Porous aromatic frameworks (PAFs) were recently synthesized with the highest surface area to date; one such PAF (PAF-1) has diamond-like structure with biphenyl building blocks and exhibits exceptional thermal and hydrothermal stabilities. Herein, we computationally design new PAFs by introducing polar organic groups to the biphenyl unit and then investigate their separating power toward CO2 by using grand-canonical Monte Carlo (GCMC) simulations. Among these functional PAFs, we found that tetrahydrofuran-like ether-functionalized PAF-1 shows higher adsorption capacity for CO2 at 1 bar and 298 K (10 mol per kilogram of adsorbent) and also much higher selectivities for CO2/CH4, CO2/N-2, and CO2/H-2 mixtures when compared with the amine functionality. The electrostatic interactions are found to play a dominant role in the high CO2 selectivities of functional PAFs, as switching off atomic charges would decrease the selectivity by an order of magnitude. This work suggests that functionalizing porous frameworks with tetrahydrofuran-like ether groups is a promising way to increase CO2 adsorption capacity and selectivity, especially at ambient pressures.