Linear-scaling Density Functional Theory Research Articles

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.

Multipurpose Black-Phosphorus/hBN Heterostructures.

Black phosphorus (BP) has recently emerged as a promising semiconducting two-dimensional material. However, its viability is threatened by its instability in ambient conditions and by the significant decrease of its band gap in multilayers. We show that one could solve all the aforementioned problems by interfacing BP with hexagonal boron nitride (hBN). To this end, we simulate large, rotated hBN/BP interfaces using linear-scaling density functional theory. We predict that hBN-encapsulation preserves the main electronic properties of the BP monolayer, while hBN spacers can be used to counteract the band gap reduction in stacked BP. Finally, we propose a model for a tunneling field effect transistor (TFET) based on hBN-spaced BP bilayers. Such BP TFETs would sustain both low-power and fast-switching operations, including negative differential resistance behavior with peak-to-valley ratios of the same order of magnitude as those encountered in transition metal dichalcogenide TFETs.

Supercell convergence of charge-transfer energies in pentacene molecular crystals from constrained DFT

Singlet fission (SF) is a multiexciton generation process that could be harnessed to improve the efficiency of photovoltaic devices. Experimentally, systems derived from the pentacene molecule have been shown to exhibit ultrafast SF with high yields. Charge-transfer (CT) configurations are likely to play an important role as intermediates in the SF process in these systems. In molecular crystals, electrostatic screening effects and band formation can be significant in lowering the energy of CT states, enhancing their potential to effectively participate in SF. In order to simulate these, it desirable to adopt a computational approach which is acceptably accurate, relatively inexpensive, and which scales well to larger systems, thus enabling the study of screening effects. We propose an electrostatically corrected constrained density functional theory (cDFT) approach as a low-cost solution to the calculation of CT energies in molecular crystals such as pentacene. Here we consider an implementation in the context of the onetep linear-scaling DFT code, but our electrostatic correction method is in principle applicable in combination with any constrained DFT implementation, also outside the linear-scaling framework. Our newly developed method allows us to estimate CT energies in the infinite crystal limit, and with these to validate the accuracy of the cluster approximation.

The potential of imogolite nanotubes as (co-)photocatalysts: a linear-scaling density functional theory study

We report a linear-scaling density functional theory (DFT) study of the structure, wall-polarization absolute band-alignment and optical absorption of several, recently synthesized, open-ended imogolite (Imo) nanotubes (NTs), namely single-walled (SW) aluminosilicate (AlSi), SW aluminogermanate (AlGe), SW methylated aluminosilicate (AlSi-Me), and double-walled (DW) AlGe NTs. Simulations with three different semi-local and dispersion-corrected DFT-functionals reveal that the NT wall-polarization can be increased by nearly a factor of four going from SW-AlSi-Me to DW-AlGe. Absolute vacuum alignment of the NT electronic bands and comparison with those of rutile and anatase TiO2 suggest that the NTs may exhibit marked propensity to both photo-reduction and hole-scavenging. Characterization of the NTs’ band-separation and optical properties reveal the occurrence of (near-)UV inside–outside charge-transfer excitations, which may be effective for electron–hole separation and enhanced photocatalytic activity. Finally, the effects of the NTs’ wall-polarization on the absolute alignment of electron and hole acceptor states of interacting water (H2O) molecules are quantified and discussed.

Anharmonic Infrared Spectroscopy through the Fourier Transform of Time Correlation Function Formalism in ONETEP.

Density functional theory molecular dynamics (DFT-MD) provides an efficient framework for accurately computing several types of spectra. The major benefit of DFT-MD approaches lies in the ability to naturally take into account the effects of temperature and anharmonicity, without having to introduce any ad hoc or a posteriori corrections. Consequently, computational spectroscopy based on DFT-MD approaches plays a pivotal role in the understanding and assignment of experimental peaks and bands at finite temperature, particularly in the case of floppy molecules. Linear-scaling DFT methods can be used to study large and complex systems, such as peptides, DNA strands, amorphous solids, and molecules in solution. Here, we present the implementation of DFT-MD IR spectroscopy in the ONETEP linear-scaling code. In addition, two methods for partitioning the dipole moment within the ONETEP framework are presented. Dipole moment partitioning allows us to compute spectra of molecules in solution, which fully include the effects of the solvent, while at the same time removing the solvent contribution from the spectra.

