Herman-Wallis Factors Research Articles

Absolute Line Intensities in the ν2 Band of 12CH335Cl at 7.5 μm

The strengths of 100 lines in the ν2 band of 12CH335Cl have been measured at high resolution in the region of 1350 cm−1, using a tunable diode-laser spectrometer. These intensities were obtained from the equivalent width method and by fitting Voigt profiles to the measured shapes of the lines. The latter method also provides the collisional widths of the lines. From these linestrength measurements, we have determined the absolute intensity of the ν2 band to be 33.46 ± 0.13 cm−2 atm−1, its transition dipole moment to be (5.006 ± 0.001) × 10−2 D, and the first Herman-Wallis factor to be (−3.05 ± 0.09) × 10−3.

Absolute Intensities in CO2: 3ν3 near 1.4 μm

Absolute intensities of about 100 lines of CO2, have been measured in the region from 6894 to6988 cm−1. Our measurements include 3ν3 (00031-00001 ) as well as the principal hot band 3ν3 + ν2 − ν2 (01131-01 101). The squared transition dipole matrix elements and Herman-Wallis factors are: [formula] The measurements were made independently in Paris and in Ottawa and were found to be in good agreement.

Absolute Line Intensities of the ν6 Band of CH335Cl at 10 μm

Strengths of individual lines in the ν6 degenerate fundamental at 10 μm of methyl chloride have been measured at room temperature using a diode laser spectrometer. From these measurements we have determined by a linearized fit two significant intensity parameters, namely, the band strength, Sv0 = 15.06 ± 0.19 cm−2 atm−1 at 297 K and the parameter α = 0.0081 ± 0.0017 of the Herman-Wallis factor F = (1 + αKΔK + ···)2.

Absolute intensities in CO 2: The laser bands near 10 μm

Absolute intensities of about 400 lines of CO 2 have been measured in the region from 760 to 1100 cm −1. The squared transition dipoles and the Herman-Wallis factors for the laser bands centered at 960.959 and 1063.735 cm −1 are: ν/cm −1 Transition |R| 2/ Debye 2 A 1 RP × 10 4 A 2 RP × 10 5 961.0 00011-10001 0.001493(45) −6.41(16) −0.917(53) 1063.7 00011-10002 0.001219(36) −2.66(24) −1.499(78) These results are in very satisfactory agreement with recent theoretical predictions and also with other experimental measurements. In addition to the laser bands, the two strongest hot bands at 927.2 (01111-11101) and 1071.5 cm −1 (01111-11102), the perpendicular band at 791.4 cm −1 (11101-10002), and the laser bands of 13C 16O 2 at 913.4 (00011-10001) and 1017.7 cm −1 (00011-10002) have also been measured.

Quadratic Herman-Wallis factors for symmetric- and asymmetric-top molecules

As a result of vibration-rotation interactions, the effective dipole moment operator of a molecule depends on the total angular momentum as well as the vibrational operators. This leads to a rotational dependence of transition moments additional to that implied by the direction-cosine matrix elements. For allowed rotational transitions in the ν i fundamental band of a symmetrictop molecule, the linestrengths S are given by S = S 0 F HW, where S 0 is given by the rotation-independent part of the effective dipole moment and the Herman-Wallis rotational correction factor F HW is F HW ={1+A i im J+A K i m K+A JJ(Q) i[ J(J + 1)−m 2 J]+A JJ(PR) i m 2 J+A KK i K 2 +A JK im Jm K} 2 , where m J = [J′(J′ + 1) − J″(J″ + 1)] 2 , m K = [k′ 2 − k″ 2] 2 , J(J + 1) = [J′(J′ + 1) + J″(J″ + 1)] 2 , and K 2 = [K′ 2 + K″ 2] 2 . The terms in m K are absent for a parallel band. If different ( J, k) transitions are mixed together, as in l-resonance, the factor in braces can be applied to the individual matrix elements. Relations are given between the A i coefficients and the θ i β, α and θ i βγ, α coefficients in the expansion of the effective dipole moment operator for both parallel and perpendicular fundamentals, and the theory is illustrated by comparing variational and perturbation calculations for ν 2 of H 3 +. Results are also given for asymmetric-top molecules, where a formula analogous to the above but with k 2 replaced by the rotational energy F( J K a K c ) is derived.

Radiative transition probalities for all vibrational levels in the X 1Σ+ state of HF

Recent analyses have led to an experimentally based potential energy curve for the ground state of HF which includes nonadiabatic corrections and which joins smoothly to the long-range potential at an accurately determined dissociation limit (De=49 362±5 cm−1). Using this potential curve and a new ab initio dipole moment function (in excellent agreement with experiment), accurate radiative transition probabilities among all vibrational levels (v=0–19 known, v=20 predicted) of the ground state of HF have been calculated for selected rotational quantum numbers. Comparisons of Einstein A spontaneous emission coefficients, dipole moment absorption matrix elements, and Herman–Wallis factors for absorption bands are presented.

