VIBRONIC THEORY OF CIRCULAR DICHROISM

The effect of molecular vibrations on optically active absorption bands is treated by assuming a total wavefunction of the form ψ(Q) χ(Q-Q̄), where ψ(Q) is the electronic wavefunction with the normal coordinates as parameters and χn (Q-Q̄) is a harmonic oscillator function in the nuclear coordinates. The electric and magnetic dipole moments of a transition G→A are determined as functions of Q, μGA(Q), MAG(Q). The rotational strength for the 0-n vibrational mode, 0(QG) |μGA(Q)| χn(Q A)〉 〈χn(QA) |MAG(Q) |χ0(QG) 〉, is evaluated by expanding μGA(O) and MAG(Q) as a power series in Q about the conformation of zero rotation. Formulas are obtained which indicate the possibility of several sign changes within a nondegenerate absorption band. The theory shows that these sign changes are possible not only for multiply excited vibrational modes but for those of a single symmetry as well.