Novel computational methods for nanostructure electronic structure calculations

Experimentally relevant nanocrystals often contain a few thousands to hundreds of thousands of atoms. Yet, to understand their electronic structures, surface and impurity effects, atomic relaxations, interior electric fields, carrier dynamics, and transports, it is often necessary to carry out atomistic simulations. Owing to the advance of recent algorithm developments and improved supercomputer powers, it is now possible to calculate such nanocrystals based on ab initio methods. In this review, we discuss the numerical algorithms (the plane-wave pseudopotential method and the real-space finite-difference method) used in conventional density-functional-theory calculations, which enable the simulations of systems up to one or two thousand atoms. We also introduce methods designed specifically for nanostructure calculations. These methods [the charge-patching method (CPM) and the linear scaling three-dimensional fragment method (LS3DF)] can be used to calculate systems with hundreds of thousands of atoms. Whereas CPM is an approximation with ab initio quality, the LS3DF method is an O(N) method with essentially the same results as the direct methods. The computational aspects of the algorithms, especially for their parallelization scalability, are also emphasized in the review.