Fig. 1. Dependence of the energy gap that separates the two highest occupied molecular orbitals (HOMO and HOMO−1) upon the lateral offset between pyrene molecules in a face-to-face dimer. Two optimized structures of pyrene were positioned in space with 352 pm vertical separation, and the lateral offset was varied from perfectly eclipsed (the configuration of AA graphene) along the coordinate through semi-eclipsed (the configuration of AB graphene) by increments of ∼28 pm. At each position we report the energy gap E_HOMO − E_HOMO−1, which is proportional to the electronic coupling between the pyrene groups,¹⁰ determined by single-point calculations using density functional theory, B3LYP functional, 6-311G(2d) basis set. We plotted ±0.04 (e bohr⁻³)^1/2 isodensity surfaces of the HOMOs at the indicated offsets.