The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

The CECAM electronic structure library and the modular software development paradigm.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

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.

Natural bond orbital analysis in the ONETEP code: applications to large protein systems.

First principles electronic structure calculations are typically performed in terms of molecular orbitals (or bands), providing a straightforward theoretical avenue for approximations of increasing sophistication, but do not usually provide any qualitative chemical information about the system. We can derive such information via post-processing using natural bond orbital (NBO) analysis, which produces a chemical picture of bonding in terms of localized Lewis-type bond and lone pair orbitals that we can use to understand molecular structure and interactions. We present NBO analysis of large-scale calculations with the ONETEP linear-scaling density functional theory package, which we have interfaced with the NBO 5 analysis program. In ONETEP calculations involving thousands of atoms, one is typically interested in particular regions of a nanosystem whilst accounting for long-range electronic effects from the entire system. We show that by transforming the Non-orthogonal Generalized Wannier Functions of ONETEP to natural atomic orbitals, NBO analysis can be performed within a localized region in such a way that ensures the results are identical to an analysis on the full system. We demonstrate the capabilities of this approach by performing illustrative studies of large proteins--namely, investigating changes in charge transfer between the heme group of myoglobin and its ligands with increasing system size and between a protein and its explicit solvent, estimating the contribution of electronic delocalization to the stabilization of hydrogen bonds in the binding pocket of a drug-receptor complex, and observing, in situ, the n → π* hyperconjugative interactions between carbonyl groups that stabilize protein backbones.

Importance of many-body effects in the Kernel of hemoglobin for ligand binding.

We propose a mechanism for binding of diatomic ligands to heme based on a dynamical orbital selection process. This scenario may be described as bonding determined by local valence fluctuations. We support this model using linear-scaling first-principles calculations, in combination with dynamical mean-field theory, applied to heme, the kernel of the hemoglobin metalloprotein central to human respiration. We find that variations in Hund's exchange coupling induce a reduction of the iron 3d density, with a concomitant increase of valence fluctuations. We discuss the comparison between our computed optical absorption spectra and experimental data, our picture accounting for the observation of optical transitions in the infrared regime, and how the Hund's coupling reduces, by a factor of 5, the strong imbalance in the binding energies of heme with CO and O(2) ligands.

Vanadium dioxide: a Peierls-Mott insulator stable against disorder.

Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this Letter, we develop and carry out state-of-the-art linear scaling density-functional theory calculations refined with nonlocal dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating M(1) phase, and which furthermore survives a moderate degree of disorder.

Interrogation of the protein-protein interactions between human BRCA2 BRC repeats and RAD51 reveals atomistic determinants of affinity.

The breast cancer suppressor BRCA2 controls the recombinase RAD51 in the reactions that mediate homologous DNA recombination, an essential cellular process required for the error-free repair of DNA double-stranded breaks. The primary mode of interaction between BRCA2 and RAD51 is through the BRC repeats, which are ∼35 residue peptide motifs that interact directly with RAD51 in vitro. Human BRCA2, like its mammalian orthologues, contains 8 BRC repeats whose sequence and spacing are evolutionarily conserved. Despite their sequence conservation, there is evidence that the different human BRC repeats have distinct capacities to bind RAD51. A previously published crystal structure reports the structural basis of the interaction between human BRC4 and the catalytic core domain of RAD51. However, no structural information is available regarding the binding of the remaining seven BRC repeats to RAD51, nor is it known why the BRC repeats show marked variation in binding affinity to RAD51 despite only subtle sequence variation. To address these issues, we have performed fluorescence polarisation assays to indirectly measure relative binding affinity, and applied computational simulations to interrogate the behaviour of the eight human BRC-RAD51 complexes, as well as a suite of BRC cancer-associated mutations. Our computational approaches encompass a range of techniques designed to link sequence variation with binding free energy. They include MM-PBSA and thermodynamic integration, which are based on classical force fields, and a recently developed approach to computing binding free energies from large-scale quantum mechanical first principles calculations with the linear-scaling density functional code onetep. Our findings not only reveal how sequence variation in the BRC repeats directly affects affinity with RAD51 and provide significant new insights into the control of RAD51 by human BRCA2, but also exemplify a palette of computational and experimental tools for the analysis of protein-protein interactions for chemical biology and molecular therapeutics.

