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Gas separations with porous materials are economically important and provide a unique challenge to fundamental materials design, as adsorbent properties can be altered to achieve selective gas adsorption. Metal-organic frameworks represent a rapidly expanding new class of porous adsorbents with a large range of possibilities for designing materials with desired functionalities. Given the large number of possible framework structures, quantum mechanical computations can provide useful guidance in prioritizing the synthesis of the most useful materials for a given application. Here, we show that such calculations can predict a new metal-organic framework of potential utility for separation of dinitrogen from methane, a particularly challenging separation of critical value for utilizing natural gas. An open V(II) site incorporated into a metal-organic framework can provide a material with a considerably higher enthalpy of adsorption for dinitrogen than for methane, based on strong selective back bonding with the former but not the latter.