Knowledge Bank

The equation $\cos \varphi =f(\alpha i,\sigma i)$, where $\varphi$ is the angle formed by three successive equivalent atoms on the skeletal chain and the $\alpha$'s and $\sigma$'s are the bond and torsion angles of the monomer unit, can be used with the $\cos =\theta f(\alpha i,\sigma i)$ equation, where $\theta$ is the helical rotation angle, to obtain an analytical solution for the unknown $\alpha$'s and $\sigma$'s or at least limit the possible configurations. The $\cos \varphi$ equation can be obtained from the repeat distance d already reported in the literature. A general discussion of the problem of determining the atomic parameters from a given set of helical parameters will be included. This knowledge is useful in x-ray and normal coordinate analyses.