1995/08/15 by Eduardo Hernández, E. Hernandez, C. M. Goringe +1 · 145 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Conjugate gradient method #Cutoff #Density functional theory #Density matrix #Eigenvalues and eigenvectors #Geometry #High-pressure geophysics and materials #Linear scale #Materials science #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Minification #Physics #Pseudopotential #Quantum mechanics #Range (aeronautics) #Scaling #Spectroscopy and Quantum Chemical Studies #Statistical physics #chem-ph #cond-mat.mtrl-sci #mtrl-th
paper · pdf · doi:10.1103/physrevb.53.7147
published in Physical review. B, Condensed matter 53(11), 7147-7157 (American Physical Society) · REVTeX file, 27 pages with 4 uuencoded postscript figures
arxiv created 1995/08/15 · openalex publication_date 1996/03/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density-functional theory in which the ground-state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes, and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated. \textcopyright 1996 The American Physical Society.