QM/MM simulation of liquid water with an adaptive quantum region.

The simulation of complex chemical systems often requires a multi-level description, in which a region of special interest is treated using a computationally expensive quantum mechanical (QM) model while its environment is described by a faster, simpler molecular mechanical (MM) model. Furthermore, studying dynamic effects in solvated systems or bio-molecules requires a variable definition of the two regions, so that atoms or molecules can be dynamically re-assigned between the QM and MM descriptions during the course of the simulation. Such reassignments pose a problem for traditional QM/MM schemes by exacerbating the errors that stem from switching the model at the boundary. Here we show that stable, long adaptive simulations can be carried out using density functional theory with the BLYP exchange-correlation functional for the QM model and a flexible TIP3P force field for the MM model without requiring adjustments of either. Using a primary benchmark system of pure water, we investigate the convergence of the liquid structure with the size of the QM region, and demonstrate that by using a sufficiently large QM region (with radius 6 Å) it is possible to obtain radial and angular distributions that, in the QM region, match the results of fully quantum mechanical calculations with periodic boundary conditions, and, after a smooth transition, also agree with fully MM calculations in the MM region. The key ingredient is the accurate evaluation of forces in the QM subsystem which we achieve by including an extended buffer region in the QM calculations. We also show that our buffered-force QM/MM scheme is transferable by simulating the solvated Cl(-) ion.

Doping Engineering of Single-Walled Carbon Nanotubes by Nitrogen Compounds Using Basicity and Alignment.

Charge transport properties in single-walled carbon nanotubes (SWCNTs) can be significantly modified through doping, tuning their electrical and thermoelectric properties. In our study, we used more than 40 nitrogen-bearing compounds as dopants and determined their impact on the material's electrical conductivity. The application of nitrogen compounds of diverse structures and electronic configurations enabled us to determine how the dopant nature affects the SWCNTs. The results reveal that the impact of these dopants can often be anticipated by considering their Hammett's constants and pKa values. Furthermore, the empirical observations supported by first-principles calculations indicate that the doping level can be tuned not only by changing the type and the concentration of dopants but also by varying the orientation of nitrogen compounds around SWCNTs.

Computational analysis of phosphopeptide binding to the polo-box domain of the mitotic kinase PLK1 using molecular dynamics simulation.

The Polo-Like Kinase 1 (PLK1) acts as a central regulator of mitosis and is over-expressed in a wide range of human tumours where high levels of expression correlate with a poor prognosis. PLK1 comprises two structural elements, a kinase domain and a polo-box domain (PBD). The PBD binds phosphorylated substrates to control substrate phosphorylation by the kinase domain. Although the PBD preferentially binds to phosphopeptides, it has a relatively broad sequence specificity in comparison with other phosphopeptide binding domains. We analysed the molecular determinants of recognition by performing molecular dynamics simulations of the PBD with one of its natural substrates, CDC25c. Predicted binding free energies were calculated using a molecular mechanics, Poisson-Boltzmann surface area approach. We calculated the per-residue contributions to the binding free energy change, showing that the phosphothreonine residue and the mainchain account for the vast majority of the interaction energy. This explains the very broad sequence specificity with respect to other sidechain residues. Finally, we considered the key role of bridging water molecules at the binding interface. We employed inhomogeneous fluid solvation theory to consider the free energy of water molecules on the protein surface with respect to bulk water molecules. Such an analysis highlights binding hotspots created by elimination of water molecules from hydrophobic surfaces. It also predicts that a number of water molecules are stabilized by the presence of the charged phosphate group, and that this will have a significant effect on the binding affinity. Our findings suggest a molecular rationale for the promiscuous binding of the PBD and highlight a role for bridging water molecules at the interface. We expect that this method of analysis will be very useful for probing other protein surfaces to identify binding hotspots for natural binding partners and small molecule inhibitors.

