Physical inorganic chemistry principles methods and models

PHYSICAL INORGANIC
CHEMISTRY


PHYSICAL INORGANIC
CHEMISTRY
Principles, Methods, and Models

Edited by

Andreja Bakac


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 : principles, methods, and models / [edited by]
Andreja Bakac.
p. cm.
Includes index.
ISBN 978-0-470-22419-9 (cloth)
1. Physical inorganic chemistry. I. Bakac, Andreja.
QD475.P49 2010
547’.13–dc22
2009051003
Printed in the United States of America
10 9 8

7 6 5 4

3 2 1


To Jojika


CONTENTS
Preface

ix

Contributors

xi

1

Inorganic and Bioinorganic Spectroscopy

1

Edward I. Solomon and Caleb B. Bell III

2

57

Fe M€
ossbauer Spectroscopy in Chemistry and Biology

39

Marlene Martinho and Eckard M€unck

3

Magnetochemical Methods and Models in Inorganic Chemistry

69

Paul K€ogerler

4

Cryoradiolysis as a Method for Mechanistic Studies in Inorganic
Biochemistry

109

Ilia G. Denisov

5

Absolute Chiral Structures of Inorganic Compounds

143

James P. Riehl and Sumio Kaizaki

6

Flash Photolysis and Chemistry of Transients and Excited States

199

Guillermo Ferraudi

7

Application of High Pressure in the Elucidation of Inorganic
and Bioinorganic Reaction Mechanisms

269

Colin D. Hubbard and Rudi van Eldik

8

Chemical Kinetics as a Mechanistic Tool

367

Andreja Bakac

9

Heavy Atom Isotope Effects as Probes of Small Molecule Activation

425

Justine P. Roth

10

Computational Studies of Reactivity in Transition Metal Chemistry

459

Jeremy N. Harvey

Index

501

vii


PREFACE
Physical inorganic chemistry is an enormous area of science. In the broadest sense, it
comprises experimental and theoretical approaches to the thermodynamics, kinetics,
and structure of inorganic compounds and their chemical transformations in solid,
gas, and liquid phases. When I accepted the challenge to edit a book on this broad
topic, it was clear that only a small portion of the field could be covered in a project of
manageable size. The result is a text that focuses on mechanistic aspects of inorganic
chemistry in solution, similar to the frequent association of physical organic
chemistry with organic mechanisms.
The choice of this particular aspect came naturally because of the scarcity of books
on mechanistic inorganic chemistry, which has experienced an explosive growth in
recent years and has permeated other rapidly advancing areas such as bioinorganic,
organometallic, catalytic, and environmental chemistry. Some of the most complex
reactions and processes that are currently at the forefront of scientific endeavor rely
heavily on physical inorganic chemistry in search of new directions and solutions to
difficult problems. Solar energy harvesting and utilization, as well as catalytic
activation of small molecules as resources (carbon dioxide), fuels (hydrogen), or
reagents (oxygen), are just a few examples.
It is the goal of this book to present in one place the key features, methods, tools,
and techniques of physical inorganic chemistry, to provide examples where this
chemistry has produced a major contribution to multidisciplinary efforts, and to point

out the possibilities and opportunities for the future. Despite the enormous importance
and use of the more standard methods and techniques, those are not included here
because books and monographs have already been dedicated specifically to instrumental analysis and laboratory techniques. The 10 chapters in this book cover
inorganic and bioinorganic spectroscopy (Solomon and Bell), Mo¨ssbauer spectroscopy (Mu¨nck and Martinho), magnetochemical methods (Ko¨gerler), cryoradiolysis
(Denisov), absolute chiral structures (Riehl and Kaizaki), flash photolysis and studies
of transients (Ferraudi), activation volumes (van Eldik and Hubbard), chemical
kinetics (Bakac), heavy atom isotope effects (Roth), and computational studies in
mechanistic transition metal chemistry (Harvey).
I am extending my gratitude to the authors of individual chapters who have given
generously of their time and wisdom to share their expertise with the reader. I am
grateful to my editor, Anita Lekhwani, for her professionalism, personal touch, and

ix


x

PREFACE

expert guidance through the entire publishing process. Finally, I thank my family,
friends, and coworkers who supported and helped me, and continued to have faith in
me throughout this long project.
ANDREJA BAKAC


CONTRIBUTORS
ANDREJA BAKAC, The Ames Laboratory and Chemistry Department, Iowa State
University, Ames, IA, USA
CALEB B. BELL III,
USA

Department of Chemistry, Stanford University, Stanford, CA,

ILIA G. DENISOV, Department of Biochemistry, University of Illinois at UrbanaChampagne, Urbana, IL, USA
GUILLERMO FERRAUDI,
Dame, IN, USA

Radiation Laboratory, University of Notre Dame, Notre

JEREMY N. HARVEY, Centre for Computational Chemistry, School of Chemistry,
University of Bristol, Bristol, UK
COLIN D. HUBBARD,

Tolethorpe Close, Oakham, Rutland, UK

SUMIO KAIZAKI, Department of Chemistry, Center for Advanced Science and
Innovation, Graduate School of Science, Osaka University, Osaka, Japan
PAUL KO¨GERLER,
Germany

Institut fu¨r Anorganische Chemie, RWTH Aachen, Aachen,

MARLE`NE MARTINHO, Department of Chemistry, Carnegie Mellon University,
Pittsburgh, PA, USA
ECKARD MU¨NCK, Department of Chemistry, Carnegie Mellon University,
Pittsburgh, PA, USA
JAMES P. RIEHL, Department of Chemistry, University of Minnesota Duluth,
Duluth, MN, USA
JUSTINE P. ROTH,
MD, USA

Department of Chemistry, Johns Hopkins University, Baltimore,

EDWARD I. SOLOMON,
USA
RUDI

Department of Chemistry, Stanford University, Stanford, CA,

¨ r Anorganische Chemie, Universita¨t ErlangenVAN ELDIK, Institut fu
Nu¨rnberg, Erlangen, Germany

xi


FIGURE 1.1 As an example, plastocyanin functions in photosynthesis as a soluble electron
carrier in the thylakoid lumen transferring electrons from the cytochrome b6/f complex to
photosystem I ultimately for ATP synthesis (bottom). Despite its relatively small size,
plastocyanin has had a large impact on the field of bioinorganic spectroscopy. The protein
has a characteristic intense blue color (hence the term blue copper protein) that was later shown
to derive from LMCT to the Cu. Hans Freeman first reported a crystal structure (light blue
ribbon diagram, PDB ID, 1PLC) for plastocyanin in 19788 showing that the Cu site was
tetrahedrally coordinated by a methionine, a cysteine, and two histidine resides. This was a
surprising result given the typical tetragonal structure for small model Cu(II) complexes. Since
that time, a tour de force of spectroscopy has been applied in blue copper research (projected on
the back are selected spectra for methods that are covered in this chapter), many of which were
developed and first used on this enzyme, as will be presented. The spectroscopic approach
combined with electronic structure calculations has allowed elucidation of the geometric and
electronic structures of the Cu site (top left blowup) that in turn has been used for structure–
function correlations in understanding plastocyanin’s biochemical role in electron transfer (ET)

and defining the role of the protein in determining geometric and electronic structure.


FIGURE 1.4 Tanabe-Sugano diagram for a d5 ion. Insets are the d electron configurations for
the indicated states.


FIGURE 1.27 Sulfur K-pre-edge XAS59 for (a) FeIII(SR)4À model complex, (b) the model
compared to several rubredoxins to illustrate the effect of the protein environment in reducing
covalency, and (c) Fe2S2-type complexes with RS4 (black) replaced by ClÀ (red) or mS2À by
mSe2À (blue).


FIGURE 2.10
Ref. 11.

FIGURE 2.11

DFT optimized structure of [(H2O)5FeIV¼O]2 þ . For details see Chapter 2,

Structure of the diferric TPA complex, [Fe2III (O)(H2O)(OH)(TPA)2]3 þ .


FIGURE 2.14 Structure of the diiron(IV) complex X (Section 2.3.2) compatible with
experimental data.

FIGURE 3.14 Representation of the highly symmetrically frustrated classical ground state of
the Fe30 spin icosidodecahedron in {Mo72Fe30} in the absence of an external magnetic field.
The 10 classical spin vectors of each of the three sublattices (green, red, and blue) assume 120
relative orientation. Next to the Fe positions, only the bridging oxygen (small black spheres) and

molybdenum (pink) positions of the {Mo72Fe30} cluster framework are shown for clarity.


FIGURE 6.5 Normalized rates of product formation at different distances from the front
window when the absorbance of the solution in the 1 cm cell is 2 (red) and 4 (green).

SCHEME 7.2 The Mo72Fe30 cluster containing 72 Mo(VI)-oxide polyhedra (purple) and 30
Fe(III) as Fe(O)6 octahedra (brown).


FIGURE 8.4 Plot of log k against pH for the oxidation of iodide ions with
L2(H2O)RhOOH2 þ . Data are from Chapter 8, Ref. 45. The line is a fit to Equation 8.107.

FIGURE 9.13

Proposed reaction mechanism for H2O2 activation in horseradish peroxidase.


FIGURE 10.2 Molecular orbitals in hydrogen fluoride, plotted using two isosurfaces, at
Æ0.02 eÀ1/2 BohrÀ3/2.


1

Inorganic and Bioinorganic
Spectroscopy
EDWARD I. SOLOMON and CALEB B. BELL III

1.1

INTRODUCTION

Spectroscopic methods have played a critical and symbiotic role in the development
of our understanding of the electronic structure, physical properties, and reactivity of
inorganic compounds and active sites in biological catalysis.1,2 Ligand field theory3
developed with our understanding of the photophysical and magnetic properties of
transition metal complexes. Ligand–metal (L–M) bonding descriptions evolved
through the connection of p-donor interactions with ligand to metal charge transfer
(LMCT) transitions and p-backbonding with metal to ligand charge transfer (MLCT)
transitions.4 X-ray absorption (XAS) spectroscopy initially focused on the use of
extended X-ray absorption fine structure5 (EXAFS) to determine the geometric
structure of a metal site in solution, but evolved in the analyses of pre-edges and
edges to probe the electronic structure and thus covalency of ligand–metal bonds.6
In bioinorganic chemistry, spectroscopy probes the geometric and electronic
structure of a metallobiomolecule active site allowing the correlation of structure
with function (Figure 1.1).7
Spectroscopies are also used to experimentally probe transient species along a
reaction coordinate, where often the sample has been rapidly freeze quenched to trap
intermediates. An important theme in bioinorganic chemistry is that active sites often
exhibit unique spectroscopic features, compared to small model complexes with the
same metal ion.8 These unusual spectroscopic features reflect novel geometric and
electronic structures available to the metal ion in the protein environment. These
unique spectral features are low-energy intense absorption bands and unusual spin
Hamiltonian parameters. We have shown that these reflect highly covalent sites (i.e.,
where the metal d-orbitals have significant ligand character) that can activate the
metal site for reactivity.9
It is the goal of this chapter to provide an overview of the excited-state spectroscopic methods, including electronic absorption, circular dichroism (CD), magnetic

Physical Inorganic Chemistry: Principles, Methods, and Models Edited by Andreja Bakac
Copyright Ó 2010 by John Wiley & Sons, Inc.

1


2

INORGANIC AND BIOINORGANIC SPECTROSCOPY

FIGURE 1.1 As an example, plastocyanin functions in photosynthesis as a soluble electron
carrier in the thylakoid lumen transferring electrons from the cytochrome b6/f complex to
photosystem I ultimately for ATP synthesis (bottom). Despite its relatively small size,
plastocyanin has had a large impact on the field of bioinorganic spectroscopy. The protein
has a characteristic intense blue color (hence the term blue copper protein) that was later shown
to derive from LMCT to the Cu. Hans Freeman first reported a crystal structure (light blue
ribbon diagram, PDB ID, 1PLC) for plastocyanin in 19788 showing that the Cu site was
tetrahedrally coordinated by a methionine, a cysteine, and two histidine resides. This was a
surprising result given the typical tetragonal structure for small model Cu(II) complexes. Since
that time, a tour de force of spectroscopy has been applied in blue copper research (projected on
the back are selected spectra for methods that are covered in this chapter), many of which were
developed and first used on this enzyme, as will be presented. The spectroscopic approach
combined with electronic structure calculations has allowed elucidation of the geometric and
electronic structures of the Cu site (top left blowup) that in turn has been used for structure–
function correlations in understanding plastocyanin’s biochemical role in electron transfer (ET)
and defining the role of the protein in determining geometric and electronic structure. (See the
color version of this figure in Color Plates section.)


LIGAND FIELD (d ! d) EXCITED STATES

3

circular dichroism (MCD), and X-ray absorption edge spectroscopies. Ground-state
methods are presented in subsequent chapters and mostly focus on the first few
wavenumbers (cmÀ1) of the electronic structure of a transition metal site. Here we first
consider ligand field (d ! d) transitions in the near-IR to visible spectral region, from
about 5000 to $20,000 cmÀ1, then charge transfer (CT) transitions in the visible to
UV regions (up to $32,000 cmÀ1 $ 4 eV), and finally X-ray edge transitions that
involve core excitations and energies up to 104 eV. We apply the concepts developed
to two cases that generally define the information content of the method: the simple
case of Cu(II) complexes with a d9 one-hole configuration and the most complex case
of Fe(III) d5 complexes with a half-occupied valence configuration. It is important
to emphasize that the rapid development of electronic structure calculations for
transition metal systems, particularly density functional theory (DFT), has made a
correlation to spectroscopy of critical importance.10 There are many ways and levels
of performing these calculations that can provide very different descriptions of
bonding and reactivity. Spectroscopy experimentally defines the electronic and
geometric structure of a transition metal site. Calculations supported by and combined
with the experimental data can provide fundamental insight into the electronic
structure and define this contribution to physical properties and the activation of a
metal site for reactivity.

1.2
1.2.1

LIGAND FIELD (d ! d) EXCITED STATES
Electronic Absorption Spectroscopy

In electronic absorption spectroscopy, we are interested in a transition from the
ground state Yg to an excited state Ye that is allowed by the transition moment
^ that derives from the interaction of the electromagnetic radiation of the

operator M
photon with the electron in a metal complex (Figure 1.2).

FIGURE 1.2 (a) The interaction of electromagnetic radiation with a metal center promotes
an electron from the ground state (Yg) to the excited state (Ye) as dictated by the transition
moment operator. This leads to the absorption band shape shown in (b).


4

INORGANIC AND BIOINORGANIC SPECTROSCOPY

This leads to an absorption band, and the quantity that connects experiment with
theory is the oscillator strength of the transition, f.
ð
fexp ¼ ð4:33 Â 10À9 Þ eðyÞdy
y in cmÀ1
ð
ftheo ¼ ð1:085 Â 10 Þy
11

Y*e

^ g dt
MY

2

transition moment integral in cmÀ1
ð1:1Þ

Experimentally, the oscillator strength is given by the integrated intensity (area) under
the absorption band,
Ð while theoretically it is given by the square of the transition
^ e dt. This leads to the selection rules for electronic
moment integral Ð Yg MY
^ e dt is nonzero, there is absorption intensity and the
transitions: when Yg MY
transition is “allowed”; when this integral is required to be zero, the transition is
“forbidden.”
When the wavelength of light is much greater than the radius of the electron on the
metal site (the long-wave approximation), the transition moment operator is given by
the multipole expansion:11
^ ¼M
^ ðelectric dipoleÞ þ M
^ ðmagnetic dipoleÞ þ M
^ ðelectric quadrupoleÞ þ Á Á Á
M

ð1:2Þ

where each term in the expansion is $10 3 times more effective than the subsequent
term. Note that green light has l $ 5000 A, while the radius of an electron in transition
metal complexes is on the order of a few angstroms. For electronic absorption
spectroscopy, we are interested in the dominant, electronic dipole term, where
^ ðelectric dipoleÞ ¼ er*Á E*. The electric vector of light (E*) projects out a specific
M
*
component of r, which operates on the electron coordinates in the transition moment
integral in Equation 1.1.

