Numerical challenges in the application of density functional theory to biology and nanotechnology

摘要

This paper summarizes our efforts to develop fast algorithms for density functional theory (DFT) calculations of inhomogeneous fluids. Our goal is to apply DFTs to a variety of problems in nanotechnology and biology. To this end we have developed DFT codes to treat both atomic fluid models and polymeric fluids. We have developed both three-dimensional real space and Fourier space algorithms. The former rely on a matrix-based Newton's method while the latter couple fast Fourier transforms with a matrix-free Newton's method. Efficient computation of phase diagrams and investigation of multiple solutions is facilitated with phase transition tracking algorithms and arclength continuation algorithms. We have explored the performance that can be obtained by application of massively parallel computing, and have begun application of the codes to a variety of two- and three-dimensional systems. In this paper, we summarize our algorithm development work as well as briefly discuss a few applications including adsorption and transport in ion channel proteins, capillary condensation in disordered porous media and confinement effects in a diblock copolymer fluid. [References: 73]