A. D. Bykov

On isotope effects in polyatomic molecules: Some comments on the method

Abstract The quantum mechanical expressions for the Hamiltonians of various isotope modifications of a polyatomic molecule are transformed to the coordinate systems connected with the molecules. Such coordinate transformations selected in the proper way permit all Hamiltonians His to be expressed as functions of the parameters rNα0, lNαλ, ζλμα, kλ⋯μ of one of them. Isotopic relations for the parameters of Watsons Hamiltonian (Mol. Phys. 15, 479–490 (1968)) of an arbitrary isotopic modification of a molecule are determined.

On the displacements of centers of vibration-rotation bands under isotope substitution in polyatomic molecules

Abstract The effect of isotope substitution in polyatomic molecules on the displacements of absorption vibration-rotation band centers is considered. Formulas are obtained that allow the band-center displacements to be calculated in harmonic approximation and with anharmonicity. The effect of resonance interactions is also considered. The results obtained are illustrated by numerical calculation for a number of molecules.

Rotation-vibration spectra of deuterated water vapor in the 9160–9390-cm−1 region☆

Abstract The absorption spectrum of mixtures of H 2 O, HDO and D 2 O has been recorded in the region 9161.5 to 9392.5 cm −1 with an absorption sensitivity of 10 −7 cm −1 and a line-center determination accuracy of 0.08 cm −1 . An attempt to identify the absorption bands of the spectrum obtained experimentally was undertaken. The justification for attributing the observed lines to the HDO bands (3 ν 1 + ν 2 ), ( ν 1 + 2 ν 2 + ν 3 ) and D 2 O bands ( ν 2 + 3 ν 3 ), ( ν 1 + ν 2 + 2 ν 3 ) is given. In this study the bands centers have been found and the molecular rotational and centrifugal constants have been determined as well.

Water-vapor absorption spectrum in the 0.59-μm region☆

Abstract The paper gives the results of investigation of the water-vapor absorption spectrum in the range of 586.9–596.6 nm. In the given range, 282 water-vapor absorption lines were recorded and were identified as belonging to the bands 4 ν 1 + ν 3 , 3 ν 1 + 2 ν 2 + ν 3 , 3 ν 1 + 2 ν 3 . Theoretical justification of the technique for interpreting the observed spectrum was made. The values of more vibration-rotation levels of energy were determined: for state (401) up to J = 10, for state (321) up to J = 10, and for state (302) up to J = 8. The rotational and centrifugal constants of the reduced Watsons Hamiltonian for the vibrational states (401), (321), (302), and (222) and constants of Fermi resonance (401)-(321), (302)-(222), and Coriolis resonance between the states (401), (321), and (302), (222) were determined.

The laser spectroscopy of highly excited vibrational states of HD16O

Abstract The absorption spectra of HD 16 O were recorded using a F 2 + :LiF color center intracavity laser spectrometer in the 0.9-μm region and an optoacoustic dye laser spectrometer in the 0.59-μm spectral region. Energy levels and rotational and centrifugal distortion constants of the (003) and (005) states were determined. Improved sets of vibrational and vibration-rotation constants have been obtained by fitting all available data for the energy levels of HDO.

On the displacements of centres of vibration-rotation lines under isotope substitution in polyatomic molecules

The general form of the corrections to the vibration-rotation hamiltonian resulting from isotope substitution of heavy nuclei has been obtained. These results are used for predicting the displacements of the vibration-rotation line centres. Some results of numerical calculations are given as an illustration.

The vibration-rotation HDO absorption spectrum between 8558 and 8774 cm−1

Abstract The absorption spectrum of HDO has been recorded in the region 8558–8774 cm −1 using a high-sensitivity intracavity F 2 − :LiF center laser spectrometer. The absorption sensitivity is 10 −7 cm −1 and the line-center determination accuracy is about 4 × 10 −2 cm −1 . The spectrum was interpreted and the absorption lines were attributed to the ν 2 + 2 ν 3 band of HDO. Energy levels up to J = 12 and rotational and centrifugal parameters of the vibrational (012) state were obtained.

Calculation of vibrational energy levels of water molecule by summing divergent perturbation theory series

The Rayleigh-Schrödinger perturbation theory is applied to a calculation of vibrational energy levels of the H2O molecule for isolated states and the states involved in the anharmonic Fermi and Darling-Dennison resonances. It is shown that in spite of the rapid divergence of the perturbation theory series caused by the resonances, the use of the summation methods of Padé, Padé-Borel, and Padé-Hermite and the moments method allows one to obtain quite satisfactory results.

Simulation of the vibrational-rotational energy levels of D218O, HD18O, D217O, and HD17O molecules by the effective Hamiltonian approach

The vibrational-rotational energy levels of the first and second triads and the first and second hexads of the D218O, HD18O, D217O, and HD17O molecules are simulated on the basis of the Watson-type Hamiltonian and the rotation operator written in terms of the Padé–Borel approximants. Rotational, centrifugal distortion, and resonance constants and mixing coefficients of the resulting wave functions are found by the least squares method. The resonance interactions are analyzed. The predictive capability of the effective Hamiltonian parameters found is examined for the long extrapolated rotational quantum numbers.

Calculation of vibrational energy levels of triatomic molecules with the C 2v and C s symmetries by summing divergent series of the Rayleigh-Schrödinger perturbation theory

The Rayleigh-Schrödinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the C2v and Cs symmetries: SO2, H2S, F2O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Padé, Padé-Borel, and Padé-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Padé-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied.