Circular dichroism (CD) is the observed difference in absorption spectra by right- and left-handed circularly polarized light (CPL) in chiral molecules and is used to reveal important structural aspects of these molecules. Currently the optics module of the linearly scaling Density Functional Theory (DFT) package ONETEP calculates spectroscopic data by approximating the angular momentum matrix elements through the assumption of an identity in the rotary strength function equation. This approximation results in nicely formed CD spectra that resemble experimental data but spoils the Hermiticity of the angular momentum matrix elements. We sought to improve the Hermiticity and provide a more consistent approach by calculating the aforementioned term directly. Using the chiral molecule methyloxirane for validations of our new design against the old one, we were able to see that our changes yielded more accurate Hermiticity values for the calculated matrix elements as well as promising CD spectra that resembled the experimental data. While the new design’s results were not ideal, they were encouraging and offer a more consistent and reliable approach to the circular dichroism part of ONETEP’s optical simulations. Future work will include modifying the general rotary function calculation (a replacement with additional energy factors for adjustment) and restoring the nonlocal commutator, which was used in the previous design and increases overall accuracy.