Gauge Dependence of the S̃ Molecular Orbital Space Decomposition of Optical Rotation

The measurement of optical rotation (OR) is a foundational technique for the detection and characterization of chiral molecules, but it is poorly understood how the observed property relates to the structure of the molecule. Over the years, several schemes have been developed to decompose the OR into more chemically intuitive contributions. In this paper, we introduce two alternative formulations of our previously developed S̃ molecular orbital space decomposition. These new expressions use the modified velocity gauge-magnetic (MVG-M) and -electric (MVG-E) definitions of OR, rather than the length gauge-magnetic (LG-M) definition used in the original paper. Comparing these formulations across a small set of previously studied chiral molecules, we find that these different definitions produce consistent physical interpretations of the OR. These results demonstrate that the S̃ methodology for investigations of structure-property relationships in chiral molecules is insensitive to the choice of gauge.