Polymer membranes incorporating carbon nanotubes (CNT) belong to two broad categories: Vertically aligned (VA-CNT) membranes, where the polymer acts solely as a matrix embedding an aligned forest of nanotubes, and thin film composite (CNT-TFC) membranes which incorporate randomly aligned nanotubes in their selective layer. The former can achieve orders-of-magnitude higher permeability than many commercial membranes but cannot be scaled up industrially. The latter are based on commercial technology but provide only modest flux increases. Furthermore, filtration in VA-CNT is based on steric hindrance determined by the tubes' diameter, whereas in CNT-TFCs, the tubes are embedded in the polymer with selectivity given by the polymer alone. In this work, a novel computational method to optimize the selectivity-permeability of an ideal CNT membrane encompassing the advantages of VA-CNTs and CNT-TFCs is presented. In analogy to the former, the tubes are all aligned with the membrane selectivity provided by their diameter; to the latter, the polymer matrix also contributed to the total membrane permeability. As nanotubes with larger internal diameter would provide higher flow, ab-initio modeling was used to improve their selectivity by functionalizing the tips of large multiwall nanotubes with PIM-1 monomers, achieving simultaneously an increase in selectivity toward small molecules (e.g. rac-fluoxetine, glucose, ethanol and water) and an increase in permeability (due to the large diameter). Results show up to 3 orders of magnitude increase in water permeability compared to a CNT-TFC membrane in the literature with randomly oriented tubes of comparable size and an increase in rejection of a factor of 2.5 and 2, for rac-fluoxetine and glucose, respectively, compared to water. The proposed methodology is of general use and requires no fitting parameters, only the chemical structure of the solutes to test and the tubes' geometry. (C) 2015 ElSevier B.V. All rights reserved.