Note that, since the electric
Ð dipole operator does not involve the electron spin, the
^ electric dipole Ye dt is nonzero only if Yg and Ye have
transition moment integral Yg M
the same spin leading to the selection rule DS ¼ 0 for a “spin-allowed” transition. For
electronic absorption spectroscopy in the ligand field region, we focus on excitation of
electrons between a ligand field split set of d-orbitals. Since d-orbitals are symmetric
*
(gerade or g) to inversion and the electric dipole operator r ¼ x; y; z is antisymmetric
to inversion (ungerade or u), all d ! d transitions are forbidden due to the total u
symmetry of the integral; these are called “parity” or “Laporte” forbidden transitions.
However, metal sites in proteins and low-symmetry complexes have no inversion
center; therefore, the d ! d transitions become weakly allowed through mixing with
higher energy electric dipole-allowed charge transfer transitions (see below). This
leads to molar extinction coefficients (e) of up to a few 100 MÀ1 cmÀ1 for spin-allowed
d ! d transitions. It is important to note that metalloprotein solutions of $1 mM in a
1 mm cuvette will give an absorbance of $0.01, which is difficult to observe
experimentally. This is particularly the case for d ! d transitions that occur at
relativity low energy as given by ligand field theory.


LIGAND FIELD (d ! d) EXCITED STATES

5

FIGURE 1.3 Effects of a ligand field (LF) on a Cu(II) d9 ion and the corresponding
Tanabe–Sugano diagram. The electron configurations leading to each state are shown.

1.2.1.1 Ligand Field Theory of Cu(II) d9 and Fe(III) d 5 Ions The ligand field
ground and excited states of a dn transition metal complex are given by the Tanabe–

Sugano diagrams,12 which quantitatively define the effects of the ligand field splittings
of the d-orbitals on the many-electron atomic term symbols of the free metal ion.
As shown in Figure 1.3, the Cu(II) d9 free ion has one hole in the fivefold
degenerate set of d-orbitals giving a 2 D atomic term symbol. In an octahedral (Oh)
ligand field, the d-orbitals are split in energy into the t2g and eg orbital sets, by 10Dq,
the spectroscopic parameter of ligand field theory. It should be mentioned that in
the original derivation by Bethe, D parameterized the crystal field electrostatic
distribution and q a radial integral over the d-orbitals.13 Now these are considered
as one parameter obtained experimentally by correlating the Tanabe–Sugano diagram
splittings to the experimentally observed transition energies. For a d9 Cu(II) ion in an
octahedral ligand field, this gives a t2g6eg3 electron configuration, thus giving a 2 Eg
ground state with a t2g5eg4 or 2 T2g first excited state at 10Dq. The Tanabe– Sugano
diagram for this simple one-hole case is shown in Figure 1.3; the 2 D splits into two
states, 2 Eg and 2 T2g , with the energy separation increasing with 10Dq.
For Fe(III), there are five valence electrons that generate the following configurations when distributed over an Oh ligand field split set of d-orbitals:
FeIIIðd5 Þ! ðt2g Þ5 ðt2g Þ4 ðeg Þ1 ðt2g Þ3 ðeg Þ2 ðt2g Þ2 ðeg Þ3 ðt2g Þ1 ðeg Þ4
Energy ¼

0

10Dq

20Dq

30Dq

40Dq

For each of these configurations, one must also consider electron–electron repulsions
that split each configuration into a number of ligand field states that can further

interact with each other, through configuration interaction (CI), leading to the
Tanabe–Sugano diagram of the d5 configuration given in Figure 1.4.


6

INORGANIC AND BIOINORGANIC SPECTROSCOPY

FIGURE 1.4 Tanabe-Sugano diagram for a d5 ion. Insets are the d electron configurations for
the indicated states. (See the color version of this figure in Color Plates section.)

