Inorganic reaction mechanisms vol 5

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A Specialist Periodical Report

Inorganic Reaction Mechanisms
Volume 5

A Review of the Literature Published between
January 1975 and June 1976

Senior Rep0 rter
A. McAuley, Department of Chemistry, University of Vidoria,
British Columbia, Canada
Reporters
J. Burgess, University of Leicester
R. D. Cannon, University of East Anglia
J . N . Davidson, Heriot-Watt University, Edinburgh
D. N . Hague, University of Kent
A. G. Lappin, Purdue University, Lafayette, Indiana, U.S.A.
P . Moore, University of Warwick
6. Stedman, University College, Swansea

The Chemical Society
Burlington House, London, WIV OBN


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I S B N : 0 85186 295 0
I SSN : 0305-8255
Library of Congress Catalog No. 73-642977

Copyright 0 1977
The Chemical Society
All Rights Reserved
No part of this book may be reproduced or transmitted
in any form or by any means - graphic, electronic,
including photocopying, recording, taping or
information storage and retrieval systems - without
written permission from The Chemical Society.

Printed in Great Britain by
Adlard & Son Ltd.
Bartholomew Press, Dorking


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Foreword

In this volume, the format, coverage, and approach in dealing with various aspects
of Inorganic Reaction Mechanisms are similar to those adopted for the previous
volumes of the series. Once again, rather than make an attempt at cataloguing all the
articles in which mention is made of mechanism, we have chosen (with an eye on
volume size and cost!) to concentrate on papers in which kinetics and mechanisms in
solution form the principal interest. This policy inevitably leads to mention of some
papers being cursory with a consequent loss of subtlety. It is our hope, however, that

any resultant oversimplification or misrepresentation is minimal. Review articles
cited are those which should be accessible to the great majority of readers.
The period of literature coverage extends from January 1975 to June 1976. The
boundaries at both ends are somewhat vague since not all libraries have issues available at the same time. Care has been taken to ensure that an overlap with Volume 4
has been maintained in all areas. Material which is derived from Chemical Abstracts
rather than from the original source is indicated by inclusion of a Chem. Abs.
citation in the reference quoted. References to the Russian literature derived from
this source quote the page number of the original article whereas those giving the
title of the English translation quote the page number of the translation.
As in previous volumes, kinetic data are reported in the form (Ea,or logA or
AH* and AS*)or units (SI or other) used in the original article, although some
conversions have been made both in the text and in the tables where comparisons are
required.
The Reporters are grateful to many of their colleagues for helpful comments. We
are particularly indebted to Drs R. W. D. Kemmitt and A. G. Sykes for their critical
reading of sections of the manuscript.
A. MCAULEY


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Contents
Part I Electron Transfer Processes
Chapter 1 Reactions Between Two Metal Complexes

3

By R. D.Cannon
1 General and Theoretical
Theory of the Electron Transfer Process
Activation Parameters
Stereoselectivity
2 Intramolecular Electron Transfer
The Precursor Complex
Optical Electron Transfer
Symmetrical Exchange Processes

6
8
10

3 Intermolecular Electron Transfer
Methods of Measurement
Complementary Reactions
Chromium(I1)
Vanadium(I1)
Titanium(Ir1)
Uranium(n1)
Neptunium(vI1)
Excited [*Ru(bipy) J2+
Europium(I1)
Other Reagents
Non-complementary Reactions

14
14
14

15
19
19
21
21
21
22
22
23

Chapter 2 Metal Ion-Ligand Redox Reactions
By A. G. Lappin

6

42

1 Chromium(v1)

42

2 Iron(II1)

50

3 Manganese(Ir1)

57

4 Manganese(vr1)

60


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vi

Contents

5 Cobalt(II1)

64

6 Vanadium(v)

67

7 Thallium(rr1)

70

8 Cerium(1v)

74

9 Copper(I1)

77

10 Miscellaneous Redox Reactions

82

11 Halogens and Halogenate Ions

95

12 Metal-ion Reductions

100

13 Pulse Radiolysis Studies

104

Chapter 3 Reactions of Oxygen and Hydrogen Peroxide
By A. McAuley

107

1 Cobalt(1r) Complexes

107

2 Iron(I1) Complexes

109

3 Copper-(I) and -(II)Complexes

111

4 Other Metal Complexes

113

5 Reactions of Hydrogen Peroxide

114

Part /I Substitution and Related Reactions
Chapter 1 Non-metallic Elements
By G. Stedman
1 Group I11
Boron
Tetrahedral Anions
Boron-Hydrogen Compounds
Boron-Nitrogen and Boron-Phosphorus Compounds
Boron-Oxygen Compounds
Aluminium
Gallium
Indium
Thallium

