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CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
3. ELECTRON SPIN RESONANCE (ESR) SPECTROSCOPY.
3.1 Background
Electron spin resonance (ESR), also known as Electron Paramagnetic Resonance (EPR), has been
used for about the last 50 years to study species which contain unpaired electrons (paramagnetic).
Such species can include organic and main group radicals and transition metal compounds with
unpaired electrons. ESR can be thought of as broadly complementary to NMR spectroscopy in that
ESR deals with paramagnetic species, while NMR deals primarily with diamagnetic species. In
ESR it is the measurement of electron spin interacting with the external magnetic field, while in
NMR it is the interaction of the nuclear spin with the magnetic field which is key.
Let us consider what happens when an electron is placed in a magnetic field. In the absence of a
magnetic field the two spin states (ms = ±½) are degenerate. When an external field is applied, the
degeneracy of the spin states (ms) is lifted, and thus two electron spin energy levels occur, with
energies given by:
E = gBBoms
Where g is called the g-factor (=2.00232 for a free electron), B is the Bohr magneton, Bo is the
magnetic field strength and ms is the electron spin quantum number. This situation can be described
by the simple graph (Figure 3.1, below).
E
ms = 1/2
A single transition, as shown by the vertical
arrow, can occur from the ms = - ½ spin state
to the ms = ½ spin state if the system is
irradiated with electromagnetic radiation of
appropriate energy.
ms = -1/2
Bo
Figure 3.1 The splitting of electron spin states
in a magnetic Field.
3.1 The EPR Experiment
The vast majority of EPR instruments are
based on the general design shown in the
schematic diagram on the right.
Microwaves are generated by the klystron
tube and the power level adjusted with the
attenuator. The circulator directs the
microwaves to the cavity where the
sample is mounted. At resonance, a
portion of the microwaves are absorbed
by the sample. The microwaves are
reflected back from the cavity and
detected by a diode detector and any
Figure 3.2 Schematic Diagram of an ESR
Spectrometer.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
excess microwaves reflected from the diode are absorbed by the load. The diode is mounted to lie in
the direction of the electric vector of the microwaves and generates a direct current proportional to
the microwave power reflected from the cavity. In principle the absorption of microwaves by the
sample could be detected by the decrease in current. In practice, such a dc measurement is too
noisy.
The solution is to introduce a small amplitude field modulation.
A small oscillating magnetic field is superimposed on the fixed
field by means of small coils built into the cavity walls. At the
resonance point the result is to sweep the field back and forth
across the resonance and the detected diode current is now an ac
current. Amplification using a frequency sensitive amplifier
eliminates much of the noise. The detected ac signal is the
change in sample absorption and so what is observed is the first
derivative of the absorption curve.
Most commonly, EPR spectra are run at one of two fixed
frequencies with an associated field strength:
X-Band 0.33T / 9GHz
Q-Band 1.4 T / 32GHZ
Figure 3.3 The Derivative Spectrum
3.2 Isotropic EPR Spectra.
An isotropic EPR spectrum, ie that of a paramagnetic molecule tumbling freely in solution, can
contain several types of useful chemical information:
i) g-value (parallels chemical shift in NMR).
ii) The hyperfine coupling pattern provides information on the number and types of
magnetic nuclei with which the unpaired electron interacts
iii) The spacing of the lines and the centre of gravity of the spectrum yield the hyperfine
coupling constants (A) and the g-values, which are related to the way in which the electron
spin density is distributed in the molecule.
iv) The integrated spectral intensity is proportional to the concentration of radicals in the
sample
v) The spectral linewidths are related to the rate of rotation and the rate of fluxional
processes.