Here the energy units are in B (cmÀ1), where B is the Racah parameter14 that
quantitates electron–electron repulsion, obtained experimentally for a given free
metal ion and allowed to reduce due to covalency (i.e., the nephelauxetic effect15).
The left-hand side of Figure 1.4 represents the high-spin t2g3eg2 (6 A1g ) ground state,
while the right-hand side represents the low-spin t2g5 (2 T2g ) ground state. The crossing
point at Dq/B ¼ 2.8 quantitates the ligand field splitting of the d-orbitals required to
overcome the electron–electron repulsion (i.e., t2g3eg2 $ t2g5eg0), which is defined as
the spin-pairing energy for this configuration. In the inset on the left-hand side of
Figure 1.4, the lowest energy ligand field excited state on the high-spin side of the d5
Tanabe–Sugano diagram (4 T1g ) corresponds to an eg(") ! t2g(#) transition. This is an
excited state due to the increased electron–electron repulsion relative to the energy
splitting of the t2 and e sets of d-orbitals. The transition to the 4 T1g from the 6 A1g
ground state is spin forbidden. In fact, all d ! d transitions for high-spin Fe(III) are
DS ¼ 1 (or 2); therefore, they are spin forbidden and will not have significant intensity
in the absorption spectrum (generally e < 0.1 MÀ1 cmÀ1).
Alternatively, for d9 Cu(II) complexes from Figure 1.3, the 2 Eg ! 2 T2g transition
at 10Dq is spin allowed. For divalent first transition row metal ions with biologically
relevant ligands, 10Dq is in the range of 10,000–12,000 cmÀ1; therefore, transitions
are expected in the near-IR spectral region. Both the ground and excited states are

orbitally degenerate and will split in energy in a characteristic way depending on the
geometry of the Cu(II) site.


LIGAND FIELD (d ! d) EXCITED STATES

7

FIGURE 1.5 Splitting of metal 3d orbitals in various ligand field environments.

1.2.1.2 Geometric Dependence of Spin-Allowed Ligand Field Transitions Ligand field theory quantitates the splittings of the one-electron d-orbitals due to their
repulsion/antibonding interactions with the ligands.
As shown in Figure 1.5a for d9 Cu(II) ions in an Oh ligand field, the ground
configuration (and state) is t2g6eg3 (2 Eg ). The extra electron in the eg set of d-orbitals is
strongly s-antibonding with the ligands, and this interaction is anisotropic. Thus, the
orbital degeneracy of the ground state leads to a Jahn–Teller distortion16 of the ligand
field to lower the symmetry, splits the eg orbital degeneracy, and lowers the energy of
the d9 complex. Generally, Cu(II) complexes are found to have a tetragonal elongated
structure (Figure 1.5b) or, in the limit of loss of the axial ligands, a square planar
structure (Figure 1.5c). Note from Figure 1.5 that the ligand field splittings of the
d-orbitals greatly change for the square planar relative to the Oh limit due to
differences in antibonding interactions of the metal ion with the ligands in a square
planar versus an Oh ligand field.
A geometric distortion that has been of considerable interest in inorganic and
bioinorganic chemistry is the square planar (D4h) to D2d distorted to tetrahedral (Td)
limit17 (Figure 1.5c–e). From the energy levels in Figure 1.5, the ligand field
transitions go down in energy from the 12,000 cmÀ1 region to the 5000 cmÀ1 region
across the series. This reflects the prediction of ligand field theory that 10Dq of a Td
complex is À4/9 10Dq of the corresponding Oh complex. As depicted in Figure 1.5,
the ligand field transition energies are a sensitive probe of the geometry of the Cu(II)

site. However, these are in the 12,000–5000 cmÀ1, near-IR, spectral region that can
have intense contributions from protein, buffer, and H2O vibrations to the absorptions


8

INORGANIC AND BIOINORGANIC SPECTROSCOPY

spectrum. In addition, due to their parity forbiddeness (i.e., low intensity), these
d ! d transitions generally are not experimentally observed in the absorption spectra
of proteins. However, based on the different selection rules associated with different
spectroscopies, these transitions can be very intense in circular dichroism and
magnetic circular dichroism spectroscopies in the near-IR spectral region.
1.2.2

Circular Dichroism Spectroscopy

CD spectroscopy measures, with high sensitivity using modulation and lock-in
detection, the difference in the absorption of left (L) and right (R) circularly polarized
*
(CP) light (the direction of rotation of the E vector as light propagates toward the
observer) in a transition between the ground and excited states (Yg ! Ye). The
spectrum is plotted as De ¼ eL À eR versus energy, and since CD has a sign as well as
a magnitude, it can often resolve overlapping bands in a broad absorption envelope,
as illustrated in Figure 1.6.
The quantity that connects theory with experiment in CD spectroscopy is the
rotational strength R. On an experimental level, R is determined by the area under a
resolved CD transition (Figure 1.6b), while from theory the rotational strength is
proportional to the projection of the electric dipole moment of a Yg ! Ye transition

FIGURE 1.6 Schematic representation of the resolution of an absorption envelope by CD
spectroscopy, due to the sign of CD transitions. Shaded area indicates R-value of a given
transition in CD.


