Herman Wallis Effect Research Articles

Line lists for X3Σ− and a1Δ vibration-rotation bands of SO

SO is found in several astronomical sources such as the atmospheres of Io and Venus. To complete our work on SO line lists, we used our previous fits for v = 0 to v = 6 for the X3Σ- state and v = 0–5 for the a1Δ state [JQSRT 272, 107772 (2021)] for line positions, and high-level ab initio calculations of electric dipole moments for line strengths for the vibration-rotation bands. LeRoy's RKR program was used to produce pointwise potential energy curves. N- and v-dependent dipole matrix elements were produced with LeRoy's LEVEL program and the final line lists were made with Western's PGOPHER program. All possible vibrational bands were calculated, and the line strengths included the Herman-Wallis effect caused by vibration-rotation interaction.

A new linelist for the A3Π–[formula omitted] transition of the NH free radical

A new linelist for the A3Π–X3Σ− electronic transition of NH has been prepared using line positions from the literature and calculated line intensities. High level ab initio calculations were performed with the MOLPRO program to obtain the A–X transition dipole moment function. Potential energy curves and line strengths were calculated with Le Roy’s RKR1 and LEVEL programs. Line intensities and Einstein A values were calculated with Western’s PGOPHER program after converting the Hund’s case (b) output of LEVEL to Hund’s case (a) input needed for PGOPHER. The Herman–Wallis effect is included in the Einstein A calculations of the bands for the levels with v′=0−2 and v″=0−6.

Improved Ultraviolet and Infrared Oscillator Strengths for OH+

Abstract Molecular ions are key reaction intermediates in the interstellar medium. OH+ plays a central role in the formation of more complex chemical species and for estimating the cosmic ray ionization rate in astrophysical environments. Here, we use a recent analysis of a laboratory spectrum in conjunction with ab initio methods to calculate infrared and ultraviolet oscillator strengths. These new oscillator strengths include branch dependent intensity corrections, arising from the Herman–Wallis effect, that have not been included before. We estimate 10% total uncertainty in the UV and 6% total uncertainty in the IR for the oscillator strengths.

Einstein A-values and oscillator strengths of the A2П–X2Σ+ system of CP

Line strengths for bands of the A2П–X2Σ+ transition of CP, including the effect of rotation on the vibrational wavefunctions (the Herman–Wallis effect), have been calculated using Western׳s PGOPHER program and Le Roy׳s LEVEL program. The potential energy functions for the A2П and X2Σ+ state were computed using spectroscopic constants obtained from high resolution spectra. The RKR potentials of the two states, and the electronic transition dipole moments of this transition calculated in a recent ab initio study have been used in Le Roy׳s LEVEL program to produce transition dipole moment matrix elements. The matrix elements have been converted from Hund׳s case (b) to (a), and then used in PGOPHER to generate a line list containing observed and calculated wavenumbers, Einstein A coefficients and f-values for 75 bands with v=0–8 for both states. The Einstein A coefficients have been used to compute radiative lifetimes for v=0–5 in the A2П state. The line list may be useful for computing the molecular opacities of CP needed to simulate the spectra of stellar and substellar sources.

EINSTEIN A COEFFICIENTS AND OSCILLATOR STRENGTHS FOR THE A 2 Π- X 2 Σ + (RED) AND B 2 Σ + -X 2 Σ + (VIOLET) SYSTEMS AND ROVIBRATIONAL TRANSITIONS IN THE X 2 Σ + STATE OF CN

Line strengths have been calculated in the form of Einstein A coefficients and f-values for a large number of bands of the A 2Π-X 2Σ+ and B 2Σ+-X 2Σ+ systems and rovibrational transitions within the X 2Σ+ state of CN using Western's PGOPHER program. The J dependence of the transition dipole moment matrix elements (the Herman-Wallis effect) has been taken into account. Rydberg-Klein-Rees potential energy functions for the A 2Π, B 2Σ+ , and X 2Σ+ states were computed using spectroscopic constants from the A 2Π-X 2Σ+ and B 2Σ+-X 2Σ+ transitions. New electronic transition dipole moment functions for these systems and a dipole moment function for the X 2Σ+ state were generated from high level ab initio calculations and have been used in Le Roy's LEVEL program to produce transition dipole moment matrix elements (including their J dependence) for a large number of vibrational bands. The program PGOPHER was used to calculate Einstein A coefficients, and a line list was generated containing the observed and calculated wavenumbers, Einstein A coefficients and f-values for 290 bands of the A 2Π-X 2Σ+ transition with v' = 0-22, v'' = 0-15, 250 bands of the B 2Σ+-X 2Σ+ transition with v' = 0-15, v'' = 0-15 and 120 bands of the rovibrational transitions within the X 2Σ+ state with v = 0-15. The Einstein A coefficients have been used to compute radiative lifetimes of several vibrational levels of the A 2Π and B 2Σ+ states and the values compared with those available from previous experimental and theoretical studies.

