In the Laboratory
Advanced Chemistry Classroom and Laboratory
Use of EPR Spectroscopy in Elucidating Electronic Structures
of Paramagnetic Transition Metal Complexes
Partha Basu
Department of Chemistry and Biochemistry, Duquesne University, Pittsburgh, PA 15282; [email protected]
Electronic structure is an important concept in many
areas of chemistry such as inorganic, physical, materials, and
biophysical. However, undergraduate students often receive
limited opportunities for hands-on exploration of the theory
(1). Among the many techniques for describing electronic
structure, electron paramagnetic resonance (EPR) spectroscopy
is unique in its ability to selectively probe paramagnetic
molecules (2). In fact, EPR spectroscopy can provide a wealth
of information about the electronic structure of paramagnetic
molecules, including those involving metal ions (3). In this
paper I describe how EPR spectroscopy can be utilized to
understand the electronic structure of metal complexes of
tetraphenyl porphyrins (TPP).
Porphyrins are among the most extensively studied biological chromophores. The interest in metalloporphyrins
spans from their unique structural and physical properties to
their ability to show a variety of chemical reactivities (4). The
practical aspects of these molecules include their catalytic
properties, biomedical applications, and development of new
materials. Thus, there is an inherent interest in porphyrin chemistry. The “rigid” ligand framework of porphyrin imparts a stable
conformation. In addition, a wealth of information is already
available on porphyrins and their metal complexes. These features prompted an examination of the electronic structure
of metalloporphyrin complexes using EPR spectroscopy. I
have chosen two S = 1/2 complexes, oxo-molybdenum(V)
(d1) and copper(II) (d9) porphyrin complexes, as examples.
This paper introduces the application of EPR spectroscopy
of transition metal complexes along with crystal field theory.
666
Background
Electrons have a magnetic dipole moment due to their
intrinsic angular momentum (or spin). For a spin angular
momentum, S, the associated magnetic moment (µe) is
µe = ᎑g e µB S
where g is a dimensionless quantity called the electron g-factor,
µB is the Bohr magneton and is equal to eh /4πmc = 9.2731 ×
10᎑24 J/T (e and m are the charge and mass of the electron,
respectively, h is Planck’s constant, and c is the speed of light).
The interaction of an applied magnetic field B0—usually along
the z axis—with the magnetic moment of an electron can be
described by a Hamiltonian, Ᏼ = ge µB B0 ᏿, where ᏿ is the
angular momentum operator. For spin angular momentum S,
2S + 1 nondegenerate energy states can be obtained. Thus, for
S = 1/2 systems, two nondegenerate energy levels are obtained
with Ms = ᎑1/2 and Ms = +1/2. This loss of degeneracy upon
application of a magnetic field is called the electronic Zeeman
effect. It should be pointed out that systems with multiple
unpaired electrons are complicated by zero field splitting.
In this paper the discussion is limited to S = 1/2 systems.
The energies of different spin manifolds are proportional
to the strength of the magnetic field (B0) (5). In EPR spectroscopy, a transition is induced between the two Ms levels
by applying a suitable electromagnetic radiation ν (10–1000
J/mol, microwave region) that satisfies the resonance condition
hν = g µB B0 (Fig. 1). For free electrons the value of the constant
g is 2.0023; however, in molecules whose unpaired electron is
Journal of Chemical Education • Vol. 78 No. 5 May 2001 • JChemEd.chem.wisc.edu
In the Laboratory
Ms = +
1
2
(E = +
1
2
geµBB0)
1
2
(E = −
1
2
geµBB0)
hν = geµBB0
Ms = −
Figure 1. Electronic Zeeman energy-level diagram of an unpaired spin
and EPR transition.
3450
3470
3490
3510
3530
3550
3450
3470
3490
3510
3530
3550
no longer free, its value varies considerably. Orbital motion,
introduced as a result of spin–orbit coupling, leads to a
departure from the free electron g value. This is particularly
important for transition metal ions, where the orbital angular
momentum is never completely absent. The energy due to
spin–orbit coupling is comparatively smaller than the energy
of the electron–field interaction. Thus, for transition metal
ions, the spin–orbit coupling effect alters g values from those
of the free electrons. This effect is very important for secondand third-row transition metals, whose spin–orbit coupling
constant is large.
