Ab initio calculation and display of the rotary strength tensor in the random phase approximation. Method and model studies

The theory of the rotatory strength tensor describing circular dichroism (CD) of electronic excitations in oriented molecules is summarized in length and velocity formulations, and we outline an ab initio implementation of the calculation of this tensor and its electric dipole — magnetic dipole and electric dipole — electric quadrupole components in the random phase approximation. Results are presented for the predominantly π → π∗ and σ → π∗ type transitions in an ethylene molecule twisted into chiral D2 conformations demonstrating the origin-sensitivity of the electric dipole-magnetic dipole and electric dipole-electric quadrupole contributions to the tensor, and demonstrating origin-invariance of the total tensor in the velocity formulation. The electric dipole-electric quadrupole contribution is small, but not insignificant for both transitions. We present a pictorial representation of the CD response, and its application to the total tensor and its components for the π → π∗ excitation.