A general measure of conjugation in biphenyls and their radical cations

Abstract

Changes in the amount of conjugation in the biphenyl system upon torsion have been investigated with quantum chemistry computations. For the unsubstituted biphenyl and its radical cation, the change in the energy for the first electronic transition as determined from time-dependent density functional theory, specifically TD-B3LYP, upon an imposed change in torsion angle appears to provide a good general measure of the delocalization of the π-electrons. Upon substitution, though, a relationship could not be established between the excitation energy and the twist across the C–C bond connecting the two phenyl rings. In contrast, the π-interaction energy, i.e., the π–π interaction across the central C–C bond, determined from a natural bond orbital analysis, provides a uniform description of conjugation in the electronically different systems, for an imposed twist as well as upon substitution. Substituent effects are found to be larger and more varied for the biphenyl radical cations. Of particular interest is the introduction of the oxidizable substituents OCH3 (methoxyl) and SCH3 (methylthio), as this leads to the smallest changes in torsion angle in the biphenyl unit upon removal of an electron from the molecule. The findings of this work could ultimately prove useful for the rational design of conductive polymer materials.