Electronic structure calculations and molecular dynamics simulations with linear system-size scaling

As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only attained by localized or randomized algorithms that have large cost prefactors in the difficult regime of low-temperature metals. Using large copper clusters in a minimal-basis semiempirical model as our reference system, we study the costs of the...

We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are compu...

Nonlocal kinetic energy density functionals (KEDFs) with density-dependent kernels are currently the most accurate functionals available for orbital-free density functional theory (OF-DFT) calculations. However, despite advances in numerical techniques and using only (semi)local density-dependent kernels, nonlocal KEDFs still present substantial computational costs in OF-DFT, limiting their application in large-scale material simulations. To address this challenge, we propose...

A parallel implementation of an eigensolver designed for electronic structure calculations is presented. The method is applicable to computational tasks that solve a sequence of eigenvalue problems where the solution for a particular iteration is similar but not identical to the solution from the previous iteration. Such problems occur frequently when performing electronic structure calculations in which the eigenvectors are solutions to the Kohn-Sham equations. The eigenvect...

TBPLaS is an open-source software package for the accurate simulation of physical systems with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an intuitive object-oriented Python application interface (API) and Cython/Fortran extensions for the performance critical parts, ensuring both flexibility and efficiency. Under the hood, numerical calculations are mainly performed by both exact diagonalizatin and the tight-binding propagation meth...

While the success of density functional theory (DFT) has led to its use in a wide variety of fields such as physics, chemistry, materials science and biochemistry, it has long been recognised that conventional methods are very inefficient for large complex systems, because the memory requirements scale as $N^2$ and the cpu requirements as $N^3$ (where $N$ is the number of atoms). The principles necessary to develop methods with linear scaling of the cpu and memory requirement...

Molecular quantum chemistry has seen enormous progress in the last few decades thanks to the more advanced and sophisticated numerical techniques and computing power. Following the recent interest in extending these capabilities to condensed-phase problems, we summarize basic knowledge of condensed-phase quantum chemistry for ones with experience in molecular quantum chemistry. We highlight recent efforts in this direction, including solving the electron repulsion integrals b...

A brief review of the SIESTA project is presented in the context of linear-scaling density-functional methods for electronic-structure calculations and molecular-dynamics simulations of systems with a large number of atoms. Applications of the method to different systems are reviewed, including carbon nanotubes, gold nanostructures, adsorbates on silicon surfaces, and nucleic acids. Also, progress in atomic-orbital bases adapted to linear-scaling methodology is presented.

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms which take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will therefore first be studied for both metals and insulators. Several approaches to construct O(N) algori...

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a ...