Differential polarization of spin and charge density in substituted phenoxy radicals

We have carried out a theoretical study of a series of para-substituted phenoxy radicals in an effort to understand the factors influencing spin and charge density distribution in open-shell systems. The calculations reveal that the distribution of spin and charge are not correlated: cases were found for which spin and charge move together, whereas for other substituents the two quantities exhibit spatially distinct intramolecular polarizations. Charge density variations across the series were found to correlate well with both the Hammett (sigma(p)) and Hammett-Brown (sigma(p)+) constants for each substituent, indicating that inductive and/or resonance effects are primarily responsible for the polarization of charge within the molecule. In contrast, the distribution of unpaired spin density could not be adequately accounted for using any of the typical Hammett-type spin delocalization constants cited in the literature. We uncovered an empirical correlation between the polarization of spin density and the alpha-HOMO-alpha-LUMO gap of the substituted phenoxy radicals: this led to the development of a simple model based on a three-electron, two-orbital bonding scheme in which mixing between the HOMO of the substituent and the SOMO of the phenoxy moiety serves to define the nature and extent of unpaired spin polarization throughout the molecule. This analysis yielded a correlation coefficient of r > 0.97 for the 15 substituents examined in the study; spin polarization effects in compounds that exhibited the greatest deviation from this correlation could also be readily explained within the context of the model. The underlying reason for the ability to differentially polarize spin and charge likely stems from the fact that net unpaired spin density is completely carried by the unpaired electron (and thus tracks the spatial characteristics of the SOMO), whereas charge density reflects the behavior of all of the electrons of the system. These results could have implications in the field of molecular magnetism, suggesting a means for synthetically tuning the magnitude of intramolecular exchange interactions, as well as providing guidance for the design of catalysts for radical-radical coupling reactions.