1
Determining g-factors with Electron Paramagnetic
Resonance
Butera, R.A., Waldeck, D.H., and Wagner, E.P. (revised June 2016)
Introduction
Electron paramagnetic resonance (EPR) spectroscopy is a technique that is useful for studying
the structure of paramagnetic species. These are species with at least one unpaired electron and
hence a magnetic moment. These species include transition metal ions, organic free radicals and
ions, and electronically excited states. EPR spectroscopy uses microwaves to induce transitions
between the electron spin energy levels of paramagnetic species. Molecules of this type can play
important roles in reaction mechanisms. Many of these species are known and can be stable for
long periods of time.
This experiment has two parts. First, you will study the organic radical DPPH on a
Helmholtz EPR instrument, which is specifically designed as a teaching tool. By measuring how
its resonance frequency shifts with the value of the applied magnetic field, you will determine
the value of its g-factor. The value of g provides a quantitative measure of the molecule’s
magnetic moment; i.e., how much the applied magnetic field shifts the energies of the molecule’s
electron spin energy sublevels. Second, you will perform a measurement of the EPR spectrum of
two inorganic complexes, Copper(II) acetylacetonate, Cu(acac)2, and Vanadyl acetylacetonate,
VO(acac)2. Your will perform these latter measurements on a Varian E-4 EPR spectrometer
which is a research grade instrument. In this study, you will interpret the general structure of the
spectrum. In addition, you will determine the g-factors of these two complexes by comparison
with the measured value of DPPH after putting a capillary tube of DPPH into your sample tubes
for use as a sort of internal standard.
Theory
The electron, like certain nuclei, behaves like a small magnet since it possesses the properties of
charge and motion (spin) about an axis. In the absence of an applied magnetic field, the spins
and magnetic moments of a group of free electrons are pointed in random directions. In the
presence of an applied field, an electron behaves like a bar magnet and takes one of two
orientations with respect to the field axis. The lower energy, and therefore preferred orientation,
is the one in which the electron is aligned parallel to the field. The higher energy orientation is
the one in which the electron is aligned antiparallel to the field. If radiation of the appropriate
frequency is applied in the presence of the field, a transition from the “parallel state” to the
“antiparallel state” may occur (Figure 1). EPR (or ESR) spectroscopy uses this phenomenon to
study molecules possessing unpaired electrons. This splitting in energy is referred to as Zeeman
splitting. The energy of interaction of the field with the electron is
𝐸 = −𝜇Β
(1)
where µ is the spin magnetic moment and Β is the magnetic field. Although Β and 𝜇 are vector
quantities, their dot product is a scalar quantity, i.e., the energy of their interaction. For an
electron in a magnetic field oriented along the z axis,
𝜇 = 𝑔𝜇𝐵 𝑚𝑠
(2)
where g is the spectroscopic splitting factor (g = 2.0023 for a “free” spin), μB is the Bohr
magneton (= eh/4πmc), and ms is the magnitude of the projection of the spin angular momentum,
𝑆⃗, on the magnetic field z axis (Figure 1). For a single electron, ms = ±1/2ℏ, corresponding to
2
Figure 1. (left) Zeeman Splitting. An unpaired electron can move between the two energy levels
by either absorbing or emitting a photon of energy hν such that the resonance condition, ∆E=
hν, is obeyed. (right) the projected magnitude (ms) of 𝑆⃗ on to the z axis, which is the in line with
the magnetic field.
the two orientations of 𝑆⃗ with respect to the field. Therefore, we expect two energy levels, with
energies E1 = -1/2 gμBB and E2 = +1/2gμBB. The energy difference between these two levels is
given by
(3)
Δ𝐸 = 𝐸𝑢𝑝𝑝𝑝𝑝 − 𝐸𝑙𝑜𝑜𝑜𝑜 = 𝑔𝜇𝐵
A transition between these energy levels may occur when electromagnetic radiation of
frequency ν is incident on the system, where ν = ΔE/h = gμBH/h (Figure 1). These transitions
may be observed in the laboratory when the population of the lower energy state is greater than
that of the upper state. At a field strength of 3.6 kilogauss, this energy spacing is only on the
order of 1 cal/mole and the two levels are almost equally populated. Despite this small
separation, the Boltzmann factor exp(-ΔE/kT) predicts a very slight excess of electrons in the
lower energy state at room temperature.
The energy of the transition can also change if the g factor value changes. While an
electron free from any orbital angular momentum affects has a g value of 2.0023, this value will
vary with orbital angular momentum (L) contributions. So the g value measured it not just g for
electron spin (S), but rather the total g value referred to as Lande g factor.
