By Gould R.F. (ed.)
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Extra info for Advanced Propellant Chemistry
In this case we have three symmetry elements: (i) the xz plane, bisecting all three atoms; (ii) the yz plane, bisecting the carbon atom, and through which the hydrogen atoms reflect each other; and (iii) a two-fold rotation axis along the z coordinate, bisecting the H—C—H angle. The two orbitals, sHH and s*HH in Fig. 14, are SSS and SAA with respect to these elements, and the atomic orbitals of carbon are SSS, SSS, ASA and SAA. Thus there are two orbitals on the right and one on the left with SSS symmetry, and the overlap integral is positive for the interactions of the sHH and both the 2s and 2pz orbitals, so that we cannot have as simple a way of creating a picture as we did with methane, where one of the possible interactions had a zero overlap integral.
Similarly, there are two antibonding orbitals, 4* and 5*, with the same energy having two nodes. Finally there is another antibonding orbital, 6*, with three nodes. Fig. 36 The p molecular orbitals of benzene The energies of the molecular orbitals can be deduced by inscribing the conjugated system inside a circle of radius 2. There is no need for dummy atoms, since the sine curves go right round the ring, and the picture is therefore 34 MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Fig. 37 The energies of the p molecular orbitals of benzene that shown in Fig.
25. In this picture of the bonding, we get no immediate appreciation of the energies of these orbitals relative to those of ethylene. The nonbonding orbital 2 is clearly on the level, that of a p orbital on carbon, and 1 is lowered by the extra p bonding and 3* is raised. To assess the energies, there is a simple geometrical device that works for linear conjugated systems. The conjugated system, including the dummy atoms at the ends of the sine curves, is inscribed vertically inside a circle of radius 2, following the convention that one p bond in ethylene defines .