General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.