𝑔 = 𝑔𝑆 + 𝑔𝐿
(4)
Quanta of energy 1 cal/mol are associated with wavelengths of about 3 cm. Hence, this
type of spectroscopy falls in the microwave (RADAR) region of the electromagnetic spectrum
and uses techniques appropriate for this wavelength scale. In practice, the sample is placed in a
resonant cavity fed by a microwave generator of fixed frequency. A transverse magnetic field is
applied to the sample and is gradually increased in strength until a sudden loss of energy from
the cavity occurs. This loss of energy indicates absorption by the sample. The change in field
strength changes ΔE and the absorption occurs when the value of ΔE satisfies the resonance
conditions. It can be shown that, in principle, electron paramagnetic resonance may take place at
any frequency provided the value of the magnetic field is adjusted to satisfy the resonance
condition given in equation 3.
In addition to the detection of unpaired electrons, EPR can provide information
concerning their environment. If the orbit of the unpaired electron interacts with an atom that
has a nucleus with a magnetic moment and spin I, then this nucleus and the electron will interact.
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The resonance line will be split into (2I + 1) lines, since the field of the nucleus may either
increase or decrease the value of the external magnetic field experienced by the unpaired
electron. If the particular case of interaction with a proton is considered, it is clear that the
proton spin and magnetic moment will be aligned either parallel or antiparallel to the applied
field. This alignment occurs because the proton itself has a spin of I= 1/2 therefore only two
orientations with components m1 = ±1/2 are allowed. The magnetic moment of the proton
produces a small additional field at the electron, which modifies the external field experienced
by the electron, as described previously. The electron experiences a magnetic field that is either
slightly greater or slightly less than the applied field. Since the interaction energy with the
magnetic field is weak (≈ 10-3 cal/mol), the protons will be almost equally distributed between
the two orientations and each of the electron levels will split into two separate levels. This
splitting is shown in Figure 1b.
In general, the resonance signal is split into N hyperfine lines by interaction with N1
nuclei of spin number I1, N2 nuclei of spin number I2,… where
(4)
N = (2 N1I1 + 1)(2 N 2 I 2 + 1)....
Here N1, N2, … refer to different nuclei or to groups of similar nuclei in different chemical
environments. The intensities of the hyperfine lines may be calculated by considering all
possible permutations of the nuclear spin’s orientation. The separation between any two
hyperfine lines is given as A (the difference in energy of the two transitions in Figure 2), and it
will be the same for a given group of nuclei. The constant A represents the strength of the
interaction between the electron and the nucleus and is called the hyperfine coupling constant.
This coupling constant will change when the type of nucleus changes or its environment
changes.
Figure 2. Zeeman splitting in a magnetic field for the case of S=½ and I = ½.
As an example, let us consider the case of the ethylene radical anion, [CH2 = CH2]– . One
possibility is that the electron interacts with all four protons (I = ½) equally, assuming that all
carbons are 12C with I = 0. In this case, we would predict (2 N I+1) transitions or 5 lines, as
shown in Figure 3.
The absolute intensities of the lines are determined by a variety of factors, but their
relative intensities are predictable.
First, we consider the different sublevels of the
ms = ½ state. Each sublevel is associated with a different set of nuclear spin states. In the case
of [CH2 = CH2]– we have five sublevels with the nuclear spin states as shown in Figure 3. In this
diagram, α and β are the directions of the individual nuclear spin orientations, (m1 = +½ and -½,
respectively) for the four protons. All possible permutations of these spin orientations are
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shown. In this case, transitions originating in the +2 and -2 sublevels would have equal
intensities because only one possible combination exists for the m1 of the four protons, all α for
+2 and all β for -2. In contrast, four possible combinations exist for the states in which m1 is +1
or -1, and six possible combinations exist for the state with m1 = 0. Thus, the statistical weights
of the transitions are 1:4:6:4:1. These statistical weights give rise to a spectrum that looks
approximately like that shown in Figure 4.
Figure 3: Energy level scheme for ethylene anion. The transitions are indicated by the doubleheaded arrows. (right) The energy sublevels and the nuclear spin states of the ethylene anion.
Note that the intensity of the signal will increase with the number of spin states in an energy
level.
a
Signal
Derivative Signal
b
Magnetic field strength
Magnetic field strength
Figure 4: Spectrum (a) and first derivative (b) spectrum for the ethylene anion.