Several other factors such as nuclear Zeeman effect and
quadrupole interaction can alter the energy levels. Nuclei
possessing spin angular momentum exhibit additional splitting
due to the nuclear Zeeman effect. Thus, nuclear spin of I,
when interacting with the electronic spin, perturbs the energy
of the system in such a way that each electronic state is split
into 2I + 1 sublevels. Since the nuclear magneton is about 1000
times smaller than the Bohr magneton, nuclear magnetic interactions are weak, so the energy separations between sublevels
are small. Transition involving these states gives rise to hyperfine splitting in a well-resolved spectrum and is designated by
“A”. Similarly, when ligand nuclei with spin angular momentum are involved, they give rise to nuclear superhyperfine
structure and are designated by “a”. Both of these interactions
can be seen clearly in the present case. Thus, n nuclei of spin
I can give rise to 2nI + 1 resonances. In this article discussion
is limited to nuclear interaction.
Experimental Procedure
Field / G
Figure 2. Room-temperature (295 K) CW-EPR spectra of MoOCl(TPP).
Top: the spectrum as a conventional first derivative; bottom: the same
spectrum as a second derivative.
The ligand, tetraphenyl porphyrin (H2TPP, 1), and
its molybdenum and copper complexes were synthesized
according to published procedures (6 ).
N
H
N
N
H
N
1
3000
2600
3100
2800
3200
3300
3000
3400
3200
3500
3400
3600
EPR spectra of two metalloporphyrin complexes, Cu(TPP)
and MoO(TPP)Cl, were recorded in toluene solutions (Figs.
2–4), in a Bruker ESP 300 E X-band spectrometer at room
temperature under nonsaturating microwave conditions. The
g values were calculated using the formula g = hν/ µB B, where
h = 6.626 × 10᎑34 J s, µB = 9.274 × 10᎑24 J/T, ν is the microwave
frequency, and B is the field position where the g values are
measured. Thus, the g value at a field 3498 G (349.8 mT), the
field position of the central resonance of the room-temperature
spectrum of MoOCl(TPP), is calculated to be 1.971.
3600
Field / G
Figure 3. CW-EPR spectra of frozen and liquid solutions of Cu(TPP)
in toluene. Top: room-temperature spectrum (297 K); bottom: lowtemperature (77 K) spectrum.
Results and Discussion
The EPR spectra of the complexes show several important
features. The room temperature spectrum of MoO(TPP)Cl
solution has one strong central peak and six satellite peaks
JChemEd.chem.wisc.edu • Vol. 78 No. 5 May 2001 • Journal of Chemical Education
667
In the Laboratory
(Fig. 2). The naturally abundant stable molybdenum isotopes
(95Mo, I = 5/2, 15.72%; 97Mo, I = 5/2, 9.46%; and I = 0
isotopes, 74.82%) give rise to this characteristic and unique
pattern for Mo(V). The large central line is due to I = 0
isotopes, which account for 75% of the integrated intensity.
Isotopes with I = 5/2 spin give rise to six satellite peaks
(2nI + 1 = 2 × 1 × 5/2 + 1 = 6) around the central signal. The
nuclear gyromagnetic ratio of the two I = 5/2 isotopes (95Mo
and 97Mo) are very similar and are not usually distinguished
by EPR spectroscopy.
The room-temperature EPR spectrum of Cu(TPP) exhibits four major resonances characteristic of the natural isotope
abundance of copper (Fig. 3). Naturally abundant copper has
two magnetic (I = 3/2) isotopes (63Cu, 65Cu) giving rise to
four (2nI + 1 = 2 × 1 × 3/2 + 1 = 4) resonances. The natural
abundance for copper is 69.17% for 63Cu and 30.83% for 65Cu.
The corresponding magnetic moments (in units of nuclear
magneton, µN) of the two isotopes are +2.2233 and +2.3817.
Under the experimental conditions employed the two isotopes
could not be differentiated.