First high-resolution analyses of the ν8 and ν8 + ν9 spectral regions of 35CIONO2: determination of the ν9 band centre

A ro-vibrational analysis of the C-type ν8 fundamental band of 35CIONO2 as well as the hot band ν8 + ν9 − ν9 has been carried out using a Fourier-transform infrared spectrum of natural chlorine nitrate recorded with a resolution of 0.000 94cm−1 at a temperature of 190 K. Accurate upper state constants have been determined for both bands including the following band centres: ν0 (ν8) = 711.207 63(9) and ν0(ν8 + ν9 − ν9) = 714.905 0(12)cm−1. These constants have been used, together with a transition moment operator that takes into account the observed Herman-Wallis effect, to successfully model the experimental spectrum. In addition, the constants of the 8191 state have been used to model the ν8 + ν9 band, allowing us to assign nearly 100 Q-branch transitions and, therefore, to determine the band centre of the ν8 + ν9 band, ν0(ν8 + ν9) = 838.626 9(15)cm−1 Consequently this allows us to obtain the band centre of ν9: ν0(ν9) = 123.721 9(20)cm−1. This establishes unambiguously that the band at 714.9cm−1 previously attributed to ν5 + ν7 − ν9 is actually the ν8 + ν9 − ν9 hot band.

Vibrational Transition Moment of the CH Radical Determined from the Herman‐Wallis Effect

The Δv = 1 emission spectrum of the CH radical was observed by a Fourier transform spectrometer. The Herman-Wallis effect observed as intensity difference in P- and R-branch transitions was analyzed to give the transition dipole moment, where we used a new method to calculate intensities of vibration-rotation spectral lines with wave functions obtained by the diagonalization of a vibration-rotation energy matrix up to v = 40. When the permanent dipole moment of 1.46 D was used, the vibrational transition moment μ10 was determined to be -0.151(10) D, with 1 standard deviation in parentheses.

Transition Dipole Moments for the Vibrational Fundamentals of HNC Determined from the Herman–Wallis Effect

The ν1and ν3fundamental bands of HNC are recorded with a Fourier transform infrared spectrometer with a resolution of 0.008 cm−1. Hydrogen isocyanide is generated in situ by dc discharge in a mixture of CH3CN (∼40 mTorr), H2(∼160 mTorr), and Ar (∼160 mTorr). The transition dipole moments for these fundamental bands are determined from the analysis of the Herman–Wallis effect, and they are compared withab initiocalculated values. It is found that theab initiovalues for the ν1and ν3bands are about 50 and 30% larger, respectively. The transition dipole moments determined are to be of use for determination of the abundance of HNC in reaction systems such as the dissociative recombination reaction of HCNH+with electrons.

A Long Path Cell for the Fourier Spectrometer Bruker IFS 120 HR: Application to the Weak ν1+ ν2and 3ν2Bands of Carbon Disulfide

The construction and properties of a White cell connected to a Bruker IFS 120 HR spectrometer are described. The maximum path length attainable is about 200 m. The cell and its use in accurate measurements where the calibration is performed with the aid of CO2laser lines in absorption has been tested with the weak bands ν1+ ν2and 3ν2of CS2. From the ground state combination differences of these bands, new, more accurate rotational constants were derived:B0= 0.109126043(50) cm−1andD0= 1.17678(31) × 10−8cm−1. The bands were fitted with a standard deviation of 4.8 × 10−5cm−1by using a model, where thel-type and Fermi resonances were included. The intensities in the bands were strikingly perturbed. These anomalies were explained and simulated with the Herman–Wallis effect.

