Ligand Substitution Reactions:Rates and 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.

Stoichiometric and Intimate Mechanisms

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.

Stoichiometric mechanism: the sequence of elementary steps in a reaction

ML

L L

L

X

L

ML

L L

L

L

ML

L L

L

Y

L

-x +Y

5 coordinate intermediate

Dissociative Mechanism, D

7 coordinate intermediate

Associative Mechanism, A

ML

L L

L

X

L

ML

L L

L

L

ML

L L

L

Y

L

-x+YX Y

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.

transition state rather than an intermediate

Interchange Mechanism, I

ML

L L

L

X

L

ML

L L

L

L

ML

L L

L

Y

L

-x+Y

X Y=|

If there is no identifiable intermediate, then we have to assume an interchange mechanism is operating

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.

Suppose for the reaction

[M(NH3)3(OH2)]n+ + Lm− → [M(NH3)3L](n-m)+ + H2O

1) there is spectroscopic evidence for the existence of a 5 coordinate intermediate;

2) 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−)

(1) tells us that we are dealing with an A stoichiometric mechanism(2) tells us that the intimate mechanism is a

The mechanism of the reaction is Aa

rate determining step

intermediate

rate determining process

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.

The mechanism would then be described as Da.

Reversible formation of a 5 coordinate intermediate

Rate-determining attack of entering ligandProduct

rate determining step

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

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.

‡

‡

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

‡

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

‡

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

Ia Id

Self-exchange reactions

M(H2O)6 + H2O* M(H2O)5(H2O*) + H2O

(eg., from line shape analysis using 17O NMR)

inert labile

Rate:• increases with ionic radius• decreases with an increase in ionic charge

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

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

• 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

d3 LFSE = -12 Dq Cr(III)d6 (LS) -24Dq + 2P Co(III)d8 -12Dq Ni(II)d7 (HS) -8Dq Co(II)d9 -6Dq Cu(II)d10 0 Zn(II)

Expected order of lability:

Co(III) < Cr(III) = Ni(II) < Co(II) < Cu(II) < Zn(II)

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 labile than expectedmore inert than expected

Observed order of lability:

Cr(III) ~ Co(III) < Ni(II) < Co(II) < Zn(II) < Cu(II)

more labile than expectedmore inert than expected

J-T distortion of d9 ion

population of eg orbitals (which are antibonding) imparts lability to a metal ion. Thus Ni2+ (d8, t2g

6eg2) is much more labile

than d3 Cr3+ (t2g3) although it has the same

LFSE

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

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

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

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)

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)

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,yze’ x2-y2, xya1’ z2

Method of Krishnamurthy and Schaap

axial ligand field

equatorial ligand field

axial

equatorial

axial

equatorial

axial

equatorial

axial

equatorial

axial

equatorial

In D3h the d orbitals transform as

e” xz,yze’ x2-y2, xya1’ z2

Symmetry requires the energies of these two oribitals to be the same

Average of 2.93 and -4.57 is -0.82

axial

equatorial

In D3h the d orbitals transform as

e” xz,yze’ x2-y2, xya1’ z2

axial

equatorial

z , a '21

x -y ; x y, e '2 2

x z ; y z , e "

7 .0 7 D q

-0 .8 2 D q

-2 .7 1 D q

z , a '21

x -y ; x y, e '2 2

x z ; y z , e "

7 .0 7 D q

-0 .8 2 D q

-2 .7 1 D q

LFSETS = 2(-2.71) – 0.82 = -6.24 Dq

LFSEGS = -12Dq

LFAE = -6.24 –(-12) Dq = 5.76 Dq

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

A

34 8 -1 -1A

19 23 -1

-1

100 cm6.626 10 Js 2.998 10 ms 10138 cm

m

2.01 10 J 6.022 10 mol

= 121 kJ mol

E h hc N

N

From this kind of approach:

D Mechanism, D3h intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 121 14 36 215 59

D Mechanism, C4v intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 42 -39 36 162 20

A Mechanism, D5h intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 89 67 12 45 44

D Mechanism, D3h intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 121 14 36 215 59

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

D Mechanism, C4v intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 42 -39 36 162 20

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

A Mechanism, D5h intermediateCr(III) Mn(III) Fe(III) Co(III) Ni(II)

LFAE /kJ mol-1 89 67 12 45 44

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

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