121
121
121
121
121

122
122
122
123

124
124


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vii

Contents

2 GroupIV
Carbon
Silicon
Germanium
Tin
Lead

125
125
125
126
126
127

3 GroupV

128
128
130
130
132
132
133
133
134
134
135

Nitrogen
Phosphorus
Oxoanions
Phosphorus-Oxygen-Sulphur Compounds
Phosphorus-Oxygen-Nitrogen Compounds
Phosphazanes
Miscellaneous Compounds
Intramolecular Processes
Arsenic
Antimony
4 GroupVI
Sulphur
Sulphur-Nitrogen Compounds
Intramolecular Processes
Selenium
Tellurium

135

135
138
138
138
139

5 GroupVII

Fluorine
Chlorine
Bromine
Iodine

139
139
140
140
140

6 GroupVIII
Xenon

141
141

Chapter 2 Inert Metal Complexes: Co-ordination Numbers Four
and Five
By J. Burgess
1 Square-planar Complexes
Platinurn@)

General
Aquation, Solvolysis, and Anation
Ligand Exchange
Entering Groups
Ring Closure

142

142
143
143
143
144
145
146


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viii

Contents

Ring-opening
Displacement of Bidentate Groups
Displacement of Alkenes
Effects of Non-leaving Ligands
Isomerization, Symmetrization, and Inversion
Photochemistry
Reactions of Co-ordinated Ligands
Palladium(rr)

Aquation and Anation
Substitution
Isomerization and Inversion
Gold(II1)
Nickel(@
Iron(@, Rhodium(r), and Iridium(1)

147
147
148
148
149
150
150
151
151
152
155
155
157
158

2 Tetrahedral Complexes

158

3 Five-co-ordinate Complexes

159

Chapter 3 Inert Metal Complexes: Co-ordination Numbers Six
and Higher
By P. Moore
1 Introduction
2 Aquation: Cobalt(II1) Complexes

Unidentate Leaving Groups
Multidentate Leaving Groups
Effects of Non-leaving Ligands
[Co(en),XY]n+ Complexes
[Co(LL),(L)XIn+and [Co(LLL)(LL)XIn+Complexes
[Co(LLLL)(L)X]n+and [Co(LLLLL)X]a+Complexes
Dioximato-complexes
Bridged Dicobalt Complexes
Solvent Variation
Catalysed Aquation
Photochemistry

162

162
169
169
174
175
175
176
178
181
182

184
184
187

3 Aquation: Chromium(Ir1) Complexes

188

Unidentate Leaving Groups
Ammonia Loss
[Cr(H,O),L] n+ Complexes
Other Complexes
Multidentate Leaving Groups

189
189
189
191
192


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ix

Contents

Effects of Non-leaving Groups
Bridged Dichromium Complexes
Non-aqueous Solvents
Catalysis

195
197
198
200

4 Aquation: Other Complexes
do: Molybdenum(v1)
do:Vanadium(v)
d l : Molybdenum(v)
d2: Molybdenum(1v)
d : Rhenium(v)
d : Molybdenum(Ir1)
d a : Technetium(1v)
d 4 : Manganese(rI1)
d : Rhenium@)
d : Molybdenum(1)
d : Iron(II1)
d 5: Ruthenium(II1)
d : Rhodium(m)
Photochemistry
d 6 : Iron(I1)
d e: Ruthenium(@
Reactions of Co-ordinated Ligands
d : Osmium(1r)

200
200
201
201

201
202
202
202
203
203
203
203
203
204
206
207
209
21 1
212

5 Base Hydrolysis
Cobalt(m) Complexes
Chromiurn(1n)Complexes
Other Metal Ions

212
212
217
217

6 Formation
do:Titanium(w) and Zirconium(1v)
d l : Molybdenum(v)
d2: Molybdenum(1v)

d 3 :Chromiurn(I1I)
d : Molybdenum(m)
d : Technetium(1v)
d 4 :Manganese(rI1)
d : Iron(Ir1)
d 5: Ruthenium(II1)
d6:Iron(r1)
d : Ruthenium@)
d s :Cobalt(II1)
d b: Rhodium(u1)
d : Platinum(rv)
Miscellaneous Metal Ions

217
217
218
218
218
220
220
220
22 1
22 1
221
223
223
228
229

230

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Contents

X

7 Ligand Exchange and Replacement
Solvent Exchange
Ligand Exchange and Replacement : Unidentate by Unidentate
Ligand Replacement : Multidentate by Unidentate
Ligand Replacement : Unidentate by Multidentate
Ligand Replacement: Multidentate by Multidentate

230
230
23 1
232
232
232

8 Metal Exchange and Displacement

234

9 Isomerization and Racemization
General
Cobalt(rI1) Complexes
Chromium(r) Complexes
Intramolecular Rearrangements of Tris-chelate Complexes

Miscellaneous

235
235
235
237
237
238

10 Co-ordination Numbers Greater than Six

Chapter 4 Labile Metal Complexes
By D. N. Hague

239

240

1 Complex Formation involving Unsubstituted Metal Ions:
Unidentate Ligands and Solvent Exchange
Univalent Ions
Bivalent Ions
Metals of Valency Three and Higher

240
240
240
243

2 Complex Formation involving Unsubstituted Metal Ions:

Multidentate Ligands
Univalent Ions
Bivalent Ions
Manganese
Cobalt
Nickel
Copper
Zinc, Cadmium, and Mercury
Metals of Valency Three and Higher

245
245
246
246
246
246
25 1
254
254

3 The Effects of Bound Ligands
Reactions in Water
Reactions in Non-aqueous Solvents

255
255
256


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xi

Contents

Chapter 5 Solvent Effects
By J. Burgess

260

1 Introduction

260

2 Pure and Mixed SoIvents
Solvent Isotope Effects
Solvent Properties
Dielectric Constant
Viscosity
Water Concentration
Solvent Parameters
Grunwald-Winstein Analysis
Other Solvent Parameters
Thermodynamic Aspects
Reactant Solvation
Solvents
Solvent Structure
Photochemistry
Pure Solvents: Miscellaneous
Solvent Exchange

Solvolysis
Ligand Exchange and Replacement
Complex Formation: Inert Cations
Complex Formation : Labile Cations
Isomerization
Miscellaneous
Mixed Aqueous Solvents: Miscellaneous
Solvolysis
Formation
Non-aqueous Solvent Mixtures

261
261
261
261
263
263
264
264
266
266
266
267
268
268
269
269
269
269
270

270
271
271
271
271
272
272

3 Salt Effects

272

Part /I/ Reactions of Biochemical Interest
By 0.N. Hague
~~

~

1 General

277

2 Metal Ion Transport through Membranes

277


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Contents

xii

3 Metal Complex Formation: Non-redox Systems
Systems involving Phosphate Groups
Carbonic Anhydrase (CA)
Carboxypeptidase
Liver Alcohol Dehydrogenase
Other Systems

280
280
283
287
288
289

4 Reactions involving Metals in Porphyrins and Related Ring
Systems
Haemoglobin and Similar Molecules
Coenzyme B, and Similar Molecules
Cytochromes and other Porphyrin-containing Systems

290
290
294
294

5 Redox Reactions involving Metals in other Biological and Model
Systems

299

Part I V

OrganometaIlic Compounds
By J. L. Davidson

Chapter 1 Substitution

305

1 Exchange Reactions

305

2 Substitution in Carbonyls:Carbon Monoxide Replacement
Simple Carbonyls
Polynuclear Carbonyls
Mixed-ligand Carbonyls

308
308
3 10
310

3 Formation of Carbonyls

318

4 Metal-Metal Bonds

320

5 Cyclopentadienyls

324

6 Olefin and Acetylene Complexes

325

7 Amine Complexes

328

8 Miscellaneous

330


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...

