Herman-Wallis Coefficients Research Articles

Detection of Vibration−Rotational Band 5−0 of 12C16O X 1Σ+ with Cavity Ringdown Absorption near 0.96 μm

We have recorded extremely weak absorption in the overtone band 5-0 of 12C16O X 1sigma+ near 0.96 microm with cavity ringdown spectroscopy; the light source was a Raman-shifted dye laser pumped with a frequency-doubled Nd:YAG laser. This band shows lines in branch P to be much more intense than corresponding lines in branch R, in contrast to all lower overtone bands v-0 (v = 1-4). This reversal in relative intensity is explained quantitatively in terms of a radial function for the electric dipolar moment of CO. We have estimated absorption line strengths for P3-P18 in band 5-0 of 12C16O; these strengths are consistent with a pure vibrational matrix element <5/p(x)/0> = (3.6 +/- 0.3) x 10(-36) C m of the electric dipolar moment p(x), a Herman-Wallis coefficient C0(5) of about -0.1, and a band strength of (5.1 +/- 1.3) x 10(-29) m at 293 K.

Line intensities of acetylene in the 3- [formula omitted]m region: New measurements of weak hot bands and global fitting

About 170 line intensities of 14 weak parallel hot bands of acetylene have been measured in the 3- μ m region. Absolute values of line intensities are obtained with a mean uncertainty of 10%, except for a few lines of 3 very weak bands (uncertainty up to 20%). Vibrational transition dipole moment and Herman–Wallis coefficients have been determined for each measured band. These measured line intensities together with previously published ones (JQSRT 2005;92:239–60) have been treated simultaneously within the framework of the effective operators approach. Using only 6 effective dipole moment parameters, it was possible to reproduce the 591 measured line intensities of the 20 bands with a root mean square of the residuals equal to 4.2%.

A multispectrum analysis of the ν2 band of H 12C 14N: Part I. Intensities, broadening, and shift coefficients

Absolute intensities, self- and air-broadening coefficients, self- and air-induced shift coefficients and their temperature dependences have been determined for lines belonging to the P- and R-branches of the ν 2 band of H 12C 14N centered near 712 cm −1. Infrared spectra of HCN in the 14-μm region were obtained at high resolution (0.002–0.008 cm −1) using two different Fourier transform spectrometers (FTS), the McMath-Pierce FTS at the National Solar Observatory on Kitt Peak and the Bruker IFS 120HR FTS at the Pacific Northwest National Laboratory. Spectra were recorded with 99.8% pure HCN as well as lean mixtures of HCN in air at various temperatures ranging between +26 and −60 °C. A multispectrum nonlinear least squares technique was used to fit selected intervals of 36 spectra simultaneously to obtain the line positions, intensities, broadening, and shift parameters. The measured line intensities were analyzed to determine the vibrational band intensity and the Herman–Wallis coefficients. The measured self-broadening coefficients vary between 0.2 and 1.2 cm −1 atm −1 at 296 K, and the air-broadening coefficients range from 0.08 to 0.14 cm −1 atm −1 at 296 K. The temperature dependence exponents of self-broadening range from 1.46 to −0.12 while the corresponding exponents for air broadening vary between 0.58 and 0.86. The present measurements are the first known determination of negative values for the temperature dependence exponents of HCN-broadening coefficients. We were able to support our self-broadening measurements with appropriate theoretical calculations. Our present measurements are compared, where possible, with previous measurements for this and other HCN bands, as well as the parameters that are included in the 2000 and 2004 editions of the high-resolution transmission (HITRAN) database.

Line intensities of acetylene at [formula omitted

More than 400 absolute line positions and intensities of acetylene have been measured for the two cold bands ν 3 and ν 2 + ( ν 4 + ν 5 ) + 0 , and four strong hot bands occuring in the 3- μ m spectral region, from Fourier-transform spectra. Accuracies are on the average 0.0005 cm - 1 for line positions and 5% for line intensities. Vibrational transition dipole moment values have been deduced, as also empirical Herman–Wallis coefficients, and comparisons have been made with previous results.

Spectral line parameters in the (2 ← 0) overtone band and the dipole moment function of the HI molecule

We present here new high-resolution experimental data on the linestrengths and pressure-broadened Lorentzian widths for the P 2(13) to R 2(12) vibration–rotation lines in the first overtone absorption band of hydrogen iodide. By combining the measured linestrengths with our previous results for the fundamental band [J. Mol. Spectrosc. 218 (2003) 75] and with other published data for the higher-overtone bands of this molecule, an improved dipole moment expansion as a function of the dimensionless reduced nuclear displacement x is obtained: μ( x)=0.4471(5)−0.0772(2) x+0.542(3) x 2−1.90(2) x 3. This experimental dipole moment function is compared with the results of a few recent non-relativistic and relativistic ab initio calculations. The agreement between theoretical and experimental Herman–Wallis coefficients for the first two vibrational bands of HI is found best as ever reported before.

