Study of H 2 O Polarizability Based on Data on Rovibrational Line Shifts by Buffer Gas Pressure
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Study of H2O Polarizability Based on Data on Rovibrational Line Shifts by Buffer Gas Pressure V. I. Starikov* Tomsk State University of Control Systems and Radioelectronics, Tomsk, 634050 Russia *e-mail: [email protected] Received September 26, 2019; revised December 3, 2019; accepted December 23, 2019
Abstract—The study of the vibrational dependence of H2O polarizability α is based on the comparison of experimental and calculated line shifts induced by argon, nitrogen, and air pressure in different H2O vibrational bands. The dependence of α on the internal coordinate θ, which describes large-amplitude bending vibration in the molecule, is expressed by a power series. The coefficients of the power series were selected so as to ensure the best agreement between the calculated matrix elements ψn|α(θ)|ψn and the polarizability values α(n) derived from the analysis of experimental H2O absorption line shifts in nν2 vibrational bands by nitrogen, oxygen, air, and argon pressure. The rotational contributions in the effective H2O polarizability are calculated and discussed. The α(θ) representation found is compared with ab initio calculations. Keywords: water molecule, polarizability, broadening and shift of spectral lines DOI: 10.1134/S102485602004017X
INTRODUCTION The bending vibration ν2 in a Н2О molecule (a change in the angle θ = НОН) strongly differs from the stretching vibrations ν1 and ν3, which describe variations in the length of OH bonds. The difference is determined by the fact that the molecular potential cross section along the θ coordinate has a low barrier to the linear configuration Н ∼ 10000 cm−1. The frequency of normal bending vibrations ω2 = 1648.5 cm−1 [1]; therefore, seven or eight vibrational energy levels (depending on the potential used in the calculation) fit up to the barrier H. An increase in the vibrational quantum number n = ν2 sharply changes the rotational structure of the energy levels in the vibrational states E(ν2), which is shown in the strong dependence on ν2 of the series of rotational and centrifugal constants from the effective centrifugal Hamiltonian of the molecule [2]. It is important to know the vibrational dependence of polarizability α of the H2O molecule for calculation of the coefficients of H2O line broadening γ and shift δ by the pressure of buffer gases. Along with the dipole moment μ, the polarizability α determines the vibrational dependence of the long-range part of the effective induction and polarization interaction potential [3]. The dependence of the dipole moment μ on the vibrational quantum numbers ν = (ν1, ν2, ν3) of water was derived in [4, 5]. In [4], the semirigid molecular model was used, where all H2O vibrations were considered small. In [5], the nonrigid model was used, where bending vibrations were considered large-amplitude.
The μ values calculated in [4, 5] for the vibrational states E(v2), close to the linear configuration of the molecule, differ. The vibrational dependence of the Н2О polarizability α, Å3, is usually
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