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Register a new userCalculations on millions of atoms with DFT: Linear scaling shows its potential
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An overview of the Conquest linear scaling density functional theory (DFT) code is given, focussing particularly on the scaling behaviour on modern high- performance computing (HPC) platforms. We demonstrate that essentially perfect linear scaling and weak parallel scaling (with fixed atoms per processor core) can be achieved, and that DFT calculations on millions of atoms are now possible.
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Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources.
Density Functional Theory (DFT) has become the quasi-standard for ab-initio simulations for a wide range of applications. While the intrinsic cubic scaling of DFT was for a long time limiting the accessible system size to some hundred atoms, the recent progress with respect to linear scaling DFT methods has allowed to tackle problems that are larger by many orders of magnitudes. However, as these linear scaling methods were developed for insulators, they cannot, in general, be straightforwardly applied to metals, as a finite temperature is needed to ensure locality of the density matrix. In this paper we show that, once finite electronic temperature is employed, the linear scaling version of the BigDFT code is able to exploit this locality to provide a computational treatment that scales linearly with respect to the number of atoms of a metallic system. We provide prototype examples based on bulk Tungsten, which plays a key role in finding safe and long-lasting materials for Fusion Reactors. We believe that such an approach might help in opening the path towards novel approaches for investigating the electronic structure of such materials, in particular when large supercells are required.
One of the key challenges to realize controlled fusion energy is tritium self-sufficiency. The application of hydrogen permeation barrier (HPB) is considered to be necessary for tritium self-sufficiency. {alpha}-Al2O3 is currently a candidate material for HPB. However, a crucial issue for {alpha}-Al2O3 is that its permeability reduction factor (PRF) will dramatically drop after ion or neutron irradiations. At present, little is known about the relevant mechanism. In order to shed light on this issue, the kinetics and energetic changes of hydrogen on defected {alpha}-Al2O3 surfaces in comparison with perfect {alpha}-Al2O3 surfaces were studied by density functional theory. For perfect {alpha}-Al2O3 surfaces, the results show that the barrier for hydrogen migration from the outermost layer into the subsurface layer is the highest, making this migration step to be a rate limiting process. In contrast, surface point defects dramatically reduce this maximum barrier. Consequently, hydrogen can preferentially permeate into the interior of the material through surface defects. The findings can help explain the possible mechanism of significant decrease of PRF under radiation.
We present an approach to the DFT+U method (Density Functional Theory + Hubbard model) within which the computational effort for calculation of ground state energies and forces scales linearly with system size. We employ a formulation of the Hubbard model using nonorthogonal projector functions to define the localized subspaces, and apply it to a local-orbital DFT method including in situ orbital optimization. The resulting approach thus combines linear-scaling and systematic variational convergence. We demonstrate the scaling of the method by applying it to nickel oxide nano-clusters with sizes exceeding 7,000 atoms.
Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides...
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