SALC and sigma and pi bonding.

1. MOLECULAR SYMMETRY AND
GROUP THEORY

2. CONTENTS
Symmetry adapted linear combination
Sigma and pi bonding in AB4 (tetrahedral)
molecule.
References

3. Symmetry adapted linear
combinations.
To determine SALC's of the s-orbitals in water

4. Determine the point group of the molecule.
H2O belongs to the C2v point group.

5. Identify the symmetrically complete sets.
H (1) and H(2) form one set while the
O forms the other

6. Determine the operation which converts the
reference vector into each of the others.

7. Determine the reducible representation of the
complete sets.

8. Determine the character of the appropriate
operation for each of the irreps

9. Construct SALC's
A1: ψ1= N1{H(1) + H(2)} & ψ2 = N2{O}
B1: ψ3 = N3{H(1) - H(2)}

10. Example, the  and  bonding in ClO4
-.
Td E 8 C3 3 C2 6 S4 6 d
 8 -1 0 0 0

11. The irreducible representation for the  bonding
is (A1 + T2),
Td E 8 C3 3 C2 6 S4 6 d
A1 1 1 1 1 1 x2 + y2 + z2
A2 1 1 1 -1 -1
E 2 -1 2 0 0 (2z2 - x2 - y2, x2 - y2)
T1 3 0 -1 1 -1 (Rx, Ry, Rz)
T2 3 0 -1 -1 1 (x, y, z) (xy, xz, yz)

12. The irreducible representation for the  bonding
is (E + T1 + T2),
Td E 8 C3 3 C2 6 S4 6 d
A1 1 1 1 1 1 x2 + y2 + z2
A2 1 1 1 -1 -1
E 2 -1 2 0 0 (2z2 - x2 - y2, x2 - y2)
T1 3 0 -1 1 -1 (Rx, Ry, Rz)
T2 3 0 -1 -1 1 (x, y, z) (xy, xz, yz)

13. Reducible representation for the ligand sigma
SALC's in tetrahedral ML4.

14. • The σ SALC of a1 symmetry is
ψ1 = 1/2[σ1 + σ2 + σ3 + σ4]

15. REFERENCES
Molecular Symmetry and Group Theory, Robert
L. Carter, Wiley publications.