A mathematical method is presented for determining helical conformations, or more precisely, positions of atoms relative to the helical axis and internal rotational angles about skeletal bonds, of a polymer molecule in crystalline state, straightforwardly from bond lengths and bond angles of the chain skeleton, and the translational distance along the helical axis and the rotational angle about the axis per one repeating unit. The treatment is confined to one-, two-, and three-atom helices, i.e., those whose stereochemical and conformational repeating units are composed of one, two, and three consecutive skeletal atoms, respectively. A nonhelical conformation also is included as a special helix. The method is illustrated by the two examples, poly-p-fluorostyrene and polypeptides, for which it was originally devised.
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Nagai et al. (1962) studied this question.