Higher-order sum rules for rotatory strengths

Abstract

Higher-order sum rules of the form , are derived for the rotatory strengths of randomly oriented and oriented molecules. In randomly oriented molecules R (n) = 0 for one-electron systems when n<5, whereas R (0)=R (2)=R (4)=0 for many-electron systems. In oriented molecules R (n)=0 for one-electron systems when n<3, whereas R (0)=R (2)=0 for many-electron systems. The remaining non-vanishing R (n) can all be evaluated as diagonal matrix elements of the ground-state wave-function. The resulting expressions are applied to the one-electron model of Condon, Altar and Eyring, and to the coupled oscillator model of Born, Oseen and Kuhn. It is found that the rotatory strengths of the latter model do not fulfil some of the general sum rules. The reason for this discrepancy is discussed. Finally the implications of the present results for the controversy of one-electron versus coupled oscillator models are discussed, and it is proposed that the non-vanishing moments be used as ‘chirality indices’ for specific groun...