LINEAR SCALING CONJUGATE-GRADIENT DENSITY-MATRIX SEARCH AS AN ALTERNATIVE TO DIAGONALIZATION FOR FIRST PRINCIPLES ELECTRONIC-STRUCTURE CALCULATIONS

Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree-Fock and density functional th eory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the O(N-3) diagonalization bottleneck as the rate determining step for very large systems. In th is work, a conjugate gradient density matrix search (CG-DMS) method ha s been successfully extended and computationally implemented for use w ith first principles calculations. A Cholesky decomposition of the ove rlap matrix and its inverse is used to transform to and back from an o rthonormal basis, which can be formed in near-linear time for sparse s ystems. Linear scaling of CPU time for the density matrix search and c rossover of CPU time with diagonalization is demonstrated for polyglyc ine chains containing up to 493 atoms and water clusters up to 900 ato ms. (C) 1997 American Institute of Physics.