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Figure 4 shows two types of spectra. In Figure 4a a normal absorption spectrum is
shown, in which the amount of microwave (or RF) power absorbed by the sample is plotted
versus the magnetic field strength. This plot of the amount of intensity lost is a common way to
present the data in many different spectroscopies, and it is this method that is used by the
Helmholtz spectrometer you will use to study DPPH. Figure 4b shows a plot of the same
spectrum in derivative form; i.e., the first derivative of the lost microwave intensity is plotted
versus the magnetic field strength. This latter manner of the presenting the spectrum is most
common in EPR spectroscopy and it is the manner in which the data is obtained from the Varian
E-4 EPR spectrometer. Lastly, you should note that if the electron does not interact equally with
all the protons, a different energy level diagram and hence a different spectrum would result for
the ethylene radical anion.
Figure 4 clearly shows the presence of hyperfine structure in the spectrum. In this
experiment, you will find that the hyperfine structure is not present in your DPPH sample, but it
is present for your spectra of the inorganic complexes. In addition, you will observe that the
spectra you obtain are not symmetric as in Figure 4b. These different features of the spectra
occur because of the difference in dynamical features of the molecules; i.e., differences in
electronic couplings and in the nuclear motion (e.g., over rotation) of the molecules.
The Experiment
This experiment consists of two parts. First, you will measure the value of g for the 2,2diphenyl-1-picrylhydrazyl organic radical (DPPH). Second, you will determine the g-factor of
two inorganic complexes by the comparison to the value obtained for DPPH.
The organic compound DPPH is a radical possessing one unpaired electron distributed
throughout the molecule (Figure 5). From the relationship between the resonance frequency v
and the field strength H (see Eq. (2)), the g-factor
for the spin of the electron can be calculated.
First, you must calibrate the apparatus for the
field strength. You will perform this task by
measuring the magnetic field with a gaussmeter
as a function of the current you apply through the
coils. The relationship between them should be
linear; i.e., the field H is proportional to the
current.
Second, you will measure the
‘spectrum’ of DPPH for 10 different field
strengths and radiofrequencies. From the results
of the analysis of these 10 scans, you will plot
Figure 5: The DPPH structure.
the radiofrequency as a function of field strength
(Figure 6). The g-factor may be calculated from the following equation that uses both the
measureable values of magnetic field strength (B (tesla) or H if in gauss units) and the absorption
frequency (n) along with Plank’s constant and the Bohr magneton (mB=9.274x10-24 J/T). This
equation can then be arranged into a simple slope-intercept equation for a line to obtain g.
ℎ
𝑣
𝑔𝑔𝑔𝑔𝑔 Δ𝐸 (𝑀𝑀𝑀)
𝑔 = �𝜇 � ∗ 𝐵 = 0.71448( 𝑀𝑀𝑀 ) �𝐻(𝑔𝑔𝑔𝑔𝑔)�
(4)
𝐵
You should also note that the commercial Varian EPR instrument used in the second half of this
experiment runs at a fix frequency of 9800 MHz while scanning the magnetic field. Therefore,
based on your results in this first part of the experiment, you should be able to predict the
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magnetic field value where you will observe an absorption for the DPPH. You will compare
your value to the literature value of DPPH and the g-factor of a free electron.
The inorganic compounds Cu(acac)2 and VO(acac)2 (Figure 7) both are EPR active. The
copper compound is a d9 species and the vanadium compound is d1. Both of these molecules
have significant hyperfine splittings, which are evident in the spectra. You should be sure that
your scans cover the whole spectral range so that you observe all of the transitions. It will be
useful to know that the nuclear spin of 63Cu is 3/2 and that the nuclear spin of 51V is 7/2.
Figure 7: Structures of the Cu(acac)2 and VO(acac)2 compounds.
You will determine the g-factor of each of these compounds by measuring their EPR
spectrum in solution (60% chloroform: 40% toluene). You should find that the g-factors for
these complexes are quite different from that of a free electron. This change in the value of g
reflects the importance of spin-orbit coupling in these metal complexes. Furthermore you will
find that one of the complexes has a g-factor that is less than that of the free electron, and the
other has a g-factor larger than that of a free electron. You will place a solid sample of DPPH
(encapsulated in a quartz tube) inside of the solution and use its EPR spectrum as an internal
reference. Because the E-4 EPR spectrometer operates at a fixed resonant frequency and scans
the magnetic field, the left hand side of Eq. 2 must be the same for the DPPH and your sample.
