A spectral scheme for Kohn-Sham Density Functional Theory of helical structures

Based on the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems - the plane-wave method - is a spectral method based on eigenfunction expansion, we formulate and implement a spectral method designed towards solving the Kohn-Sham equations for helical structures. Various important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons and miscellaneous chiral structures from chemistry and biology constitute examples of helical structures, and such systems are often associated with fascinating material properties.

The electronic states in helical structures can be characterized by means of special solutions to the single electron problem called helical Bloch waves. Such solutions allow us to block-diagonalize the Kohn-Sham Hamiltonian and arrive at the governing equations. We write out these equations in helical coordinates and expand unknowns in terms of helical waves, i.e. helical symmetry adapted Laplacian eigenfunctions. We discuss the use of fast transforms for carrying out the eigenfunction expansion and the use of iterative techniques for diagonalization. We present example calculations involving nanotubes and nanoribbons to illustrate various computational aspects of our method.