O(N) methods in electronic structure calculations

Linear scaling methods, or O(N) methods, 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 number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. 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. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

Implementation and benchmark of a long-range corrected functional in the density functional based tight-binding method

Bridging the gap between first principles methods and empirical schemes, the density functional based tight-binding method (DFTB) has become a versatile tool in predictive atomistic simulations over the past years. One of the major restrictions of this method is the limitation to local or gradient corrected exchange-correlation functionals. This excludes the important class of hybrid or long-range corrected functionals, which are advantageous in thermochemistry, as well as in the computation of vibrational, photoelectron and optical spectra. The present work provides a detailed account of the implementation of DFTB for a long-range corrected functional in generalized Kohn-Sham theory. We apply the method to a set of organic molecules and compare ionization potentials and electron affinities with the original DFTB method and higher level theory. The new scheme cures the significant overpolarization in electric fields found for local DFTB, which parallels the functional dependence in first principles density functional theory (DFT). At the same time the computational savings with respect to full DFT calculations are not compromised as evidenced by numerical benchmark data

Parallel Simulation of Biomacromolecules using the DFTB method

Cilem teto prace je akcelerace DFTB metody pouzivane k simulaci biomakromolekul. Casove nejnarocnejsi casti simulace jsou identifikovany a akcelerovany s pouzitim internich moznosti puvodniho reseni, paralelizace pomoci OpenMP a moznosti pouzit knihovnu MAGMA, ktera vyuziva hybridnich CPU/GPU algoritmu ke zrychleni operaci linearni algebry. Jednotlive metody akcelerace jsou popsany a otestovany na systemech vod ruznych velikosti. Vysledky testu, prokazujici zrychleni oproti jinym knihovnam implementujicim operace linearni algebry, minimalni dopad paralelizace kodu a problemy s pouzitim interni akcelerace, jsou prezentovany v zaveru prace.The purpose of this work is to accelerate DFTB method used for biomacromolecule simulation by paralellization. The most time consuming parts of simulation are identified and parallelized using internal options and CPU and GPU acceleration of used linear algebra routines and the code itself. Possibility to use MAGMA - hybrid GPU/CPU linear algebra library and OpenMP parallelization of the code were implemented. All of those methods are described and tested on water systems of different size. Test results of MAGMA acceleration, parallelization and problems with internal optimizations are presented at the end of the work

Siesta: Recent developments and applications

A review of the present status, recent enhancements, and applicability of the Siesta program is presented. Since its debut in the mid-1990s, Siesta?s flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of Siesta combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin?orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as wannier90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering Siesta runs, and various post-processing utilities. Siesta has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.SIESTA development was historically supported by different Spanish National Plan projects (Project Nos. MEC-DGES-PB95-0202, MCyT-BFM2000-1312, MEC-BFM2003-03372, FIS2006-12117, FIS2009-12721, FIS2012-37549, FIS2015-64886-P, and RTC-2016-5681-7), the latter one together with Simune Atomistics Ltd. We are thankful for financial support from the Spanish Ministry of Science, Innovation and Universities through Grant No. PGC2018-096955-

Siesta: Recent developments and applications

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-1990s, SIESTA’s flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a realspace grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin–orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as WANNIER90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various post-processing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments. Published under license by AIP Publishing.Siesta development was historically supported by different Spanish National Plan projects (Project Nos. MEC-DGES-PB95-0202, MCyT-BFM2000-1312, MEC-BFM2003-03372, FIS2006-12117, FIS2009-12721, FIS2012-37549, FIS2015-64886-P, and RTC-2016-5681-7), the latter one together with Simune Atomistics Ltd. We are thankful for financial support from the Spanish Ministry of Science, Innovation and Universities through Grant No. PGC2018-096955-B. We acknowledge the Severo Ochoa Center of Excellence Program [Grant Nos. SEV-2015-0496 (ICMAB) and SEV-2017-0706 (ICN2)], the GenCat (Grant No. 2017SGR1506), and the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143). P.G.-F. acknowledges support from Ramón y Cajal (Grant No. RyC-2013-12515). J.I.C. acknowledges Grant No. RTI2018-097895-B-C41. R.C. acknowledges the European Union’s Horizon 2020 Research and Innovation Program under Marie Skłodoswka-Curie Grant Agreement No. 665919. D.S.P, P.K., and P.B. acknowledge Grant No. MAT2016-78293-C6, FET-Open No. 863098, and UPV-EHU Grant No. IT1246-19. V. W. Yu was supported by a MolSSI Fellowship (U.S. NSF Award No. 1547580), and V.B. and V.W.Y. were supported by the ELSI Development by the NSF (Award No. 1450280). We also acknowledge Honghui Shang and Xinming Qin for giving us access to the honpas code, where a preliminary version of the hybrid functional support described here was implemented. We are indebted to other contributors to the Siesta project whose names can be seen in the Docs/Contributors.txt file of the Siesta distribution, and we thank those, too many to list, contributing fixes, comments, clarifications, and documentation for the code.Peer reviewe

ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives