The molar rotation of a solution of a natural alpha amino acid is changed in the positive direction by addition of a strong acid. Three decades ago, an attempt to rationalize this old rule, named for Clough, Lutz, and Jirgensons (CLJ), was made by assigning circular dichroism octants for overlapping carbonyl n to pi* transitions. Modern quantum chemical methods allow us to take a new look at this phenomenon. Time-dependent density functional theory was used to model the electronic structure and transitions responsible for CLJ. We show that sector rules originally developed for circular dichroism (CD) can be applied to the optical rotation in this case, but with some restrictions, and with great caution, due to the change of the overall charge of the acids upon protonation and the distortion of the COO- chromophore in the zwitterions. We have prepared sector maps based on first-principles computations to study the correspondence between CD and optical rotation for zwitterionic and protonated l-amino acid chromophores. The CLJ effect is correctly obtained from the computations for all 12 amino acids studied in this work.