5.

04, Principles of Inorganic Chemistry II

MIT Department of Chemistry
Lecture 15: ML6
Complexes

The basis set needs to be expanded for metal complexes with ligands containing

orbitals. Let’s consider ligands with two orthogonal
orbitals, e.g. CO, CN-, O2-, X-,
to the  bond:

L1

L5

L6 M L4 represents 2 orthogonal p
bonds

L3
L2

The arrow is indicative of a directional phase of the p orbitals. Owing to their ungerade
symmetry:

• a p orbital, i.e. arrow, transforming into itself contributes +1

• a p orbital transforming into minus itself contributes -1
• a p orbital that moves, contributes 0

Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3h 6d

 6 0 0 2 2 0 0 0 4 2  a1g + t1u + eg

12 0 0 0 -4 0 0 0 0 0  t1g + t1u + t2g + t2u

On the basis of geometrical considerations, the following is true:

( )

unmoved =

atoms
x,y,z =  + 

Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3h 6d

 6 0 0 2 2 0 0 0 4 2  a1g + t1u + eg
T1u=x, y, z 3 0 -1 1 -1 -3 -1 0 1 1
+
18 0 0 2 -2 0 0 0 4 2  a1g+eg+t1g+2t1u+t2g+t2u


= t1g + t1u + t2g + t2u

The  SALCs have already been derived

We will derive the
orbitals pictorially (mirror metal ao symmetry)… other methods
may also be applied.

5.04, Principles of Inorganic Chemistry II Lecture 15

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 t1u

and 2 others (in xz and yz plane…with

± overlap between py and px)

1
2
(

3 +
4 +
5 +
6 ) ± pz

non-bonding SALC’s (can verify symmetry by considering transformation properties)

the bonding SALC…

with the dxy orbital
t1g (and 2 others) t2u (and 2 others) t2g (and 2 others)

For a
donor complex, such as CoF63

for Co ion:

t1u (ML* and ML
*)

3.8 eV 4px, 4py, 4pz

a1g (ML*)

7.3 eV 4s

eg (ML*)
decreased energy gap (relative to
-only case) owing to participation
t2g (ML
*) of t2g orbitals as m-L
antibond
2 2 2
3dz , 3dx -y
9.4 eV
3dxy, 3dxz, 3dyz
t1g
formed from px
t2g
n.b. t1g, t2u 12L
and py orbitals
t1u
(VOIE = -19 eV)
t2u

(ML) t1u

(ML
) t2g

a1g
6L eg formed from pz (VOIE
t1u t1u = 19 eV) the s orbital
on F too low in energy to
(ML) eg
participate in M-L bonding
a1g (VOIE = 40eV)

5.04, Principles of Inorganic Chemistry II Lecture 15

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For a
-accepting ligand set, orbitals have the same form (or symmetry) as

donors…

t1u t2g
1 * 1 *
2
(

3 +
*4 +
*5 +
*6 ) 2
(

1 +
*4 
*2 
*6 )

… the only difference is the relative placement of the
* orbitals to the metal ao’s:

t1u (ML* and ML
*)

px, py, pz
(ML
) t2g
a1g (ML*) t1g
t
(n.b.) t2u, t1g 12L
 2g from L
*, p , p
t1u x y
s t2u
t1u
(ML*, ML
)
eg (ML*)

2 2 2
dx -y , dz
dxy, dxz, dyz

t2g (ML
)

t1u
6Lp eg from L lp, pz
t1u a1g

ML eg

a1g

5.04, Principles of Inorganic Chemistry II Lecture 15

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