3.2.1 Hyperfine Coupling
As observed in NMR spectroscopy, coupling can be observed to nuclei with I ≠ 0. The energies of
the resulting spin states are given by the equation:
E = gBBoms + AmsmI
Where A is the hyperfine coupling constant (broadly equivalent to J in NMR) and m I is the nuclear
spin quantum number. In the same way as in NMR spectroscopy, coupling to n nuclei with nuclear
spin I leads to 2nI+1 lines in the spectrum. Consider the effect of the coupling of a nucleus of spin I
= 3/2 to an electron in a magnetic field. The energy levels are given by substituting values of Ms ( =
± ½ ) and mI (= -3/2, -1/2, 1/2, 3/2) into the above equation. The energy levels obtained are shown
in the figure below:
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
E
mI
+3/2
+1/2
-1/2
-3/2
-3/2
-1/2
+1/2
+3/2
ms = +1/2
ms = -1/2
Figure 3.4 The effect of Coupling to a
Nuclear Spin I = 3/2
B
As seen previously, the electron spin energy levels are split by the magnetic field. In addition there
is further splitting due to the four possible values of m I. Since the coupling is to a nucleus of spin I
= 3/2, there should be 2n(I + 1) lines (ie 2.1.(3/2 +1) = 4 lines). The four transitions are shown on
the diagram. There are only four transitions because, as in all forms of spectroscopy, there are
selection rules. In this case the selection rules state that Δms = 1 and ΔmI = 0. Note that the energy
of each transition is the same (fixed microwave frequency) but that they occur at different fields (B
is scanned).
3.3 Anisotropy
Isotropic spectra are obtained from solutions and from species with cubic (tetrahedral or octahedral)
symmetry. In less symmetric species, and particularly in solid state samples, we see the effects of
anisotropy. We have considered the g-factor to be a scalar quantity, but in fact it is a symmetric
tensor. Such a tensor can be diagonalised to give three principle g-factors, gxx, gyy and gzz. In
solution these are averaged by molecular motion to give a single isotropic g-factor, and in systems
with cubic symmetry, gxx = gyy = gzz. For a system with axial symmetry two of the terms are the
same giving rise to two distinct g-factors, g|| and g. For lower symmetries, all three terms are
inequivalent.
Let us consider the case of distortion in octahedral transition metal complexes. A pure octahedral
complex will give a simple isotropic spectrum. However, if we compress or extend one axis (eg
Jahn-Teller distortion), put different ligands on one axis, or remove ligands from one axis (ie go to a
square planar complex) then we generate a system with axial symmetry. This is often referred to as
a tetragonal distortion, and gives rise to a spectrum in which two g-factors are observed, g|| and g.
This is shown schematically below.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
L
L
L
L
L
L
L
M
M
L
L
Compression or
elongation of axis
(exaggerated)
L
L
L
L
L
L
L
L
M
M
L
L
L
L
L
L'
L
L
M
L
L
L'
Figure 3.5 Tetragonal Distortion in Octahedral Complexes and the Resulting Spectral Form
Further distortion or change of the ligand set, destroying the axial symmetry gives rise to what is
known as a rhombic distortion, characterised by three unique g-factors, gxx, gyy and gzz (NB
sometimes the symbols gx, gy and gz are used). Again this is shown schematically below.
L
L
L
M
L
L
L
L
L
L
L'
M
M
L
L
L
L'
L
L
L'
L
L''
M
L''
L
L'
Figure 3.6 Rhombic Distortion in Octahedral Complexes and the Resulting Spectral Form
3.4 Other Observations.
It should be noted that ESR is a remarkably sensitive technique. Samples with concentrations as low
as 10-9 M can be detected in favourable cases. This is in contrast to NMR which ideally requires
samples of at least 10-2 M.
ESR is also versatile, in that a range of sample types can be studied. It is best for magnetically
dilute systems, where the paramagnetic species is surrounded by diamagnetic material, such that
there is no interaction of neighbouring electron spins. Solutions are most widely used and give the
more easily interpreted spectra. Frozen solutions (often referred to as glasses) are also widely used.
Spectra from powdered solids can be more complex, but are OK. For the most detailed studies, ESR
from single crystals, or from doped crystals (paramagnetic ions doped at low concentrations in a
crystalline, diamagnetic host matrix) enables the precise orientation of the molecules in the field,
giving access to a great deal of information regarding the electronic structure of the molecule.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
Interpretation of ESR spectra at a superficial level is fairly straightforward. Approximate values of
g and A can be extracted, although second order effects and anisotropy can make it difficult to
obtain accurate parameters. The g-values are indicative of the electron environment. The magnitude
of the hyperfine coupling constant A is usually a good indicator of where an electron is located
within the molecule in question. In transition metal complexes, the unpaired electron is usually
located in a metal based orbital. Consequently, if the metal has a non-zero nuclear spin, the value of
A will be large. Coupling to other nuclei will be much smaller. There are now sophisticated
computer programmes readily available which can simulate the spectra and give a far more detailed
quantum mechanical analysis.