248 research outputs found
Weighted Trace-Penalty Minimization for Full Configuration Interaction
A novel unconstrained optimization model named weighted trace-penalty
minimization (WTPM) is proposed to address the extreme eigenvalue problem
arising from the Full Configuration Interaction (FCI) method. Theoretical
analysis shows that the global minimizers of the WTPM objective function are
the desired eigenvectors, rather than the eigenspace. Analyzing the condition
number of the Hessian operator in detail contributes to the determination of a
near-optimal weight matrix. With the sparse feature of FCI matrices in mind,
the coordinate descent (CD) method is adapted to WTPM and results in WTPM-CD
method. The reduction of computational and storage costs in each iteration
shows the efficiency of the proposed algorithm. Finally, the numerical
experiments demonstrate the capability to address large-scale FCI matrices
ELSI -- An open infrastructure for electronic structure solvers
Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets. Program summary: Program title: ELSI Interface CPC Library link to program files: http://dx.doi.org/10.17632/473mbbznrs.1 Licensing provisions: BSD 3-clause Programming language: Fortran 2003, with interface to C/C++ External routines/libraries: BLACS, BLAS, BSEPACK (optional), EigenExa (optional), ELPA, FortJSON, LAPACK, libOMM, MPI, MAGMA (optional), MUMPS (optional), NTPoly, ParMETIS (optional), PETSc (optional), PEXSI, PT-SCOTCH (optional), ScaLAPACK, SLEPc (optional), SuperLU_DIST Nature of problem: Solving the electronic structure from given Hamiltonian and overlap matrices in electronic structure calculations. Solution method: ELSI provides a unified software interface to facilitate the use of various electronic structure solvers including cubic scaling dense eigensolvers, linear scaling density matrix methods, and other approaches
A spectral scheme for Kohn-Sham density functional theory of clusters
Starting from the observation that one of the most successful methods for
solving the Kohn-Sham equations for periodic systems -- the plane-wave method
-- is a spectral method based on eigenfunction expansion, we formulate a
spectral method designed towards solving the Kohn-Sham equations for clusters.
This allows for efficient calculation of the electronic structure of clusters
(and molecules) with high accuracy and systematic convergence properties
without the need for any artificial periodicity. The basis functions in this
method form a complete orthonormal set and are expressible in terms of
spherical harmonics and spherical Bessel functions. Computation of the occupied
eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a
combination of preconditioned block eigensolvers and Chebyshev polynomial
filter accelerated subspace iterations. Several algorithmic and computational
aspects of the method, including computation of the electrostatics terms and
parallelization are discussed. We have implemented these methods and algorithms
into an efficient and reliable package called ClusterES (Cluster Electronic
Structure). A variety of benchmark calculations employing local and non-local
pseudopotentials are carried out using our package and the results are compared
to the literature. Convergence properties of the basis set are discussed
through numerical examples. Computations involving large systems that contain
thousands of electrons are demonstrated to highlight the efficacy of our
methodology. The use of our method to study clusters with arbitrary point group
symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational
Physic
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