LIGAND FIELD (d ! d) EXCITED STATES

onto its magnetic dipole moment (Equations 3a and 3b, respectively):18
ð
De
dn
Rexp ¼ 22:9 Â 10À40
n

9

ð1:3aÞ

ð
ð
^ electric dipole Ye dt Á Yg M
^ magnetic dipole Ye dt ð1:3bÞ
Rtheory ¼ 4:7 Â 10À24 Im Yg M
This form derives from the fact that circularly polarized light excites electrons in a
helical motion, requiring the electronic excitation to undergo both translational
(electric dipole (x, y, z)) and rotational (magnetic dipole (Rx, Ry, Rz)) operations.
Note from Equation 3b that only optically active molecules (point groups, Cn, Dn, or
C1 for a protein active site) can have a nonzero projection of the electric dipole and
magnetic dipole moments for a given Yg ! Ye transition (i.e., this transition must be
^

^ y; zÞ; therefore, M
^ i and R
^ i must
allowed by the same component of Mðx;
y; zÞ and Rðx;
transform as the same irreducible representation in the point group of the molecule).
Generally electronic transitions are electric dipole allowed or gain electric dipole
character through low-symmetry site distortions such as in a protein active site;
therefore, the magnetic dipole operator dominates the rotational strength.
^ Á H*, where the H* vector of light
^ ðmagnetic dipoleÞ in Equation 1.2 is given by bL
M
^i (i¼x,y,z). Again, Yg and Ye must have the same
projects out a specific component of L
spin to be magnetic dipole allowed (leading to the selection rule DS ¼ 0) as
^ ðmagnetic dipoleÞ does not affect the spin part of the wavefunction.
M
We now consider the spin-allowed ligand field transitions of optically active Cu(II)
^i operator on electrons in
complexes. The table below gives the effect of the L
d-orbitals.3
^x dxz ¼ Àidxy
L
pffiffiffi
^x dyz ¼ i 3dz2 þ idx2 Ày2
L
^x dxy ¼ idxz
L
^x dx2 Ày2 ¼ Àidyz
L

pffiffiffi
^x dz2 ¼ Ài 3dyz
L

pffiffiffi
^y dxz ¼ Àidx2 Ày2 Ài 3dz2
L
^y dyz ¼ idxy
L
^y dxy ¼ Àidyz
L
^y dx2 Ày2 ¼ Àidxz
L
pffiffiffi
^y dz2 ¼ i 3dxz
L

^z dxz ¼ idyz
L
^z dyz ¼ Àidxz
L
^z dxy ¼ À2idx2 Ày2
L
^z dx2 Ày2 ¼ 2idxy
L
^z dz2 ¼ 0
L

^z
From Figure 1.5, many Cu(II) complexes have one hole in the dx2 Ày2 orbital and L

^
^
will allow the ligand field excitation of a dxy electron into this hole, while Lx and Ly will
allow magnetic dipole excitation of the dyz and dxz electrons into the dx2 Ày2 orbital. In
general, d ! d (ligand field) transitions will be magnetic dipole allowed, have
significant rotational strength, and appear with reasonable intensity in the CD spectrum.
It is common to define the Kuhn anisotropy factor, g ¼ De=e, which is the intensity
of a given Yg ! Ye transition in the CD relative to the absorption spectrum. For
reasonable values of f and R, it is generally found that g (not to be confused with the
EPR g-values) > 0.01 for magnetic dipole-allowed transitions.19
From the above, d ! d transitions in the near-IR spectral region will be moderately intense in CD, while vibrations of the protein and solvent will not, allowing CD