Practical methods for ab initio calculations on thousands of atoms

We describe recent progress in developing practical ab initio methods for w hich the computer effort is proportional to the number of atoms: linear sca ling or O(N) methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then de scribe our scheme, which operates within density functional theory. Efficie nt methods for reaching the electronic ground state are summarized, both fo r finding the density matrix and in varying the localized orbitals. (C) 200 0 John Wiley & Sons, Inc.