A far wing line shape theory and its application to the water continuum absorption in the infrared region. I

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Abstract
A theory is presented for the calculation of the continuous absorption due to the far wing contributions of allowed lines. The theory is based on the quasistatic approximation for the far wing limit and the binary collision approximation of one absorber molecule and one bath molecule. In line space, the motion of the dipole moment of the absorber molecule, determined by the time displacement Liouville operator related to the total Hamiltonian of the absorber molecule and the bath molecule, is approximately expressed as the ordered product of two time displacement Liouville operators, one related to the intermolecular potential and the other to the unperturbed Hamiltonian. Using a Laplace transformation, the spectral density is expressed in terms of a Cauchy integral whose integrand is a product of two resolvent operators corresponding to the interaction and to the unperturbed Hamiltonian, respectively. After isolating the effects of the bath variables, the spectral density and subsequently the absorption coefficient are expressed in terms of the individual line coupling functions, or the individual line shape functions. By using two average line shape functions instead of the individual ones, the expression of the absorption coefficient closely matches empirical models. The validity of the present theory is discussed, and some numerical results of the water continuum absorption in the infrared region are presented for comparison with experimental data. A good agreement in both the magnitude and the temperature dependence of the absorption coefficients is obtained. Some further extensions and applications of the present theory are also discussed briefly.