Hence, if the transitions occur at different magnetic field strengths, then the g-factors must also
be different. In general,
H
(5)
g sample = g DPPH DPPH
H sample
In order to determine the magnetic field strength at which the transitions are observed for the
inorganic complexes, you will need to understand and interpret their spectra. The shifts in the gvalue are caused by the influence of spin-orbit coupling. To explain these trends, you must
consider how the ligand field splits the energies of the d-orbitals (see References 3 and 6).
Laboratory Procedure
To begin, you will perform measurements on the DPPH sample using the EPR simulation
system (typically referred to as the Helmholtz setup, which describes the two large wire
windings that will create the magnetic field). This step will familiarize you with the underlying
principles of the EPR measurement and you will determine the g value for a “free” electron. In
the second part, you will perform your measurement of the copper and vanadium complexes on
the Varian E-4 EPR spectrometer with the DPPH as a “standard”.
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Measurement of g using the Helmholtz Coil Instrument
The Instrument
This apparatus uses radiofrequency waves rather than microwaves as the source of
radiation. The EPR apparatus consists of 6 components: 1) a radiofrequency (RF) control unit
(probe holder), 2) a magnetic field (mf) control unit, 3) a pair of Helmholtz coils, 4) a multimeter
(used here as a voltmeter), 5) a phase shifter, and 6) an oscilloscope. A photograph and a
schematic diagram of the apparatus are shown in Figure 8. The apparatus is interfaced to a
personal computer. A menu-driven program provides for the acquisition and analysis of data.
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a
2
6
1
3
7
5
4
1- Magnetic field probe, 2- RF field generator (coarse adjustment is on the back, fine adjustment
on top), 3- Helmholtz coils, 4- Gaussmeter, 5- Magnetic field control unit, 6- Voltmeter,
7- oscilloscope with typical waveform displayed, 8- phase shifter (note: phase can also be
adjusted through the magnetic field controller)
b
c
1
3
3
2
Figure 8: (a) Photograph of the Helmholtz coil instrument. (b) Rear view of RF field generator
and magnetic field probe (gaussmeter). (c) Schematic diagram of system.
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The radiofrequency (RF) unit controls the frequency and amplitude of the RF field. The
dial on top of the unit provides the radiofrequency control and can be varied from 25 MHz to 100
MHz. You should utilize the tuning range from 30 MHz to 65 MHz when doing this experiment.
The RF frequency is locked during the course of an experimental run and its exact value is
displayed on the magnetic field control unit. Absorption of RF energy by the sample, which is
placed inside the coil, causes a reduction in the transmitted RF power. This loss of RF power
causes a drop in the voltage that is sent to the y-axis on the oscilloscope; hence the y-axis on the
scope is proportional to the absorbed RF power. The RF course amplitude adjustment (on the
back) should be set to the highest allowable level. The RF field collapses when this maximum
value is exceeded and 0.00 MHz will be displayed on the LED output screen.
The magnetic field (mf) control unit provides for independent control of the AC and DC
components of the magnetic field strength. The magnetic field is generated by a set of
Helmholtz coils, i.e., loops of wire through which electrical current flows in order to generate a
magnetic field. The coils are oriented so that the RF probe (containing the sample) resides on an
axis through the centers of both coils. The coils should be placed symmetrically about the RF
probe and separated by 2.5 inches, the radius of one coil. The sample and the field probe need to
be placed in the center of the two coils where the magnetic field is most stable and homogeneous
(Figure 9).
Figure 9: Cross sectional view of the Helmholtz
coils. The dark circles are the coil windings and the
circular contours show the magnitude of the
magnetic field near the coil pair. Inside the central
'octopus' the field is within 1% of its central value
B0. The five contours are for field magnitudes of
0.5B0, 0.8B0, 0.9B0, 0.95B0, and 0.99B0
In this arrangement, the field strength at the sample can be calculated when the current through
both coils is known. The magnetic field control unit is capable of driving up to 3 amps DC into
the coils (maximum field strength of 52 G) and is regulated by the left-most dial on the front
panel. Connection to the current supply is made through the banana plug connectors on the front
of the control unit. The coils are wired in parallel to each other and are in series with a shunted
voltmeter. The voltmeter shunt is a calibrated resistor, and the voltage across the resistor is
proportional to the current. The proportionality constant that converts the voltage to current is
the value of the resistance (Ohm’s law V = IR. The resistor is nominally 0.1 Ω and its actual
value is marked on the box in which it is enclosed. Note that:
• The wire connected to the mf control unit’s ground receptor should be plugged into the
grounded side of the ammeter.
