coefficients of 408 ν₂ transitions with quantum numbers as high as J″ = 21 and K = 18, where K″ = K′ ≡ K (for a parallel band). The measured self-broadening coefficients range from 0.0349 to 0.0896 cm⁻¹ atm⁻¹ at 296 K. All the measured pressure-shifts are negative. The reported pressure-induced self-shift coefficients vary from about −0.004 to −0.008 cm⁻¹ atm⁻¹. We have examined the dependence of the measured broadening and shift parameters on the J″, and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = −J″, J″, and J″ + 1 in the ^QP-, ^QQ-, and ^QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 3.6%. A semiclassical theory based upon the Robert-Bonamy formalism of interacting linear molecules has been used to calculate these self-broadening and self-induced pressure-shift coefficients. In addition to the electrostatic interactions involving the octopole and hexadecapole moments of CH₃D, the intermolecular potential includes also an atom-atom Lennard-Jones model. For low K (K ? 3) with |m| ? 8 the theoretical results of the broadening coefficients are in overall good agreement (3.0%) with the experimental data. For transitions with K approaching |m|, they are generally significantly underestimated (8.8%). The theoretical self-induced pressure shifts, whose vibrational contribution is derived from results in the ^QQ-branch, are generally smaller in magnitude than the experimental data in the ^QP-, and ^QR-branches (15.2%).