Quantum mechanical basis for kinetic diameters of small gaseous molecules

Kinetic diameters are often invoked in discussing gas adsorption and permeation in porous and polymeric materials. However, how these empirical kinetic diameters relate to the size and shape of the molecules as manifested by their "electron cloud" is unclear. In this paper, we obtain the quantum mechanical (QM) diameters of several common gaseous molecules by determining the cross-sectional sizes of their iso-electronic density surfaces at a predetermined small value. We show that the QM diameters are in good agreement with the kinetic diameters. For example, the trends for important gas pairs such as O2 versus N2 and CO2 versus N2 are consistent between the QM diameters and the most often quoted kinetic diameters. Hence, our work now provides a quantum mechanical basis for the empirical kinetic diameters and will be useful for designing separation media for small gaseous molecules according to their sizes.