Accelerating Materials Discovery through Bezier Interpolation of Electronic Band Structure

One important part of DFT calculations is the numerical integral of the electronic band structure. Unfortunately, this critical step of DFT simulation is the most computationally expensive, because each k-point requires solving the Kohn-Sham equations, an eigenproblem, in a large basis set. Almost all of the error in the band energy integral comes from misrepresenting the Fermi surface, so the most important part of any integration technique is approximating the Fermi surface correctly. Current DFT codes approximate the bands using three-dimensional Riemann sums, which represent the Fermi surface very poorly. We present an integration technique of interpolating the bands using Bezier surfaces in order to more accurately represent the Fermi surface, and thereby achieve the same accuracy with fewer k-points. We also explore further improvement by using an adaptive mesh refinement technique in those integration regions which contain the Fermi surface. Preliminary results suggest that 1 meV accuracy can be achieved using ~10× fewer k-points.