The convexity condition of density-functional theory.

It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.

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.

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.

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.

Dynamical Screening of Local Spin Moments at Metal-Molecule Interfaces.

Transition-metal phthalocyanine molecules have attracted considerable interest in the context of spintronics device development due to their amenability to diverse bonding regimes and their intrinsic magnetism. The latter is highly influenced by the quantum fluctuations that arise at the inevitable metal-molecule interface in a device architecture. In this study, we have systematically investigated the dynamical screening effects in phthalocyanine molecules hosting a series of transition-metal ions (Ti, V, Cr, Mn, Fe, Co, and Ni) in contact with the Cu(111) surface. Using comprehensive density functional theory plus Anderson's Impurity Model calculations, we show that the orbital-dependent hybridization and electron correlation together result in strong charge and spin fluctuations. While the instantaneous spin moments of the transition-metal ions are near atomic-like, we find that screening gives rise to considerable lowering or even quenching of these. Our results highlight the importance of quantum fluctuations in metal-contacted molecular devices, which may influence the results obtained from theoretical or experimental probes, depending on their possibly material-dependent characteristic sampling time-scales.

Monolayer Capping Provides Close to Optimal Resistance to Laser Dewetting of Au Films.

Next-generation heat-assisted magnetic recording (HAMR) relies on fast, localized heating of the magnetic medium during the write process. Au plasmonic near-field transducers are an attractive solution to this challenge, but increased thermal stability of Au films is required to improve long-term reliability. This work compares the effect of nanoscale Al, AlOx, and Ta capping films on Au thin films with Ti or Ta adhesion layers for use in HAMR and other high-temperature plasmonic applications. Thermal stability is investigated using a bespoke laser dewetting system, and SEM and AFM are extensively used to interrogate the resulting dewet areas. The most effective capping layers are found to be 0.5-1 nm of Al or AlOx, which can eliminate dewetting under certain conditions. Even one monolayer of AlOx is shown to be highly effective in reducing dewetting. In the case of thicker capping layers of Ta and AlOx, the Au film can easily dewet underneath, leaving an intact capping layer. It is concluded that thinner capping layers are most effective against dewetting as the Au cannot dewet without breaking them and pulling them apart during the dewetting process. A simple model based on energetics considerations is developed, which explains how thinner capping layers can more effectively protect the metal from pore or fissure creation. The model provides some convenient guidelines for choosing both the substrate and capping layer, for a given metal, to maximize the resistance to laser-induced damage.

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.

Adhesion of thin metallic layers on Au surfaces.

We carried out first-principles density-functional theory calculations to study the work of separation for five different metal-metal interfaces, each of them comprising thin layers of selected metals (Cr, W, Ta, Al or Ti) lying on top of Au surfaces. We found that the highest work of separation is obtained for one-atom-thick layers. Increasing the number of atomic layers leads the work of separation to oscillate with the thickness, and ultimately tend to a limiting value for a large number of layers. Interestingly, for most cases the lowest work of separation is obtained for two-atom layers. We find that this behaviour is mirrored by the quantity of charge transferred between the two metals on the one hand, and their spatial distance on the other.

Electric Field Tunability of Photoluminescence from a Hybrid Peptide-Plasmonic Metal Microfabricated Chip.

Enhancement of fluorescence through the application of plasmonic metal nanostructures has gained substantial research attention due to the widespread use of fluorescence-based measurements and devices. Using a microfabricated plasmonic silver nanoparticle-organic semiconductor platform, we show experimentally the enhancement of fluorescence intensity achieved through electro-optical synergy. Fluorophores located sufficiently near silver nanoparticles are combined with diphenylalanine nanotubes (FFNTs) and subjected to a DC electric field. It is proposed that the enhancement of the fluorescence signal arises from the application of the electric field along the length of the FFNTs, which stimulates the pairing of low-energy electrons in the FFNTs with the silver nanoparticles, enabling charge transport across the metal-semiconductor template that enhances the electromagnetic field of the plasmonic nanoparticles. Many-body perturbation theory calculations indicate that, furthermore, the charging of silver may enhance its plasmonic performance intrinsically at particular wavelengths, through band-structure effects. These studies demonstrate for the first time that field-activated plasmonic hybrid platforms can improve fluorescence-based detection beyond using plasmonic nanoparticles alone. In order to widen the use of this hybrid platform, we have applied it to enhance fluorescence from bovine serum albumin and Pseudomonas fluorescens. Significant enhancement in fluorescence intensity was observed from both. The results obtained can provide a reference to be used in the development of biochemical sensors based on surface-enhanced fluorescence.

Enhanced Spin-Orbit Coupling in Heavy Metals via Molecular Coupling.

