Electron paramagnetic resonance (EPR)

Introduction to technique:

• The theory of EPR can be found in any number of textbooks, including ones by Drago [R.S. Drago, Physical Methods for Chemists, HBJ Publishing, Ft. Worth, TX, 1992], Abragam [A. Abragam, Electron Paramagnetic Resonance of Transition Metal Ions, Oxford, Clarendon Publishing, New York, 1970], and more recently, Solomon and Lever [A. Bencini, D. Gatteschi, in: E.I. Solomon, A.B.P. Lever (Eds.), Inorganic Electronic Structure and Spectroscopy, vol. 1, Wiley, New York, 1999, p. 93].
• EPR spectroscopy examines the transitions between electron spin states separated by the presence of an external magnetic field. These states are separated by an energy dependent on the g value of the observed species (for the theoretical ‘free’ electron, g=2.0023) and the magnetic field applied, as shown in Fig.1 

Figure. 1.         The spin state transitions observed in the EPR are shown here for a system with both electron spin S=1/2 and nuclear spin I=1/2.

• Values of g in vanadyl EPR spectra are typically less than the free electron value, usually ca.1.95.
• The transition is induced by microwave radiation of frequency υ, such that hυ=gβH, where h is Planck’s constant, β is the Bohr magneton, and H is the magnitude of the applied field.
• Note that unlike NMR, in the EPR experiment, the frequency is held constant, and it is the strength of the magnetic field, which is varied. These electronic states are then split by their interaction with the spin of the nucleus—termed hyperfine coupling.
• For the case of vanadium(IV), the nuclear spin of 51V is I=7/2, so the states are split into 2I+1=8 different energy states each, separated by the hyperfine coupling constant, A. Almost all (>99%) vanadium is 51V, so there are no additional isotopes with nuclear spin to complicate the spectrum. Further splitting of states by nearby nuclei, such as 14N is referred to as superhyperfine coupling. For the vanadyl case, due to the electron residing in a σ-non-bonding orbital pointing away from the ligands in the equatorial (xy) plane, superhyperfine coupling to nitrogen-containing ligands is not resolved in a typical X-band (9 GHz) EPR spectrum. Therefore, there is no additional splitting of the EPR absorption. EPR transitions are electronic in nature,
• Selection rules can be expressed as ΔMs = ±1, ΔM_I = ±0, as shown in Fig. 1. For a vanadium(IV) complex, this gives rise to an eight-line spectrum.