A multispectrum analysis of the ν1 band of H 12C 14N: Part I. Intensities, self-broadening and self-shift coefficients

The infrared spectrum of HCN in the region between 3150 and 3450 cm −1 has been recorded at 0.005 and 0.008 cm −1 resolution using two different Fourier transform spectrometers, the McMath–Pierce Fourier transform spectrometer located at the National Solar Observatory (on Kitt Peak) and the Bruker-120HR Fourier transform spectrometer situated at the Pacific Northwest National Laboratory at Richland, Washington. Room temperature measurements were made of positions, absolute intensities, self-broadening and self-shift coefficients for individual lines belonging to the HCN ν 1 band centered near 3311 cm −1 . These are to our knowledge the first extensive set of self-broadening and self shift measurements in the band. In addition, intensities, self-broadening and self-shift coefficients for several lines of the ν 1+ ν 2 1− ν 2 1 hot band and several intensities for lines in the H 13C 14N and H 12C 15N isotopomers were also determined. A multispectrum nonlinear least-squares fitting algorithm was used to fit the entire spectral region covering the 3200– 3400 cm −1 region of up to 27 spectra simultaneously. The measured line intensities in the ν 1 band were further analyzed to derive the vibrational band intensity and the Herman–Wallis coefficients. Differences in line intensities between 5 and 10% are found with respect to present measurements and the values given in the HITRAN database for m values beyond 25 in the P branch and 5 in the R branch.

Strengths of absorption features in vibration-rotational band v=6← v=0 of 14N 16O X 2Πr in the near infrared region

The strengths or integrated absorption intensities of individual features in band v=6← v=0 of gaseous 14N 16O X 2 Π r are measured at (297.35 ± 0.4) K with spectral resolution 6 m −1. For unresolved features near band heads in R branches, partition of total intensity enables estimates for each transition, apart from spin-rotation doubling and hyperfine effects. As a sum of these strengths of lines, the strength of the entire band centred near 1 083 606 m −1, including sub-bands for both 2 Π 1/2 and 2 Π 3/2, is (5.63±0.28)×10 −27 m. We compare measured strengths with those calculated from deduced values of transition moment for electric dipolar moment and Herman–Wallis coefficient.

High-resolution FTIR measurement of the line parameters in the fundamental band of HI

The linestrengths and self-broadening coefficients are determined from high-resolution measurements for P ( 1 ) – P ( 10 ) and R ( 0 ) – R ( 15 ) lines in the fundamental vibration–rotation band of hydrogen iodide at different gas pressures in the range of 2–280 Torr. Dipole matrix elements are calculated from the linestrength data. New values of the Herman–Wallis coefficients obtained, C 10 = 0.1319 , D 10 = 4.41 × 10 - 3 , are in a better agreement with theory than previously reported. A significant influence of the hyperfine splitting on the spectral line profiles is demonstrated.

Absolute intensity measurements of the [formula omitted] laser bands near [formula omitted

Line intensities of the two 12 C 16 O 2 laser bands ( ν 3– ν 1 and ν 3–2 ν 2 0) centered near 960.9 and 1063.7 cm −1 , respectively, were obtained from analysis of 30 room temperature long path laboratory absorption spectra recorded at 0.0028 and 0.0053 cm −1 resolution with the McMath–Pierce Fourier transform spectrometer at the National Solar Observatory (located on Kitt Peak). The spectra were analyzed simultaneously with the multispectrum nonlinear least-squares fitting procedure. The measured line intensities were further analyzed to derive the vibrational band intensities and Herman–Wallis coefficients.

The spectrum of acetylene in the 5-μm region from new line-parameter measurements

Abstract Using Fourier Transform spectra (unapodized FWHM: 0.002 cm −1 ) of acetylene 12C2H2, absolute line positions have been obtained in the 5-μm region for about 490 lines belonging to 15 hot bands arising from the v4=1 or v5=1 lower vibrational level, improving the data available in this spectral region. Absolute line intensities have been measured for about 410 lines, from which vibrational transition dipole moments squared could be determined, as well as empirical Herman-Wallis coefficients when it was possible. The self-broadening coefficients of more than 370 lines have been measured at room temperature, showing that no vibrational dependence exists for the bands of acetylene already studied, and allowing a significant determination of their rotational dependence. Furthermore, about 120 measured values of self-shifting coefficients are tentatively proposed. Combining results published for other bands, and using the smoothed line-parameter values obtained in this work, a HITRAN-format line list of the acetylene molecule has been set up in this spectral region.

