McConnell relation

The simplest theoretical orbital-based estimate of the coupling interaction, is provided by the McConnell relation ... 

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... 

For 7r-conjugated hydrocarbon radicals, it is well known that the HFC constant of a hydrogen, aH, is proportional to the spin density of nr orbital on a carbon atom bonded with the hydrogen atom, pc, which is the so-called McConnell relation ... 

Theoretical Calculations. According to the McConnell relation, Eq. (9), the proton hyperfine sphtting constants are proportional to p , the unpaired tt electron density of the carbon atom bonded to the proton. Using quantum mechanics p can be calculated at different levels of approximation. The approach outlined here is one of the simplest, the Hiickel molecular orbital (HMO) method. This model assumes that a tt molecular orbital, delocalized over n atoms, can be written as a hnear combination of n atomic orbitals (z is perpendicular to the molecular plane). 

For the benzosemiquinone radical anion, one has nine tt electrons, with two each in the fonr lowest levels and the nnpaired electron residing in 5. Using the HMO resnlts in the tables, calcnlate p for the carbons attached to the protons and compare with the valnes obtained from your experimental results and the McConnell relation [Eq. (9)] with Q = -22.5 ganss. Note that the calculations provide a basis for assignment of the hyper-fine splitting constants to specific ring protons in orfAo-benzosemiqninone. Draw out the possible valence-bond resonance structures for both ortho and para compounds and dis-cnss the relative importance of these. 

C. Spin-Density The Semi-Empirical McConnell Relation... 

The values of the hyperfine coupling constants are collected in Table 1. Because the hfs constants for aromatic protons are proportional to the spin densities at the adjacent carbon atoms through the McConnell relation,8 these values provide a clear-cut picture of the spin density distribution within the molecular framework of radical cation l+ The hfs constants for the nitrogen atoms should reflect, besides the spin density at the nitrogen atom itself, the spin density at the adjacent atoms as well as the nature of their bonds to the nitrogen.7... 

And finally, these lines will be seen to be further split by the three methyl protons into 1 3 3 1 quartets with splittings 1.045 mT. Note that the McConnell relation cannot be applied to calculate these latter splittings, but the software generates them directly from calculated spin densities on the methyl hydrogens. The computed splittings agree well with experiment at the ortho positions (0,60 mT) and at the methyl hydrogens (1.19 mT), but less well at the meta positions (0.145 mT). 

The McConnell relation does not provide quantitative estimates of electronic propagation because (a) it does not include the influence of antibonding orbitals, (b) it neglects through-space nonnearest neighbour interactions, and... 

The origin of the proton hyperfine splitting in the ESR spectra of hydrocarbon radicals can be explained by quantum-mechanical calculations. These results give rise to the well-known McConnell relation [2]... 

The n-electron spin density p(C) at the carbon atom can be estimated from the measured coupling constant of the adjacent H atom by the McConnell relation. 

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