Contents

XI1 1

Chapter 2 Metal-Alkyl, -Aryl, and -Ally1 Bond Formation and
Cleavage

333

1 General

333

2 GroupIV

333

3 GroupV
Vanadium

334
334

4 GroupVI

335
335

Chromium
5 GroupVII

Manganese

335
335

6 Group VIII
Iron
Cobalt
Rhodium and Iridium
Nickel
Palladium
Platinum

335
335
337
339
340
341
342

7 Group1
Gold

344
344

8 Actinides

345

Chapter 3 Homogeneous Catalysis

346

1 General

346

2 Isomerization

346
346
349

Strained Carbocyclic Systems
Alkenes
3 Disproportionation

352

4 Oligomerization

355

5 Co-addition and Co-oligomerization

360

6 Homogeneous Hydrogenation

362


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Contents

xiv
7 Hydrogen Exchange

364

8 Homogeneous Oxidation

367

9 Exchange Reactions

368

10 Carbonylation, Hydroformylation, and Hydration

370

11 Decarbonylation

372

12 Hydrosilylation

372

Chapter 4 Insertion Reactions

374

1 Alkenes and Akynes

374

2 Carbon Monoxide

378

3 Sulphur Dioxide

379

4 Miscellaneous
Carbon Disulphide
Carbon Dioxide
Oxygen
Isocyanides
Carbenes
Stannous Chloride

380
380
381
38 1
381
382
382

Chapter 5 Reactions of Co-ordinated Ligands

383

1 Carbonyls and Nitrosyls
Carbonyls
Nitrosyls

383
383
383

2 Alkenes and Alkynes

384
384
387
390
392

Linear Alkenes and Alkynes
Cyclic Alkenes
Cycloaddition
Isomerization and Exchange
3 Isocyanides

396


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xv

Contents

Chapter 6 Oxidative Addition and Reductivc Elimination

398

1 GroupVIII
Iron
Cobalt
Rhodium
Iridium
Nickel
Platinum
Oxidative Addition
Reductive Elimination

398
398
398
398
400
400
402
402
404

2 Group1

406

406

Gold

Chapter 7 lsomerization : Intramolecular Processes

408

1 Groups IV and V

405

2 GroupVI

411

3 GroupVII

416

4 Group VIII: Iron Triad
Iron
Six-co-ordinate Complexes
Rotational Isomerization
Ruthenium and Osmium

41 8
418
421
424

425

5 Group VIII: Cobalt Triad
Cobalt
Rhodium
Iridium

429
429
430
433

6 Group VIII: Nickel Triad
General
Nickel
Palladium
Platinum

434
434
434
434
437

7 Group11
Mercury

439
439

8 Actinides

439

Author Index

440


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Abbreviations for Ligands and Solvents
Abbreviations which appear only once in the text are generally defined at their point
of use; those which appear more than once are defined below.

General
R
L
LL
LLL
LLLL
X

alkyl, aryl
uni dentate 1igand
bidentate ligand
terdentate ligand
quadridentate ligand
halide (except where otherwise stated)

Specific

acac
ADP
2’-AMP
3’-AMP
5’-AMP
AN
asp
ATP
big
biPY
bzac
bzbz
cal
CDP
cod
CP
CTP
cyclam
cydta
dacoda
diars
dien
dien -H
dimetn
diphos
DMF
dmg

acetylacetonate
adenosine-5’-diphosphate
adenosine-2’-monophosphate
adenosine-3’-monophosphate
adenosine-5’-monophosphate
acetonitrile
aspartate
adenosine-5’-triphosphate
biguanide
2,2’-bipyridyl
benzoylacetonate (1 -phenylbut ane-1,3-dionate)
1,3-diphenylpropanel,3-dionate
calmagite [1-(1-hydroxy-4-methyl-2-phenylazo)-2-naphthol-4sulphonate]
cytosine-5’-diphosphate
cyclo-octadiene
cyclopentadienyl
cytosine-5’-triphosphate
1,4,8,11 -tetra-azacyclotetradecane
cyclohexane-l,2-diaminetetra-acetate
1,5-diazacyclo-octane-NN’-diacetate
o-phenylenebisdimethylarsine
diethylenetriamine
diethylenetriamine minus one nitrogen proton