A "Stepping Stone" Approach for Obtaining Quantum Free Energies of Hydration.

We present a method which uses DFT (quantum, QM) calculations to improve free energies of binding computed with classical force fields (classical, MM). To overcome the incomplete overlap of configurational spaces between MM and QM, we use a hybrid Monte Carlo approach to generate quickly correct ensembles of structures of intermediate states between a MM and a QM/MM description, hence taking into account a great fraction of the electronic polarization of the quantum system, while being able to use thermodynamic integration to compute the free energy of transition between the MM and QM/MM. Then, we perform a final transition from QM/MM to full QM using a one-step free energy perturbation approach. By using QM/MM as a stepping stone toward the full QM description, we find very small convergence errors (<1 kJ/mol) in the transition to full QM. We apply this method to compute hydration free energies, and we obtain consistent improvements over the MM values for all molecules we used in this study. This approach requires large-scale DFT calculations as the full QM systems involved the ligands and all waters in their simulation cells, so the linear-scaling DFT code ONETEP was used for these calculations.

Energy landscape and band-structure tuning in realisticMoS2/MoSe2heterostructures

While monolayer forms of two-dimensional materials are well characterized both experimentally and theoretically, properties of bilayer heterostructures are not nearly so well known. We employ high-accuracy linear-scaling density functional theory calculations utilizing nonlocal van der Waals functionals to explore the possible constructions of the ${\mathrm{MoS}}_{2}/{\mathrm{MoSe}}_{2}$ interface. Utilizing large supercells, we vary rotation, translation, and separation of the layers without introducing unrealistic strain. The energy landscape shows very low variations under rotation, with no strongly preferred alignments. By unfolding the spectral function into the primitive cells, we show that the monolayers are more independent than in homo-bilayers and that the electronic band structure of each layer is tunable through rotation, thus influencing hole effective masses.

Large-scale density functional theory simulation of inorganic nanotubes: a case study on Imogolite nanotubes

The high experimental control over inorganic Imogolite-like open-ended nanotubes (Imo-NTs) composition, dimensions and monodispersity together with the potentially huge range of tuneable properties that can be introduced by chemical functionalisation and doping make Imo-NTs appealing substrates for nanotechnology, as artificial ion-channels and in chemical separation. Investigation of Imo-NTs electronic and spectroscopic properties has so far been hampered by the large size of the systems repeat unit (+300 atoms), which pose severe challenges and accuracy-viability compromises for standard plane-wave (fixed atomic basis set) density functional theory (DFT) simulations. These challenges can, however, be met by linear-scaling DFT (LS-DFT) approaches based on in situ optimisation of minimal basis sets. Here, we illustrate the applicability of LS-DFT to Imo-NTs by providing structural and electronic characterisation of periodic and finite models of aluminosilicate (AlSi) and methylated-AlSi Imo-NTs. It is shown that adoption of moderate kinetic energy cutoff (1000 eV) and basis set truncation radius (8 Bohr) leads to optimal accuracy-viability compromised for geometrical optimisation of Imo-NTs. These results should be useful for future LS-DFT investigation of Imo-NTs and other AlSi-based functional materials.

Electronic transport calculations in the onetep code: Implementation and applications

We present an approach for computing Landauer–Büttiker ballistic electronic transport for multi-lead devices containing thousands of atoms. The method is implemented in the onetep linear-scaling density-functional theory code and uses matrix elements calculated from first-principles. Using a compact yet accurate basis of atom-centred non-orthogonal generalised Wannier functions that are optimised in situ to their unique local chemical environment, the transmission and related properties of very large systems can be calculated efficiently and accurately. Other key features include the ability to simulate devices with an arbitrary number of leads, to compute eigenchannel decompositions, and to run on highly parallel computer architectures. We demonstrate the scale of the calculations made possible by our approach by applying it to the study of electronic transport between aligned carbon nanotubes, with system sizes up to 2360 atoms for the underlying density-functional theory calculation. As a consequence of our efficient implementation, computing electronic transport from first principles in systems containing thousands of atoms should be considered routine, even on relatively modest computational resources.

Accurate and efficient linear scaling DFT calculations with universal applicability.

