The u 3 orbital has energy too different from the other ones to be conveniently
combined by symmetry rules. The remaining ones give rise, by the use of the
projection operator, to symmetry-adapted combinations associated to the C 2v
symmetry of H 2 O.
Considering the representation table for the six base orbitals
C 2v
E
C 2
r v (xz)
r v (yz)
u 1
u 1
u 2
u 2
u 1
u 2
u 2
u 1
u 1
u 2
u 4
u 4
u 4
u 4
u 4
u 5
u 5
Àu 5
u 5
Àu 5
u 6
u 6
Àu 6
Àu 6
u 6
u 7
u 7
u 4
u 7
u 7
and having as objective the construction of the six symmetry-adapted linear
combinations of atomic orbitals (SALC)
2A 1 u 1 þ u 2 þ u 4 ; u 7 ! u 1 þ u 2 þ u 4
1B 2 À u 1 þ u 2 þ u 6
3A 1 u 1 þ u 2 À u 7 À u 4
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2 Symmetry Orbitals for Different Bis and Polyatomic Molecules