Multispectrum fitting measurements of line parameters for 5-μm cold bands of acetylene

Using FT spectra (unapodized FWHM: 0.002 cm −1 ) of acetylene 12 C 2 H 2 , absolute line positions have been measured (average accuracy: ±0.0002 cm −1 ) between 1860 and 2180 cm −1 in the 3 ν 5 1, (2 ν 4+ ν 5) 1I, and (2 ν 4+ ν 5) 1II cold bands, improving the wavenumbers previously published by Plı́va under a resolution of about 0.03 cm −1 . Absolute intensities have been obtained for more than 130 lines, with a mean accuracy of ±5%, the accuracy of the amount of 12 C 2 H 2 in the sample being estimated to be better than 2%. For each band, the vibrational transition dipole moment squared has been determined, as well as empirical Herman–Wallis coefficients. Self-broadening coefficients have been measured at room temperature for more than 120 lines. No striking vibrational dependence has been observed for the self-broadening coefficients, and a polynomial expansion describing the rotational dependence is given. Furthermore, self-shifting coefficients have been measured for 89 lines, together with more than 150 absolute line positions. A multispectrum fitting procedure has been used to retrieve the line parameters from the spectra, and cross comparisons have been performed on a few lines between two different codings of this procedure.

Line intensities of hot bands in the [formula omitted] spectral region of acetylene 12C 2H 2

Using FTS spectra (apodized FWHM: 0.0014 cm −1 ), absolute intensities have been measured for 355 hot lines of 12C 2H 2 in the 13.6 μm spectral region, with an accuracy of ±5%. Intensities of lines with J values up to 31 have been obtained for the five following hot bands: 2 ν 5 0− ν 5 1, 2 ν 5 2− ν 5 1, ( ν 4+ ν 5) + 0− ν 4 1, ( ν 4+ ν 5) − 0− ν 4 1, and ( ν 4+ ν 5) 2− ν 4 1. The vibrational transition dipole moment squared and the Herman–Wallis coefficients have been determined for each band. On the whole, the measured line intensities have been found greater than the 1996 HITRAN values by about 11%.

Line intensities in the ν5 band of acetylene 12C 2H 2

Using FTS spectra (apodized FWHM: 0.0014 cm −1) , absolute intensities have been measured for about 80 lines of the ν 5 band of 12C 2H 2 at 13.6 μm , with an accuracy of ±5%, improving the already published measured values. The vibrational transition dipole moment squared has been determined: |R 0| 2=(9.81±0.11)×10 −2 D 2 (1 D=3.33546×10 −30 C m), as also the Herman–Wallis coefficients: A 1 RP =(−9.34±1.85)×10 −4, and A 2 RP =(4.30±0.89)×10 −5. On the whole, the measured line intensities have been found greater than the 1996 HITRAN values by about 14%.

Analytical expressions for the Herman–Wallis coefficients in the Raman Q-branch transitions of a diatomic molecule

The matrix elements of the dynamic polarizability isotropy and anisotropy in the Raman Q-branch transitions of diatomic molecules are investigated. These matrix elements are given by 〈vJ| f |v′J〉=〈v 0| f |v 0′〉G vv′(m) where m= J( J+1) and G vv′ ( m) is the rotational factor. By using a nonconventional approach to the Rayleigh–Schrödinger perturbation theory, this rotational factor can be written in the form G vv′ ( m)=∑ i=0 A i m i where A i are the Herman–Wallis coefficients for the Q-branch. These coefficients are given by analytic expressions in terms of Ψ v ( i) and Ψ v′ ( i) defined in the conventional perturbation theory. The order of correction in G vv′ ( m) is not limited, it is left to the precision needed by the user. A numerical application is presented for the ground states of the molecule N 2, H 2 and CO. A comparison with numerical calculation and published results shows the validity and the good accuracy of the present formulation.

Emission spectra of HCN/HNC in the 2–5 μm range of astrophysical interest

Emission from H 12C 14N observed with a Fourier transform spectrometer from a radio-frequency excited plasma is reported in the 2400–3400 cm −1 spectral range of astrophysical interest. The molecular constants, for 21 vibration–rotation bands are given, as well as estimates of the first-order Herman-Wallis coefficients for 11 bands. These constants are derived from about 900 observed transitions in HCN, and are used to generate a sequential linelist of about 1400 calculated line positions, within a standard deviation equal to 3×10 −4 cm −1. The relative intensities of the observed lines are also reported, as well as those for the ν 1 band of H 14N 12C, at 3650 cm −1, simultaneously observed from the same plasma.

