One-Electron Rotatory Power

Abstract

It is shown that a single electron moving in a field of suitable dissymmetry can give rise to optical rotatory power in a medium containing molecules of this type. This effect is called one‐electron rotatory power and is in striking contrast to the models developed by Born, Oseen, Gray and others in which a dynamic coupling between several electronic oscillators is responsible for the rotatory power. The detailed calculations are carried out for the potential function, $$\mathrm{V=}\frac{1}{2}{\mathrm{(k}}_1{x}^2{\mathrm{+k}}_2{y}^2{\mathrm{+k}}_3{z}^2\mathrm{)+Axyz,}$$ which shows rotatory power both quantum mechanically and classically. Next it is shown how fields of this type may be adapted to an approximate description of the field in which the chromophoric electrons of a molecule move, the constants k₁, k₂, k₃ and A being largely determined by the average charge on the different atoms of the molecule as found from additivity of dipole moments due to the bonds in the molecule. As illustrations of the theory absolute calculations are made for the contribution of the nitrite group to the rotatory power of methyl phenyl carbinol nitrite which agrees satisfactorily with experimental data, for the phenyl group contribution of the same molecule and for the hydroxyl group contribution in secondary butyl alcohol. In the latter two instances the theoretical values are much too small but as there is a great deal of freedom in the choice of the configuration because of free rotation these results merely indicate need for more detailed calculations. The general quantum‐mechanical theory of circular dichroism is developed and a quantum‐mechanical derivation of Natanson's rule is given. The quantum‐mechanical definition of Kuhn's ``anisotropy factor'' is given and an alternative measure of the contribution of an absorption band to rotatory power called the rotatory strength is defined and discussed. It is shown that spin magnetic moments may generally be neglected in calculation of rotatory power owing to the weakness of spin‐orbit interaction. Interpretation of experiments of Schwab, Rost and Rudolph on the catalytic dehydration of butyl alcohol on active quartz is discussed and kinetic arguments advanced to show how the relative configuration of quartz and butyl alcohol may be inferred from such data. The relation of one‐electron rotatory power to known dipole moment and solvent effects on rotatory power is briefly discussed.