Systematic prediction of crystal structures: An application to s p3 -hybridized carbon polymorphs

A general systematic method of predicting hypothetical crystal structures could enable important advances in many areas of science. We describe a recently developed approach based on graph theory and density functional theory and apply it to enumerate systematically a number of sp³ -hybridized carbon polymorphs with four atoms per unit cell. The calculations predict three unknown structures that are potentially metastable under appropriate pressure and temperature conditions. The theoretical properties of these hypothetical polymorphs and their relative stability with respect to diamond are discussed.