Sum rules for atomic polar and axial tensors from vibronic coupling theory

Abstract

Sum rules for the electronic parts of the atomic polar tensors and atomic axial tensors are developed in the vibronic coupling theoretical (VCT) formalism for vibrational circular dichroism (VCD) intensities. These sum rules provide alternative means to judge the accuracy of VCD calculations. Implemented at the ab initio level of theory, these sum rules are tested for various sized molecules and basis sets. Calculations indicate that the atomic axial tensors computed in the distributed origin (DO) gauge obey the sum rule better than those in the common origin (CO) gauge.