Line parameter measurements of trace gases in the near infrared region

The absorption spectra of CO 2, CO, and N 2O in the near infrared region were measured with a high-resolution Fourier transform spectrometer to examine the uncertainties of the line parameters of spectroscopic databases. The line strengths and half-widths of these molecules were determined by a nonlinear least squares technique. We compared our results with the values compiled in the HITRAN databases. Large differences between the measured line strengths and the compiled ones in the HITRAN databases were found for the weak bands of each molecule. The Herman-Wallis coefficient was determined for the first overtone band of CO. Self-broadened half-widths of CO 2 and N 2O agreed with the HITRAN96 values; while self-broadened half-widths of CO were different from the HITRAN96 values. N 2 − and O 2 − -broadened half-widths of CO were very close to the values previously reported by others.

Line Positions and Absolute Intensities in the Laser Bands of Carbon-12 Oxygen-17 Isotopic Species of Carbon Dioxide

Infrared spectra of a carbon dioxide sample enriched with oxygen-17 have been recorded with a resolution of about 0.0025 cm−1in the region of the laser bands near 10 and 9 μm, using the long path difference Fourier Transform Spectrometer of the LPMA in Paris. The two laser bands of the16O12C17O and17O12C18O species have been analyzed for the first time. Line intensities for several isotopic species have been measured in this region and the rotationless transition dipole moments and Herman–Wallis coefficients of the corresponding bands have been reported. In particular intensities, alternation in the spectra of17O12C17O has been analyzed.

Explicit pure rotational effect for diatomic molecule in infrared transitions

The rovibrational matrix element M v′J′ vJ=〈Ψ vJ| γ|Ψ v′J′〉 is considered in the pure rotational case ( v=v′) for i.r. spectra (| J′− J|=1). The explicit rotational effect in M v′J′ vJ is sought by introducing the parameter m=[ J′( J′+1)− J( J+1)]/2, and by using an unconventional approach of the Rayleigh–Schrödinger perturbation theory. It is proved that: (i) Ψ vJ = ∑ n=0 π n m n where π n are simple combinations of Ψ v0 and its first `rotational corrections'; and (ii) Ψ vJ′ = ∑ n=0 π n (−m) n , then (iii) M v′J′ vJ = ∑ n=0 μ n m n where μ n are simple combinations of simple integrals of the form 〈 y 1| γ| y 2〉 where y 1 and/or y 2 stand for Ψ v0 or one of its rotational corrections. The use of the present formulation to derive analytical expressions for the Herman–Wallis coefficients C v, D v,… shows that C v=0, D v=2 μ 2/ μ 0,… . These results are valid for any potential (either analytical or numerical), any vibrational level v (even near the dissociation), and any operator γ. The numerical application shows that high accuracy is obtained with a simple algorithm and simple numerical analysis tools.

Infrared Fundamental and First Hot Bands of O12C17O Isotopic Variants of Carbon Dioxide

Infrared spectra of16O12C17O,17O12C17O, and17O12C18O in a carbon dioxide sample enriched with oxygen-17 have been recorded with a resolution of about 0.0025 cm−1in the regions of the fundamental bands, ν2(600–800 cm−1) and ν3(2200–2400 cm−1), and in the region of the “forbidden” band, ν1(1200–1400 cm−1), using the long path difference Fourier transform spectrometer of the LPMA in Paris. For each species, the first hot band in the 4.5-μm region and two hot bands at least in the 15-μm region have been studied for the first time, and a simultaneous reduction of wavenumbers measured in different spectral regions has been carried out yielding new or improved spectroscopic constants. Line intensities have been measured in the region of the ν2and ν3bands of16O12C17O, and the corresponding rotationless transition dipole moments and Herman–Wallis coefficients have been reported.

Fourier Transform Spectroscopy of18O-Enriched Carbonyl Sulfide from 1825 to 2700 cm−1

We have measured the Fourier transform spectrum of carbonyl sulfide from 1825 to 2700 cm−1, using a sample enriched in both18O (94.0%) and17O (1.54%). A careful calibration yields a line-position accuracy between 1.5 and 3.0 10−5cm−1. We have observed and analyzed 118 infrared bands of which 93 are measured for the first time: 55 for18O12C32S, 20 for18O12C34S, 11 for18O12C33S, 1 for18O12C36S, 12 for17O12C32S, 4 for17O12C34S, 2 for17O12C33S, and 13 for18O13C32S. Intensities are also reported and analyzed for all those bands. The intensity accuracy is better than 10%, and the precision of approximately 1% allows us to determine some Herman–Wallis coefficients.