• The wire connected to the mf control unit’s high (+) side contains an in-line 3 amp fuse.
This wire always must be used to protect against an accidental short-circuit.
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•
The voltmeter should be used on the 200 mV scale.
The shunted voltmeter measures only the DC component of the coil current. A 60 Hz AC
component is superimposed on the DC current by using the dial at the center of the mf control
unit. This procedure allows you to choose a magnetic field strength with the DC dial to vary it
over a narrow range with the AC dial. Since the field strength is proportional to the current and
in phase with the current, the field strength is modulated at 60 Hz. The modulated voltage across
the shunt resistor (also in phase with the current) is used to drive the x-axis on the oscilloscope.
Unfortunately, because of capacitance in the cables, the voltage displayed on the scope lags
behind the current and field strength. (Remember ELI and ICE man from first-year physics).
The lag results in a slight phase shift of one peak with respect to the other. An in-line phase
shifter is used to compensate for this phase lag.
Experiencing both a preset RF field and a modulated magnetic field, the sample will
absorb radiation when the resonance condition described by equation 2 is met. The x-axis on the
oscilloscope is the change in the magnetic field strength and the y-axis on the oscilloscope is the
RF power. A menu-driven program for the acquisition and analysis of data is provided. The
program can be accessed by double clicking on the icon on the desktop.
Experimental Procedure
The computer program has two primary components. The first component is used to
calibrate the magnetic field created by the current running through the Helmholtz coils. The
second component is used to collect the RF power loss spectrum as a function of the magnetic
field strength.
Part I. Alignment and Calibration: In this part of the procedure you will measure the magnetic
field near the sample as a function of the amount of DC current that you run through the
Helmholtz coils. It is best to set the AC current on the mf control unit to zero. You will use a
gaussmeter (Magnetic Instrumentation Inc., Model 907) to measure the magnetic field. The TA
will demonstrate how to use the meter. You will need to ramp the magnetic field from a value
near 0 Gauss to a field strength of about 30 Gauss. For the calibration program, you will need to
collect at least 20 points. You will enter the field strength in G into the program, and it will
calculate a current value in V (to be used later as a method of conversion).
• Before running the program, verify your use of the Hall probe and gaussmeter then Zero
the gaussmeter.
o Turn on the meter and press “menu”
o Press “next” until the “utilities” option appears.
o Press “enter”, then “next” until the “auto zero” appears.
o Press “enter”. The Gaussmeter will begin the auto zeroing.
o When prompted with “shield the probe”, put the shield helmet over the top
of the probe. It will probably be easier to do this if you remove the probe
from its holder and hold it upright.
o Once shielded, press “reset”. The meter is now ready for use.
• Put the probe back in its holder and optimize its orientation and position in the holder by
maximizing the value of the field that you measure. The Helmholtz coil must be on at this
point.
• When you run the acquisition program, you will be prompted to input a filename. Your
data will be stored under this filename in the “eprdata” folder on the hard drive.
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•
•
•
•
•
You will be prompted to run the calibration procedure. When ready to begin, click OK.
Once you start, the computer will prompt you for the magnetic field strength in Gauss.
After you enter the field strength, the computer will determine the current through the
Helmholtz coils by measuring the voltage drop across the calibrated resistor.
At this point, the program gives you two options, Calibration or Take Spectra If you
have previously calibrated the system, you can choose to skip the calibration procedure
and proceed directly to taking spectra.
To complete the calibration procedure, you need to collect 20 values for the magnetic
field and voltage and enter into the program. Try to make the points evenly spread from
around 0 to around 30 Gauss. After you collect 20 or more values, you can choose to end
the calibration and begin the experiment. After each calibration point taken, you will be
prompted to ‘Take Another Calibration Value’. Change the DC value on the mf control
unit. The digital multimeter should display the value of the voltage drop across the
calibrated resistor. After a few seconds, the system should stabilize and you can read a
new magnetic field strength and enter the value into the computer. Repeat this process
until you have collected at least 20 points.
When you complete the calibration, a file that contains a collection of x,y points (x is the
voltage drop V and y is the magnetic field H) will be written to the hard disk. Later, you
will need to plot these points and fit them to a line (H = mV + b) using a linear regression
algorithm. The parameters of the fit will provide you with the means to convert the
measured field voltage into a magnetic field strength. Because these parameters are used
to determine the field strength along the x axis, Be careful not to change the geometry
of the coils. If you move the coils, you will have to recalibrate the apparatus.
Part II. Sample Runs.