NN’-dimethylpropane-1,3-diamine
1,2-bisdiphenylphosphinoethane
dimethylformamide
dimethylglyoximate

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Abbreviations .for Ligands and Solvents
dmP
DMSO
dmtu

DNA
dPt
dtc
dto
dtP
dtpa
edda
eddda
edds
edma
edta
egta
en
Et ,dien
ete
gedta
glu
glY
Hb
hedta
hfac
himda
his
hm

ida
ind
isn
ma1
Me,dien - H
Me ma1
Me,t ren
met u
mida
mnt
mq
NADH
niox
nta
ox
pada
pdta
phen
Pn
PY

xvii

2g-dimethyl-1,lo-phenanthroline
dimethyl sulphoxide
NW-dimethylthiourea
deoxyribonucleic acid
dipropylenetriamine
dithiocarbamate
dithio-oxalate

diethyldithiophosphate
diethylenetriaminepenta-acetate
ethylenediaminediacetate
ethylenediaminediacetatedipropionate
NN’-et hylenediaminedisuccinate
ethylenediaminemonoacetate
ethylenediaminetetra-acetate
ethylene glycol bis-(Zaminoethyl ether)-tetra-acetate
ethylenediamine
NNN”N”-tetraethyldiethylenetriamine
4,8-dithia-1711-diazaundecane

2,2’-ethylenedioxybis(ethyleneiminodiacetate)
glutamate
glycinate
Haemoglobin
N-(2-hydroxyethyl)ethylenediaminetriacetate
hexafluoroacetylacetonate
hydroxymethyliminodiacetate
histidine
histamine
iminodiacetate
indenyl
isonicotinamide
malonate
NNN”N”-tetramethyldiethylenetriamineminus the nitrogen proton
methylmalonate anion
2,2’, 2”- tris-(NN-dimethylamino)tr ieth ylamine
N-methylthiourea
N-methyliminodiacetate

maleonitriledithiolate
2-meth yl-S-quinolinate
nicotinamide adenine dinucleotide (reduced form)
nioxime
nitrilotriacetate
oxalate
pyridine-2-azo-p-dimethylaniline
propylenediaminetetra-acetate
1,lo-phenanthroline
propylenediamine
pyridine


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xviii
salen
tar
tcne
tea
terPY
2,3,2-tet
tet-a, tet-b
tetren
tfac
thiox
tmd
tmeda
TP
trarts-14-diene

tren
trien
trigly
ttha
tu
XYl

Abbreviations for Ligands and Solvents

NN’-bis(salicyla1dehydo)ethylenediamine
tartrate
tetracyanoethylene
triethanolamine
2,2’,2”-terpyridyl
1,4,8,11 -tetra-azaundecane
5,7,7,12,14,14-hexamethyl1,4,8,11 -cyclotetra-azatetradecane
tetraethylenepentamine
1,1,1-trifluoroacetylacetonate
monothio-oxalate
trimethylenediamine
NNN’N’-tetramethylethylenediamine
tripolyphosphate
5,7,7,12,14,14-hexamethyl1,4,8,11-tetra-azacyclotetradeca-4,11diene
triaminotriethylamine
triethylenetetramine
triglycine
triethylenetetraminehexa-acetate
thiourea
xylenol orange

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Part I
ELECTRON TRANSFER PROCESSES

BY
R. D. CANNON
A. G. LAPPIN
A. McAULEY


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1
Reactions Between Two Metal Complexes
BY R. D. CANNON

1 General and Theoretical
Theory of the Electron Transfer Process.-A lengthy review of electron-transfer
theory has appeared in a companion publication to this series,l and a further review
is promised in the next volume.* New studies have also appeared of outer-sphere
electron transfer in solution,2covering the intermediate range between adiabatic and
non-adiabatic conditions, and of inner-sphere transfer in the solid ~ t a t e .The
~
relationship between electron transfer and magnetic exchange interactions has been
pointed out. Antiferromagnetic coupling has been demonstrated in copper(i1)copper(n) dimers with no direct inner-sphere bridging ligands, and it is suggested

that further work on such systems will lead to a better understanding of outer-sphere
electron transfer in solution? There is continuing discussion of the possibility of
electron transfer over long distances, but the evidence for such a process in solution
still seems inconcl~sive.~-~
Of more direct interest to kineticists is a reconsideration by Marcus and Sutin of
the basis for the well known equation (1) relating activation free energies AG* to
AG* = A(l

