Hyperfine multiplet

Measurements by photographic photometry require careful calibration due to the nonlinear response of photographic plates saturation effects can lead to erroneous values. Line profiles can be recorded photoelectrically, if the stability of the source intensity and the wavelength scanning mechanism are adequate. Often individual rotational lines are composed of incompletely resolved spin or hyperfine multiplet components. The contribution to the linewidth from such unresolved components can vary with J (or TV). In order to obtain the FWHM of an individual component, it is necessary to construct a model for the observed lineshape that takes into account calculated level splitttings and transition intensities. An average of the widths for two lines corresponding to predissociated levels of the same parity and J -value (for example the P and R lines of a 1II — 1E+ transition) can minimize experimental uncertainties. A theoretical Lorentzian shape is assumed here for simplicity, but in some cases, as explained in Section 7.9, interference effects with the continuum can result in asymmetric Fano-type lineshapes. 

Figure 2. Derivative spectrum of N2 in irradiated Ba(N3)2, showing hyperfine multiplet of five lines spaced 20 gauss apart. The arrows indicate sateUite lines of unexplained origin.

Before the advent of magnetic resonance spectroscopy, nuclear spins and moments were determined almost entirely by optical spectroscopy. When a hyperfine multiplet is observed with good resolution, the value of the nuclear spin / is obtained immediately from the multiplicity, provided that / < J. In practice, the resolution has proved to be adequate for the stable isotopes of odd Z, that are all odd-proton isotopes Tb, Ho and Tm (each 100% abundant) La,... 

We shall briefly review the relationship between spectroscopic observables and nuclear properties/ These properties include spins, magnetic dipole and electric quadrupole moments, as well as the variation in the mean square charge radius within a sequence of isotopes. They manifest themselves in the hyperfine structures and isotope shifts. The hyperfine energies of the different F states within a hyperfine multiplet / - / F J + I, given by the well-known formula... 

Local fields at the site of the observed electron spin Nare induced by nuclear spins and other electron spins in the vicinity. The nuclear spins are much more abundant and are usually of more interest. The h5q>erfine coupling to a nuclear spin / results in a local field that is proportional to the magnetic quantum number mi, so that each level with magnetic quantum number ms splits into 2/ -h 1 hyperfine sublevels. Accordingly, each allowed EPR transition with Anis = 1 splits into 21 + 1 transitions that give rise to the lines of a hyperfine multiplet. The hyperfine coupling consists of the Fermi-contact contribution caused by spin density of the electron at the site of the nucleus and a dipolar contribution that acts through space. As only orbitals have nonzero spin density at... 

The direct observation of hyperfine resonances of the T7 ground state of isotopically enriched Er in a powdered gold matrix was reported by Sjostrand and Seidel (1975). In weak external fields for 5=2 and / =, two hyperfine multiplets, F=3 and 4, are expected. The appropriate isotropic spin Hamiltonian is given by... 

The tliree-line spectrum with a 15.6 G hyperfine reflects the interaction of the TEMPO radical with tire nitrogen nucleus (/ = 1) the benzophenone triplet caimot be observed because of its short relaxation times. The spectrum shows strong net emission with weak E/A multiplet polarization. Quantitative analysis of the spectrum was shown to match a theoretical model which described the size of the polarizations and their dependence on diffrision. 

The remainder of equation (38) describes the multiplet effect, and it can be seen that whether an individual line in the multiplet corresponds to emission or absor ption depends on the signs of the hyperfine coupling constants but is independent of Hq. The nature of the hyperfine field is such that the integral over the whole multiplet is zero if Ag = 0. 

Pulse techniques, coupled with the observation of the decay of enhancement (Atkins et al., 1970a, b Glarum and Marshall, 1970 Smaller etal., 1971) constitute the most sensitive procedure for detecting CIDEP. Both net and multiplet polarization have been described. As with CIDNP, the former is believed to arise essentially from the Zeeman interaction and the latter from the hyperfine term. Qualitative rules analogous to Kaptein s rules should be capable of development. 

Nuclear hyperfine coupling results in a multi-line ESR spectrum, analogous to the spin-spin coupling multiplets of NMR spectra. ESR spectra are simpler to understand than NMR spectra in that second-order effects normally do not alter the intensities of components on the other hand, ESR multiplets can be much more complex when the electron interacts with several high-spin nuclei, and, as we will see in Chapter 3, there can also be considerable variation in line width within a spectrum. 

When several magnetically equivalent nuclei are present in a radical, some of the multiplet lines appear at exactly the same field position, i.e., are degenerate , resulting in variations in component intensity. Equivalent spin-1/2 nuclei such as 1H, 19F, or 31P result in multiplets with intensities given by binomial coefficients (1 1 for one nucleus, 1 2 1 for two, 1 3 3 1 for three, 1 4 6 4 1 for four, etc.). One of the first aromatic organic radical anions studied by ESR spectroscopy was the naphthalene anion radical,1 the spectrum of which is shown in Figure 2.2. The spectrum consists of 25 lines, a quintet of quintets as expected for hyperfine coupling to two sets of four equivalent protons. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

The multiplet hyperfine pattern of ESR lines in organic radicals is most frequently due to electron-proton interactions, but other nuclei with nonzero spin may also cause hyperfine structure. Weak satellite lines arising from interactions between the unpaired electron and C13 nuclei are sometimes observed C13 has and the analysis is straightforward. Nitrogen-containing radicals may show hyperfine splittings due to N14, which has 7 1. The possible Mj values are 1, 0, and -1, so that an electron... 

A seven-line like signal was detected from carboxymethyl cellulose irradiated with ultraviolet light of 254 nm (Figure 7). When this sample was warmed to ambient temperature for 60 seconds, this multiplet spectrum was transformed rapidly into a prominent doublet signal with a hyperfine splitting constant of 20 gauss. This indicated that the primary free radicals... 

Holmium has a nucleus with 7 = 7/2 spin in a natural abundance of 100%. Each sublevel of the J = 8 ground multiplet is split into an octet by the hyperfine interaction between the (4/)10 system and the nucleus. All observed step positions are... 

The data show that the quadmpole hyperfine patterns of the rotational transitions are different between the two states, due to changes of the relative positions of some of the hyperfine components within the multiplet. The rotational spectrum of a pyrrole dimer is consistent with essentially a T-shaped structure, in which the planes of the two pyrrole monomers form an angle of 55.4(4)° and the nitrogen side of one ring is directed to the 7t-electron system of the other ring establishing a weak H bond <1997JCP504>. 

---