Enhancing thermoelectric properties of single-walled carbon nanotubes using halide compounds at room temperature and above.

Carbon nanotubes (CNTs) are materials with exceptional electrical, thermal, mechanical, and optical properties. Ever since it was demonstrated that they also possess interesting thermoelectric properties, they have been considered a promising solution for thermal energy harvesting. In this study, we present a simple method to enhance their performance. For this purpose, thin films obtained from high-quality single-walled CNTs (SWCNTs) were doped with a spectrum of inorganic and organic halide compounds. We studied how incorporating various halide species affects the electrical conductivity, the Seebeck coefficient, and the Power Factor. Since thermoelectric devices operate under non-ambient conditions, we also evaluated these materials' performance at elevated temperatures. Our research shows that appropriate dopant selection can result in almost fivefold improvement to the Power Factor compared to the pristine material. We also demonstrate that the chemical potential of the starting CNT network determines its properties, which is important for deciphering the true impact of chemical and physical functionalization of such ensembles.

Time averaging of NMR chemical shifts in the MLF peptide in the solid state.

Since experimental measurements of NMR chemical shifts provide time and ensemble averaged values, we investigated how these effects should be included when chemical shifts are computed using density functional theory (DFT). We measured the chemical shifts of the N-formyl-L-methionyl-L-leucyl-L-phenylalanine-OMe (MLF) peptide in the solid state, and then used the X-ray structure to calculate the (13)C chemical shifts using the gauge including projector augmented wave (GIPAW) method, which accounts for the periodic nature of the crystal structure, obtaining an overall accuracy of 4.2 ppm. In order to understand the origin of the difference between experimental and calculated chemical shifts, we carried out first-principles molecular dynamics simulations to characterize the molecular motion of the MLF peptide on the picosecond time scale. We found that (13)C chemical shifts experience very rapid fluctuations of more than 20 ppm that are averaged out over less than 200 fs. Taking account of these fluctuations in the calculation of the chemical shifts resulted in an accuracy of 3.3 ppm. To investigate the effects of averaging over longer time scales we sampled the rotameric states populated by the MLF peptides in the solid state by performing a total of 5 micros classical molecular dynamics simulations. By averaging the chemical shifts over these rotameric states, we increased the accuracy of the chemical shift calculations to 3.0 ppm, with less than 1 ppm error in 10 out of 22 cases. These results suggests that better DFT-based predictions of chemical shifts of peptides and proteins will be achieved by developing improved computational strategies capable of taking into account the averaging process up to the millisecond time scale on which the chemical shift measurements report.

Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons.

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mechanical calculations. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calculating properties at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

The True Amphipathic Nature of Graphene Flakes: A Versatile 2D Stabilizer.

The fundamental colloidal properties of pristine graphene flakes remain incompletely understood, with conflicting reports about their chemical character, hindering potential applications that could exploit the extraordinary electronic, thermal, and mechanical properties of graphene. Here, the true amphipathic nature of pristine graphene flakes is demonstrated through wet-chemistry testing, optical microscopy, electron microscopy, and density functional theory, molecular dynamics, and Monte Carlo calculations, and it is shown how this fact paves the way for the formation of ultrastable water/oil emulsions. In contrast to commonly used graphene oxide flakes, pristine graphene flakes possess well-defined hydrophobic and hydrophilic regions: the basal plane and edges, respectively, the interplay of which allows small flakes to be utilized as stabilizers with an amphipathic strength that depends on the edge-to-surface ratio. The interactions between flakes can be also controlled by varying the oil-to-water ratio. In addition, it is predicted that graphene flakes can be efficiently used as a new-generation stabilizer that is active under high pressure, high temperature, and in saline solutions, greatly enhancing the efficiency and functionality of applications based on this material.

Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

Water structuring and collagen adsorption at hydrophilic and hydrophobic silicon surfaces.

