Density matrix search using direct inversion in the iterative subspace as a linear scaling alternative to diagonalization in electronic structure calculations

For electronic structure calculations on large systems, solving the self-consistent-field (SCF) equations is one of the key bottlenecks. Density matrix search methods provide an efficient linear scaling approach for circumventing the traditional O(N-3) diagonalization procedure for solving the SCF equations. The conjugate gradient density matrix search (CG-DMS) method is a successful implementation of this approach. An alternative density matrix search method, QN-DMS, employs direct inversion in the iterative subspace using a quasi-Newton (QN) step to estimate the error vector. For linear polyglycine chains of 10-100 residues, the present approach scales linearly and is 30% faster than CG-DMS. For clusters of up to 300 water molecules, this method shows smoother and efficient convergence, and displays nearly linear scaling. (C) 2003 American Institute of Physics.