Journal ArticleDOI
Assessment of density matrix methods for linear scaling electronic structure calculations
TLDR
Purification and minimization methods for linear scaling computation of the one-particle density matrix for a fixed Hamiltonian matrix are compared and it is investigated how the convergence speed for the different methods depends on the eigenvalue distribution in theHamiltonian matrix.Abstract:
Purification and minimization methods for linear scaling computation of the one-particle density matrix for a fixed Hamiltonian matrix are compared. This is done by considering the work needed by each method to achieve a given accuracy in terms of the difference from the exact solution. Numerical tests employing orthogonal as well as non-orthogonal versions of the methods are performed using both element magnitude and cutoff radius based truncation approaches. It is investigated how the convergence speed for the different methods depends on the eigenvalue distribution in the Hamiltonian matrix. An expression for the number of iterations required for the minimization methods studied is derived, taking into account the dependence on both the band gap and the chemical potential. This expression is confirmed by numerical tests. The minimization methods are found to perform at their best when the chemical potential is located near the center of the eigenspectrum. The results indicate that purification is considerably more efficient than the minimization methods studied even when a good starting guess for the minimization is available. In test calculations without a starting guess, purification is more than an order of magnitude more efficient than minimization.read more
Citations
More filters
Journal ArticleDOI
O(N) methods in electronic structure calculations.
TL;DR: The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers.
Journal ArticleDOI
Large-Scale Computations in Chemistry: A Bird's Eye View of a Vibrant Field.
Alexey V. Akimov,Oleg V. Prezhdo +1 more
Journal ArticleDOI
Recent progress with large-scale ab initio calculations: the CONQUEST code
TL;DR: In this paper, the authors report recent progress in the development of the \textsc{Conquest} code, which performs density functional theory (DFT) calculations on parallel computers, and has demonstrated ability to handle systems of over 10,000 atoms.
Journal ArticleDOI
Linear-scaling self-consistent field methods for large molecules
TL;DR: This review gives a brief overview of selected linear‐scaling QM approaches at the Hartree–Fock and density‐functional theory level with a particular emphasis on density matrix‐based approaches.
Journal ArticleDOI
O(N) methods in electronic structure calculations
TL;DR: Linear scaling methods as mentioned in this paper have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the size of atoms.
References
More filters
Book
Numerical Recipes 3rd Edition: The Art of Scientific Computing
TL;DR: This new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded, and adopts an object-oriented style particularly suited to scientific applications.
Journal ArticleDOI
Linear scaling electronic structure methods
TL;DR: In this paper, the physical decay properties of the density matrix were studied for both metals and insulators, and several strategies for constructing O(N) algorithms were presented and critically examined.
Journal ArticleDOI
Density functional and density matrix method scaling linearly with the number of atoms.
TL;DR: A variational principle for $n({r,r}^{\ensuremath{'}})$ is derived in which, by the use of a penalty functional, the (difficult) idempotency of $n(r, r)$ need not be assured in advance but is automatically achieved.
Journal ArticleDOI
Density-matrix electronic-structure method with linear system-size scaling.
TL;DR: A method is introduced for the solution of the electronic-structure problem in the independent-electron approximation based upon a variational solution for the density matrix, which is truncated to zero beyond a real-space radius R c and becomes exact as R c →∞.