Electron-Nuclei Hyperfine Coupling Constants

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

In order to explain qualitatively how CIDNP arises, the simple case of a radical pair in which only one component contains a nucleus (spin J) coupled to an electron (spin through a hyperfine coupling constant will be considered. 

Once a description of the electronic structure has been obtained in these terms, it is possible to proceed with the evaluation of spectroscopic properties. Specifically, the hyperfine coupling constants for oligonuclear systems can be calculated through spin projection of site-specific expectation values. A full derivation of the method has been reported recently (105) and a general outline will only be presented here. For the calculation of the hyperfine coupling constants, the total system of IV transition metal centers is viewed as composed of IV subsystems, each of which is assumed to have definite properties. Here the isotropic hyperfine is considered, but similar considerations apply for the anisotropic hyperfine coupling constants. For the nucleus in subsystem A, it can be... 

The electron spin resonance (E.S.R.) spectra of a paramagnetic organic molecule, e.g. free radical, radical cation or radical anion, is directly related to its unpaired electron distribution (spin density). In the region of a magnetic nucleus the hyperfine interaction between the magnetic moments of the nucleus and the electron is a function of the spin density. It has been shown that, for an atom N, a direct correlation exists between its observed hyperfine coupling constant, and [pa—pP), the unpaired electron population of its atomic orbitals 1). 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

This hyperfine coupling is of two kinds An isotropic interaction arises from the possibility that the electronic wave-function, x , be non-zero at the nucleus, N. This is the Fermi contact term and the hyperfine coupling constant is given by ... 

Fig. 3. First derivative electron spin resonance spectra. (A) ESR spectrum of an unpaired electron. (B) ESR spectrum of an unpaired electron interacting with a nitroxide resulting in a nitrogen hyperfine coupling constant aN. (C) ESR spectrum of an unpaired electron interacting with a H nucleus and a l4N nucleus as is typical for PBN radical adducts. (D) ESR spectrum of an unpaired electron interacting with the l3C nucleus, the H nucleus and the 14N nucleus of the trichloromethyl radical adduct of PBN, where the carbon tetrachloride was labeled with 13C.

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