A far-wing line shape theory that satisfies the detailed balance principle is applied to the H2O–H2O system. Within this formalism, two line shapes are introduced, corresponding to band averages over the positive and negative resonance lines, respectively. Using the coordinate representation, the two line shapes can be obtained by evaluating 11-dimensional integrations whose integrands are a product of two factors. One depends on the interaction between the two molecules and is easy to evaluate. The other contains the density matrix of the system and is expressed as a product of two three-dimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively. If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature. The 11-dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished. Numerical tests show that by taking into account about 107 random selections, one is able to obtained converged results. We find that it is necessary to consider frequency detuning, because this makes significant and opposite contributions in the two band-averaging processes and causes the lines to be asymmetric. Otherwise, the two line shapes become symmetric, are the same, and equal to the mean of the two shapes obtained including the frequency detuning effects. For the pure rotational band, we find that the magnitude of the line shape obtained from the positive line average is larger than that obtained from the negative line average for ω>0 and vice versa for ω<0, and their relative gap increases as the frequency displacement from the line center increases. By adopting a realistic potential model and optimizing its parameters, one is able to obtain these two line shapes and calculate the corresponding absorption coefficients that are in good agreement with laboratory data. Also, this same potential yields good theoretical values for other physical properties of the dilute H2O gas.
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