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Register a new userLinear scaling DFT calculations for large Tungsten systems using an optimized local basis
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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.
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Given the widespread use of density functional theory (DFT), there is an increasing need for the ability to model large systems (beyond 1,000 atoms). We present a brief overview of the large-scale DFT code Conquest, which is capable of modelling such large systems, and discuss approaches to the generation of consistent, well-converged pseudo-atomic basis sets which will allow such large scale calculations. We present tests of these basis sets for a variety of materials, comparing to fully converged plane wave results using the same pseudopotentials and grids.
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.
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.
We introduce numerical optimization of multi-site support functions in the linear-scaling DFT code CONQUEST. Multi-site support functions, which are linear combinations of pseudo-atomic orbitals on a target atom and those neighbours within a cutoff, have been recently proposed to reduce the number of support functions to the minimal basis while keeping the accuracy of a large basis [J. Chem. Theory Comput., 2014, 10, 4813]. The coefficients were determined by using the local filter diagonalization (LFD) method [Phys. Rev. B, 2009, 80, 205104]. We analyse the effect of numerical optimization of the coefficients produced by the LFD method. Tests on crystalline silicon, a benzene molecule and hydrated DNA systems show that the optimization improves the accuracy of the multi-site support functions with small cutoffs. It is also confirmed that the optimization guarantees the variational energy minimizations with multi-site support functions.
We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor five and the memory by a factor of six compared to localized, orthogonal orbitals. For jellium, we demonstrate that the total energy is converged for orbitals truncated within spheres with radii 7-8 $r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.
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