Origin Invariant Molecular Orbital Decomposition of Optical Rotation

Optical rotation (OR) is a sensitive electronic property for which there are no clear structure-property relations. We proposed an approach to decompose the OR tensor in terms of one-electron transitions between occupied-virtual molecular orbital pairs, called the Sia method. This method allows to select the transitions with the largest magnitude that determine the overall value of the OR for a specific molecule, thus providing useful insights for characterization. However, the individual Sia values are origin-dependent even if the total OR is origin invariant. In this work, we explicitly identify the reason for the origin dependence of the Sia original formulations and we propose two ways to eliminate this spurious effect and define an origin invariant S ̃ia within the modified velocity gauge formalism. One approach is based on averaging the electric and magnetic-perturbed density Sia definitions (which have equal and opposite origin dependence that cancels out in the average), while the second approach is based on the equal distribution of the electronic response to an external field via Cholesky decomposition of the response matrix. Numerical results prove that the new Sia definitions are indeed origin invariant and they provide the same physical picture for the OR tensor decomposition. At the same time, we show that setting the origin of the coordinate system at the center of mass of the molecule also provides the same physical picture when using the original Sia formulation, which confirms that this is a robust approach for investigating structure-property relations in chiral molecules.