• Raise the AC current on the magnetic field unit to around the 3rd marking on the dial.
• Set the RF frequency between 35 and 65 MHz. (We advise starting with a high
frequency and working toward the low end.)
• Vary the DC current until you see two downward facing peaks on the oscilloscope. Try
to center the peak on the oscilloscope. You can imagine the spectrum on the oscilloscope
to be a cylinder where the phase dial can rotate the entire 3D spectrum. It is important
that you put the two peaks as close together as possible for more accurate data.
• In the data collection program, choose ‘Acquire an EPR Spectrum’. First you will be
prompted to enter the RF frequency. Next you are given the opportunity to verify that
everything is ready before you proceed to collecting a spectrum. When you click ‘OK’, a
new screen appears and data collection begins.
• The collection program shows you a number of curves. On the left is the spectrum
collected for each sweep and on the right panel is the spectrum for all of the averaged
sweeps you have collected. The number of cycles you take is also displayed on the
screen.
• Once you are satisfied with the quality of the averaged data, stop the scan and the
information will be written to a file.
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Figure 11: Typical signal as observed on the oscilloscope (left) and on the computer (right).
Note that the display on the oscilloscope is the raw signal (no averaging) and will not look as
“clean” as the averaged signal on the computer. Try to get the peaks closer together than those
seen above.
• You will need to assign the value of the field voltage at which the spectrum shows its
absorption (dip). Because of the phase shift in the circuit, you will probably see two
peaks on your spectrum. You could spend time overlapping these by adjusting the phase
shift control and collecting the spectrum in an iterative manner. You may also choose to
take the average of the peak positions when assigning the magnetic field strength for the
resonance. Either way is appropriate, but more accurate data will have peaks at least close
together even if they are not on top of one another.
• When you are finished collecting the spectrum, you may want to do a “print screen” and
save the image for your report. The data for the averaged spectrum is written to a file
(ASCII format of x,y pairs where x is the field voltage and y is the RF power level). The
filename is ‘field#’, where # is the integer value of the RF frequency that you are using.
You can use Excelto read the data file and assign the peak positions.
• Repeat this procedure for 10 resonance frequencies.
• When you are finished with this procedure, you should power down the electronics of the
Helmholtz system. Be sure to also turn off the guassmeter.
EPR Spectra on the Varian E-4 Spectrometer
EPR Sample Preparation
Both of the samples will be dissolved in a solution of 60% chloroform (CHCl3): 40%
toluene, by volume. These samples should be prepared freshly; i.e., right before you perform the
measurement. In both cases you will need to prepare a concentrated solution of the sample
(either VO(acac)2, or Cu(acac)2) in the chloroform:toluene solution. The concentration should be
about 10-2 M.
After preparing the solutions, you should place them in the quartz EPR tubes provided.
Use a pipet for this procedure. Be careful with the EPR tubes since they are made of quartz and
rather expensive. Inside of each sample tube, you should place the DPPH reference. This
reference sample is a piece of solid DPPH which has been encased in quartz tubing. Your
instructor will provide you with this sample. The easiest way to get the right amount of sample
into the tube is to carefully slide the DPPH reference sample into the tube and to pipette your
sample until it is a little higher than the DPPH tube (the tube will float, so don’t continue to add
sample).
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A photograph of the E-4 EPR spectrometer is shown in Figure 12. The EPR instrument
has two major components, a variable field 8 kilogauss (kG) magnet/microwave bridge and a
control unit. Between the poles of the magnet, a quartz sample holder is located in the
microwave resonant cavity. It is here that you will place the sample and tune the cavity’s
frequency via the Teflon screwdriver. The control unit has a pen recorder for recording your
spectrum. In addition, you will need to optimize this unit’s settings as described below. The
components you should focus on are the Field Controller, the 100 kHz module and the
oscilloscope.
•
Before turning the instrument on, make sure that the MODE control on the magnet is set
to STANBY and that the ATTENUATION/POWER control is set at zero milliwatts
(mW) of radiofrequency (RF) power.
Turn on the instrument using the MAIN POWER switch located just below the lower left
hand corner of the control module and allow it to warm up, i.e., unitl a trace appears on
the small oscilloscope on the right hand side of the control unit.
Place your sample, contained in the EPR sample tube, into the quartz dewar and then
place the dewar into the sample holder between the magnetic housing.
Set the power level to 1~2 mW.
Turn the MODE switch to TUNE.
At this point, you should see a broad peak on the oscilloscope (see Figure 13a).
