We present theoretical calculations of the millimeter wave foreign continuum due to colliding pairs of H_(2)O-N_(2) and H_(2)O-O_(2) molecules. The calculations are based on an idea that the millimeter water vapor continuum is caused by all lines of the pure rotational band of H_(2)O, but not individual ones. By treating this band as a whole, one is able to calculate the continuum directly. In practice, this idea is realized by using three powerful tools: the Lanczos algorithm, the coordinate representation, and the Monte Carlo method. Based on this procedure, we have calculated the foreign continuum from the H_(2)O-N_(2) and H_(2)O-O_(2) pairs for a range of temperatures relevant to the atmosphere. The calculated results of H_(2)O-N_(2) are compared to laboratory measurements and to widely used empirical models. For easy use, we fit our results for the absorption coefficient to a simple analytic function of frequency applicable up to 450 GHz and temperature ranging from 200 K to 300 K.
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