CHM 501 Lecture



MO theory for polyatomics

Orbitals are treated as objects that can be labeled by their irreducible representations
This can be done within either the VBT or LCAO-MO approaches

VBT: Find the irreducible reps of the bond pairs; this allows us to label the bonds into different energy groups but gives no indication of the relative energy of each type of irred. rep.

CH4



Td
E
8C3
3C2
6S4
6d
   
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)
bonds
4
1
0
0
2
   

These transform as a1 + t2

a1 is also an s orbital; t2 is also px, py, pz orbitals which implies an sp3 hybrid

SF4 find irred reps of bonds; find hybrid



C2v
E
C2
v(xz)
v'(yz)
   
a1
1
1
1
1
z
x2, y2, z2
a2
1
1
-1
-1
Rz
xy
b1
1
-1
1
-1
x, Ry
xz
b2
1
-1
-1
1
y, Rx
yz
bonds
4
0
2
2
   
lp
1
1
1
1
   

bonds 2a1 + b1 + b2 sp3 hybrid?
lp a1 dsp3 hybrid!


LCAO MO:

Must be able to interpret MO diagrams for polyatomic molecules.

H2O


The bonding and antibonding orbitals are spread out over all atoms. The nodal properties determine the relative energies of the orbitals.

Benzene