Isotropic EPR spectra (X-band, 9.5 GHz) ?

EPR spectrum of methyl radical CH3.
Data are from F. Gerson, W. Huber, Electron Spin Resonance Spectroscopy of Organic Radicals, Wiley-VCH: Weinheim, 2003, Ch. 7.
The structure of TEMPO is shown below.

Data are from ...
The structure of the hydrogen adduct of spin trap DMPO is shown below. The nuclei participating in hyperfine interaction are highlighted in red.

Data are from Spin Trap Database, ref. 963.
One fo the resonance structures of the methyl viologen radical cation is shown below. The sets of non-equivalent nuclei participating in hyperfine interaction are highlighted in different colours.

Data are from W. R. Dunham, J. A. Fee, L. J. Harding, H. J. Grande, J. Magn. Reson., 1980, 40, 351.
Take-home message: 1st derivative spectra in general show better resolution than 1st integral spectra, which is very convenient in EPR, as we often have to deal with overlapping lines.
EPR lines have a Voigt shape which in simple terms is a mixture of a Gaussian and a Lorentzian shape. The exact shape depends on the structure of the radical and the experimental parameters.

Lorentzian shape has very wide wings. The spectrum on the screen seems to be well contained within the plot boundaries. Click on the "2nd integral" button to bring up the green trace. Look at the Y axis - it should go to 100 for the full peak, but it only reaches ca. 95. This means that 5% of the peak is outside the plot boundaries.

Untick the "Separate Y axes for saved spectra" button. Click on the "Save this spectrum?" button and then click and hold the down triangle on the "% Lorentzian" box. You will see the red peak getting taller and narrower. When you get to the purely Gaussian shape ("% Lorentzian" = 0), you will see that the spectrum lost its long wings and is completely contained within 3389 - 3391 G region. Its double integral trace is steep and you can now clearly see that the blue trace for Lorentzian peak is lower than the green one for the Gaussian peak. This is because Lorentzian peaks are extremely wide, and one has to integrate a very wide spectrum to measure their intensity fully.

Take-home message: Lorentzian lines have much wider wings than the Gaussian lines of the same width.
Take-home message: Height of EPR peaks could be misleading! It is very difficult to compare EPR intensities of peaks with different line width, for instance, peaks of different radicals.
The number of lines in the EPR spectrum is 2nI+1, just like in the NMR. Here n is the number of equivalent nuclei and I is nuclear spin. Let's check how this works.

We will start with just one nucleus. Click "Add nucleus" button. You see two lines of equal intensity - this is because we have one nucleus with spin I = ½. Now click on the "Nuclear spin" box and choose the value "1.5". You see 2×1.5 + 1 = 4 lines of equal intensity. Try other spin values!

Set the nuclear spin back to I = ½ and choose 3 as the "No of equivalent nuclei". You will see a 1:3:3:1 quartet which is consistent with the formula: 2×3×½ + 1 = 4 lines. Choose other values of equivalent nuclei and other spin values. For I = ½, the relative intensities are described by the Pascal triangle.

Take-home message: The number of lines in EPR spectra is determined by the 2nI+1 formula. Hyperfine interaction with one nucleus gives lines of equal intensity, interaction with a set of several equivalent nuclei gives a multiplet with lines of different intensities.
What determines the relative intensities in the EPR multiplets? Let's do an experiment. Click on the "Add nucleus" button. You see how one line got split into a doublet from the hyperfine interaction of unpaired electron with one I = ½ nucleus. Set line width to 0.05 G, and click "Save this spectrum?" button.

Now add another nucleus, and set the hyperfine of this second nucleus to 4.8 G. You now see how each of the two components of the orange spectrum again got split into a doublet. The inner lines of the two new doublets are very close to each other; set the hyperfine back to 5 G to see how they overlap to give one line of double intensity. This is how we get the 1:2:1 triplet.

Click "Delete saved spectra" button, then "Save this spectrum?" button again, add another nucleus and set its hyperfine to 4.8 G. You see how each component of the orange triplet gets split into new doublets. The smaller orange lines at the ends gave smaller red doublets, and the bigger orange line in the middle gave a bigger red doublet. Set the hyperfine back to 5 G and see how the lines overlap to yield a 1:3:3:1 quartet.

Take-home message: To calculate the intensities of the lines in a multiplet, consider splitting from equivalent nuclei one by one, and count the intensities of the overlapped components.
Hyperfine constants are the differences between energy levels for EPR transitions. Strictly speaking, hyperfine constants should therefore be given in energy units. It is however more conventional to quote them in frequency (e.g., MHz) or wavenumber (e.g., cm-1) units.

If the hyperfine constants are small (which is often the case for organic radicals), the hyperfine interaction splits EPR signals into a set of equidistant lines with the the distances between the lines equal the hyperfine constant. Therefore, small hyperfine values are often quoted in the field units (e.g., G or mT). This is how they can be directly read from the spectra:

Click on "Examples" button and choose the spectrum of methyl radical. You see four equidistant lines. Click the mouse at the position where the first peak crosses the zero point on the Y axis. Now shift the mouse to the position where the 2nd line crosses the zero point. The distance between the lines (Δx) is displayed on the blue background in the top left corner of the spectrum. It should match the value of the hyperfine given in the parameters above the spectrum (23 G). Use the hν = gμBB equation to convert this value into other units, you should get around 64.5 MHz or 0.00215 cm-1.

Take-home message: Relatively weak hyperfine interaction splits EPR signal into a set of equidistant lines. The distance between them equals hyperfine constant. The distance is measured between the positions where the 1st derivative lines cross the zero point on the Y axis.
For isotropic spectra, g factor is at the very centre of the spectrum. You can convert the position in the magnetic field units into g factor by using the following equation:

hν = gμBB

Here h is the Planck's constant, ν is microwave frequency, g is g factor, μB is the Bohr magneton, and B is the magnetic field. Make sure you use the same magnetic field units for Bohr magneton and magnetic field. You can convert G into T as 1 T = 10000 G. Frequency units should also match the Planck's constant units.

Load any of the example spectra on this page (click Examples button), bring the mouse cursor to the centre of the spectrum, make note of the field position (you can zoom in by dragging the mouse in the spectrum), and of the g factor which is shown in the top left corner of the spectrum. Use the above equation to calculate your own g value from the field position and see if it matches the shown value. The value should also match the giso value in the spectrum parameters above the spectrum.

Take-home message: g factor is at the centre of the EPR spectrum of a given radical.
Many EPR spectra present complex patterns. The analysis is not straightforward, particularly if more than one component is present. Sometimes some smaller features are not recorded. For instance, click on the "Examples" button and choose the methyl viologen radical cation. A spectrum like this will be difficult to analyze! Note that some features at both ends of the spectrum are hardly visible. Zoom in at either end and you will find a small singlet peak, then a doublet, then a triplet, and then things get complicated. If the spectrum had been noisy, these lines would have been easily overlooked.

Spectrum analysis usually starts from the end of the spectrum. The spectra should be symmetrical (if only one component is present) so it does not matter which end you start from.

Let's illustrate spectrum assignment using an example. Click on the "Examples" button and load the spectrum of DMPO-H spin adduct. Start analysing at the left edge of the spectrum. You see one line, and then another line of the same intensity. Measure the distance between them (left-click at the first peak, and move the mouse to the second, the distance will be shown on a blue background in the top left corner), it should be 16.6 G. Several lines with the same intensity come from a hyperfine interaction with one nucleus. Are there other lines? Measure out 16.6 G from the second line and you will find another line. Measure out yet another 16.6 G and you will not find any further lines. So, this component is a 1:1:1 triplet and according to the 2nI+1 rule, it comes from one nucleus with I = 1.

Sometimes lines overlap, and this changes relative intensities - but the distances between the lines are not affected.

What else do we see in the spectrum? There are three higher intensity lines in the middle, the distance between them is also 16.6 G (check this!), so this is a second 1:1:1 triplet. Finally, there are three remaining lines on the right, again with 16.6 G separation - the third 1:1:1 triplet. So we have three 1:1:1 triplets, with the one in the middle twice as intense as the ones at the ends, e.g., they are in a 1:2:1 ratio. According to the 2nI+1 rule, this ratio corresponds to two equivalent nuclei with I = ½. To measure the hyperfine constant for this interaction, you need to measure the distance between the components of the 1:2:1 triplet, e.g., the distance from the 2nd small line (the centre of the first 1:1:1 multiplet) and the second large line (the centre of the second 1:1:1 multiplet). You should get 22.5 G.

Take-home message: Complex spectra are difficult to analyse! Start from the side and look for patterns of equidistant lines. Do not forget that lines can overlap.
The orange line is the EPR spectrum of ethyl radical CH2CH3. Let's simulate it! Data are from F. Gerson, W. Huber, Electron Spin Resonance Spectroscopy of Organic Radicals, Wiley-VCH: Weinheim, 2003, Ch. 7.