Practical methods for ab initio calculations on thousands of atoms

We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or {article}{empty}{document}O(N){document} methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then describe our scheme, which operates within density functional theory. Efficient methods for reaching the electronic ground state are summarized, both for finding the density matrix and in varying the localized orbitals.