Transition Moment Operator Research Articles

Third-order derivatives of the dipole moment function for the ozone molecule

The third-order contributions to the dipole moment function of ozone has been evaluated from available experimental values of the transition moment parameters for the second overtone and ternary combination vibration–rotation bands. The calculations are based on the formalism of effective dipole moment operators. The purely vibrational part of the transformed transition moment operators for three-quanta bands is presented in the form suitable for an iterative programming. It allows one to determine the values and to make the optimal choice of signs of the third derivatives of the dipole moment function using the transition moment parameters deduced from experimental spectra. The estimation of the errors have been done by an error propagation of uncertainties in anharmonicity parameters of the potential function and previously determined first- and secondorder dipole moment derivatives.

New High-Resolution Analysis of the ν3 Band of the 15N16O2 Isotopomer of Nitrogen Dioxide by Fourier Transform Spectroscopy

New high-resolution Fourier transform absorption spectra of an 15N16O2 isotopic sample of nitrogen dioxide were recorded at the University of Bremen in the 6.3-μm region. Starting from the results of a previous study [Y. Hamada, J. Mol. Struct. 242, 367–377 (1991)], a new and more extended analysis of the ν3 band located at 1582.1039 cm−1 has been performed. The spin–rotation energy levels were satisfactorily reproduced using a theoretical model which takes into account both the Coriolis interactions between the spin–rotation energy levels of the (001) vibrational state with those of the (020) and (100) states and the spin–rotation resonances within each of the NO2 vibrational states. Precise vibrational energies and rotational, spin–rotation, and coupling constants were obtained in this way for the first triad of 15N16O2 interacting states {(020), (100), (001)}. Finally, a comprehensive list of line positions and line intensities of the {ν1, 2ν2, ν3} interacting bands of 15N16O2 was generated, using for the line intensities the transition moment operators which were obtained previously for the main isotopic species.

A Tensorial Formalism Adapted to the Rovibronic Couplings in the Colored Hexafluorides: Application to the ν5(F2g) and ν3(F1u) Modes

A tensorial formalism adapted to the case of transition-metal hexafluorides in a degenerate electronic state has been developed on the basis of preceding works about spherical-top molecules in a nondegenerate electronic state. We have introduced electronic operators constructed using group theory features and some physical considerations. Vibronic couplings (Jahn–Teller effect, etc.) have been reviewed for the triply degenerate vibrational modes ν5(F2g) and ν3(F1u) leading to the identification of the main vibronic parameters. For the first time, an effective rovibronic Hamiltonian as well as the effective transition moment operators (dipole moment and polarizability) for rovibronic transitions have been studied qualitatively thanks to the tensorial algebra properties.

A quantitative study of non-Condon effects in the S2O C̃→X̃ emission spectrum

A novel technique has been developed for the quantitative study of vibronically-resolved transition intensities in polyatomic molecules beyond the Condon approximation. Matrix elements of coordinate-dependent transition moment operators are evaluated analytically with the pertinent vibrational wave functions obtained by means of Lie algebraic methods. Experimentally-observed S2O C̃ 1A′–X̃ 1A′(π*−π) emission intensities, in conjunction with previous Franck–Condon calculations, reveal pronounced non-Condon effects for vibronic bands terminating on higher-lying vibrational levels of the ground electronic state. The transition dipole moment is examined as a function of both the S–O and S–S local stretching coordinates.

Spectroscopy of XY5Z (C4v) Molecules: Development of the Hamiltonian and the Transition Moment Operators Using a Tensorial Formalism

We present a development of the Hamiltonian, dipole moment, and polarizability operators of XY5Z (C4v) molecules using a tensorial formalism derived from the one developed previously in Dijon for XY6 molecules. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for all these operators.