+

AG*/4A)2

(1)

standard free-energy changes AGe. Equation (1) is commonly illustrated by diagrams
of the type of Figure 1 (cf. Figures 2 and 3, pp. 9 and 10). For restricted ranges of
AGe, it predicts an approximate linear correlation of AG* with AGe, with slope a
[equation (2)], such that when AG* is close to zero, a is ca. 0.5, and this has been
verified in several cases :O
a=---

aAG*

- +(1

+

AG*/4A)

However, equation (2) also predicts that as AGe becomes more negative a decreases,

until when AG < -4A further decrease in AG* leads to an increase in AG *. Marcus

*
1
2

3
4

5
6

7
8
9

Two other reviews are inaccessible at the time of writing (see refs. 114 and 11 5).
P. P. Schmidt, in ‘Electrochemistry’, ed. H. R. Thirsk (Specialist Periodical Reports), The
Chemical Society, London, 1975, Vol. 5, p. 21.
S. G. Christov, Ber. Bunsengesellschaftphys. Chem., 1975, 79, 357.
J. Mulak and K. W. H. Stevens, 2.phys. ( B ) , 1975, 20, 21.
E. J. Laskowski, D. M. Duggan, and D. N. Hendrickson, Inorg. Chem., 1975, 14,2449.
K. I. Zamaraev and R. F. Khairutdinov, Chem. Phys., 1974, 4, 181.
A. G. Rykov and N. B. Blokhin, Russ. J. Phys. Chem., 1975,49,737 (2hur.ji.z. Khim., 1975,49,
1262).
R. F. Khairutdinov and K. I. Zamaraev, Doklady Phys. Chem., 1975,222,521 (Doklady Akad.
Nauk S.S.S.R., 1975, 222, 654).
R A. Marcus and N. W i n , Inorg. Chem., 1975, 14, 213.
J. E. Earley, Progr. Znorg. Chem., 1970,13, 243.

3


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4

Inorganic Reactiori Mechanisms

Figure 1 Reaction profiles for electron-transfer reactions (x= reaction co-ordinate,
G = free energy), showing the cases (i) AGe= 0, (ii) O > AGe> -4A, (iii)
AGe c - 4A [cf. equation (1) of text]. The dotted curve represents a possible
electronically excited state of (iii)
and Sutin now point out that this is not to be expected. The region AGe< - 4 A
corresponds to intersection of reactants’ and products’ curves on the left-hand side
of the diagram ( x < O , point b, Figure 1)’ in contrast to ‘normal’ intersections at
x > 0 (point c), and this requires a non-adiabatic transition. It is suggested that for
these transitions nuclear tunnelling may become important, and that as a result AG *
will not increase with decreasing AGe but will remain constant, with the specificrate
at the diffusion-controlled limit. An analogous situation has indeed already been
recognized for electron transfer between organic molecules. Over a range of AGe
from - 5 to + 5 kcal mol-l, Rehm and Weller ObtainedlO a parabolic plot of AG *
against AGO, but from AGe= - 5 to -62 kcal mol-l AG* remained constant.
Another theory based on the non-adiabatic description leads to a linear dependence
of AGe on AG* in this region,ll but constancy of AG* can also be explained in a
different way:12 it has been suggested that when the ground-state products’ curve
passes the minimum on the reactants’ curve (point d), other curves for higher electronic levels become available, as for example the dotted curve (iii) in Figure 1;
hence the reaction may still proceed with zero thermal activation energy along the
route a -+d+e. More sophisticated quantum mechanical models involving multiple
energy states have also been disc~ssed.~~J*
The minimum value of AG * (on the old theory) or the limiting value (on the new)

is expected to be zero only if the work terms are negligible, and if there are no rapid
l o D. Rehm and A. Weller, Israel J. Chem., 1970, 8, 259.

