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We have performed a detailed ab initio computation of the dipole moment surface, the vibrational transition moments, and the spectral lines for the water molecule. A total of 412 vibrational eigenstates were identified below 30 000 cm-1, corresponding to ≈85 000 vibrational transitions. In principle there are many billions of allowed vibration-rotation transitions between these eigenstates. In our most complete test calculations we constructed a list of 3 billion ($3\times 10^9$) lines. At room temperature, the computed monochromatic absorption coefficient is in good overall agreement with the hitra