Density functional theory calculations are computationally extremely expensive for systems containing many atoms due to their intrinsic cubic scaling. This fact has led to the development of so-called linear scaling algorithms during the last few decades. In this way it becomes possible to perform ab initio calculations for several tens of thousands of atoms within reasonable walltimes. 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 system with linear scaling walltimes requiring only a moderate demand of computing resources. We prove the effectiveness of our method on a wide variety of systems with different boundary conditions, for single-point calculations as well as for geometry optimizations and molecular dynamics.

Optimized multi-site local orbitals in the large-scale DFT program CONQUEST.

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: Condens. Matter Mater. Phys., 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.

Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10000+ Atoms.

The recent progress of linear-scaling or O(N) methods in density functional theory (DFT) is remarkable. Given this, we might expect that first-principles molecular dynamics (FPMD) simulations based on DFT could treat more realistic and complex systems using the O(N) technique. However, very few examples of O(N) FPMD simulations exist to date, and information on the accuracy and reliability of the simulations is very limited. In this paper, we show that efficient and robust O(N) FPMD simulations are now possible by the combination of the extended Lagrangian Born-Oppenheimer molecular dynamics method, which was recently proposed by Niklasson ( Phys. Rev. Lett. 2008 , 100 , 123004 ), and the density matrix method as an O(N) technique. Using our linear-scaling DFT code Conquest, we investigate the reliable calculation conditions for accurate O(N) FPMD and demonstrate that we are now able to do practical, reliable self-consistent FPMD simulations of a very large system containing 32768 atoms.

Expanding the Scope of Density Derived Electrostatic and Chemical Charge Partitioning to Thousands of Atoms.

The density derived electrostatic and chemical (DDEC/c3) method is implemented into the onetep program to compute net atomic charges (NACs), as well as higher-order atomic multipole moments, of molecules, dense solids, nanoclusters, liquids, and biomolecules using linear-scaling density functional theory (DFT) in a distributed memory parallel computing environment. For a >1000 atom model of the oxygenated myoglobin protein, the DDEC/c3 net charge of the adsorbed oxygen molecule is approximately -1e (in agreement with the Weiss model) using a dynamical mean field theory treatment of the iron atom, but much smaller in magnitude when using the generalized gradient approximation. For GaAs semiconducting nanorods, the system dipole moment using the DDEC/c3 NACs is about 5% higher in magnitude than the dipole computed directly from the quantum mechanical electron density distribution, and the DDEC/c3 NACs reproduce the electrostatic potential to within approximately 0.1 V on the nanorod's solvent-accessible surface. As examples of conducting materials, we study (i) a 55-atom Pt cluster with an adsorbed CO molecule and (ii) the dense solids Mo2C and Pd3V. Our results for solid Mo2C and Pd3V confirm the necessity of a constraint enforcing exponentially decaying electron density in the tails of buried atoms.

Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils

We present a hybrid MPI-OpenMP implementation of Linear-Scaling Density Functional Theory within the ONETEP code. We illustrate its performance on a range of high performance computing (HPC) platforms comprising shared-memory nodes with fast interconnect. Our work has focused on applying OpenMP parallelism to the routines which dominate the computational load, attempting where possible to parallelize different loops from those already parallelized within MPI. This includes 3D FFT box operations, sparse matrix algebra operations, calculation of integrals, and Ewald summation. While the underlying numerical methods are unchanged, these developments represent significant changes to the algorithms used within ONETEP to distribute the workload across CPU cores. The new hybrid code exhibits much-improved strong scaling relative to the MPI-only code and permits calculations with a much higher ratio of cores to atoms. These developments result in a significantly shorter time to solution than was possible using MPI alone and facilitate the application of the ONETEP code to systems larger than previously feasible. We illustrate this with benchmark calculations from an amyloid fibril trimer containing 41,907 atoms. We use the code to study the mechanism of delamination of cellulose nanofibrils when undergoing sonification, a process which is controlled by a large number of interactions that collectively determine the structural properties of the fibrils. Many energy evaluations were needed for these simulations, and as these systems comprise up to 21,276 atoms this would not have been feasible without the developments described here.

Large-Scale Density Functional Theory Transition State Searching in Enzymes.

