1. Ligand Substitution Reactions:
Rates and Mechanisms
Chapter 2

2. Stoichiometric and Intimate Mechanisms
We can think of a reaction mechanism at two different levels.
– The reaction may occur through a series of distinct steps each of which can be written as a chemical equation.
» This series of steps is a stoichiometric mechanism.
– We can also consider what is happening during each of these individual steps.
» These details constitute the intimate mechanism of the reaction.

3. Stoichiometric Mechanism
Each step in the stoichiometric mechanism has a rate or equilibrium constant associated with it.
The stoichiometric mechanism looks at the reactants, products and intermediates that are involved in a reaction.
Each species considered exists in potential minimum along the reaction coordinate.

4. Dissociative Mechanism, D
Stoichiometric mechanism: the sequence of elementary steps in a reaction
5 coordinate intermediate
Dissociative Mechanism, D

5. Associative Mechanism, A
7 coordinate intermediate
Associative Mechanism, A

6. In general, a D mechanism requires evidence for the existence (structural, spectroscopic) of an intermediate with reduced coordination number. An A mechanism requires evidence of an intermediate with increased coordination number.

7. Interchange Mechanism, I
If there is no identifiable intermediate, then we have to assume an interchange mechanism is operating
transition state rather than an intermediate
Interchange Mechanism, I

8. Intimate mechanism: this describes the nature of the process in the rate-determining step.
If the rate is strongly dependent on the nature of the entering group, then the intimate mechanism is associative. We say the reaction is under associate activation. The symbol is a subscript a.

9. The mechanism of the reaction is Aa
Suppose for the reaction
[M(NH3)3(OH2)]n+ + Lm− → [M(NH3)3L](n-m)+ + H2O
there is spectroscopic evidence for the existence of a 5 coordinate intermediate;
the rate of the reaction is strongly dependent on the nature of L (for example, if L = H2O the reaction occurs 4 orders of magnitude slower than if L = CN−)
tells us that we are dealing with an A stoichiometric mechanism
tells us that the intimate mechanism is a
The mechanism of the reaction is Aa

10. rate determining step

11. rate determining process
intermediate
rate determining process

12. The mechanism would then be described as Da.
Whilst less common the situation could arise where the reaction proceeds through an intermediate of reduced coordination number (D) and this is followed by rate-determining attach of entering L on the intermediate (a).
The mechanism would then be described as Da.

13. The mechanism would then be described as Da.
Reversible formation of a 5 coordinate intermediate
Product
Rate-determining attack of entering ligand

14. rate determining step

15. In a Ad reaction, formation of the intermediate of higher coordination number occurs relatively rapidly; the rate-determining step is the dissociation of a ligand from the intermediate

16. If there is no experimental evidence for an intermediate, then we have to assume an interchange, I, mechanism. In this mechanism, bond breaking and bond making occur simultaneously and there is no well-defined intermediate along the reaction coordinate. ‡

17. An interchange, I, mechanism could be under either associative or dissociative activation, i.e., Ia or Id ‡

18. ‡
If the rate of the reaction is strongly dependent on the nature of the entering group and is weakly dependent on the nature of the leaving group, then bond making is more important than bond breaking.
The reaction is under associative activation.
We say the mechanism is an Associative Interchange Mechanism, Ia

19. ‡
If the rate of the reaction is weakly dependent on the nature of the entering group and is strongly dependent on the nature of the leaving group, then bond breaking is more important than bond making in the approach to the transition state.
The reaction is under dissociative activation.
We say the mechanism is a Dissociative Interchange Mechanism, Id

20. Ia Id

21. Self-exchange reactions
M(H2O)6 + H2O*  M(H2O)5(H2O*) + H2O
(eg., from line shape analysis using 17O NMR)
inert
labile

22. Rate:
increases with ionic radius
decreases with an increase in ionic charge

23. Rate:
increases with ionic radius
decreases with an increase in ionic charge
Inertness  q r __
Inertness  ion
 Self exchange reactions at metal centres are usually under dissociative activation

24. For the transition metals...
Inertness  ion
Jahn-Teller distortion of high spin d4 and d9 complexes imparts on them significant lability.
These two will exchange very rapidly because of the long (and therefore weak) M-L bonds.
This is an example of how a ground state structural effect can influence kinetics