R. P. Van Duyne and S. F. Fisher, Chem. Phys., 1974,5, 183.
S. Efrima and M. Bixon, Chem. Phys. Letters, 1974, 25, 34.
l3 J. Ulstrup and J. Jortner, J. Chem. Phys., 1975, 63, 4358.
l4 W. Schmickler, J.C.S. Faraday 11, 1976, 72, 307.
11

l2


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Reactions Between Two Metal Complexes

5

equilibrium steps preceding the electron-transfer process. Previously, Hyde et al.15
had found a non-linear correlation of AG* with AGO, for a reaction of a series of
reductants with the common oxidant [Co(H20),l3+.The limiting value of AG* was
found to be ca. 9 kcal mol-l. Ekstrom et all7have now added an additional point for
the reaction Co3+ U3+,which fits well on to the curve, but they point out that data
for a large number of cation-cation reactions involving oxidants other than
[CO(H~O)~]~+
also cluster quite well round the same curve and Falcinella et al.ls have
produced an analogous correlation for reactions of T12+, acting alternatively as
oxidant and reductant.
The limiting value, AG * E 9 kcal mol-l, had previously been felt to be rather
high, and one possible explanation considered was a rapid equilibrium between the
two spin states of cobalt(m) ( t f ,+t&e,) prior to the electron transfer. The data from

other oxidants have weakened if not altogether removed the necessity for this. It has
moreover been argued from ligand-field considerations that for the hexa-aquocobalt(m) ion the spin-change free energy may in any case be quite small.l@
It is accordingly now argued that the high limiting value is sufficiently accounted
for by the work terms, i.e. the limiting rate constant does represent the diffusioncontrolled value for the reactants in equation. The specificcollision rate calculated by
the Debye equation17for the reaction U3++ Co3+is 1.7 x lo41 mol-1 s-l (at 25 "C,
zero ionic strength), to be compared with the experimental 7.1 x lo31 mol-1 s-l. In
theory there should be different limiting rates depending on the ionic charges, and it
is perhaps a cause for concern that reactions as diverse as Co3+fNpO2+,UOZ2++
Eu2+,and FeS++U3+all fall near the same curve.
Activation Parameters.-Negative heats of activation have previously been reported
for some outer-sphere reactions,20p21and it has been suggested that some special
factor, not covered by the simple Marcus theory, might need to be invoked to
explain them. (It will be recalled that negative heats of activation of some innersphere reactions have been rationalized in terms of the energetics of formation of
precursor complexes.)22Marcus and Sutin point out,s however, that negative A H *
values are theoretically predicted, under certain conditions. On differentiating
equation (1) with respect to temperature, they obtain

+

A H * = -a(AG*/T)/a(l/T)

-

+ $AH*(l + 28)
+ *ASO(l + 2p)

= A H A ( ~ 4p2)

A S * = -a(AG*)/aT = A s ~ ( 1- 4b2)

(3a)

(3b)

where AHA and ASA are activation parameters corresponding to the intrinsic freeenergy barrier A [equation (l)] and p=2AG0/A. The term p may be positive or
negative, but is usually small; hence if the overall enthalpy change is sufficiently
negative AH& may be negative even when AHA is positive. A complete calculation
requires a knowledge of AHA and ASA, from the appropriate cross-reactions,as well
l5
l6
17

1s
19
20

21
28

M. R. Hyde, R. Davies, and A. G. Sykes, J.C.S. Dalton, 1972, 1838.
A. Ekstrom, A. B. McLaren, and L. E. Smythe, Inorg. Chem., 1975, 14, 1035.
A. Ekstrom, A. B. McLaren, and L. E. Smythe, Inorg. Chem., 1975, 14, 2899.
B. Falcinella, P. D. Felgate, and G. S. Laurence, J.C.S. Dalton, 1975, 1 .
I. Bodek and G. Davies, Coordination Chem. Rev., 1974, 14, 269.
J. N. Braddock and T. J. Meyer, J. Amer. Chem. Soc., 1973,95, 3158.
J. L. Cramer and T. J. Meyer, Inorg. Chem., 1974, 13, 1250.
R. C. Patel, R. E. Ball, J. F. Endicott, and R. G. Hughes, Inorg. Chem., 1970, 9, 23,