The SIESTA method for ab initio order-N materials simulation (original) (raw)
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Advances in Density-Functional Calculations for Materials Modeling
Annual Review of Materials Research, 2019
During the past two decades, density-functional (DF) theory has evolved from niche applications for simple solid-state materials to become a workhorse method for studying a wide range of phenomena in a variety of system classes throughout physics, chemistry, biology, and materials science. Here, we review the recent advances in DF calculations for materials modeling, giving a classification of modern DF-based methods when viewed from the materials modeling perspective. While progress has been very substantial, many challenges remain on the way to achieving consensus on a set of universally applicable DF-based methods for materials modeling. Hence, we focus on recent successes and remaining challenges in DF calculations for modeling hard solids, molecular and biological matter, low-dimensional materials, and hybrid organic-inorganic materials.
A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density functional equation is solved implicitly for the density response, eliminating the instabilities that arise in conventional techniques for simulations of large, metallic or inhomogeneous systems. The auxiliary system is not required to be fermionic, and an example bosonic auxiliary density functional is presented which captures the key aspects of the fermionic Kohn-Sham behaviour. This bosonic auxiliary scheme is shown to provide good performance for a range of bulk materials, and a substantial improvement in the scaling of the calculation with system size for a variety of simulation systems.
Numerical Methods for Electronic Structure Calculations of Materials
SIAM Review, 2010
The goal of this article is to give an overview of numerical problems encountered when determining the electronic structure of materials and the rich variety of techniques used to solve these problems. The paper is intended for a diverse scienti£c computing audience. For this reason, we assume the reader does not have an extensive background in the related physics. Our overview focuses on the nature of the numerical problems to be solved, their origin, and on the methods used to solve the resulting linear algebra or nonlinear optimization problems. It is common knowledge that the behavior of matter at the nanoscale is, in principle, entirely determined by the Schrödinger equation. In practice, this equation in its original form is not tractable. Successful, but approximate, versions of this equation, which allow one to study nontrivial systems, took about £ve or six decades to develop. In particular, the last two decades saw a ¤urry of activity in developing effective software. One of the main practical variants of the Schrödinger equation is based on what is referred to as Density Functional Theory (DFT). The combination of DFT with pseudopotentials allows one to obtain in an ef£cient way the ground state con£guration for many materials. This article will emphasize pseudopotentialdensity functional theory, but other techniques will be discussed as well.
Density functional theory calculations using the finite element method
We propose a method to solve Kohn-Sham equations and to calculate electronic states, total energy, and material properties of non-crystalline, non-periodic structures with l-dependent fully non-local real-space ab initio pseudopotentials using finite elements. Contrary to the variety of well established k-space methods, which are based on Bloch's theorem and applicable to periodic structures, we do not assume periodicity in any respect. Precise ab initio environment-reflecting pseudopotentials that have been applied in the k-space, plane wave approach so far, are connected with real space finite-element basis in this work. The main expected asset of the present approach is the combination of efficiency and high precision of ab initio pseudopotentials with applicability not restricted to periodic environment.
Density Functional Theory Methods for Computing and Predicting Mechanical Properties
Over the past few decades, tremendous progress has been made in the development of computational methods for predicting the properties of materials. At the heart of this progress is density functional theory (DFT) [13, 17, 31, 39, 65], one of the most powerful and efficient computational modeling techniques for predicting electronic properties in chemistry, physics, and material science. Prior to the introduction of DFT in the 1960s [31, 39] the only obvious method for obtaining the electronic energies of materials required a direct solution of the many-body Schrödinger equation [62]. While the Schrödinger equation provides a rigorous path for predicting the electronic properties of any material system, analytical solutions for realistic systems having more than one interacting electron are out of reach. Moreover, since the Schrödinger equation is inherently a many-body formalism (3N spatial coordinates for N strongly interacting electrons), numerically accurate solutions of multi-electron systems are also impractical. Instead of the full 3N-dimensional Schrödinger equation, DFT recasts the electronic problem into a simpler yet mathematically equivalent 3-dimensional theory of non-interacting electrons (cf. Fig. 4.1). The exact form of this electron density, .D n.r//, hinges on the mathematical form of the exchange-correlation functional, E xc OEn.r/, which is crucial for providing accurate and efficient solutions to the many-body Schrödinger equation. Unfortunately, the exact form of the exchange-correlation functional is currently unknown, and all modern DFT functionals invoke various degrees of approximation.
N-scaling algorithm for density-functional calculations of metals and insulators
Physical review, 1994
An algorithm for minimization of the density-functional energy is described that replaces the diagonalization of the Kohn-Sham Hamiltonian with block diagonalization into explicit occupied and partially occupied (in metals) subspaces and an implicit unoccupied subspace. The progress reported here represents an important step toward the simultaneous goals of linear scaling, controlled accuracy, efficiency, and transferability. The method is specifically designed to deal with localized, nonorthogonal basis sets to maximize transferability and state-by-state iteration to minimize any charge-sloshing instabilities. It allows the treatment of metals, which is important in itself, and also because the dynamics of "semiconducting" systems can result in metallic phases. The computational demands of the algorithm scale as the particle number, permitting applications to problems involving many inequivalcnt atoms. I. INTRODUCTION Meaningful simulation of the microscopic behavior of condensed-matter systems requires a reliable description of interatomic forces. More than 20 years of experience have shown that the local-density-functional approximation (LDA) can accurately predict structure and properties of many classes of materials, including crystals, interatomic compounds, surfaces, and small molecules. Consequently, LDA represents a general framework for the study of important material-science issues, e. g., crystal growth, defect properties, catalytic chemistry, and materials degradation and failure. Since the seminal paper of Car and Parrinello, ' a great deal of effort has been devoted to making LDA calculations more efficient. However, until very recently, all LDA algorithms scaled with N, where N is the number of inequivalent atoms in the system. The outlook for treating large systems changed with the publications of Yang and Baroni and Giannozzi, which showed that linear scaling with N is in principle attainable in LDA. Although there are more rigorous, and, in general, more accurate, methods than LDA for the solution of electronic structure problems, none clearly shows the promise of applicability to even modestly complex systems, since they all scale rapidly with system size.
Grid-based density functional calculation of many-electron systems
2010
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for 3 atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems.
A new density functional method for electronic structure calculation of atoms and molecules
arXiv: Chemical Physics, 2019
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradi...