Molecular diameter is an essential molecule-size descriptor
that
is widely used to understand, e.g., the gas separation preference
of a permeable membrane. In this contribution, we have proposed two
new molecular diameters calculated respectively by the circumscribed-cylinder
method (D
n
′) and the group-separated method (D
n), and compared them with the already known
kinetic diameter (D
k), averaged diameters
(D
pa), and maximum diameters (D
pm and D
mm) in correlating
with the penetration barriers of small gas molecules on a total of
14 porous carbon-based monolayer membranes (PCMMs). D
1
′ and D
2
′ give the best barrier–diameter correlations with average
Pearson’s correlation coefficients of 0.91 and 0.90, which
are markedly larger than those (0.77, 0.76, 0.60, 0.48, 0.33, and
0.32) for D
1, D
2, D
k, D
pa, D
pm, and D
mm. Our results manifest that the choice of vdW radii set does not
drastically change the barrier–diameter correlation. Our newly
defined D
1
′, D
2
′, D
1, and D
2, especially D
1
′ and D
2
′, show universal applicability in predicting the relative permeability
of small gas molecules on different PCMMs. The circumscribed-cylinder
method proposed here is a facile approach that considers the molecule’s
directionality and can be applicable to larger molecules. The excellent
linear correlation between D
n
′ and gas penetration barrier
implies that the computationally less demanding molecular diameter D
n
′ can be an alternative to the penetration barrier in diagnosing the
gas separation preference of the PCMMs.