Analysis of the ν8+ ν9Band of HNO3, Line Positions and Intensities, and Resonances Involving thev6=v7= 1 Dark State

Using a high-resolution (R= 0.0025 cm−1) Fourier transform spectrum of nitric acid recorded at room temperature in the 1100–1240 cm−1region, it has been possible to perform a more extended analysis of the ν8+ ν9band of HNO3centered at 1205.7075 cm−1. As in a recent analysis of this band [W. F. Wang, P. P. Ong, T. L. Tan, E. C. Looi, and H. H. Teo,J. Mol. Spectrosc.183, 407–413 (1997)], the Hamiltonian used for the line positions calculation takes into account, for the upper state, the ΔK= ±2 anharmonic resonance linking the rotational levels of thev8=v9= 1 “bright” vibrational state and those of the “dark”v6=v7= 1 vibrational state. More than 4800 lines were assigned in the ν8+ ν9band, which involve significantly higher rotational quantum numbers than in previous works. On the other hand, and surprisingly as compared to previous studies, the ν8+ ν9band appears to be a hybrid band. In fact, nonnegligibleB-type transitions could be clearly identified among the much strongerA-type lines. Accordingly, a set of individual line intensities were measured for lines of both types and were introduced in a least-squares fit to get theA- andB-type components of the transition moment operator. Finally, a synthetic spectrum of the 8.3-μm region of HNO3has been generated, using for the line positions and line intensities the Hamiltonian constants and the expansion of the transition moment operator which were determined in this work. In this way, theB-type and theA-type components of the ν8+ ν9band appear to contribute for about 14 and 34, respectively, to the total band intensity.

Line Intensities for the 8-μm Bands of SO2

Using both high-resolution (R= 0.003 cm−1) and medium-resolution (R= 0.12 cm−1) Fourier transform spectroscopy, it has been possible to measure accurately a large set of individual line intensities for the ν1and ν3bands of SO2in the 950–1400 cm−1spectral region. These intensities were introduced into a least-squares fit calculation allowing one to obtain the expansion of the transition moment operator of the ν1and ν3bands. For these intensity calculations, the theoretical model takes into account the vibration–rotation interactions linking the upper levels involved in the ν1, 2ν2, and ν3interacting SO2bands. Finally, a synthetic spectrum of the 8-μm SO2bands has been generated using the dipole moment expansion determined in this work and the molecular parameters and the Hamiltonian matrix given in a previous analysis.

The {ν1+ 2ν2, ν1+ ν3} Bands of14N16O2: Line Positions and Intensities; Line Intensities in the ν1+ ν2+ ν3− ν2Hot Band

High resolution Fourier transform absorption spectra of the14N16O2molecule recorded in the 2630–3510 cm−1spectral region have been analysed and lines of the ν1+ ν3band of this molecule have been assigned forKavalues ranging from 0 to 10 andNvalues up to 55. The spin–rotation energy levels were very satisfactorily reproduced using a theoretical model which takes explicitly into account both the Coriolis interaction between the spin–rotation levels of the (101) vibrational state and those of (120) and the spin–rotation resonances within (101) and (120). As a consequence, precise vibrational band centers and rotational, spin–rotation, and coupling constants were obtained for the {(120), (101))} interacting states of14N16O2. In addition, using a large set of individual ν1+ ν3experimental line intensities we have determined precisely the ν1+ ν3transition moment constants. Also from ν1+ ν2+ ν3− ν2line intensities measured in this work, the transition moment operator of the ν1+ ν2+ ν3− ν2hot band was found to be in agreement with the transition dipole moment of the corresponding cold band, namely, ν1+ ν3. Finally, a comprehensive list of line positions and intensities of the ν1+ ν3band of14N16O2has been generated at 3.4 μm.

An IPA procedure for bound-continuum diatomic transition intensities

An inversion procedure for determining a repulsive diatomic molecule potential energy curve and a function of the electronic transition moment operator from structured bound-continuum transition intensity data is proposed. The method is based on the first-order perturbation inversion of node positions differences in an experimental spectrum and its zeroth order simulation. This approach is free from the restrictions of the RKR-like procedure of Child, Essen and Le Roy (J. Chem. Phys. 78 (1983) 6732). The method is tested for the 7Li 2 (3 3 Π g ( ν = 17, N = 0)) → a 3 Σ u + and 7Li 2(3 3 Σ g +( ν = 10, N = 10) → a 3 Σ μ +) model bound-free transitions spectra.