25. There is a strong correlation between Ligand Field Stabilisation Energy (LFSE) and inertness
For example, low spin Co3+ and Cr3+ are amongst the most inert transition metal ions

26. d3 LFSE = -12 Dq Cr(III)
d6 (LS) -24Dq + 2P Co(III)
d Dq Ni(II)
d7 (HS) -8Dq Co(II)
d9 -6Dq Cu(II)
d Zn(II)
Expected order of lability:
Co(III) < Cr(III) = Ni(II) < Co(II) < Cu(II) < Zn(II)

27. Expected order of lability:
Co(III) < Cr(III) = Ni(II) < Co(II) < Cu(II) < Zn(II)
Observed order of lability:
Cr(III) ~ Co(III) < Ni(II) < Co(II) < Zn(II) < Cu(II)
more inert than expected
more labile than expected

28. Observed order of lability:
Cr(III) ~ Co(III) < Ni(II) < Co(II) < Zn(II) < Cu(II)
more inert than expected
more labile than expected
population of eg orbitals (which are antibonding) imparts lability to a metal ion. Thus Ni2+ (d8, t2g6eg2) is much more labile than d3 Cr3+ (t2g3) although it has the same LFSE
J-T distortion of d9 ion

29. Hence:
LFSE (a thermodyamic parameter) is a rough guide to the rate of self-exchange reactions at metal centres (a kinetic parameter).

30. 2nd and 3rd transition series
Usually very inert
High LFSE
Strong M-L bonds because of good overlap between ligand orbitals and the more expansive (compared to 3d) 4d and 5d orbitals

31. Ground state  Transition state
Clearly the LFSE contributes to the kinetic behaviour of a metal ion, i.e., there must be a ligand field contribution to the activation energy (LFAE)
Ground state  Transition state
LFSEGS
LFSETS
LFAE = LFSETS - LFSEGS

32. [Cr(H2O)6]3+  {[Cr(H2O)5(H2O)]3+}‡
EXAMPLE
[Cr(H2O)6]3+  {[Cr(H2O)5(H2O)]3+}‡
LFSEGS = -12Dq
LFSETS
Assumptions:
the reaction is under dissociative activation
the departing ligand in the TS is far from the metal centre, i.e., that the TS is approximately 5-coordinate
The LFSE of the TS will depend on the geometry of the TS, and two reasonable geometries can be envisaged, viz., square pyramidal (C4v) and trigonal bipyramidal (D3h)

33. The LFSE of the TS will depend on the geometry of the TS, and two reasonable geometries can be envisaged, viz., square pyramidal (C4v) and trigonal bipyramidal (D3h)

34. Method of Krishnamurthy and Schaap to estimate LFSE of geometries that are neither Oh nor Td
D3h
In D3h the d orbitals transform as
e” xz,yz
e’ x2-y2, xy
a1’ z2

35. Method of Krishnamurthy and Schaap
axial ligand field
equatorial ligand field

36. axial
equatorial

37. axial
equatorial

38. axial
equatorial

39. axial
equatorial

40. In D3h the d orbitals transform as
e” xz,yz
e’ x2-y2, xy
a1’ z2
axial
equatorial
Symmetry requires the energies of these two oribitals to be the same
Average of 2.93 and is -0.82

41. In D3h the d orbitals transform as
e” xz,yz
e’ x2-y2, xy
a1’ z2
axial
equatorial

42. axial
equatorial

43. LFSETS = 2(-2.71) – 0.82 = Dq
LFSEGS = -12Dq
LFAE = –(-12) Dq = 5.76 Dq

44. For Cr(III), Dq = 1760 cm-1 (from electronic spectroscopy), so LFAE= 10138 cm-1

45. From this kind of approach:

46. Predicted rate:
Co(III) < Cr(III) < Ni(II) < Fe(III) < Mn(III)

47. Predicted rate:
Co(III) < Cr(III) < Fe(III) < Ni(II) < Mn(III)

48. Predicted rate:
Cr(III) < Mn(III) < Co(III) ~ Ni(II) < Fe(III)

49. Experimental rate:
Cr(III) < Co(III) < Fe(III) < Ni(II) < Mn(III)
Hence, probably a D mechanism, possibly with a C4v intermediate.
There is other evidence to suggest that many Cr(III) reactions have a distinctly associative character, explaining the very inert nature of Cr(III) complexes