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We extend our linear-scaling approach for the calculation of Hartree–Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree–Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results. [ABSTRACT FROM AUTHOR]

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson–Boltzmann equation (P–BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P–BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages. [ABSTRACT FROM AUTHOR]

Density functional theory (DFT) is often used for simulating extended materials such as infinite crystals or surfaces, under periodic boundary conditions (PBCs). In such calculations, when the simulation cell has non-zero charge, electrical neutrality has to be imposed, and this is often done via a uniform background charge of opposite sign ("jellium"). This artificial neutralization does not occur in reality, where a different mechanism is followed as in the example of a charged electrode in electrolyte solution, where the surrounding electrolyte screens the local charge at the interface. The neutralizing effect of the surrounding electrolyte can be incorporated within a hybrid quantum–continuum model based on a modified Poisson–Boltzmann equation, where the concentrations of electrolyte ions are modified to achieve electroneutrality. Among the infinite possible ways of modifying the electrolyte charge, we propose here a physically optimal solution, which minimizes the deviation of concentrations of electrolyte ions from those in open boundary conditions (OBCs). This principle of correspondence of PBCs with OBCs leads to the correct concentration profiles of electrolyte ions, and electroneutrality within the simulation cell and in the bulk electrolyte is maintained simultaneously, as observed in experiments. This approach, which we call the Neutralization by Electrolyte Concentration Shift (NECS), is implemented in our electrolyte model in the Order-N Electronic Total Energy Package (ONETEP) linear-scaling DFT code, which makes use of a bespoke highly parallel Poisson–Boltzmann solver, DL_MG. We further propose another neutralization scheme ("accessible jellium"), which is a simplification of NECS. We demonstrate and compare the different neutralization schemes on several examples. [ABSTRACT FROM AUTHOR]

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem – with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K+, and Cl−. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface. [ABSTRACT FROM AUTHOR]

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms. [ABSTRACT FROM AUTHOR]

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals. [ABSTRACT FROM AUTHOR]

A new method for finite-temperature density functional theory calculations which significantly increases the number of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic system, described in terms of a set of non-orthogonal, localized functions which are optimized in situ using a periodic-sinc basis set, equivalent to plane waves. Most parts of the calculation, including the demanding operation of building the Hamiltonian matrix, have a computational cost that scales linearly with the number of atoms in the system. Also, this approach ensures that the Hamiltonian matrix has a minimal size, which reduces the computational overhead due to diagonalization, a cubic-scaling operation that is still required. Large basis set accuracy is retained via the optimization of the localized functions. This method allows accurate simulations of entire metallic nanostructures, demonstrated with calculations on a supercell of bulk copper with 500 atoms and on gold nanoparticles with up to 2057 atoms. [ABSTRACT FROM AUTHOR]

Density Functional Theory (DFT) calculations with computational effort which increases linearly with the number of atoms (linear-scaling DFT) have been successfully developed for insulators, taking advantage of the exponential decay of the one-particle density matrix. For metallic systems, the density matrix is also expected to decay exponentially at finite electronic temperature and linear-scaling DFT methods should be possible by taking advantage of this decay. Here we present a method for DFT calculations at finite electronic temperature for metallic systems which is effectively linear-scaling (O(N)). Our method generates the elements of the one-particle density matrix and also finds the required chemical potential and electronic entropy using polynomial expansions. A fixed expansion length is always employed to generate the density matrix, without any loss in accuracy by the application of a high electronic temperature followed by successive steps of temperature reduction until the desired (low) temperature density matrix is obtained. We have implemented this method in the ONETEP linear-scaling (for insulators) DFT code which employs local orbitals that are optimised in situ. By making use of the sparse matrix machinery of ONETEP, our method exploits the sparsity of Hamiltonian and density matrices to perform calculations on metallic systems with computational cost that increases asymptotically linearly with the number of atoms. We demonstrate the linear-scaling computational cost of our method with calculation times on palladium nanoparticles with up to ∼13 000 atoms. [ABSTRACT FROM AUTHOR]

Hypothesis Silanol groups at the silica–water interface determine not only the surface charge, but also have an important role in the binding of ions and biomolecules. As the pH is increased above pH 2, the silica surface develops a net negative charge primarily due to deprotonation of the silanol group. An improved understanding of the energetics and mechanisms of this fundamentally important process would further understanding of the relevant dynamics. Simulations Density Functional Theory ab initio molecular dynamics and geometry optimisations were used to investigate the mechanisms of surface neutralisation and charging in the presence of OH - and H 3 O + respectively. This charging mechanism has received little attention in the literature. Findings The protonation or deprotonation of isolated silanols in the presence of H 3 O + or OH - , respectively, was shown to be a highly rapid, exothermic reaction with no significant activation energy. This process occurred via a concerted motion of the protons through ‘water wires’. Geometry optimisations of large water clusters at the silica surface demonstrated proton transfer to the surface occurring via the rarely discussed ‘proton holes’ mechanism. This indicates that surface protonation is possible even when the hydronium ion is distant (at least 4 water molecules separation) from the surface. [ABSTRACT FROM AUTHOR]

