A method of using a crystallographic framework of sterically bulky calixarene molecules to selectively separate and/or store volatile gas components. Sterically bulky calix[4]arenes or their derivatives form a crystalline lattice that has relatively large lattice voids, is nonporous, and is held together predominately by van der Weals forces. The calix[4]arene lattice can form a guest-host assembly by absorbing a desired volatile gas guest component into the crystalline lattice without any phase shift or other change to the lattice structure. The crystalline calixarene can also be desirably used to purify a gas mixture by removing one or more volatile gas contaminants or by removing and storing the desired volatile gas component. This method can preferably be used to purify a hydrogen gas stream by removing the carbon dioxide and carbon monoxide contaminants or to remove and store oxygen from the air or carbon dioxide and carbon monoxide from combustion gases.