While a thorough understanding of quantum mechanics may be essential in order to understand the fundamental origin of the EPR signal it is not required to comprehend how EPR spectroscopy can be useful for the detection and quantification of free radical species and metalloprotein complexes in biological systems. As such (with apologies to my biophysics colleagues) here is a description of how EPR works.

Unpaired electrons are spinning charges (hence the preponderance of the word ‘spin’ in EPR) and a spinning charge generates a magnetic field. Consequently, each unpaired electron is a magnetic dipole (something like a tiny bar magnet with a ‘North’ and ‘South’ pole). Magnetic dipoles align themselves along magnetic fields (this is what makes a compass needle point to magnetic north) or stated another way; the presence of an external magnetic field creates a situation in which it is energetically favorable for the dipole to point in a particular direction. In order to rotate the dipole (rotate the compass needle away from pointing north) energy has to be applied. While it is possible to force a compass needle to any angle away from north and so generate a continuum of energetic states, the magnetic dipole of an electron can only take on two energy states (it is quantized). Consequently, the amount of energy required to flip the electron from its favorable direction to its unfavorable direction is a discrete value. It follows that if you supply this discrete amount of energy the system will absorb the energy as the electrons are flipped, and the detection of this absorbed energy is the basis of the EPR signal. For an electron in a magnetic field of about 0.35 T or 3500 G

^{1}, the energy required is in the X-band microwave range (about 9.5 GHz), and most spectrometers operate in this range (hence ‘X-band EPR’). The EPR spectrometer is basically a machine that shines microwave radiation on a sample and measures how much of that radiation is absorbed by the sample as a function of externally applied magnetic field. The fundamental equation of EPR spectroscopy is shown in

equation 1, where ν is the frequency of the microwaves,

*h* is Plank's constant, B is the external

magnetic field, β is another constant referred to as the Bohr magneton, and g is a dimensionless constant that is characteristic of the sample under study. To take an EPR spectrum, the microwave frequency (ν) is held constant and the magnetic field is swept across the desired range. When this equation is true (referred to as the resonance condition), energy will be absorbed. The detection of absorbed microwave energy as a function of magnetic field is referred to as the continuous wave EPR spectrum as shown in . There are two important things to notice about . First, there is no y-axis. The intensity of an EPR spectrum is measured on a machine-dependent arbitrary scale, and so the y-axis is usually omitted. Second, the spectrum is a first derivative. Due to the way the EPR spectrum is detected, the readout from the detector is a first derivative of the absorption spectrum. With modern computation power it is trivial to integrate this signal to get back to the absorption spectrum (), but the first derivative representation has become the standard way to present EPR data and most EPR spectra are presented in this format. For quantitative purposes, it is the area under the absorption spectrum () that is proportional to the number of unpaired electrons in the sample. As a result the first derivative spectrum needs to be integrated twice (once to get the absorption spectrum and once again to get the area under the absorption spectrum) and compared with a standard in order to determine the concentration of unpaired electrons. For accurate quantification it is important to use a stable radical standard that exhibits an absorption at a similar magnetic field (i.e. a similar g-value) to the sample.

Each feature of an EPR spectrum can be defined by a specific value of g (or ‘g-value’). As can be seen from

Equation 1, h and β are fundamental constants and ν is held constant for the experiment, and so H is inversely proportional to g. As H increases, g decreases. For this reason features at high magnetic field have low g-values and features at low magnetic field have high g-values. Although the g-value (or more correctly the g-tensor, as it is directional) is a fundamental property of the unpaired electron(s) under study, it is conventional to refer to parts of the EPR spectrum as (for example) the ‘g=6 region’ or the ‘g=2 region’. One g value that is of particular interest is that of the free electron, which has a value of 2.0023. The difference in g-value between an unpaired electron in an atom/molecule and the free electron can give important information about the magnetic properties of the microenvironment of the unpaired electron. The EPR spectrum also reports the presence of paramagnetic nuclei in the vicinity of the unpaired electron. Such nuclei (which include the proton, and the

^{14}N nucleus as the two most common in biological molecules) also have spin and are contain one or more tiny quantum mechanical magnets that can only point in one of two directions. So the presence of these nuclei can either add or subtract from the external magnetic field applied by the spectrometer. The result of this is that the actual magnetic field experienced by the unpaired electron may not be the field you apply but may be either more or less than this depending on orientation of the local magnetic nuclei. As an example, a proton nucleus in close association with the unpaired electron will have the effect of adding or subtracting from the magnetic field experienced by the electron. Due to the fact that approximately half of the magnetic dipoles generated by the protons will be aligned with the external field and half will be aligned against the field, the effect will be that about half of the unpaired electrons will experience a larger magnetic field and half will experience a lower magnetic field than expected. The result of this is that the resonance condition described by

equation 1 will be true at different values of H for these two populations and so instead of a single EPR feature there will be two of roughly equal intensity (). This effect is referred to as the hyperfine effect and is usually reported as the difference in magnetic field between the two EPR features (i.e. a

_{H}=6.2 G means that that the two EPR lines are 6.2 G apart and is referred to as the hyperfine splitting constant

^{2}). The g value, in this case, will be the point equidistant between the two EPR lines. The nitrogen nucleus is a slightly different case as each nucleus can be thought of as containing two of these tiny quantum mechanical magnets. Consequently you have three possible combinations of alignment that are approximately equally populated; namely both aligned with the field, both aligned against the field and one with and one against the field. In the latter case the contribution to the external field will be zero, and so the effect will be to generate 3 EPR features of equal intensity, with the middle one positioned at the g-value (). From this discussion it can be seen that a combination of magnetic nuclei will rapidly multiply the number of EPR features and this gives rise to complex hyperfine splitting patterns. For example 5 protons will give rise to 32 EPR lines some of which may completely or partially overlap. In order to aid interpretation of complex EPR spectra and also to help examination of situations where more than one radical species is present in the experiment, spectral simulation tools have been developed such as the WinSim program developed at NIEHS to analyze isotropic spectra [

1].

Both the g-value and the hyperfine splitting constants are tensors, in that they have a different value in every direction. If the molecule is freely diffusing, these values average out to single directionless values (referred to as the isotropic value). However, in frozen solution, the molecule orientations will be random and fixed, such that all possible values will be present in the spectrum (referred to as a powder spectrum). In this case, the g-value and the hyperfine constant are given as three orthogonal values in the x, y and z directions (e.g. g_{x}, g_{y} and g_{z}). In metal complexes, depending on the symmetry of the complex, the values in the x and y direction can be identical giving only two values that are referred to as g-perpendicular and g-parallel. These terms are often used to describe the EPR spectra of NO/metal complexes as will be seen later.

This background information is simplistic and incomplete but should be sufficient to understand the following discussion. For a more complete and robust description of EPR spectroscopy the reader is referred to the following texts [

2,

3].