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6 Introduction to Carbon Materials (a) (c) H H H (b) H C CC CC 0 120 Figure 1.4: (a) Schematic view of the sp2 hybridisation. The orbitals form angles of 120o. (b) Benzene molecule (C6H6). The 6 carbon atoms are situated at the corners of a hexagon and form covalent bonds with the H atoms. In addition to the 6 covalent σ bonds between the C atoms, there are three π bonds indicated by the doubled line. (c) The quantum-mechanical ground state of the benzene ring is a superposition of the two configurations which differ by the position of the π bonds. The π electrons are, thus, delocalised over the ring. (d) Graphene may be viewed as a tiling of benzene hexagons, where the H atoms are replaced by C atoms of neighbouring hexagons and where the π electrons are delocalised over the whole structure. is elongated in the +x (−x) direction for the |sp+⟩ (|sp−⟩) states [Fig. 1.3 (a)]. This hybridisation plays a role, e.g., in the formation of the acetylene molecule H–C≡C–H, where overlapping sp1 orbitals of the two carbon atoms form a strong covalent σ bond [Fig. 1.3 (b)]. The remaining unhybridised 2p orbitals are furthermore involved in the formation of two additional π bonds, which are weaker than the σ bond. 1.1.2 sp2 hybridisation – graphitic allotopes In the case of a superposition of the 2s and two 2p orbitals, which we may choose to be the |2px⟩ and the |2py⟩ states, one obtains the planar sp2 hy- HC H (d)PDF Image | Physical Properties of Graphene
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