First-Principles Diffusivity Ratios for Kinetic Isotope Fractionation of Water in Air

Kinetic isotope fractionation between water vapor and liquid water or ice depends on the ratio of the diffusivities of the isotopic species in air, but there is disagreement as to the values of these ratios and limited information about their temperature dependence. We use state-of-the-art intermolecular potential-energy surfaces for the water-nitrogen and water-oxygen pairs, along with the kinetic theory of molecular gases, to calculate from first principles the diffusivities of water isotopologues in air. The method has sufficient precision to produce accurate diffusivity ratios. For the HDO/H₂O ratio, we find that the often used hard-sphere kinetic theory is significantly in error, and confirm the 1978 experimental result of Merlivat. For the ratios involving ¹⁷O and ¹⁸O, the simple kinetic theory is relatively close to our more rigorous results. We provide diffusivity ratios from 190 K to 500 K, greatly expanding the range of temperatures for which these ratios are available.