Knowledge Bank

Equations for helical parameters can be expressed in the atomic parameters of bond length (I), bond angle ($\alpha$), and torsion angle ($\sigma$) of the skeletal chain for any type polymer. A conceptually simple method for the derivation of these equations is presented in such a way that other useful equations are also obtained. An important new restriction on the possible configurations of a polymer with a given helical rotation angle ($\theta$) and repeat distance (d) is obtained by making use of the invariancy of the repeat parameter ($\varphi$). The differentials of the equations for $\theta$, d, and $\rho$ (the radial distance) as f (l, $\alpha ,\sigma$) set equal to zero give immediately the geometric redundancy conditions for helical molecules. Application of the equations to finite molecules is also discussed.