Abstract by Nathan Foulk
Physics and Astronomy
Two-Dimensional Integration of Band Structure through Quadratic Interpolation
One of the most important parts of density functional theory (DFT) is the numerical integral of the electronic band structure. Unfortunately, this critical step of DFT simulations is also the most computationally expensive. For this integral, each sampling point requires solving an eigenvalue problem in a large basis set. Almost all of the error in this 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 the conventional "midpoint rule". We present an integration technique of interpolating the bands using Bezier surfaces in order to represent the Fermi surface much more accurately. 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.