2. Lecture 7: M-M bonds d-bonds and bonding in metal clusters
Schedule
Last week: p-Acceptor Ligands and Biology CO, O2, N2 and NO complexes, introduction to M-M bonds
Lecture 7: M-M bonds d-bonds and bonding in metal clusters
Lecture 8: Rates of reaction Ligand-exchange reactions, labile and inert metal ions
Demos: charles law (2.3), CO2 density (2.1), star wars (4.3)
Brief mention of 3 states of matter.
Lecture 9: Redox reactions Inner and outer-sphere reactions

3. Summary of Course – week 6
Metal-metal bonding
be able to predict bond order for M2Lx dimers using d-electron count and s, p and d molecular orbital diagram
be able to predict bond order in larger metal-halide clusters using d-electron count shared over edges of cluster
be able to predict bond order in metal carbonyl clusters using 18 e- rule
Reaction mechanisms
be able to describe ligand exchange mechanisms
be able to explain role of metal charge and LFSE in rate of ligand exchange
be able to describe electron transfer reaction mechanisms
be able to predict relative rate of outer sphere reaction for different metals
Resources
Slides for lectures 7-9
Shriver and Atkins “Inorganic Chemistry” Chapter 18.11, 21.20,

4. Summary of Last Lecture
Metal-N2 complexes
N2 is isoelectronic with CO but M-N2 bonding is much weaker
N2 is non-polar and bond is strong
NO complexes
Can bond as 1 electron donor (NO-: bent M-NO)
Can bond as 2 electron donor (NO+ linear M-NO)
Today’s lecture
Metal-Metal bonding in complexes

5. Maximum Bond Order – d-Block
3dsu
the maximum bond order is 5
but…complexes also contain ligands which use some of the d-orbitals reducing number of bonds
3dpu
3dpg
3ddg
3ddu
dx2-y2 + dx2-y2
dxy + dxy
2 × 3d 3d
dxz + dxz dyz + dyz
2 ×
3dsg
dz2 + dz2

6. Maximum Bond Order – d-Block
dx2-y2 + dx2-y2
dxy + dxy
2 ×
2 ×
dxz + dxz dyz + dyz
2 ×
2 ×
dz2 + dz2

7. Complexes Containing d-d Bonds
In complexes, not all of these molecular orbitals will form as some of the d-orbitals will be involved in bonding to ligands
[Re2Cl8]2- contains two ~square planar ReCl4 units
there must be a Re-Re bond as the two units are attached
the geometry is eclipsed
[Re2Cl8]2- ≡ 2Re3+ (d4) + 8Cl-

8. Quadruple Bonds
In complexes, not all of these molecular orbitals will form as some of the d-orbitals will be involved in bonding to ligands
[Re2Cl8]2- contains two ~square planar ReCl4 units
dx2-y2 bonds with the four ligands
leaving:
dz2 (s), dxz, dyz (p) and dxy (d) to form M-M bonds

9. Quadruple Bonds 2 × 2 × 2 × Re3+ (d4)  8 e- (s)2(p)4(d)2
3dsu
2 × Re3+ (d4)  8 e-
(s)2(p)4(d)2
quadruple bond:
3dpu
3dpg
3ddu
dx2-y2 + dx2-y2
dxy + dxy
2 × 3d 3d
3ddg
dxz + dxz dyz + dyz
2 ×
3dsg
dz2 + dz2

10. Quadruple Bonds [Re2Cl8]2- quaduple bond:
(s)2(p)4(d)2: a s-bond, two p-bonds and one d-bond
the sterically unfavourable eclipsed geometry is due to the d-bond

11. Quadruple Bonds [Re2Cl8]2- [Re2Cl8]2- ≡ 2Re3+ (d4) + 8Cl-
2 × Re3+ (d4)  8 e-
(s)2(p)4(d)2
bond order = 4 (quadruple bond)
d-bond: eclipsed geometry
3dsu
3dpg
3ddu
[Re2Cl8]4-
[Re2Cl8]4- ≡ 2Re2+ (d5) + 8Cl-
2 × Re2+ (d5)  10 e-
(s)2(p)4(d)2(d*)2
bond order = 3 (triple bond)
no d-bond: staggered geometry
3ddg
3dpu
3dsg

12. Larger Clusters – M3 ReCl3 exists Re3Cl9 clusters
detailed view of cluster bonding more involved…
Re3Cl9 ≡ 3Re3+ (d4) + 9Cl-
3 × Re3+ (d4)  12 e- or 6 pairs
3 × Re-Re connections in triangle
number of pairs / number of edges = 6/3 = 2
3 × Re=Re double bonds

13. Larger Clusters – M6 [Mo6Cl14]2-
Mo6 octahedron with 8Cl capping faces and 6 Cl on edges
[Mo6Cl14]2- ≡ 6Mo2+ (d4) + 14Cl-
6 × Mo2+ (d4)  24 e- or 12 pairs
12 × Mo-Mo connections in octahedron
number of pairs / number of edges = 12/12 = 1
12 × Mo-Mo single bonds

14. Larger Clusters – M6 [Nb6Cl12]2+ Nb6 octahedron with 12Cl on edges
[Nb6Cl12]2+ ≡ [Nb6] Cl-
6 × Nb (d5)  30 e-
[Nb6]14+ so…
number for M-M bonding is 30 – 14 = 16 e- or 8 pairs
12 × Nb-Nb connections in octahedron
number of pairs / number of edges = 8/12 = 2/3
12 × Nb-Nb bonds with bond order = ⅔

15. Carbonyl Clusters
In carbonyl clusters, some of the metal orbitals are used to s and p-bond to the CO ligands
The number and order of the M-M bonds is easily determined by requiring that all of the metals obey the 18 e- rule
Mn2(CO)10
total number of electrons = 2 × 7 (Mn) + 10 × 2 (CO)  34 e-
Mn2 so each Mn has 34/2 = 17 e-
to complete 18 e- configuration, a Mn-Mn single bond is formed

16. Carbonyl Clusters
In some cases, the CO ligands bridge two metals – this does not effect the method as CO always donates 2e- to the cluster
Fe2(CO)9
total number of electrons = 2 × 8 (Fe) + 9 × 2 (CO)  34 e-
Fe2 so each Fe has 34/2 = 17 e-
to complete 18 e- configuration, a Fe-Fe single bond is formed

17. Carbonyl Clusters Larger clusters are again possible Os3(CO)12
total number of electrons = 3 × 8 (Os) + 12 × 2 (CO)  48 e-
Os3 so each Os has 48/3 = 16 e-
to complete 18 e- configuration, each Os makes two Os-Os bonds
Os3 triangle results

18. Summary By now you should be able to
Draw out the MO diagram for L4ML4 complexes
Complete this diagram by filling in the appropriate number of electrons
Explain the appearance of eclipsed geometries due to d-bonding
In larger clusters, use the total number of pairs of metal electrons and number of metal-metal connections to work out the bond order
In carbonyl clusters, use the 18 e- rule to work out how many bonds have to be formed
Next lecture
Ligand-substitution reactions

19. Practice

20. Practice What is the Mo-Mo bond order in the complex [Mo2(CH3CO2)4]?
What is the Os-Os bond order in the cluster Os4(CO)12?