12C 16O: Experimental determination of the linear coefficient of the Herman-Wallis factor

From intensity measurements of the rovibrational lines of 12C 16O in absorption, we have determined the linear coefficient of the Herman-Wallis factor with a precision of a few percent. No experimental determination has ever been done before for this molecule. The experimental results are compared to the theoretical calculations. The agreement with these calculations is very good (∼10%).

Absolute intensities in CO 2: The ν2 fundamental near 15 μm

About 925 absolute intensities have been measured in 18 bands of CO 2 in the region of the ν 2 fundamental near 15 μm. In addition to the band intensities many Herman-Wallis factors have also been determined. The results for the fundamental and the three strongest hot bands of the main isotope are summarized below: v 2 |R| 2 = 0.03294(5)[1+0.00096(2)m] 2 (P,R) v 1(l=0)−v 2 |R| 2 = 0.01505(4)[1+0.00107(7)m] 2 (P,R) = 0.01505(4)[1+0.000022(2)J(J+1)] 2 (Q) 2v 2(l=2)−v 2 |R| 2 = 0.0641(1)[1+0.00096(3)m] 2 (P,R) 2v 2(l=0)−v 2 |R| 2 = 0.01722(3)[1+0.00096(5)m] 2 (P,R) = 0.01721(3)[1+0.000031(2)J(J+1)] 2 (Q)

Spectral intensities in the v 3-band of 12CH3 35Cl at 13 μm

A tunable diode laser spectrometer was used to perform measurements of absolute intensities for 98 lines in the v 3-fundamental of methyl chloride. From these data, the vibrational band strength S 0 v was calculated at 296K and for hundred percent of the 12CH3 35Cl-species to be S 0 v = 90·7 ± 1·3cm-2 atm-1 with the uncertainty covering three times the standard deviation. Furthermore the α1-coefficient involved in the Herman-Wallis factor F = (1 + α1 m + …)2 was significantly derived, α1 = -0·00120 ± 0·00018. These results can be used for further applications such as sensing and determination of atmospheric methyl chloride via its absorption in the 13 μm spectral region.

Quadratic Herman-Wallis factors in the fundamental bands of linear molecules

General theoretical formulas are derived for the coefficients in the terms M ̃ 12 and M ̃ 13 of the effective molecular dipole moment operator, and applied to the parallel and perpendicular fundamentals of linear molecules. The Herman-Wallis factors for P- and R-branch lines are F PR = [1 + A 1m + A 2 PRm 2 ] 2 , m = δ J( J ′ + J ″ + 1)/2 and for Q-branch lines F Q = [1 + A 2 QJ ( J + 1)] 2 The quadratic coefficients A 2 PR and A 2 Q depend on up to cubic potential derivatives and quadratic dipole derivatives. Calculated A 2 PR and A 2 Q values for the fundamentals of CO 2 do not agree well with recent measurements of Johns, and possible reasons for the discrepancies are discussed.

Absolute intensity and pressure broadening measurements of CO 2 in the 4.3-μm region

Absolute intensity measurements of about 340 lines in the spectrum of CO 2 have been made in the vicinity of 4.3 μm. The intensity of the fundamental of 12C 16O 2 is found to be 2219(40) cm −2/atm at 300 K. Because the extensive measurements cover both P- and R-branch regions it has also been possible to measure the Herman-Wallis factors. It is found that the squared transition dipole moment for this band can be expressed (in Debye 2): | R| = 0.1026[1 − 0.000145 m + 0.0000026 J ′( J ′ + 1)] 2 Several hot bands have also been measured including 01 11-01 10, 02 01-02 00, 02 21-02 20, and 10 01-10 00 as well as the stronger bands of the less abundant isotopic species. Self broadening and some nitrogen broadening coefficients have been measured in good agreement with previous experimental results on other vibrational levels. Some disagreement is found with theoretical predictions at low values of J.

The high-resolution infrared spectra of the ν2 and ν3 bands of HOCl

The infrared spectra of the a-type transitions of the ν 2 and ν 3 bands of HO 35Cl and HO 37Cl have been obtained under high resolution. Line assignments of both bands have been made, and the spectroscopic constants have been obtained for both bands using a Watson Hamiltonian. Lines of the K a = 5 subband of the ν 2 band of the HO 35Cl molecule were found to be slightly shifted by an interaction with the K a = 4 level of the 2 ν 3 vibrational state. The b-type transitions permitted for both bands were too weak to observe. Relative intensities of selected lines of both bands have been measured, and empirical Herman-Wallis factors have been determined.