Analysis of the 2 ν1 + 2 ν3 band of ozone: Line positions and intensities

The 2 ν 1 + 2 ν 3 band of ozone, appearing in the 4150 cm −1 region has been observed for the first time, using the high resolution Reims FTS and a large p × l product of 3616 cm × 48 torr. 275 transitions have been assigned, involving J and K a up to 55 and 9, respectively. The fit on the 193 corresponding energy levels using single Watson type Hamiltonian leads to a standard deviation of 1.4 × 10 −3 cm −1, on the order of experimental accuracy. Line intensities are also measured and calculated with suitable transition moment operators. We report here the set of parameters as well as transition moment operators. A complete list, with a cut-off of: 1 × 10 −26 cm −1/mol.cm −1 has been generated which leads to a band intensity S V(2 ν 1 + 2 ν 3) = 1.175 × 10 −22 cm −1/mol.cm −2.

Line Intensities in the Far-Infrared Spectrum of H2O2

Using high resolution Fourier transform spectra (resolution 0.002 cm−1) recorded at the Instituto Ricerca Onde Electromagnetiche Firenze and at the Justus Liebig University Giessen, it has been possible to measure the relative intensities of lines in the far-infrared spectrum of H2O2in the 25–400 cm−1spectral region. These intensities were used as input data in a least-squares fit calculation in order to obtain the expansion parameters of the transition moment operator of the pure torsional–rotational transitions of H2O2. For these intensity calculations, the theoretical model takes into account the cos γ-type dependence of the dipole moment due to the large amplitude motion of the H atoms relative to the O–O bond, where 2γ is the torsion angle. The value of the dipole moment obtained from the fit of the observed intensities was then scaled to the value obtained from Stark effect measurements. Finally, a synthetic spectrum of the far infrared band of H2O2was generated, using the dipole moment expansion determined in this work for the line intensities and the parameters and the Hamiltonian matrix given in a previous analysis (C. Camy-Peyret, J.-M. Flaud, J. W. C. Johns, and M. Noel,J. Mol. Spectrosc.155,84–104 (1992)) for the line positions. In addition to the (Δn= ±1, ΔKa= ∓2) torsional–rotational resonances within the ground vibrational state, which are usually observed for H2O2, the Hamiltonian model takes explicitly into account both the vibration–rotation resonances involving the ground state and thev3= 1 vibrational state and the “staggering” effect which is due to thecispotential barrier.

Line Positions and Intensities for the 2ν1 + ν2 + ν3 Band of 16O3

The 2ν1 + ν2 + ν3 band of 16O3 has been recorded and analyzed for the first time at high resolution (0.006 cm−1) with a Fourier transform spectrometer. To increase the absorption strength of this very weak band a White-type cell with path lengths of up to 36 m and pressures from 45 to 55 Torr was used. This band, located at 3850 cm−1, lies in the region of the ν1 and ν3 H2O absorption bands. So, the whole experimental setup including the sections between the source, the detector, and the tank of the interferometer was put under vacuum in order to minimize the presence of water vapor lines. The 286 rotational levels of the (211) band (J up to 40, Ka up to 12) were satisfactorily reproduced with the aid of a single Watson-type Hamiltonian with a standard deviation of 1.8 × 10−3 cm−1. Line intensities were also measured for this band and were reproduced with suitable transition moment operators. Finally, a complete list of line positions, intensities, and lower state energies was generated for the 2ν1 + ν2 + ν3 band of 16O3.