Calculation of the Herman–Wallis effect in Π–Σ vibrational overtone transitions in a linear molecule: Comparison with HCN experimental results

The high sensitivity of cavity ring-down spectroscopy has allowed us to observe a few perpendicular vibrational overtone transitions of HCN in the visible. These transitions display a sizable Herman–Wallis effect, that is an asymmetry in the relative intensities of the R and P branch lines. We have developed a theory for the first-order Herman–Wallis effect based upon using variational vibrational wave functions but treating the vibration–rotation interaction by first-order perturbation theory. In the specific case of perpendicular transitions, the first-order effect is dominated by Coriolis mixing of Σ and Π overtone states. We used the empirical energy surface by Carter, Mills, and Handy [J. Chem. Phys. 99, 4379 (1993)] restricted to the stretching degrees of freedom. Bending was included by multiplication of these stretching wave functions by harmonic wave functions of the bend. Vibrational transition moments were calculated using a polynomial surface fit to ab initio CCSD(T) dipole moment points by Botschwina et al. [Chem. Phys. 190, 345 (1995) and private communication]. We expected that this treatment would be accurate but the calculated Herman–Wallis effect is about one order of magnitude too large. To gain further insight into the poor agreement between theory and experiment, we have calculated the sensitivity of the Herman–Wallis coefficient and of the transition moment to the dipole and energy surface parameters. From this, it appears that the dipole surface, while producing accurate band intensities, could at the same time be inadequate to account for the Herman–Wallis effect. A similar possibility stands for the energy surface, which however is highly constrained by the requirement to fit the observed band origins.

Fourier Transform Emission Spectroscopy of the Δv = 1 Bands of the CD Radical

The gas-phase vibration-rotation emission spectrum of the CD radical in the X2Π state was observed in the 1832-2150 cm−1 region with a high-resolution Fourier transform spectrometer. The CD radicals were generated by a dc discharge in a CD4 and He mixture. The spectra of the ν = 1 - 0 and 2 - 1 bands were analyzed by an effective Hamiltonian in Hund′s case (a) parity-conserving basis set written in the N2-formalism. Molecular constants of the vibrationally excited states were determined for the first time with a high precision, and the equilibrium molecular constants were determined: ωe = 2100.3457(10) cm−1, ωexe = 34.15582(39) cm−1, Be = 7.807826(33) cm−1, and αe = 0.212255(80) cm−1, with one standard deviation given in parentheses. The internuclear distance, re was also determined to be 1.117915(10) Å from the corrected equilibrium rotational constant for the second-order electronic contribution to the rotational constant. Quantitative discussions on the Herman-Wallis effect are presented for the CH and CD radicals. The analysis of this effect on the CH radical led to the transition moment of -0.190(11) D for the ν = 1 - 0 band.

The ν1 Band of HOBr

The ν1 band of HOBr centered at 3614.903 cm−1 has been observed at 0.006 cm−1 resolution. The band is a hybrid type with |(∂μb/∂Q1)/(∂μa/∂Q1)| ≈ 0.84. The spectra of both bromine isotopes have been simultaneously fitted with a single calculation which includes all the previously reported rotational transitions. There appear to be no strong local perturbations to complicate the fitting of the line positions. Precise parameters are reported for the upper states as well as improved parameters for the ground states of both species. There is a prominent Herman-Wallis effect for the b-type transitions, which is well described by linear and quadratic terms in Ka. The equilibrium structure has been calculated.

FTIR Absorption Spectrum of Indium Hydride InH

A high-resolution FTIR spectrum of InH produced in a heat pipe cell was observed in absorption; 122 transitions for two isotopic species were measured, and the molecular constants were refined by simultaneous analysis of these transitions with those of the previous measurements ( Chem. Phys. Lett. 155, 269-272, 1989). Analysis of the Herman-Wallis effect of this molecule gave μ e/( dμ/ dr) e = 0.67 (15) A, which was compared with the results for A1H and GaH reported recently ( J. Mol. Spectrosc. 164, 379-389, 1994.)

The Infrared Spectra of the Diatomic Hydrides AlH and GaH and Intensity Analyses from FTIR Measurements

High-resolution infrared spectra of aluminum hydride and gallium hydride produced in a heat pipe cell by the reaction of corresponding metals with hydrogen at high temperature were successfully observed with an FTIR spectrometer. The 88 and 111 transitions for AIH and GaH were measured and the molecular constants were refined by fitting the newly observed and already reported transitions simultaneously. Intensity analyses were carried out to estimate the Herman-Wallis effect. The sensitivity of the FTIR method is discussed by comparing it with that of infrared diode laser method.

