physical inorganic chemistry: reactions, processes, and applications

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PHYSICAL INORGANIC CHEMISTRY

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PHYSICAL INORGANIC
CHEMISTRY
Reactions, Processes, and Applications

Edited by

Andreja Bakac

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Copyright Ó 2010 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Physical inorganic chemistry : reactions, processes and applications / [edited by]
Andreja Bakac.
p. cm.
Includes index.
ISBN 978-0-470-22420-5 (cloth)
1. Physical inorganic chemistry. I. Bakac, Andreja.
QD476.P488 2010
5470 .13–dc22
2009051078
Printed in the United States of America
10 9 8

7 6 5 4

3 2 1

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To Jojika

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CONTENTS
Preface

ix

Contributors

xi

1

Electron Transfer Reactions

1

Ophir Snir and Ira A. Weinstock

2

Proton-Coupled Electron Transfer in Hydrogen
and Hydride Transfer Reactions

39

Shunichi Fukuzumi

3

Oxygen Atom Transfer

75

Mahdi M. Abu-Omar

4

Mechanisms of Oxygen Binding and Activation
at Transition Metal Centers

109

Elena V. Rybak-Akimova

5

Activation of Molecular Hydrogen

189

Gregory J. Kubas and Dennis Michael Heinekey

6

Activation of Carbon Dioxide

247

Ferenc Joo´

7

Chemistry of Bound Nitrogen Monoxide and Related
Redox Species

281

Jose A. Olabe

8

Ligand Substitution Dynamics in Metal Complexes

339

Thomas W. Swaddle

9

Reactivity of Inorganic Radicals in Aqueous Solution

395

David M. Stanbury

10

Organometallic Radicals: Thermodynamics, Kinetics,
and Reaction Mechanisms

429

Tamas Kegl, George C. Fortman, Manuel Temprado, and Carl D. Hoff

vii

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viii

11

CONTENTS

Metal-Mediated Carbon–Hydrogen Bond Activation

495

Thomas Brent Gunnoe

12

Solar Photochemistry with Transition Metal Compounds Anchored
to Semiconductor Surfaces
551
Gerald J. Meyer

Index

589

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PREFACE
This book is a natural extension of “Physical Inorganic Chemistry: Principles,
Methods, and Models,” a 10-chapter volume describing the methods, techniques,
and capabilities of physical inorganic chemistry as seen through the eyes of a
mechanistic chemist. This book provides an insight into a number of reactions that
play critical roles in areas such as solar energy, hydrogen energy, biorenewables,
catalysis, environment, atmosphere, and human health. None of the reaction types
described here is exclusive to any particular area of chemistry, but it seems that
mechanistic inorganic chemists have studied, expanded, and utilized these reactions
more consistently and heavily than any other group. The topics include electron
transfer (Weinstock and Snir), hydrogen atom and proton-coupled electron transfer
(Fukuzumi), oxygen atom transfer (Abu-Omar), ligand substitution at metal centers

(Swaddle), inorganic radicals (Stanbury), organometallic radicals (Kegl, Fortman,
Temprado, and Hoff), and activation of oxygen (Rybak-Akimova), hydrogen (Kubas
and Heinekey), carbon dioxide (Joo´), and nitrogen monoxide (Olabe). Finally, the
latest developments in carbon–hydrogen bond activation and in solar photochemistry
are presented in the respective chapters by Gunnoe and Meyer.
I am grateful to this group of dedicated scientists for their hard work and
professionalism as we worked together to bring this difficult project to a successful
conclusion. I am also thankful to my family, friends, and colleagues who provided
invaluable support and encouragement throughout the project, and to my editor,
Anita Lekhwani, who has been a source of ideas and professional advice through the
entire publishing process.
ANDREJA BAKAC

ix

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CONTRIBUTORS
MAHDI M. ABU-OMAR, Department of Chemistry, Purdue University, West
Lafayette, IN, USA
GEORGE C. FORTMAN, Department of Chemistry, University of Miami, Coral
Gables, FL, USA
SHUNICHI FUKUZUMI, Department of Material and Life Science, Graduate School of
Engineering, Osaka University, Suita, Osaka, Japan
THOMAS BRENT GUNNOE, Department of Chemistry, University of Virginia,
Charlottesville, VA, USA