The 3ν 1 and ν 1 + 3ν 3 − ν 2 Absorption Bands of 16O 3

Using a high-pressure × path length sample of ozone it has been possible to record at high resolution (0.006 cm −1) the 3-μm absorption region of this molecule. A thorough analysis of the spectra has been performed allowing one to assign for the first time the 3ν 1 band of 16O 3. Also, during the course of the analysis it became clear that, in this spectral region, another band almost as strong as 3ν 1 was absorbing: it is the ν 1 + 3ν 3 − ν 2 hot band. The (300) rotational levels were reproduced together with the (003), (102), and (201) ones [ J. Mol. Spectrosc. 141, 134-144 (1990)] using a Hamiltonian matrix which takes explicitly into account the Darling-Dennison and the Coriolis interaction terms affecting the levels. The band centers ν 0(3ν 3) = 3046.0878, ν 0(ν 1 + 2ν 3) = 3083.7030, ν 0(2ν 1 + ν 3) = 3186.4110, and ν 0(3ν 1) = 3289.9297 cm −1 were derived as well as precise rotational and coupling constants. Line intensities were also measured for 3ν 1 as well as for ν 1 + 3ν 3 − ν 2 and were reproduced with suitable transition moment operators. Finally a complete line list of the bands of 16O 3 absorbing around 3 μm has been generated.

The ν1, 2 ν2, and ν3 interacting bands of 14N 16O 2: Line positions and intensities

High-resolution Fourier transform spectra have been used in the 1200–1850 cm −1 spectral region to measure the positions of lines with K a = 0–15 for the ν 1 and ν 3 bands of 14N 16O 2, as well as lines with K a = 0, 1, 2, and 6 for the 2 ν 2 band up to very high N values. The spin-rotation energy levels were very satisfactorily reproduced using a theoretical model which takes explicitly into account both the Coriolis interactions between the spin-rotation levels of the (001) vibrational state with those of (100) and (020), and the spin-rotation resonances in each vibrational state. In this analysis, precise band centers and rotational, spin-rotation, and coupling constants were obtained for the triad {(100), (020), (001)} of interacting states for 14N 16O 2. In addition, using a large set of individual line intensities we have determined precisely the ν 1, 2 ν 2, and ν 3 transition moment operators of 14N 16O 2. Finally, a comprehensive list of line positions and intensities of the interacting ν 1, 2 ν 2, and ν 3 bands of 14N 16O 2 has been generated.

The ν2 bands of 16O 17O 16O and 16O 16O 17O: Line positions and intensities

Using a 0.005-cm −1 resolution Fourier transform spectrum of 17O-enriched ozone, the first extensive analysis of the ν 2 bands of the two isotopic species 16O 17O 16O and 16O 16O 17O has been performed. For each isotopic species, the infrared vibration-rotation energies obtained from this analysis together with the available microwave transitions in the ground state were reproduced within their experimental uncertainties using a Watson A-type Hamiltonian. The band centers v 2( 16O 17O 16O) = 697.07934 cm −1 v 2( 16O 16O 17O) = 692.43473 cm −1 were obtained as well as precise rotational and centrifugal distortion constants for both the ground state and the first vibrational state (010) of these two isotopic species. In addition, appropriate expansions of the transformed transition moment operators of the two ν 2 bands were used to generate a complete list of line positions, intensities, and lower state energy levels for the 16O 17O 16O and 16O 16O 17O isotopic species.

The ν2 bands of 18O 3, 18O 16O 18O, and 16O 18O 18O: Line positions and intensities

Using 0.005 cm −1 resolution Fourier transform spectra of an 18O-enriched ozone sample, an extensive analysis of the ν 2 bands of the three isotopic species 18O 3, 18O 16O 18O, and 16O 18O 18O has been performed for the first time. For each isotopic species, the infrared vibration-rotation energies obtained from this analysis, together with the available microwave transitions in the ground state, were reproduced within their experimental uncertainties using a Watson A-type Hamiltonian. The following band centers were obtained: v 2( 18O 3) = 661.49248 cm −1 v 2( 18O 16O 18O) = 668.08496 cm −1 v 2( 16O 18O 18O) = 677.50382 cm −1. In addition, precise rotational and centrifugal distortion constants were obtained both for the ground state and for the first vibrational state (010) of the three isotopic species. Appropriate expansions of the transformed transition moment operators of the three ν 2 bands were used to generate a complete list of line positions, intensities, and lower-state energy levels for the 18O 3, 18O 16O 18O, and 16O 18O 18O isotopic species.

