In Parts I and II we only considered paramagnets with a single unpaired electron. Many important paramagnetic species have two or more unpaired electrons, e.g. transition ions and many photoexcited species. Here we consider spin triplet species (s = 1); these include, for example six-coordinate Ni(II) ions, optically excited aromatics, triplet carbenes, etc.
For an isolated s = 1 we have three sub-levels (ms = ±1,0; hence “spin triplet”). If these levels are degenerate in zero-field, then the Zeeman splitting will give rise to equidistant spacing of the levels and the two allowed EPR transitions (ms = -1→0 and 0→+1) will appear at the same field. However, in general this is not true and there is a zero-field splitting (ZFS). The origin of this is the electron-electron dipolar interaction and also spin-orbit coupling. We can introduce two ZFS parameters, D and E (axial and rhombic, respectively). The D parameter has the effect of splitting the states in zero-field according to ms2D. Hence, ms = ±1 and 0 are separated by D in zero-field. The Zeeman splitting now looks like:
and the two EPR transitions are separated by a function of D in field units. This is the “fine structure” in EPR spectra. This tends to be dominant over hyperfine structure (hence the name) because of the electron’s large magnetic moment. For axial symmetry E = 0. In rhombic symmetry non-zero E can mix states differing by ms = ±2; for the triplet this means mixing (hence splitting) ms = ±1 in zero-field.
The picture above is for a single orientation. ZFS is inherently anisotropic: typical powder patterns for axial and rhombic spectra are shown below together with their zero-field level spacings.
These spectra are for the situation where hυ >> |D|. When this condition is not fulfilled, then very different spectra may result or it is even possible that no spectrum is observed at all (e.g. if hυ << |D| for a triplet, it may not be possible to excite an allowed EPR transition in the available field window). This is a good reason for measuring EPR spectra of such species at higher frequencies.
The spin triplet arises in the first place from the exchange interaction between the two unpaired electrons. In species where the two electrons are constrained to the same paramagnetic centre (as in the examples above), the exchange interaction is extremely strong, giving the triplet as the ground state (by Hund’s rule) and a singlet state many thousands of cm-1 away (possibly detectable by optical spectroscopy). If the two electrons belong to different paramagnetic centres, e.g. radical dimers, then J can often be determined by magnetometry. Under favourable circumstances J can be determined by EPR, for example, via variable temperature (Boltzmann) effects on the singlet and triplet populations, or where J is of the same magnitude as hyperfine splitting causing singlet – triplet mixing and new transitions in the spectra.
A hugely important application of modern EPR is distance determination between distant spin labels via their weak dipolar interaction (and where the exchange is negligible). Because of the large electron magnetic moment, such distances can be measured by pulsed EPR methods up to ca. 8 nm.