Application of geometric algebra for the description of polymer conformations

In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length $(l)$⁠, valence angle $(θ)$⁠, and rotation angle $(φ)$ of each of the preceding bonds in the chain. Hence, the set of geometrical parameters ${li,θi,φi}$ yields all the position coordinates $pi$ of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.