D. MICHAEL HEINEKEY,
Seattle, WA, USA
CARL D. HOFF,
USA

Department of Chemistry, University of Washington,

Department of Chemistry, University of Miami, Coral Gables, FL,

FERENC JOO´, Institute of Physical Chemistry, Hungarian Academy of Sciences,
University of Debrecen and Research Group of Homogeneous Catalysis,
Debrecen, Hungary
TAMA´S KE´GL, Department of Organic Chemistry, University of Pannonia,
Veszprem, Hungary
GREGORY J. KUBAS, Chemistry Division, Los Alamos National Laboratory, Los
Alamos, NM, USA
GERALD J. MEYER, Department of Chemistry, Johns Hopkins University,
Baltimore, MD, USA
JOSE´ A. OLABE, Department of Inorganic, Analytical and Physical Chemistry,
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,
Buenos Aires, Argentina
ELENA RYBAK-AKIMOVA,
MA, USA

Department of Chemistry, Tufts University, Medford,

OPHIR SNIR, Department of Chemistry, Ben-Gurion University of theNegev, Beer
Sheva, Israel
DAVID M. STANBURY,
USA

Department of Chemistry, Auburn University, Auburn, AL,
xi

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xii

CONTRIBUTORS

THOMAS W. SWADDLE,
Canada
MANUEL TEMPRADO,
FL, USA

Department of Chemistry, University of Calgary, Calgary,
Department of Chemistry, University of Miami, Coral Gables,

IRA A. WEINSTOCK, Department of Chemistry, Ben-Gurion University of the Negev,
Beer Sheva, Israel

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1

Electron Transfer Reactions
OPHIR SNIR and IRA A. WEINSTOCK

1.1

INTRODUCTION

Over the past few decades, applications of the Marcus model to inorganic electron
transfer reactions have become routine. Despite the many approximations needed
to simplify the theoretical descriptions to obtain a simple quadratic model, and the
assumptions then needed to apply this model to actual reactions, agreement between
calculated and observed rate constants is remarkably common. Because of this, the
Marcus model is widely used to assess the nature of electron transfer reactions. The
intent of this chapter is to make this useful tool more accessible to practicing chemists.
In that sense, it is written from a “reaction chemist’s”1 perspective. In 1987, Eberson
published an excellent monograph that provides considerable guidance in the context
of organic reactions.2 In addition to a greater focus on inorganic reactions, this chapter
covers electrolyte theory and ion pairing in more detail, and worked examples are
presented in a step-by-step fashion to guide the reader from theory to application.
The chapter begins with an introduction to Marcus’ theoretical treatment of outersphere electron transfer. The emphasis is on communicating the main features of the
theory and on bridging the gap between theory and practically useful classical models.
The chapter then includes an introduction to models for collision rates between
charged species in solution, and the effects on these of salts and ionic strength, which
all predated the Marcus model, but upon which it is an extension. Collision rate and
electrolyte models, such as those of Smoluchowski, Debye, H€uckel, and others, apply
in ideal cases rarely met in practice. The assumptions of the models will be defined,
and the common situations in which real reacting systems fail to comply with them
will be highlighted. These models will be referred to extensively in the second half of
the chapter, where the conditions that must be met in order to use the Marcus model
properly, to avoid common pitfalls, and to evaluate situations where calculated values
fail to agree with experimental ones will be clarified.
Those who have taught themselves how to apply the Marcus model and crossrelation correctly will appreciate the gap between the familiar “formulas” published
in numerous articles and texts and the assumptions, definitions of terms, and physical

Physical Inorganic Chemistry: Reactions, Processes, and Applications Edited by Andreja Bakac
Copyright Ó 2010 by John Wiley & Sons, Inc.

