Electron McConnell equation

There is a relationship (the McConnell equation) between the unpaired electron density on a given atom and the polarization interaction with each attached proton ... 

The external magnetic field Bq induces currents in bonds, lone pairs and inner shell orbitals of our molecular systems, and these currents are the source of the chemical shifts. Adopting the picture of localized bond orbitals, through-space contributions are caused by charge distributions of bonds that are not directly connected to the nucleus under consideration. Provided that the charge distributions are sufficiently far away so that their electron density in the vicinity of the nucleus can be neglected, this type of interaction can be approximated by the McConnell equation ... 

The McConnell equation (Equation 1.18) expresses the relationship of the observed coupling constant (an) to the unpaired spin population on the adjacent carbon atom (pc) The constant Q is different from one situation to another, but when an electron in a pz orbital on a trigonal carbon atom couples to an adjacent hydrogen, it is about -24 G. Applied to aromatic hydrocarbons, where it is particularly easy to generate radical cations and anions, there proves to be a good correlation between coupling constants and the calculated coefficients in the HOMO and LUMO, respectively.62... 

Spin densities (p) are theoretical quantities, defined as the sum of the squared atomic orbital coefficients in the nonbonding semi-occupied molecular orbital (SOMO) of the radical species (Hiickel theory). For monoradical species, the spin density is connected to the experimental EPR hyperfine coupling constant a through the McConnell equation [38]. This relation provides the opportunity to test the spin density dependence of the D parameter [Eq. (8)] for the cyclopentane-1,3-diyl triplet diradicals 10 by comparing them with the known experimental hyperfine coupling constants (ap) of the corresponding substituted cumyl radicals 14 [39]. The good semiquadratic correlation (Fig. 9) between these two EPR spectral quantities demonstrates unequivocally that the localized triplet 1,3-diradicals 9-11 constitute an excellent model system to assess electronic substituent effects on the spin density in cumyl-type monoradicals. 

The unpaired electron density (or spin density) in this equation is measured in units of electrons/volume. A related dimensionless quantity giving the probability of finding the unpaired electron at a specific atom is also commonly used employing the same symbol p and referred to as spin density . The McConnell equation [18] applying to the hyperfine coupling constant of an H atom in a n-electron radical, >Ca -H provides an example ... 

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)... 

Devaux et al. have described in some detail the use of the Bloch equations to relate electron spin-spin interactions between spin-labeled lipids to diffusion constants. This method was originally employed by Trauble and Sackmann,50 Scandella et al.,42 Devaux and McConnell,10 and Devaux et al.11 to measure diffusion constants in multibilayer model membranes and in biological membranes. In all cases diffusion constants of the order of those reported previously were obtained. 

Semiempirical VB and MO plus Cl calculations by McConnell and others yielded the following theoretical equation for aH, the coupling constant (in units of gauss) between the unpaired n electron and a ring proton of an aromatic radical18 ... 

A great deal of the electron resonance work has been done with aromatic radical ions, produced by adding or removing a tt electron from the neutral molecule by the action of a reducing or oxidizing agent.14 Correlation of data for many systems with molecular orbital calculations of v electron distributions has led to a quantitative expression, the McConnell relation (Equation 9.4), which... 

Equation (17) was put on a firm theoretical basis by McConnell and Chesnut (1958) but from their treatment it was not clear which excited states were primarily involved, nor to what extent Q might be expected to vary as the properties of the e-electrons in the C—H bond change. 

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