A Mathematical Approach that Includes the Fourier Transform (Plane Wave Decomposition Using Spherical Coordinates) and Simultaneously Assesses Complex Movements, Such as Rotations and Displacements, in Complicated Molecular Constructions

Abstract

A multimodal mathematical approach is proposed that makes it possible to consider the Fourier objects that arise when macromolecules are described in spherical coordinates. With spherical coordinates, it is relatively simple to identify certain symmetries that may occur in macromolecules. The approach also includes plane wave decomposition (intended to describe macromolecules) in a series of spherical functions and thus provides the ability to simultaneously consider both rotations and displacements of an entire macromolecule in space.