1

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2

ELECTRON TRANSFER REACTIONS

constants needed to apply them. This chapter will fill that gap in the service of those
interested in applying the model to their own chemistry. In addition, the task of
choosing compatible units for physical constants and experimental variables will be
simplified through worked examples that include dimensional analysis.
The many thousands of articles on outer-sphere electron transfer reactions involving
metal ions and their complexes cannot be properly reviewed in a single chapter. From
this substantial literature, however, instructive examples will be selected. Importantly,
they will be explaining in more detail than is typically found in review articles or
treatises on outer-sphere electron transfer. In fact, the analyses provided here are quite
different from those typically found in the primary articles themselves. There, in nearly
all cases, the objective is to present and discuss calculated results. Here, the goal is to
enable readers to carry out the calculations that lead to publishable results, so that they
can confidently apply the Marcus model to their own data and research.

1.2

THEORETICAL BACKGROUND AND USEFUL MODELS

The importance of Marcus’ theoretical work on electron transfer reactions was
recognized with a Nobel Prize in Chemistry in 1992, and its historical development
is outlined in his Nobel Lecture.3 The aspects of his theoretical work most widely
used by experimentalists concern outer-sphere electron transfer reactions. These are
characterized by weak electronic interactions between electron donors and acceptors
along the reaction coordinate and are distinct from inner-sphere electron transfer
processes that proceed through the formation of chemical bonds between reacting
species. Marcus’ theoretical work includes intermolecular (often bimolecular) reactions, intramolecular electron transfer, and heterogeneous (electrode) reactions. The
background and models presented here are intended to serve as an introduction to
bimolecular processes.
The intent here is not to provide a rigorous and comprehensive treatment of the
theory, but rather to help researchers understand basic principles, classical models
derived from the theory, and the assumptions upon which they are based. This focus is
consistent with the goal of this chapter, which is to enable those new to this area to
apply the classical forms of the Marcus model to their own science.
For further reading, many excellent review articles and books provide more in-depth
information about the theory and more comprehensive coverage of its applications to
chemistry, biology, and nanoscience. Several recommended items (among many) are
a highly cited review article by Marcus and Sutin,4 excellent reviews by Endicott,5
Creutz and Brunschwig,6 and Stanbury,7 a five-volume treatise edited by Balzano,8 and
the abovementioned monograph by Eberson2 that provides an accessible introduction
to theory and practice in the context of organic electron transfer reactions.
1.2.1

Collision Rates Between Hard Spheres in Solution

In 1942, Debye extended Smoluchowski’s method for evaluating fundamental
frequency factors, which pertained to collision rates between neutral particles D

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THEORETICAL BACKGROUND AND USEFUL MODELS

3

SCHEME 1.1

and A, randomly diffusing in solution, to include the electrostatic effects of charged
reacting species in dielectric media containing dissolved electrolytes.9–11 Debye’s
colliding sphere model was derived assuming that collisions between Dn (electron
donors with a charge of n) and Am (electron acceptors of charge m) resulted in the
transient formation of short-lived complexes, Dn À Am. Rate constants for these
reactions vary in a nonlinear fashion as functions of ionic strength, and the models are
intimately tied to contemporary and later developments in electrolyte theory.
Marcus12 and others13 extended this model to include reactions in which electron
transfer occurred during collisions between the “donor” and “acceptor” species, that
is, between the short-lived DnÀAm complexes. In this context, electron transfer within
transient “precursor” complexes ([Dn À Am] in Scheme 1.1) resulted in the formation
of short-lived successor complexes ([D(n ỵ 1) A(m1)] in Scheme 1.1). The
Debye–Smoluchowski description of the diffusion-controlled collision frequency
between Dn and Am was retained. This has important implications for application of
the Marcus model, particularly where—as is common in inorganic electron transfer
reactions—charged donors or acceptors are involved. In these cases, use of the Marcus
model to evaluate such reactions is only defensible if the collision rates between the
reactants vary with ionic strength as required by the Debye–Smoluchowski model.
The requirements of that model, and how electrolyte theory can be used to verify
whether a reaction is a defensible candidate for evaluation using the Marcus model,
are presented at the end of this section.