For both compounds, the room-temperature spectra were
used to estimate the average metal hyperfine coupling. The
average metal hyperfine constant for Cu(TTP) is 95 G; that
for MoO(TTP)Cl is 48 G. This difference in magnitude is
primarily due to the larger magnetic moment of the copper
nucleus. Both room- and low-temperature spectra exhibit rich
ligand superhyperfine structure (see below).
The g values obtained from the room temperature spectra
of Cu(TPP) and MoO(TPP)Cl exhibit resonance at g ~ 2.117
and 1.971, respectively. While the g value of the Cu(TPP)
is more than the free electron value of 2.0023, that for
MoO(TPP)Cl is less. The deviation from the free electron
value is more for copper (∆g = | g – ge| = 0.1147) and less for
molybdenum (∆g = |ge – g | = 0.0313). The frozen toluene
solution spectrum of MoO(TPP)Cl showed only one peak
for I = 0 isotopes, indicating that anisotropy is too small to
be detected (Fig. 4). No nitrogen superhyperfine coupling
could be detected.
Interestingly, the frozen solution spectrum of Cu(TPP)
exhibits a rich superhyperfine structure due to interactions
with the porphyrin nitrogen atoms. The complex spectral
pattern in Cu(TPP) complicates the evaluation of anisotropic g
values (g || = 2.195, g⊥ = 2.078). Fortunately, two well-resolved
low-field transitions allowed us to evaluate the g || component.
The g⊥ component was evaluated from the average g values
using the relationship gav = g || + 2g⊥. The anisotropic g values
were used to understand the electronic structure of the metal
ion in Cu(TPP).
One of the most revealing features of the spectra of Figures
3 and 4 is the rich superhyperfine structure. The superhyperfine structure is due to the interaction of the unpaired electron
with the nitrogen atoms of the porphyrin macrocycle. The
most abundant isotope of natural nitrogen 14N (99.63%) has
a spin of 1. The nuclear magnetic moment of 14N (+0.4038)
is smaller than that of copper or molybdenum. Thus, the
magnitude of the interaction with a nitrogen isotope is small
compared to that with a Mo or a Cu nucleus. Because there are
four porphyrin nitrogen atoms and all of them can interact
with the unpaired electron, one could potentially observe 2 ×
4 × 1 + 1 = 9 resonances. The room-temperature EPR spectrum
of Cu(TPP) exhibits 9 distinct lines due to the coupling with
668
2.2
2.1
2.0
1.9
1.8
g
3300
3400
3500
3600
3700
Field / G
Figure 4. EPR spectra of MoOCl(TPP) in toluene. Top: room temperature (297 K) spectrum; bottom: low-temperature (77 K) spectrum.
R
R
N
N
R
N
N
N
X
N
N
R
R
R
N
Y
R
R
Cu(II)TPP
Mo(V)O(TPP)Cl
3dx 2−y 2
4dxy
Figure 5. Half-filled orbitals for Cu(II) and Mo(V).
the porphyrin nitrogen atoms (Fig. 3). In contrast, the firstderivative spectrum of MoO(TPP)Cl does not clearly show 9
resonances (Fig. 2, top), although 9 resonances can be observed
in the second derivative spectrum (Fig. 2, bottom). The
superhyperfine structure indicates that all four nitrogen atoms
are interacting with the unpaired electron.
The average aN for Cu(TPP) is 14 G, and that for
MoO(TPP)Cl is 2.7 G. The half-filled 4d orbital of molybdenum is more diffuse than the half-filled 3d orbital of copper.
Keeping other factors constant, this should lead to better
interaction with the nitrogen nucleus, which in turn should lead
to a larger nitrogen superhyperfine constant for MoO(TPP)Cl.
This difference can be explained from the shape of the d orbitals. Crystal field theory predicts that the unpaired electron
in Cu(TPP) should reside on the metal 3d x ᎑y orbital, which
points directly toward the nitrogen atoms positioned along
Y and Y axes (Fig. 5). In contrast, the half-filled 4d xy orbital
in MoO(TPP)Cl points in between the nitrogen atoms.