The 2ν3 Band of 32S16O2: Line Positions and Intensities

The room temperature high resolution infrared spectrum of the 2ν3 band of 32S16O2 in the 3.7 μm region has been studied with a difference-frequency laser spectrometer and completely analyzed. The rotational levels of the upper state (002) have been reproduced to an accuracy of ±0.00008 cm−1 using a Hamiltonian matrix which explicitly takes into account the weak Fermi-type interaction coupling the rotational levels of the (002) state with those of the (130) state yielding a band origin ν0 = 2713.382660(6) cm|−1 and a complete set of rotational constants and a Fermi-type interaction constant. This band exhibits a pronounced Herman-Wallis effect. However, the intensities have been very satisfactorily fit leading to a precise vibrational transition moment for the 2ν3 band. Finally, a comprehensive set of line positions and intensities has been generated. For this band, the integrated band intensity has been found to be Sv (T = 296 K) 9.81(20) × 10−5 cm−1 Pa−1 m−1 (0.0995(20) cm−2 atm−1). A set of harmonic frequencies and vibrational anharmonic constants have been obtained. The effects of Darling-Dennison interaction appear to be very small.

Rovibrational intensities for the Δv=1 bands of the X 3Σ− NH radical: Experiment and theory

The vibrational transition dipole moment for the highly reactive radical species, NH, in its ground electronic state is obtained via the Herman–Wallis effect manifest in emission spectra produced in a plasma reactor. The results of these experiments on the five lowest Δv=1 bands, are in good agreement with high quality ab initio calculations of the electric dipole moment function.

On the dipole moment functions of ClO and OH

The electric dipole moment of ClO in the ground and first excited vibrational levels of the 2Π3/2, J=3/2 state was measured using molecular beam electric resonance. The results are 1.2974(10) (v=0) and 1.2758(12) D (v=1), with μ(v=1)−μ(v=0) being more accurately determined as −0.0216(7) D. Combination of the dipole moments with relative intensity data lead to a fundamental transition moment of −0.034(5) D. This is in excellent agreement with the results of Herman–Wallis effect measurements −0.0364(33) and −0.044(12) D and the most recent ab initio calculation, −0.0360 D. For OH, values for the v=0 through v=2 dipole moments show that the maximum of the dipole moment function occurs at an internuclear separation 0.20 to 0.25 Å larger than the equilibrium internuclear separation. The curvature about the maximum is also determined by the dipole moment measurements, however, the asymmetry about the maximum is not. Estimation of the asymmetry from ab initio calculations leads to an estimate of 28(18) S−1 for the Einstein transition probability of the 1–0 band of OH.

Infrared measurements of the ClO radical

High-resolution infrared spectra of the fundamental ( v = 1–0) and first overtone ( v = 2–0) bands of the ClO ( X 2 Π 3 2 , 2 Π 1 2 ) radical have been observed using a Fourier transform spectrometer and a diode laser. Frequencies and relative absorption line intensities have been measured and analyzed. An improved set of rovibrational constants for both 35ClO and 37ClO and a table of line positions and intensities are given. Relative intensity measurements are used to determine the rotational dependence of the intensities, and thereby determine the Herman-Wallis effect. An integrated band intensity of 11.3 ± 2.0 cm −2 atm −1 is determined for v = 1–0 from the first Herman-Wallis constant in a manner independent of any concentration determination.

Calculation of vibration-rotation line intensities of polyatomic molecules based on the formalism of irreducible tensorial sets

Irreducible tensorial sets of the point-symmetry groups are used to determine the general formulae for calculating the matrix elements of the reduced dipole moment operator of a polyatomic molecule. These general expressions allow different types of intramolecular interactions and accidental resonances to be considered. Transitions from one type of molecule to another are accounted for by substitution of isoscalar factors and 9 Gamma symbols of the point-symmetry group in the formulae. As an illustration the general expressions obtained are used to analyse the dependences of matrix elements of the reduced dipole moment on the rotational quantum numbers for some vibrational absorption bands of molecules with D3h, C3v and Td symmetries. For allowed transitions contributions to the reduced dipole moment operator which are linear and quadratic in Jalpha are taken into account. for forbidden transitions the main contributions are taken into account. It is shown that the general formulae obtained describe the generalised Herman-Wallis effect (1955) for polyatomic molecules.