Theuse of the Zwanzig equation in the calculation of single-stepperturbations to provide first-principles (ab initio) quantum mechanics (QM) correction terms to molecular mechanics(MM) free energy cycles is well established. A rigorous test of theability to converge such calculations would be very useful in thiscontext. In this work, we perform a direct assessment of the convergenceof the MM to QM perturbation, by attempting the reverse QM to MM perturbation.This required the generation of extensive QM molecular dynamics trajectories,using density functional theory (DFT), within the representative biologicalsystem of a DNA adenosine–thymidine dimer. Over 100 ps of dynamicswith the PBE functional and 6.25 ps with the LDA functional were generated.We demonstrate that calculations with total potential energies arevery poorly convergent due to a lack of overlap of phase space distributionsbetween ensembles. While not theoretically rigorous, the use of interactionenergies provides far superior convergence, despite the presence ofnonclassical charge transfer effects within the DFT trajectories.The source of poor phase space overlap for total energies is diagnosed,the approximate quantification of overlaps suggesting that even forthe comparatively simple system considered here convergence of totalenergy calculations within a reasonable simulation time is unfeasible. [ABSTRACT FROM AUTHOR]

A comprehensive conformational analysis of both 2,3-difluorobutane diastereomers is presented based on density functional theory calculations in vacuum and in solution, as well as NMR experiments in solution. While for 1,2-difluoroethane the fluorine gauche effect is clearly the dominant effect determining its conformation, it was found that for 2,3-difluorobutane there is a complex interplay of several effects, which are of similar magnitude but often of opposite sign. As a result, unexpected deviations in dihedral angles, relative conformational energies and populations are observed which cannot be rationalised only by chemical intuition. Furthermore, it was found that it is important to consider the free energies of the various conformers, as these lead to qualitatively different results both in vacuum and in solvent, when compared to calculations based only on the electronic energies. In contrast to expectations, it was found that vicinal syn-difluoride introduction in the butane and by extension, longer hydrocarbon chains, is not expected to lead to an effective stabilisation of the linear conformation. Our findings have implications for the use of the vicinal difluoride motif for conformational control. [ABSTRACT FROM AUTHOR]

Most of them are clustered along the diagonal of the matrix which in turn implies that the bulk of the communication and computation will be performed during super-steps which involve diagonal or near-diagonal processor-processor blocks. B Figure 11. b Parallel speed-ups per one NGWF iteration on a SUN V40z server with four AMD OPTERON processors for a 1000-atom block of crystalline silicon (left) and a 988-atom protein (right). The speed-up as a function of the number of processors is given for the generation of the local potential integrals according to Section 3.1, the electronic charge density according to Section 3.2, the NGWF gradient according to Section 3.3 and the total wall-clock time taken for one NGWF iteration. [Extracted from the article]

ONETEP: linear-scaling density-functional theory with local orbitals and plane waves (Phys. B Figure 2. b Three localised orbitals (non-orthogonal generalised Wannier functions) generated by ONETEP for the same oligopeptide molecule as Figure 1. B Figure 4. b Total energy convergence with respect to density-kernel cut-off I r i SB I K i sb for a Ti SB 38 sb O SB 76 sb cluster. [Extracted from the article]

The article discusses the role that density functional theory (DFT) plays as a quantum mechanics method in materials simulation, referencing a study within the issue co-authored by scientist K. Lejaeghere.

CeO 2 (ceria) is a material of significant industrial and technological importance, used in solid oxide fuel cells and catalysis. Here, we explore the usage of linear-scaling density functional theory as implemented in the ONETEP code, which allows to use larger simulation cells. By using DFT+ U calculations we revise the defect chemistry of ceria, including point defects, Frenkel and Schottky defects. We found that the ground state of an oxygen vacancy is associated to two neighbouring reduced cerium sites. A cerium vacancy is the least favourable point defect, where holes localise on neighbouring oxygen sites. It is more favourable to displace an oxygen interstitial defect away from the octahedral interstitial site, with the formation of a stable peroxide species. Our simulations show that a cerium interstitial is best accommodated in the octahedral interstitial site, as this minimises the distortion of the lattice. Placing a vacancy and an interstitial defect at a separation of 5.18 Å for the OF¡110¿ and 4.77 Å for the CeF¡111¿, stable Frenkel defects can be formed. We also studied the effect of different supercell size on the energetic ordering of Schottky defects, where the S¡111¿ is more favourable than the S¡110¿ for a given simulation cells containing 324 or more atoms. • Linear-scaling density functional theory simulations with bulk materials. • Large simulation cells containing defects in bulk cerium oxide. • Point defect formation at more dilute concentrations. • Structural and electronic properties of point defects. • Energetic ordering of Frenkel and Schottky defects at increasing simulation size. [ABSTRACT FROM AUTHOR]

Many studies of heterogeneous catalysis, both experimental and computational, make use of idealized structures such as extended surfaces or regular polyhedral nanoparticles. This simplification neglects the morphological diversity in real commercial oxygen reduction reaction (ORR) catalysts used in fuel-cell cathodes. Here we introduce an approach that combines 3D nanoparticle structures obtained from high-throughput high-precision electron microscopy with density functional theory. Discrepancies between experimental observations and cuboctahedral/truncated-octahedral particles are revealed and discussed using a range of widely used descriptors, such as electron-density, d-band centers, and generalized coordination numbers. We use this new approach to determine the optimum particle size for which both detrimental surface roughness and particle shape effects are minimized. [ABSTRACT FROM AUTHOR]