The adsorption of a collagen fragment on both a hydrophobic, hydrogen-terminated and a hydrophilic, natively oxidised Si surface is investigated using all-atom molecular dynamics. While favourable direct protein-surface interactions via localised contact points characterise adhesion to the hydrophilic surface, evenly spread surface/molecule contacts and stabilisation of the helical structure occurs upon adsorption on the hydrophobic surface. In the latter case, we find that adhesion is accompanied by a mutual fit between the hydrophilic/hydrophobic pattern within the protein and the layered water structure at the solid/liquid interface, which may provide an additional driving force to the classic hydrophobic effect.

Recent progress in linear-scaling density functional calculations with plane waves and pseudopotentials: the ONETEP code.

The ONETEP program employs the single-particle density matrix reformulation of Kohn-Sham density functional theory to achieve computational cost and memory requirements which increase only linearly with the number of atoms. As the code employs a plane wave basis set (in the form of periodic sinc functions) and pseudopotentials it is able to achieve levels of accuracy and systematic improvability comparable to those of conventional cubic-scaling plane wave approaches. The code has been developed with the aim of running efficiently on a variety of parallel architectures ranging from commodity clusters with tens of processors to large national facilities with thousands of processors. Recent and ongoing studies which we are performing with ONETEP involve problems ranging from materials to biomolecules to nanostructures.

Novel structural features of CDK inhibition revealed by an ab initio computational method combined with dynamic simulations.

The rational development of specific inhibitors for the approximately 500 protein kinases encoded in the human genome is impeded by a poor understanding of the structural basis for the activity and selectivity of small molecules that compete for ATP binding. Combining classical dynamic simulations with a novel ab initio computational approach linear-scalable to molecular interactions involving thousands of atoms, we have investigated the binding of five distinct inhibitors to the cyclin-dependent kinase CDK2. We report here that polarization and dynamic hydrogen bonding effects, so far undetected by crystallography, affect both their activity and selectivity. The effects arise from the specific solvation patterns of water molecules in the ATP binding pocket or the intermittent formation of hydrogen bonds during the dynamics of CDK/inhibitor interactions and explain the unexpectedly high potency of certain inhibitors such as 3-(3H-imidazol-4-ylmethylene)-5-methoxy-1,3-dihydro-indol-2-one (SU9516). The Lys89 residue in the ATP-binding pocket of CDK2 is observed to form temporary hydrogen bonds with the three most potent inhibitors. This residue is replaced in CDK4 by Thr89, whose shorter side-chain cannot form similar bonds, explaining the relative selectivity of the inhibitors for CDK2. Our results provide a generally applicable computational method for the analysis of biomolecular structures and reveal hitherto unrecognized features of the interaction between protein kinases and their inhibitors.

Biomolecular Force Field Parameterization via Atoms-in-Molecule Electron Density Partitioning.

Molecular mechanics force fields, which are commonly used in biomolecular modeling and computer-aided drug design, typically treat nonbonded interactions using a limited library of empirical parameters that are developed for small molecules. This approach does not account for polarization in larger molecules or proteins, and the parametrization process is labor-intensive. Using linear-scaling density functional theory and atoms-in-molecule electron density partitioning, environment-specific charges and Lennard-Jones parameters are derived directly from quantum mechanical calculations for use in biomolecular modeling of organic and biomolecular systems. The proposed methods significantly reduce the number of empirical parameters needed to construct molecular mechanics force fields, naturally include polarization effects in charge and Lennard-Jones parameters, and scale well to systems comprised of thousands of atoms, including proteins. The feasibility and benefits of this approach are demonstrated by computing free energies of hydration, properties of pure liquids, and the relative binding free energies of indole and benzofuran to the L99A mutant of T4 lysozyme.

Constrained geometric simulation of the nicotinic acetylcholine receptor.

Constrained geometric simulations have been performed for the recently published closed-channel state of the nicotinic acetylcholine receptor. These simulations support the theory that correlated motion in the flexible ß-sheet structure of the extracellular domain helps to communicate a "conformational wave", spreading from the acetylcholine binding pocket. Furthermore, we have identified key residues that act at the interface between subunits and between domains that could potentially facilitate rapid communication between the binding site and the transmembrane gate.