On the vibration-rotational matrix elements for diatomic molecules

Theoretical expressions for the vibro-rotational matrix elements of powers of the reduced displacement from equilibrium, corresponding to the infrared and Raman transitions vJ→ v′J′ with v′⩽ v+4, are obtained in terms of quartic polynomials in m (or J), including contributions from theDunham potential-energy coefficients a 1, a 2, a 3. It is shown that it is preferable to consider the coefficients of the vibration-rotation interaction function [F v′ v(m)] 1 2 rather than the Herman-Wallis factors. Two formalisms derived from power series expansion of the vibration-rotational internuclear potential function have been applied to the infrared transitions v→ v′ (with v = 0, 10, 20) of the ground electronic state of CO.

Dipole moment function of hydrogen chloride

Abstract The dipole moment function of hydrogen chloride has been determined from the combined data of dipole moments, transition moments, and Herman-Wallis factors for HCl and DCl, which include the recent measurements of vibration-rotation transitions up to the v = 7 level. The direct numerical diagonalization of vibration and vibration-rotation Hamiltonian matrices has been used to obtain the radial part wavefunctions. The sextic and septic dipole moment functions thus obtained give much improved overall fit to the experimental data. The results also agree well with those obtained from the RKR procedure. Some of the features of the present dipole moment functions are discussed.

Diode laser measurements of line strengths and widths in the 4.5-μm bands of N 2O

We have made line-strength measurements in the N 2O ν 3-fundamental region using a tunable diode-laser spectrometer. From these measurements and the Herman-Wallis factor determined by Boissy et al., we find the ν 3-fundamental band strength to be S v = 1203 ± 22 cm −2 atm −1 at 297 K. Line-broadening parameters for two ν 3-fundamental lines were determined using nitrogen (N 2) as the broadening gas. Measured strengths and N 2 line-broadening parameters for several ( ν 1 2 + ν 3 − ν 1 2) hot-band lines are also presented.

HCl vibrational fundamental band: Line intensities and temperature dependence of self-broadening coefficients

Self-broadening in the vibrational fundamental of HCl is inversely proportional to the temperature for transitions which lie near the Boltzmann rotational maximum and becomes monotonically less temperature-dependent as the rotational quantum number increases. The rotationless transition moment was found to have the value of 5.57 + or - 0.13 x 10 to the -3rd (Debye)-squared and the first Herman-Wallis factor, C = -2.543 + or - 0.019 x 10 to the -2nd.

Errata: A line parameter list for the v2 and v4 bands of 12CH4 and 13CH 4, extended to J′ = 25 and its application to planetary atmospheres

Two errors in the manuscript by Orton and Robiette are discussed. One involves the formulation of the Herman-Wallis factor. The other involves a correction of the total intensity of the v 2 and v 4 bands of CH 4 to a value of 5.28 × 10 -18 cm molecule -1, as indicated by recent experimental studies.

Herman-wallis factors for higher overtone bands: Application to HCl

Theoretical expressions for the Herman-Wallis factors in terms of the Dunham potential-energy parameters and dipole-moment coefficients were derived for higher overtone bands by the method of computer algebra. These results were applied to an analysis of the vibration-rotational intensities of HCl, leading to a good fit of the data and a dipole-moment function that is improved and extended by comparison with previous results.

Line strengths of the ν1 + ν4 band of 12CH 4

The line strengths of the ν 1 + ν 4 band of 12CH 4 at 4223.5 cm −1 were measured using a leastsquares procedure that iterates between the observed spectrum and a synthetic spectrum calculated at correct instrumental and gas sample conditions. The methane spectrum was recorded at 0.011 cm −1 resolution with signal-to-noise ratios of 300 to 1 or better using a Fourier transform spectrometer at Kitt Peak National Observatory. Line assignments were evaluated and extended to upper state J of 13. The observed line strengths reflect significant perturbation by other states so that only portions of the band can be used to determine a band strength of 6.92 (2) cm −2 atm −1 at 296 K with a Herman-Wallis factor of (1 – 0.0035(2)m) 2.

Determination of the ν4 band strength of 12CH 4 from diode laser line strength measurements

The strengths of over 50 lines in the ν 4 region of 12CH 4 were measured using a diode laser spectrometer. Forty-nine lines were assigned to transitions of the ν 4 band. Analysis of the strengths of these 49 lines leads to a value of the integrated band strength S 4 0 = 127 ± 4 cm −2 atm −1 at 295.7 K; this value is compared to other recent band strength determinations. The Herman-Wallis factor, expressing the dependence of the transition moment on rotational quantum number, is also discussed.