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We show that two graphene layers stacked directly on top of each other (AAstacking) form strong chemical bonds when the distance between planes is 0.156nm. Simultaneously, C-C in-plane bonds are considerably weakened from partialdouble-bond (0.141 nm) to single bond (0.154 nm). This polymorphic form ofgraphene bilayer is meta-stable w.r.t. the one bound by van der Waals forces ata larger separation (0.335 nm) with an activation energy of 0.16 eV/cell.Similarly to the structure found in hexaprismane, C forms four single bonds ina geometry mixing 90^{0} and 120^{0} angles. Intermediate separations betweenlayers can be stabilized under external anisotropic stresses showing a richelectronic structure changing from semimetal at van der Waals distance, tometal when compressed, to wide gap semiconductor at the meta-stable minimum.

Strong covalent bonding between two graphene layers