Locality and Sparsity of Ab Initio One-Particle Density Matrices and Localized Orbitals

The cost of Hartree−Fock and local correlation methods is strongly dependent on the locality of the one-particle density matrix and localized orbitals. In this paper the locality and sparsity of the one-particle density matrix is investigated numerically and theoretically, primarily at the Hartree−Fock level, for linear alkanes containing up to 320 carbon atoms. A method for the calculation of localized, atom-centered, occupied orbitals is presented and compared with the Boys' localization procedure. The atom-centered orbitals are ideally suited for use in local-correlation calculations. The connection between the size of optimally localized orbitals, the locality of the density matrix, and the onset of linear scaling is investigated.