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.

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.

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.

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.

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.

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.

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 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.

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.

Polarized Protein-Specific Charges from Atoms-in-Molecule Electron Density Partitioning.

Atomic partial charges for use in traditional force fields for biomolecular simulation are often fit to the electrostatic potentials of small molecules and, hence, neglect large-scale electronic polarization. On the other hand, recent advances in atoms-in-molecule charge derivation schemes show promise for use in flexible force fields but are limited in size by the underlying quantum mechanical calculation of the electron density. Here, we implement the density derived electrostatic and chemical charges method in the linear-scaling density functional theory code ONETEP. Our implementation allows the straightforward derivation of partial atomic charges for systems comprising thousands of atoms, including entire proteins. We demonstrate that the derived charges are chemically intuitive, reproduce ab initio electrostatic potentials of proteins and are transferable between closely related systems. Simulated NMR data derived from molecular dynamics of three proteins using force fields based on the ONETEP charges are in good agreement with experiment.

Assessing the accuracy of inhomogeneous fluid solvation theory in predicting hydration free energies of simple solutes.

Accurate prediction of hydration free energies is a key objective of any free energy method that is applied to modeling and understanding interactions in the aqueous phase. Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. IFST has found wide application in understanding hydration phenomena in biological systems, but quantitative applications have not been comprehensively assessed. In this study, we report the hydration free energies of six simple solutes calculated using IFST and independently using free energy perturbation (FEP). This facilitates a validation of IFST that is independent of the accuracy of the force field. The results demonstrate that IFST shows good agreement with FEP, with an R(2) coefficient of determination of 0.99 and a mean unsigned difference of 0.7 kcal/mol. However, sampling is a major issue that plagues IFST calculations and the results suggest that a histogram method may require prohibitively long simulations to achieve convergence of the entropies, for bin sizes which effectively capture the underlying probability distributions. Results also highlight the sensitivity of IFST to the reference interaction energy of a water molecule in bulk, with a difference of 0.01 kcal/mol changing the predicted hydration free energies by approximately 2.4 kcal/mol for the systems studied here. One of the major advantages of IFST over perturbation methods such as FEP is that the systems are spatially decomposed to consider the contribution of specific regions to the total solvation free energies. Visualizing these contributions can yield detailed insights into solvation thermodynamics. An insight from this work is the identification and explanation of regions with unfavorable free energy density relative to bulk water. These regions contribute unfavorably to the hydration free energy. Further work is necessary before IFST can be extended to yield accurate predictions of binding free energies, but the work presented here demonstrates its potential.

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.

Electrostatic considerations affecting the calculated HOMO-LUMO gap in protein molecules.

A detailed study of energy differences between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps) in protein systems and water clusters is presented. Recent work questioning the applicability of Kohn-Sham density-functional theory to proteins and large water clusters (Rudberg 2012 J. Phys.: Condens. Matter 24 072202) has demonstrated vanishing HOMO-LUMO gaps for these systems, which is generally attributed to the treatment of exchange in the functional used. The present work shows that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Practical solutions for ensuring the gap is maintained when the system size is increased are demonstrated. This work has important implications for the use of large-scale density-functional theory in biomolecular systems, particularly in the simulation of photoemission, optical absorption and electronic transport, all of which depend critically on differences between energies of molecular orbitals.

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.

Toward Ab Initio Optical Spectroscopy of the Fenna-Matthews-Olson Complex.

We present progress toward a first-principles parametrization of the Hamiltonian of the Fenna-Matthews-Olson pigment-protein complex, a molecule that has become key to understanding the role of quantum dynamics in photosynthetic exciton energy transfer. To this end, we have performed fully quantum mechanical calculations on each of the seven bacteriochlorophyll pigments that make up the complex, including a significant proportion of their protein environment (more than 2000 atoms), using linear-scaling density functional theory exploiting a recent development for the computation of excited states. Local pigment transition energies and interpigment coupling between optical transitions have been calculated and are in good agreement with the literature consensus. Comparisons between simulated and experimental optical spectra point toward future work that may help to elucidate important design principles in these nanoscale devices.

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.

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.

Ligand Discrimination in Myoglobin from Linear-Scaling DFT+U.

Myoglobin modulates the binding of diatomic molecules to its heme group via hydrogen-bonding and steric interactions with neighboring residues, and is an important benchmark for computational studies of biomolecules. We have performed calculations on the heme binding site and a significant proportion of the protein environment (more than 1000 atoms) using linear-scaling density functional theory and the DFT+U method to correct for self-interaction errors associated with localized 3d states. We confirm both the hydrogen-bonding nature of the discrimination effect (3.6 kcal/mol) and assumptions that the relative strain energy stored in the protein is low (less than 1 kcal/mol). Our calculations significantly widen the scope for tackling problems in drug design and enzymology, especially in cases where electron localization, allostery, or long-ranged polarization influence ligand binding and reaction.

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.