Linear-scaling quantum mechanical density functional theory calculations have been applied to study the rearrangement of chorismate to prephenate in large-scale models of the Bacillus subtilis chorismate mutase enzyme. By treating up to 2000 atoms at a consistent quantum mechanical level of theory, we obtain an unbiased, almost parameter-free description of the transition state geometry and energetics. The activation energy barrier is calculated to be lowered by 10.5 kcal mol(-1) in the enzyme, compared with the equivalent reaction in water, which is in good agreement with experiment. Natural bond orbital analysis identifies a number of active site residues that are important for transition state stabilization in chorismate mutase. This benchmark study demonstrates that linear-scaling density functional theory techniques are capable of simulating entire enzymes at the ab initio quantum mechanical level of accuracy.

Optimised three-dimensional Fourier interpolation: An analysis of techniques and application to a linear-scaling density functional theory code

The Fourier interpolation of 3D data-sets is a performance critical operation in many fields, including certain forms of image processing and density functional theory (DFT) quantum chemistry codes based on plane wave basis sets, to which this paper is targeted. In this paper we describe three different algorithms for performing this operation built from standard discrete Fourier transform operations, and derive theoretical operation counts. The algorithms compared consist of the most straightforward implementation and two that exploit techniques such as phase-shifts and knowledge of zero padding to reduce computational cost. Through a library implementation (tintl) we explore the performance characteristics of these algorithms and the performance impact of different implementation choices on actual hardware. We present comparisons within the linear-scaling DFT code ONETEP where we replace the existing interpolation implementation with our library implementation configured to choose the most efficient algorithm. Within the ONETEP Fourier interpolation stages, we demonstrate speed-ups of over 1.55×.

Photoexcitation of Light-Harvesting C–P–C60 Triads: A FLMO-TD-DFT Study

The recently proposed linear-scaling time-dependent density functional theory (TD-DFT) [ J. Chem. Comput. 2011 , 7 , 3643 ] is employed to capture more than 300 low-lying excited states for three light-harvesting C-P-C60 triads composed of β-carotenoid polyene (C), diaryl-based porphyrin (P), and pyrrole-fullerene (C60). The simulated optical absorption spectra are grossly in good agreement with experimental observations. To gain insights on the structure-property relations, both top-down and bottom-up analyses of the excited states are made in terms of the underlying fragment localized molecular orbitals (FLMO). A maximum occupation method is further proposed for finding excited-state solutions of self-consistent-field equations and is applied to long-range charge-transfer states that cannot be described by TD-DFT with pure density functionals.

Quantifying Environmental Effects on the Decay of Hole Transfer Couplings in Biosystems.

In the past two decades, many research groups worldwide have tried to understand and categorize simple regimes in the charge transfer of such biological systems as DNA. Theoretically speaking, the lack of exact theories for electron-nuclear dynamics on one side and poor quality of the parameters needed by model Hamiltonians and nonadiabatic dynamics alike (such as couplings and site energies) on the other are the two main difficulties for an appropriate description of the charge transfer phenomena. In this work, we present an application of a previously benchmarked and linear-scaling subsystem density functional theory (DFT) method for the calculation of couplings, site energies, and superexchange decay factors (β) of several biological donor-acceptor dyads, as well as double stranded DNA oligomers composed of up to five base pairs. The calculations are all-electron and provide a clear view of the role of the environment on superexchange couplings in DNA-they follow experimental trends and confirm previous semiempirical calculations. The subsystem DFT method is proven to be an excellent tool for long-range, bridge-mediated coupling and site energy calculations of embedded molecular systems.

Renormalization of myoglobin–ligand binding energetics by quantum many-body effects

We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory. This combination of methods explicitly accounts for dynamical and multireference quantum physics, such as valence and spin fluctuations, of the 3d electrons, while treating a significant proportion of the protein (more than 1,000 atoms) with DFT. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long-standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of the many-body effects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin.

Large-scale DFT simulations with a linear-scaling DFT code CONQUEST on K-computer

In oder to realize the DFT simulations on large-scale complex systems, we have been developing a linear-scaling DFT code Conquest. In this paper, we report the parallel efficiency of the code on K-computer and show that it has almost ideal parallel efficiency even when we use more than 200,000 cores. Using the code on such large-scale parallel computers, we are now ready to do actual DFT study on million-atom systems. By showing our current study on the nucleation of Ge dimers on three-dimensional Ge nano-islands on Si(001), we demonstrate that accurate, efficient and robust structure relaxation based on the DFT is possible in the actual scientific research on complex nano-structured materials.