As a result, the interaction of the unpaired electron with the
nitrogen atoms in MoO(TPP)Cl is small compared to that
in Cu(TPP). Interestingly, no nitrogen superhyperfine splitting can be detected in the X-band CW-EPR spectrum of
VO(TPP), where the unpaired electron resides on the 3d xy
orbital of vanadium. This illustrates that the 4d orbitals are
Journal of Chemical Education • Vol. 78 No. 5 May 2001 • JChemEd.chem.wisc.edu
2
2
In the Laboratory
Therefore, the magnitude of the shift will depend on the
energy of the d–d transition1 and the magnitude of the spin–
orbit coupling constant. Since the two ions have spin–orbit
coupling constants of similar magnitude (Cu(II), 830 cm᎑1;
Mo(V), 900 cm᎑1), this factor is not the primary contributor
to the magnitude of the deviation from the free-electron value.
This leaves the separation in energy of the two orbitals involved
in mixing as the major contributor to the difference in the
magnitude of the shift, nλ/∆E. Thus, the energy separation for
copper(II) system is larger than that of the molybdenum(V)
system.
Z2
6
6
2
XZ
YZ
2
2
2
2
X −Y
2
2
XY
8
Figure 6. Magic pentagon for evaluating the value of n of eq 1.
Summary
more diffuse than their 3d counterparts. Thus, nitrogen
superhyperfine structure provides direct information about
the electronic structure of the metal ions.
The g value deviation (∆g) from the free electron (g0)
along any direction can be explained by applying a simplified
theory described in eq 1
g = g 0 ± nλ
(1)
∆E
where n defines the amount of orbital mixing, λ is the ground
state spin–orbit coupling constant, and ∆E is the transition
energy. The plus sign applies to the case of mixing with a
filled orbital and the minus sign to the empty orbital. Thus,
the g value for copper(II) (more-than-half-filled d9 system,
S = 1/2) would be more than the free electron value, whereas
that for molybdenum(V) (less-than-half-filled d1 system, S =
1/2) complex would be less than the free electron value. This
feature has been observed experimentally. Therefore, from the
first approximation, the g value for less-than-half-filled configurations such as Mo(V) should be <2.0023 and that for
more-than-half-filled configurations should be >2.0023.
The value of n can be taken from the magic pentagon,
which defines orbital mixing (Fig. 6). For example, the doubleheaded arrows in the magic pentagon indicate that the dz
orbital can only mix with dxz and dyz orbitals, and n is the
number on the line linking the two orbitals. This information
can be used in defining the electronic structure of the metal
ion. For Cu(II) ion, a d9 system, the unpaired electron can
be in either d x ᎑y orbital or dz orbital. For an unpaired electron
residing in the dz orbital g || = g0 and g⊥ = g0 + 6λ/∆E(d x ᎑ y –
dxz,yz). On the other hand, for an unpaired electron residing
in d x ᎑y one can write g || = g0 + 8 λ /∆E(d x ᎑y – dxy) and g⊥ =
g0 + 2λ/∆E(d x ᎑y – dxz,yz). These relationships indicate whether
the unpaired electron resides in the d x ᎑y orbital. Both g components should be larger than the free-electron value, which
has been determined experimentally. This indicates that the
unpaired electron in Cu(TPP) resides in the d x ᎑y orbital.
Therefore the electronic structure of Cu(TPP) derived from
the g values supports our earlier assignment of the electronic
structure on the basis of the nitrogen superhyperfine structure.
Similarly, for a d1 system with an unpaired electron in
the dxy orbital, the value of n is similar to that for a d9 system
with an unpaired electron in the d x ᎑y orbital and this will
not contribute to the magnitude of the g-value shift, ∆g.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
This report describes an experimental approach to teaching the electronic structure of the paramagnetic transition
metal–porphyrin complex. The EPR spectra provide a direct
and convenient way to teach the concept of crystal field
theory, shapes of orbitals, and isotopic abundance and their
influence on the spectra. In addition, students can learn how
to extract chemical information from EPR spectra.
Acknowledgments
I am indebted to Arnold M. Raitsimring for experimental
assistance and to Jeffry Madura for discussions. I thank F.
Ann Walker and John H. Enemark for encouraging me to
communicate this investigation to this Journal.
Note
1. The g value is further influenced by a charge-transfer
transition involving metal and ligand orbitals; however, the CT
transition is not invoked in the present discussion.
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