Related papers: Numerically exact O($N^{7/3}$) method for large-sc…

Linear scaling methods provide total energy, but no energy levels and canonical wavefuctions. From the density matrix computed through the density matrix purification methods, we propose an order-N (O(N)) method for calculating both the…

With the widespread use of self-consistent field methods, including Hartree-Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction construction with…

We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…

We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The…

A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was…

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…

We present new efficient (O(N log N)) methods for computing three quantities crucial to electronic structure calculations: the ionic potential, the electron-ion contribution to the Born-Oppenheimer forces, and the electron-ion contribution…

We present a new method for computing the Near-To-Far-Field (NTFF) transformation in FDTD simulations which has an overall scaling of $O(N^3)$ instead of the standard $O(N^4)$. By mapping the far field with a cartesian coordinate system the…

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…

Orbital-free density functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the…

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets…

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…

The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…

An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this…

An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…

Collisional fragmentation is a ubiquitous phenomenon arising in a variety of astrophysical systems, from asteroid belts to debris and protoplanetary disks. Numerical studies of fragmentation typically rely on discretizing the size…

Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids…

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…

Electronic density of states (DOS) is a key factor in condensed matter physics and material science that determines the properties of metals. First-principles density-functional theory (DFT) calculations have typically been used to obtain…