After electron transfer (transition along the reaction coordinate from Dn Am to
(n ỵ 1) – (mÀ1)
A
in Scheme 1.1), the successor complex dissociates to give the nal
D
products of the electron transfer, D(n ỵ 1) and A(mÀ1). The distinction between the
successor complex and final products is important because, as will be shown, the
Marcus model describes rate constants as a function of the difference in energy
between precursor and successor complexes, rather than between initial and final
products.
1.2.2

Potential Energy Surfaces

As noted above, outer-sphere electron transfer reactions are characterized by the
absence of strong electronic interaction (e.g., bond formation) between atomic or
molecular orbitals populated, in the donor and acceptor, by the transferred electron.
Nonetheless, as can be appreciated intuitively, outer-sphere reactions must require
some type of electronic “communication” between donor and acceptor atomic or
molecular orbitals. This is referred to in the literature as “coupling,” “electronic
interaction,” or “electronic overlap” and is usually less than $1 kcal/mol. Innersphere electron transfer reactions, by contrast, frequently involve covalent bond

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ELECTRON TRANSFER REACTIONS

FIGURE 1.1 Potential energy surfaces for outer-sphere electron transfer. The potential

energy surface of reactants plus surrounding medium is labeled R and that of the products plus
surrounding medium is labeled P. Dotted lines indicate splitting due to electronic interaction
between the reactants. Labels A and B indicates the nuclear coordinates for equilibrium
configurations of the reactants and products, respectively, and S indicates the nuclear configuration of the intersection of the two potential energy surfaces.

formation between the reactants and are often characterized by ligand exchange or
atom transfer (e.g., of O, H, hydride, chloride, or others).
The two-dimensional representation of the intersection of two N-dimensional
potential energy surfaces is depicted in Figure 1.1.4 The curves represent the energies
and spatial locations of reactants and products in a many-dimensional (N-dimensional) configuration space, and the x-axis corresponds to the motions of all atomic
nuclei. The two-dimensional profile of the reactants plus the surrounding medium is
represented by curve R, and the products plus surrounding medium by curve P. The
minima in each curve, that is, points A and B, represent the equilibrium nuclear
configurations, and associated energies, of the precursor and successor complexes
indicated in Scheme 1.1, rather than of separated reactants or separated products. As
a consequence, the difference in energy between reactants and products (i.e., the
difference in energy between A and B) is not the Gibbs free energy for the overall
reaction, DG , but rather the “corrected” Gibbs free energy, DG0 . For reactions of
charged species, the difference between DG and DG0 can be substantial.
The intersection of the two surfaces forms a new surface at point S in Figure 1.1.
This (N À 1)-dimensional surface has one less degree of freedom than the energy
surfaces depicted by curves R and P. Weak electronic interaction between the
reactants results in the indicated splitting of the potential surfaces. This gives rise
to electronic coupling (resonance energy arising from orbital mixing) of the reactants’
electronic state with the products’, described by the electronic matrix element, HAB.
This is equal to one-half the separation of the curves at the intersection of the R and

