Matrix model to predict specific optical rotations of acyclic chiral molecules

This paper constructs a new matrix model to analyze the relationship of the stereogenic center and its substituents to the specific optical rotation. The variables used as matrix elements include (1) the substituentsʹ comprehensive masses (m), (2) radii (r), (3) symmetries (s), and (4) the electronegativities (χ) of the atoms or groups which are bound to the stereogenic center. Solution of the matrix determinants was postulated to give scalar numbers proportional to the magnitudes of the specific rotations of the molecules being considered. A total of 94 example calculations were performed to predict the relative magnitude and direction of rotation at the sodium D line. Only two calculations failed to predict the correct direction of rotation and this occurred only when their optical rotation values were less than 0.01°. The B3LYP functional at the aug-cc-pVDZ basis set level was also used to compute the optical rotations of the 66 example chiral molecules whose geometries were previously obtained at the B3LYP/6-31G(d) level. The expected successful predictions for these acyclic moleculesʹ optical rotation values did not appear. Overall, the matrix model is one approach to understand the optical rotation.