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PNAS Plus Significance Statements

Nanocarbons can be characterized by their curvature— that is, positively curved fullerenes, zero-curved graphene, and negatively curved schwarzites. Schwartzites are fascinating materials but have not been synthesized yet, although disordered materials with local properties similar to schwarzites (“random schwarzites”) have been isolated. A promising synthetic method allows for the interior surfaces of zeolites to be templated with sp carbon, but theoretical study of these zeolite-templated carbons (ZTCs) has been limited because of their noncrystalline structures. In this work, we develop an improved molecular description of ZTCs, show that they are equivalent to schwartzites, and thus make the experimental discovery of schwarzites ex post facto. Our topological characterization of ZTCs lends insights into how template choice allows for the tunability of ordered microporous carbons. (See pp. E8116–E8124.)