•
•
•
•
•
5
2
quartz dewar
9
8
10
3
6
sample tube
10
11
4
1
left magnet housing
7
sample cavity
You will not be using
these controls
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chart recorder
Figure 12: E-4 EPR spectrometer. 1-main power, 2&3- field set, 4- field span (scan range), 5receiver gain, 6- modulation amplitude, 7- time constant, 8- power mode, 9- AFC output , 10detector current, 11- attenuation power, 12- frequency adjustment.
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a
b
Figure 13: Typical EPR oscilloscope signal profiles. (a) Before the cavity is tuned.
(b) Absorption dip is shown after the cavity is properly tuned.
•
•
•
•
•
Adjust the FREQUENCY control knob (on the magnetic housing) until a ‘dip’ appears in
the peak (see Figure 13b). The dip should be offset to the right.
Using the special Teflon screwdriver, adjust the CAVITY CONTROL SCREW behind
the sample holder in the magnet until the dip is ~10% above the baseline. DO NOT,
UNDER ANY CIRCUMSTANCES, USE A METAL SCREWDRIVE. YOU
SHOULD KEEP ALL MAGNETIC MATERIALS AWAY FROM THE MAGNET.
THIS INCLUDES TOOLS, WATCHES, BANK AND CREDIT CARDS.
Turn the MODE control to OPERATE. (NOTE: Do not remove the sample from the
cavity unless the MODE control is set to TUNE or STANBY.)
Turn the POWER knob back up to between 10 and 30 Db so that the DETECTOR
CURRENT METER reads ~200 to 300. Carefully adjust the RF FREQUENCY control
(on magnet) to set the needle on the AFC output meter at the center of the range.
Once the cavity is adjusted, move to the control unit and adjust the magnetic field to the
desired value using the MAGNET THOUSANDS and HUNDREDS controls (located on
the Field Controller module). This knob sets the approximate value of the magnetic field
in the center of your scan. For example, if the field is set at 3000 G and the SCAN
RANGE at 1000 G, you will be sweeping the magnetic field from 2500 – 3500 G. These
are reasonable starting parameters for this experiment.
Signal Optimization:
The most important adjustments for optimizing the signal level will be the Detector Level
GAIN and the MODULATION AMPLITUDE, which are located on the 100 kHz control
module. Note that these each have an inner and outer knob. The outer dial controls the setting
while the inner knob adjusts the multiplier. Higher gains will result in large but noisier signals.
The peak intensities can also be amplified using he MODULATION AMPLITUDE, but too large
a value will results in broader peaks. A good rule of thumb is to keep the MODULATION
AMPLITUDE less than the width of the EPR line. Leave the TIME CONSTANT at a relatively
low value (1 sec). The TIME CONSTANT is an electronic filter and higher values yield quieter
signals, but also a much slower pen response. This can artificially broaden peaks and potentially
cause you to miss small peaks entirely.
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Initially, try settings of second for the TIME CONSTANT, 1.0 for the MODULATION
AMPLITUDE and 4 × 102 for the RECEIVER gain. These are not ‘magic’ values. You
may change them as necessary.
Turn on the chart recorder and set the pen control to UP.
Manually move the recorder arm out of the way to the left. Note: “manually” does not
mean moving the bar with your hand, it means using the buttons on the bottom
right of the plotting area to move the bar. Now, remove the platen from the chart
recorder. The recorder holds paper by suction, so the platen should always be left
covering the recorder bed whenever the instrument is not being used.
Slide a piece of EPR spectrum paper onto the bed.
Insert a pen into its holder, then mount the holder ron the recorder arm.
Check that the needle on the AFC METER is centered. If it is not centered, adjust the
frequency, power, and/or cavity control screw to recenter it.
Perform a slow manual sweep of the recorder arm to the right looking for peaks. The
EPR signal of your sample should be found at the field value near 3000 G. (You may
have to adjust the MODULATION AMPLITUDE and RECEIVER GAIN in order to see
a signal.)
When the signal is located, adjust the field so that the peak(s) is/are centered on the
paper. You should obtain two types of spectra: one which shows all of the lines on a
single sweep and one which is expanded to show the shift between the DPPH reference
and the center lines of the sample.
Adjust the RECEIVER GAIN and PEN ZERO controls to maximize the signal.
Now, move the recorder arm to the left, set the PEN CONTROL to AUTO, set the SCAN
TIME to 2 min, and then press the right arrow button on the SCAN controls. You should
now obtain a plot of the EPR signal.
When the scan is complete, remove the paper and fill in the information form with the
parameters of your experiment.
