Hyperfine coupling constants hydrogen

Table 18.2 Hyperfine coupling constant for a hydrogen atom when the Is orbital is represented as an uncontracted sum of n primitives...

Here, /3 and / are constants known as the Bohr magneton and nuclear magneton, respectively g and gn are the electron and nuclear g factors a is the hyperfine coupling constant H is the external magnetic field while I and S are the nuclear and electron spin operators. The electronic g factor and the hyperfine constant are actually tensors, but for the hydrogen atom they may be treated, to a good approximation, as scalar quantities. 

Arnold s o -scaIe (Arnold, 1986 Dust and Arnold, 1983 Wayner and Arnold, 1984), which reflects the spin-density distribution in meta- and para-substituted benzylic radicals and leads to parameters similar to those derived from other sources (Jackson, 1986), provide a good example. Arnold s scheme is based on the hypothesis that hyperfine coupling constants of the a-hydrogen in substituted benzylic radicals give information regarding the effect of substituents on the distribution of spin throughout the radical and that this is connected with the stability of the benzylic radical. 

Arnold s scale is derived for the action of a single substituent on the benzylic 7c-system. It cannot be used to estimate the influence of several substituents on the system under consideration. In this way it is, therefore, not possible to gain insight into the problem of captodative stabilization of a radical centre. The investigation of the spin-density distribution in benzylic radicals has been extended (Korth et al., 1987) to include multiple substitution patterns. Three types of benzylic radicals were considered a,p-disubsti-tuted a-methylbenzyl radicals [17], a-substituted p-methylbenzyl radicals [18] and a-substituted benzyl radicals [19]. In [17] and [18] the hyperfine coupling constants of the methyl hydrogens were used to determine the spin-density... 

This property of the — SiMes group has also been quite clearly demonstrated in an extremely elegant manner by Bedford et al. (77). It has been amply demonstrated that in an electron spin resonance spectrum the isotropic hyperfine coupling constant, an, of a hydrogen atom attached to an sp2 hybridised carbon atom having an unpaired electron in the 2p—orbital is given approximately by an Equation (3) due to McConnel (18)... 

We have also performed the calculation of hyperfine coupling constants the electric quadrupole constant B and magnetic dipole constant A, with inclusion of nuclear finiteness and the Uehling potential for Li-like ions. Analogous calculations of the constant A for ns states of hydrogen-, lithium- and sodiumlike ions were made in refs [11, 22]. In those papers other bases were used for the relativistic orbitals, another model was adopted for the charge distribution in the nuclei, and another method of numerical calculation was used for the Uehling potential. 

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