now the HOMO. For more about orbital symmetry and chemical reactions see e.g.
the book by Woodward and Hoffmann [ 38 ].
4.3.5.2 Stability as Indicated by Energy Levels, and Aromaticity
The MO energy levels obtained from an SHM calculation must be filled with
electrons according to the species under consideration. For example, the neutral
ethene molecule has twopelectrons, so the diagrams of Fig.4.19a(cf. Fig.4.15)
with one, two and threepelectrons, would refer to the cation, the neutral and the
anion. We might expect the neutral, with its bondingporbitalc 1 full and its
antibondingporbitalc 2 empty, to be resistant to oxidation (which would require
removing electronic charge from the low-energyc 1 ) and to reduction (which would
require adding electronic charge to the high-energyc 2 ).
CCCC+
- 2 nodes
C C CC+–
- 1 node
CCCC+- no nodes
C C C C
++ –+
- 3 nodes
+++ +- –
++
- or just
Draw+
+conrotationHHMeMeMeMe
++HHMeMeHHsameenergyandy 4y 3y 2y 2y 1Fig. 4.18 The stereochemistry of many reactions is easily predicted from the symmetry of
molecular orbitals, usually the highest occupiedpMO (pHOMO). In the ring closure of 1,3-
butadiene to cyclobutene the phase (þor") of the HOMO (c 2 ) at the end carbons (the atoms that
bond) is such that closure must occur in a conrotatory sense, giving a definite stereochemical
outcome. In the example above there is only one product. Thereverseprocess is actually
thermodynamically favored, and thecisdimethyl cyclobutene opens to thecis,transdiene. No
attempt is made here to show quantitatively the positions of the energy levels or to size the AOs
according to their contributions to the MOs
134 4 Introduction to Quantum Mechanics in Computational Chemistry