Optical activity of oriented molecules III. The absorption process and the vibrational coupling effects for the tensor of rotation

Equations for the rotation and the ellipticity of samples exhibiting linear and circular birefringence and dichroism (i.e. for small elliptical birefringence and dichroism) are given. By this a second presentation of the frequency dependence for linear and circular birefringence of anisotropic solutions is developed. The absorption coefficients of anisotropic solutions for linearly polarized light are calculated from the H-matrix of Gō. For a special type of orientational distribution function the absorption behaviour is analysed. Within the adiabatic approximation and by neglecting the variation of the electronic transition moments with the nuclear distances, the structure of a circular dichroism band is independent of the orientational distribution function. Empirically, this is not the case for α, β-unsaturated keto steroids. By including this variation in the adiabatic approximation the coordinates of the tensor of rotation R^NnKk_ij are altered by different amounts due to the coupling by vibrations of the involved states with other electronic states of the system (Herzberg-Teller method). As a consequence of this coupling electric dipole and magnetic dipole/electric quadrupole transition moments not belonging to the observed transition |K⁰> ← |N⁰> are added to the zeroth order tensor of rotation R^NK_ij. Le., first order tensor of rotation R^LM/PR_ij = $\text{1}\text{4}$ <μ_k>_LM|ε_kli <C_tj>_PR + ε_klj<C_lj>_PR}, multiplied by a mixing parameter depending on the type of vibration have to be added to R^NK_ij. As a consequence, the structure of the CD band will depend on the orientational distribution function. The model developed is demonstrated for molecules with symmetry D₂.