We study the conformational dependence of circular dichroism (CD) spectra of amino acid molecules by means of an efficient ab initio DFT approach which is free from the typical gauge invariance issues arising with the use of localized basis sets and/or real-space grids. We analyze the dependence of the chiroptical spectra on the backbone dihedrals in the specific case of alanine and consider the role of side chain degrees of freedom at the examples of leucine, phenylalanine, and serine, whose side chains have different physicochemical properties. The results allow one to identify the most diagnostic regions of the CD spectra and to critically compare the conformations which match the experimental CD data with conformations extracted from the rotamer library. The inclusion of a solvation shell of explicit water molecules and its effect on the CD spectrum are analyzed at the example of alanine.