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### Symmetry

The idea is to let symmetry help in the determination of molecular orbitals. We have already seen that in H2O, (  mixes with 2pzO and  mixes with 2pyO. Combinations such as  are called symmetry orbitals. Note that symmetry orbitals can only be combinations of the same type (s,p..) on different atoms. Note also that
 (46)
demonstrates that symmetry orbitals of different symmetry do not mix.
Because of this the secular matrix  for H2O has the form

 1sO 2sO 2pzO 1sA+1sB 2pyO 1sA-1sB 2pxO 1sO .. .. .. .. 0 0 0 2sO .. .. .. .. 0 0 0 2pzO .. .. .. .. 0 0 0 1sA+1sB .. .. .. .. 0 0 0 2pyO 0 0 0 0 .. .. 0 1sA-1sB 0 0 0 0 .. .. 0 2pxO 0 0 0 0 0 0 ..

In otherwords, the secular problem has been reduced from a 77 to three problems, 44,22 and 11.

Next: Group Theory Up: Contents - Previous: Valence-Bond Theory

Nicholas Handy

1998-09-23