The 3.3-μm bands of ozone: Line positions and intensities

Abstract The analysis of high-resolution (0.010 cm −1 ) Fourier transform spectra of 16 O 3 has provided an extensive set of rotational energy levels belonging to the (003), (102), and (201) vibrational states of this molecule. These experimental energy levels were then satisfactorily reproduced with a Hamiltonian taking explicitly into account the various resonances (Coriolis and Darling-Dennison) affecting the levels, and precise vibrational energies and rotational and coupling constants were determined. In particular, the following band centers were derived: ν 0 (003) = 3046.0882, ν 0 (102) = 3083.7024, ν 0 (201) = 3186.4097 cm −1 . Also, line intensities were measured with an accuracy of about 3% for the strongest lines and satisfactorily reproduced with suitable transition moment operators expanded with respect to rotational operators. Finally, an extensive list of line positions, intensities, and lower state energy levels was generated for the 3 ν 3 , ν 1 + 2 ν 3 , and 2 ν 1 + ν 3 bands of 16 O 3 .

Thev3andv4interacting bands of HNO3line positions and line intensities

Very high resolution Fourier transform spectra of HNO3 recorded in the 1230–1370 cm-1 spectral region have been extensively analysed leading to precise line positions and intensities for the v 3 and v 4 bands of this molecule. Then, using a hamiltonian which takes explicitly into account the Fermi and Coriolis resonances between these two bands, it has been possible to reproduce satisfactorily the majority of the v 3 and v 4 interacting rotational levels. Moreover resonances due to unobserved vibrorotational levels are discussed. Intensities of 218 individual transitions belonging to the v 3 and v 4 bands were measured allowing a precise determination of the constants involved in the expansion of the corresponding transition moment operators. Finally a complete synthetic spectrum of the v 3 and v 4 bands of HNO3 has been computed.

The ν2 bands of 16O18O16O and 16O16O18O: Line positions and intensities

Using 0.005-cm−1 resolution room temperature Fourier transform spectra of 18O-enriched ozone samples, an extensive analysis of the ν2 bands of the two isotopes 16O18O16O and 16O16O18O was performed. Vibration-rotation energy levels of both species deduced from these analyses together with the available microwave data were then reproduced using a Watson A-type Hamiltonian leading to accurate vibrational energies and rotational constants for the ground states (000) and first excited vibrational states (010) of these two isotopic species. The following band centers were obtained: ν2(16O18O16O) = 693.3057 cm−1, ν2(16O16O18O) = 684.6134 cm−1. Finally, appropriate expansions of the transformed transition moment operators of the two ν2 bands were used to generate a complete list of line positions, intensities, and lower state energies for the two isotopes 16O18O16O and 16O16O18O.

The ν1 and ν3 bands of 16O 3: Line positions and intensities

Using 0.005 cm −1 resolution Fourier transform spectra of samples of ozone, the ν 1 and ν 3 bands of 16O 3 have been reanalyzed to obtain accurate line positions and an extended set of upper state rotational levels ( J up to 69, K a up to 20). Combined with the available microwave data, these upper state rotational levels were satisfactorily fitted using a Hamiltonian which takes explicitly into account the strong Coriolis interaction affecting the rotational levels of these two interacting states. In addition, 350 relative line intensities were measured from which the rotational expansions of the transition moment operators for the ν 1 and ν 3 states have been deduced. Finally, a complete listing of line positions, intensities, and lower state energies of the ν 1 and ν 3 bands of 16O 3 has been generated.