Combining AOs to Build MOs

Molecular orbitals, which we will also later use as group orbitals can be built from AOs in exactly the same way as MO-programs do, except that we can use the LCAO principle qualitatively to understand the AO-combination process. We will consider a simple example, methylene, CH2, in order to illustrate the principles involved. We can then use the MOs obtained as generic orbitals for the fragment or group AH2, where A can be any main group element, in order to explain the shapes of these molecules, and also as group orbitals in order to build the MOs of more complicated molecules like ethylene or cyclopropane. 

The MOs of methylene are built from the AOs of one carbon and two hydrogens within the LCAO approximation. However, because the two hydrogens are symmetrically equivalent, their AOs cannot be considered separately, but must be combined to symmetry-adapted combinations. This is because the CH2 molecule has 2v -symmetry, for which the most relevant symmetry element in this discussion is the mirror plane shown in Fig. 2.9. An introduction to symmetry elements will be given in Sect. 5.1. 

The symmetry-adapted combinations of hydrogen s-orbitals that we use to build the methylene MOs must be either symmetric or antisymmetric with respect to reflection in this plane. The individual AOs do not fulfill this condition, but can be combined to give the two symmetry-adapted combinations shown in Fig. 2.9. These combinations can then be used to build the MOs. 

Once we have built symmetry-adapted combinations of AOs for all equivalent sets of atoms, we can begin to combine them to form the MOs 

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