Set the PEN CONTROL to UP and insert another piece of paper. Repeat the scan for
your partner.
After obtaining all spectra which you desire, turn the power down to ZERO and set the
MODE CONTROL switch to STANDBY.
Remove your sample from the sample holder and replace it with a new sample. Perform
the above procedure again for this new sample. If you have obtained all the spectra you
need for all of your samples, proceed with the shutdown procedure outlined below.
Shutdown Procedure
• Make sure that the POWER has been turned down to ZERO and that the MODE
CONTROL switch is set on STANDBY.
• Clean the EPR tubes by rinsing them with absolute ethanol.
• Remove and cap the pen (leave it in its holder and sitting on the table). Replace the
platen on the chart recorder and turn the recorder off.
• Remove the teflon screwdriver and set it back on the table.
• CLEAN UP THE LAB AREA AND THE PREPARATION ROOM!
• Turn the main power off.
15
Data Analysis
In the report, you should present the data that you obtained experimentally and any plots
that you made in the data analysis. You should report your experimentally determined values of
g and compare your values with the literature values. Last, you should address the questions
below.
g Value of DPPH
The data analysis should be performed after you have performed the calibration curve
and taken all ten spectra.
To calibrate the magnetic field strength, you will need to make a plot of the measured
magnetic field H to the measured field voltage V. Fit the data to a line of the form
H(gauss) = mV(volts) + b.
The procedure for determining the resonance frequency shift with magnetic field is more
involved. First you will need to assign the field voltage at which your resonance peaks are
observed (If your spectrum has two peaks because of the phase shift problem, compute the
average of the field voltages.). Once you have assigned to field voltage for each resonance, you
can convert it to magnetic field strength using your calibration curve. Hence, you can make a
plot of the RF frequency versus the magnetic field strength. It is the slope of such a plot that
provides you with the value of g (see Equation 4).
g Value of Metal Complexes
You will find the effective g value of each complex by obtaining the center field value in
the spectrum and comparing it to DPPH. This analysis has two parts. First, you should find the
center field value by finding the average field between the two center peaks in the spectrum.
Second, you should compare this field value with the field at which the DPPH spectrum is
observed. The ratio of these fields and the g value of DPPH will provide the effective g value.
Items to include in your discussion
1. Explain why the spectra for the copper and vanadium complexes are different. In particular,
explain the splitting pattern observed for the two different complexes, the degree of peak
separation (coupling constant), and the relative intensities of peaks in a spectrum.
2. The g factor for a ‘free’ electron (one not perturbed by a local chemical environment) has a
value of 2.00232. The g value you measured for the coordinated compounds is probably
different from that of a free electron. What aspect in the coordinated compound significantly
affects the g factor and make it different from the free electron g value? Explain how this
specifically affected the g factors measured in each compound studied in this experiment.
3. Explain why the splitting of the electron spin energy levels is larger than that of the nuclear
spin sublevels, at the same magnetic field strength. What frequency would be required to
observe the proton NMR transitions of DPPH at your experimental magnetic field strength in
the Helmholtz apparatus? At the magnetic field strength of the Varian E-4 spectrometer?
4. Consider the DPPH spectra you obtained (on the Helmholtz apparatus and on the Varian E-4
spectrometer). For the highest magnetic field measurement on the Helmholtz apparatus,
compute the population difference between the two spin sublevels of the molecule. Perform
a similar calculation for these sublevels at the magnetic field strength of the spectrum which
you obtained on the EPR spectrometer. Why is this population ratio important when trying to
observe an EPR absorption spectrum?
16
References
Atkins, P. W. (1998). Physical Chemistry, 6th ed. New York: Wiley.
Wertz, J.E., Bolton, J.R. (1972). Electron Spin Resonance: Elementary Theory and Practical
Applications, New York: McGraw-Hill.
Drago, R.S. (1992). Physical Methods in Chemistry, 2nd ed. Philadelphia: Saunders.
Gersmann, H.R., Swalen, J.D. (1962). J. Chem. Phys. 36, 3221.
Rogers, R.N., Pake, G.E. (1960). J. Chem. Phys. 33, 1107.
Douglas, B., McDaniel, D., Alexander, J. (1983). Concepts and Models of Inorganic Chemistry.
New York: Wiley.
Ophart, E.O., Strupgia, S. (1984). J. Chem. Educ. 61, 1102.
Carrington, A., McLachlan, A.D. (1967). Introduction to Magnetic Resonance.
New York: Harper & Row.