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THEORETICAL BACKGROUND AND USEFUL MODELS

5

P surfaces. The dotted lines represent the approach of two reactants with no electronic
interaction at all.
This diagram can be used to appreciate the main difference between inner- and
outer-sphere processes. The former are associated with a much larger splitting of the
surfaces, due to the stronger electronic interaction necessary for the “bonded”
transition state. A classical example of this was that recognized by Henry Taube,
recipient of the 1983 Nobel Prize in Chemistry for his work on inorganic reaction
mechanisms. In a famous experiment, he studied electron transfer from CrII(H2O)62 ỵ
(labile, high spin, d4) to the nonlabile complex (NH3)5CoIIICl2 ỵ (low spin, d6) under
acidic conditions in water. Electron transfer was accompanied by a change in color of
the solution from a mixture of sky blue CrII(H2O)62 ỵ and purple (NH3)5CoIIICl2 ỵ to
the deep green color of the nonlabile complex (H2O)5CrIIICl2 ỵ (d3) and labile
CoII(H2O)62 ỵ (high spin, d7) (Equation 1.1).14,15
ẵCrII H2 Oị6 2ỵ ỵẵNH3 ị5 CoIII Cl2ỵ ỵ5Hỵ !ẵH2 Oị5 CrIII Cl2ỵ ỵẵCoII H2 Oị6 2ỵ ỵ5NH4ỵ
blue

purple

green
1:1ị

Using radioactive Cl in (NH3)5CoIIICl2 ỵ , he demonstrated that even when ClÀ
was present in solution, electron transfer occurred via direct (inner-sphere) ClÀ
transfer, such that the radiolabeled ClÀ remained coordinated to the (now) nonlabile
CrIII product.
1.2.3

Franck–Condon Principle and Outer-Sphere Electron Transfer

The mass of the transferred electron is very small relative to that of the atomic nuclei.
As a result, electron transfer is much more rapid than nuclear motion, such that nuclear
coordinates are effectively unchanged during the electron transfer event. This is the
Franck–Condon principle.
Now, for electron transfer reactions to obey the Franck–Condon principle, while
also complying with the first law of thermodynamics (conservation of energy),
electron transfer can occur only at nuclear coordinates for which the total potential
energy of the reactants and surrounding medium equals that of the products and
surrounding medium. The intersection of the two surfaces, S, is the only location in
Figure 1.1 at which both these conditions are satisfied. The quantum mechanical
treatment allows for additional options such as “nuclear tunneling,” which is
discussed below.
1.2.4

Adiabatic Electron Transfer

The classical form of the Marcus equation requires that the electron transfer be
adiabatic. This means that the system passes the intersection slowly enough for the
transfer to take place and that the probability of electron transfer per passage is large
(near unity). This probability is known as the transmission coefficient, k, defined later
in this section. In this quantum mechanical context, the term “adiabatic” indicates that

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6

ELECTRON TRANSFER REACTIONS

nuclear coordinates change sufficiently slowly that the system (effectively) remains
at equilibrium as it progresses along the reaction coordinate. The initial eigenstate of
the system is modified in a continuous manner to a final eigenstate according to the
Schr€
odinger equation, as shown in Equation 1.2. At the adiabatic limit, the time
required for the system to go from initial to final states approaches innity (i.e.,
[tf ti] ! Ơ).
jyx; tf ịj2 6ẳ jyðx; ti Þj2

ð1:2Þ

When the system passes the intersection at a high velocity, that is, the above
condition is not met even approximately, it will usually “jump” from the lower R
surface (before S along the reaction coordinate) to the upper R surface (after S). That
is, the system behaves in a “nonadiabatic” (or diabatic) fashion, and the probability
per passage of electron transfer occurring is small (i.e., k ( 1). The nuclear
coordinates of the system change so rapidly that it cannot remain at equilibrium.
At the nonadiabatic limit, the time interval for passage between the two states at
point S approaches zero, that is, (tf À ti) ! 0 (infinitely rapid), and the probability
density distribution functions that describe the initial and final states remain
unchanged:



2
jyx; tf ịj2 ẳ
yðx; ti Þ

ð1:3Þ

Another cause of nonadiabicity is very weak electronic interaction between the
reactants. This means that k is inherently much smaller than 1, such that the splitting
of the potential surfaces is small. In other words, electronic communication between
reactants is too small to facilitate a change in electronic states, from reactant to
product, at the intersection of the R and P curves. Graphically, this means that the
splitting at S is small, and the adiabatic route (passage along the lower surface at S) has
little probability of occurring.
The “fast” and “slow” changes described here, which refer to “velocities” of
passage through the intersection, S, correspond to “high” and “low” frequencies of
nuclear motions. Hence, “nuclear frequencies” play an important role in quantum
mechanical treatments of electron transfer.

1.2.5

The Marcus Equation

In his theoretical treatment of outer-sphere electron transfer reactions, Marcus related
the free energy of activation, DGz, to the corrected Gibbs free energy of the reaction,
DG0 , via a quadratic equation (Equation 1.4).2,4,13
DGz ẳ



z1 z2 e2
l
DG0 2
1ỵ

expwr12 ị ỵ
Dr12
l
4

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1:4ị


THEORETICAL BACKGROUND AND USEFUL MODELS

7

The terms DG0 and l in Equation 1.4 are represented schematically in Figure 1.1, and
w is the reciprocal Debye radius (Equation 1.5).11,16
!1=2
4pe2 X 2
wẳ
ni z i
1:5ị
DkT i
In Equation 1.5, D is the dielectric constant
medium, e is the charge of an
Pof the
electron, k is the Boltzmann constant, and
ni z2i ¼ 2m, where m is the total ionic
strength of an electrolyte solution containing molar concentrations, ni, of species i of
P
charge z (ionic strength m is defined by m  12 ni z2i ).

The first term in Equation 1.4 was retained from Debye’s colliding sphere model:
the electron-donor and electron-acceptor species were viewed as spheres of radii r1
and r2 that possessed charges of z1 and z2, respectively. This term is associated with
the electrostatic energy (Coulombic work) required to bring the two spheres from
an infinite distance to the center-to-center separation distance, r12 ẳ r1 ỵ r2, which is
also known as the distance of closest approach (formation of the precursor complex
[DnÀAm] in Scheme 1.1). The magnitude of the Coulombic term is modified by
a factor exp(Àwr12), which accounts for the effects of the dielectric medium (of
dielectric constant D) and of the total ionic strength m.
The corrected Gibbs free energy, DG0 , in Equation 1.4 is the difference in free
energy between the successor and precursor complexes of Scheme 1.1 as shown in
Figure 1.1. The more familiar, Gibbs free energy, DG , is the difference in free energy
between separated reactants and separated products in the prevailing medium. The
corrected free energy, DG0 , is a function of the charges of the reactants and products.
It is calculated using Equation 1.6, where z2 is the charge of the electron donor and z1
is the charge of the electron acceptor.
DG0 ẳ DG ỵ z1 z2 1ị

e2
expwr12 ị
Dr12

1:6ị

If one of the reactants is neutral (i.e., its formal charge is zero), the work term in
Equation 1.4 equals zero. As a consequence of this (and all else being equal), highly
negative charged oxidants may react more rapidly with neutral electron donors than
with positively charged electron donors. This is somewhat counterintuitive because
one might expect negatively charged oxidants to react more rapidly with positively
charged donors, to which the oxidant is attracted. In other words, attraction between

oppositely charged species is usually viewed as contributing to the favorability of
a reaction. For example, the heteropolyanion, CoIIIW12O405 (E ẳ ỵ 1.0 V), can
oxidize organic substrates with standard potentials as large as ỵ 2.2 V. This is because
the attraction between the donor and acceptor in the successor complex, generated by
electron transfer, leads to a favorable attraction between the negative heteropolyanion
and the oxidized (now positively charged) donor. This attraction makes the corrected
free energy more favorable, the activation energy smaller, and the electron transfer
reaction kinetically possible.2,17

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