Electron density, delocalization

The increase of the exocyclic C—C bond stretching frequency from 1208 cm in toluene to 1264 cm in the benzyl radical and the simultaneous decrease of the C—C ring bond stretching frequencies (from 1494 and 1460cm to 1469 and 1446cm , respectively) result from electron density delocalization in the benzyl system. Furthermore, the force constant value for the C—C bond in the C6H5CH2 radical (5.5 X 10 N m ) is between the values for the ordinary C—C bond (4.5 x 10 N m ) and the double C=C bond (9.0 X 10 N m ) and is close to the corresponding force constant in the allyl radical (5.8 x 10 N m ). 

The X-ray and neutron diffraction data mentioned previously have been used in conjunction with the technique of polarized neutron diffraction (at 4.2 K) to deduce spin-density distributions in [MnPc].519,520 In further investigations514 it proved possible to determine individual 3d and 4s orbital populations on the manganese ion together with an estimate of 24% for the d-orbital electron density delocalized in the macrocyclic ring. From these studies it appears that the charge on the manganese is approximately +1 this charge appears to be achieved primarily by the loss of a 3d electron rather than a 4s electron. 

Native lignin arises via an oxidative coupling of the aforementioned alcohols with each other and (more important) with a growing polymer end unit. The oxidation produces a phenolic radical with unpaired electron density delocalized to positions... 

These models were developed with respect to the metal-centered breathing modes (analogous to combining Limits 1 and 2 so that = ( ml + "mb))- The electron density delocalized, in an adiabatic description of the reaction coordinate, is a minimum at the PE minima and a maximum at the transition state, and consequently the electronic coupling matrix element in the adiabatic description is a function of the reaction coordinate (/ da = aO- This deseription can be transformed into a diabatic description in which the electronic coupling, /da, is independent of the nuclear coordinates. In the diabatic description, the PE is a linear (i.e., dPEjdr f 0), as well as quadratic function of the reaction coordinate and the diabatic potential can be written. 

The simplest MOs are constructed using the LCAO (linear combination of atomic orbitals) method introduced by Eq. 4.25, adding atomic orbital wave-functions centered on different nuclei in different proportions to obtain one MO wavefunction, often with the electron density delocalized across several nuclei. Extended to several nuclei, Eq. 4.25 becomes... 

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