Order-Nmethods in self-consistent density-functional calculations

We discuss the potential impact of N-scaling algorithms on self-consistent density-functional calculations. N-scaling algorithms can increase numerical efficiency in two qualitatively different ways: First, by eliminating the O(${\mathit{N}}^3$) scaling of numerical diagonalizations or orthogonalizations, and second, through the transferability of localized electronic-structure information between chemically related, but globally different systems. We argue that the second aspect is potentially of great practical importance to self-consistent density-functional calculations. We describe how the transferability of electronic-structure information can be exploited and give numerical examples.