Hyperfme

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Thus, by measuring the intemiolecular vibrations of a WBC, ultimately with resolution of the rotational, tuimelling and hyperfme stmcture, the most sensitive measure of the IPS is accessed directly. The difficulty of measuring these VRT spectra is the fact that they lie nearly exclusively at THz frequencies. As expected, the stiffer die interaction, the higher in frequency these modes are found. In general, the total 0.3-30 THz interval must be accessed, although for the softest or heaviest species the modes rarely lie above 10-15 THz. 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

Hence, a measurement of hyperfme coupling constants provides infonnation on spin densities at certain positions in the molecule and thus renders a map of tlie electronic wavefiinction. 

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

The coupling constants of the hyperfme and the electron Zeeman interactions are scalar as long as radicals in isotropic solution are considered, leading to the Hamiltonian... 

ELDOR is tlie acronym for electron-electron double resonance. In an ELDOR experiment [28] one observes a rednction in the EPR signal intensity of one hyperfme transition that results from the saturation of another EPR transition within the spin system. ELDOR measurements are still relatively rare bnt the experiment is fimily established in the EPR repertoire. 

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

An alternative 2D ESEEM experiment based on the four-pulse sequence depicted in figure B 1.15.12(B) has been proposed by Meliring and coworkers [40]. In the hyperfme sublevel correlation (HYSCORE) experiment, the decay of the echo intensity as a fimction of is governed by -relaxation, whereas the echo decay along the t2-axis is... 

The ESEEM methods are best suited for the measurement of small hyperfme couplings, e.g. for the case of... 

Even for a single radical tire spectral resolution can be enlianced for disordered solid samples if the inliomogeneous linewidth is dominated by iimesolved hyperfme interactions. Whereas the hyperfme line broadening is not field dependent, tire anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

By examining the expression for Q ( equation (B1.16.4)). it should now be clear that the nuclear spin state influences the difference in precessional frequencies and, ultimately, the likelihood of intersystem crossing, tlnough the hyperfme tenn. It is this influence of nuclear spin states on electronic intersystem crossing which will eventually lead to non-equilibrium distributions of nuclear spin states, i.e. spin polarization, in the products of radical reactions, as we shall see below. 

Figure Bl.16.5. An example of the CIDNP net effect for a radical pair with one hyperfme interaction. Initial conditions g > g2, negative and the RP is initially singlet. Polarized nuclear spin states and schematic NMR spectra are shown for the recombination and scavenging products in the boxes.

Figure Bl.16.6. An example of CIDNP net effeet for a radieal pair with two hyperfme interaetions. Part A shows the spin levels and sehematie NMR speetnim for unpolarized prodnet. Part B shows the spin levels and sehematie NMR speetnim for polarized prodnet. Populations are indieated on eaeh level. Initial eonditions ...

Figure Bl.16.8. Example of CIDNP multiplet effect for a syimnetric radical pair with two hyperfme interactions on each radical. Part A is the radical pair. Part B shows the spin levels with relative Q values indicated on each level. Part C shows the spm levels with relative populations indicated by the thickness of each level and the schematic NMR spectrum of the recombination product.

DH has only one non-negligible hyperfme, = -1-19.0 G while D has two significant hyperfmes, = -13.96 G and = -1-19.24 G. Clearly, these two radicals will lead to very different polarizations in the CIDNP spectmm of both cage and escape products. 

As for CIDNP, the polarization pattern is multiplet (E/A or A/E) for each radical if Ag is smaller than the hyperfme coupling constants. In the case where Ag is large compared with the hyperfmes, net polarization (one radical A and the other E or vice versa) is observed. A set of mles similar to those for CIDNP have been developed for both multiplet and net RPM in CIDEP (equation (B1.16.8) and equation (B1.16.9)) [36]. In both expressions, p is postitive for triplet precursors and negative for singlet precursors. J is always negative for neutral RPs, but there is evidence for positive J values in radical ion reactions [37]. In equation (B 1.16.8),... 

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