5d metals are used in electronics because of their high spin-orbit coupling (SOC) leading to efficient spin-electric conversion. When C60 is grown on a metal, the electronic structure is altered due to hybridization and charge transfer. In this work, we measure the spin Hall magnetoresistance for Pt/C60 and Ta/C60, finding that they are up to a factor of 6 higher than those for pristine metals, indicating a 20-60% increase in the spin Hall angle. At low fields of 1-30 mT, the presence of C60 increased the anisotropic magnetoresistance by up to 700%. Our measurements are supported by noncollinear density functional theory calculations, which predict a significant SOC enhancement by C60 that penetrates through the Pt layer, concomitant with trends in the magnetic moment of transport electrons acquired via SOC and symmetry breaking. The charge transfer and hybridization between the metal and C60 can be controlled by gating, so our results indicate the possibility of dynamically modifying the SOC of thin metals using molecular layers. This could be exploited in spin-transfer torque memories and pure spin current circuits.

Surface Modification and Subsequent Fermi Density Enhancement of Bi(111).

Defects introduced to the surface of Bi(111) break the translational symmetry and modify the surface states locally. We present a theoretical and experimental study of the 2D defects on the surface of Bi(111) and the states that they induce. Bi crystals cleaved in ultrahigh vacuum (UHV) at low temperature (110 K) and the resulting ion-etched surface are investigated by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) as well as spectroscopy (STS) techniques in combination with density functional theory (DFT) calculations. STS measurements of cleaved Bi(111) reveal that a commonly observed bilayer step edge has a lower density of states (DOS) around the Fermi level as compared to the atomic-flat terrace. Following ion bombardment, the Bi(111) surface reveals anomalous behavior at both 110 and 300 K: Surface periodicity is observed by LEED, and a significant increase in the number of bilayer step edges and energetically unfavorable monolayer steps is observed by STM. It is suggested that the newly exposed monolayer steps and the type A bilayer step edges result in an increase to the surface Fermi density as evidenced by UPS measurements and the Kohn-Sham DOS. These states appear to be thermodynamically stable under UHV conditions.

Single Indium Atoms and Few-Atom Indium Clusters Anchored onto Graphene via Silicon Heteroatoms.

Single atoms and few-atom nanoclusters are of high interest in catalysis and plasmonics, but pathways for their fabrication and placement remain scarce. We report here the self-assembly of room-temperature-stable single indium (In) atoms and few-atom In clusters (2-6 atoms) that are anchored to substitutional silicon (Si) impurity atoms in suspended monolayer graphene membranes. Using atomically resolved scanning transmission electron microscopy (STEM), we find that the symmetry of the In structures is critically determined by the three- or fourfold coordination of the Si "anchors". All structures are produced without electron-beam induced materials modification. In turn, when activated by electron beam irradiation in the STEM, we observe in situ the formation, restructuring, and translation of the Si-anchored In structures. Our results on In-Si-graphene provide a materials system for controlled self-assembly and heteroatomic anchoring of single atoms and few-atom nanoclusters on graphene.

Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules.

We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.

Flexing Piezoelectric Diphenylalanine-Plasmonic Metal Nanocomposites to Increase SERS Signal Strength.

Piezoelectric quasi-1D peptide nanotubes and plasmonic metal nanoparticles are combined to create a flexible and self-energized surface-enhanced Raman spectroscopy (SERS) substrate that strengthens SERS signal intensities by over an order of magnitude compared to an unflexed substrate. The platform is used to sense bovine serum albumin, lysozyme, glucose, and adenine. Finite-element electromagnetic modeling indicates that the signal enhancement results from piezoelectric-induced charge, which is mechanically activated via substrate bending. The results presented here open the possibility of using peptide nanotubes on conformal substrates for in situ SERS detection.

Plasmonic performance of AuxAgyCu1-x-y alloys from many-body perturbation theory.

We present a detailed appraisal of the optical and plasmonic properties of ordered alloys of the form AuxAgyCu1-x-y, as predicted by means of first-principles many-body perturbation theory augmented by a semi-empirical Drude-Lorentz model. In benchmark simulations on elemental Au, Ag, and Cu, we find that the random-phase approximation (RPA) fails to accurately describe inter-band transitions when it is built upon semi-local approximate Kohn-Sham density-functional theory band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow d-bands which contribute strongly throughout the low-energy spectral range (0-6 eV), may be modeled very expediently using band-stretching operators that imitate the effect of a perturbative [Formula: see text] self-energy correction incorporating quasiparticle (QP) mass renormalization. We thereby establish a convenient work-flow for carrying out approximated [Formula: see text] spectroscopic calculations on alloys and, in particular here, we have considered alloy concentrations down to 12.5% in [Formula: see text], including all possible crystallographic orderings of face-centred cubic type. We develop a pragmatic procedure for calculating the Drude plasmon frequency from first principles, including self-energy effects, as well as a semi-empirical scheme for interpolating the plasmon inverse lifetimes between stoichiometries. A distinctive M-shaped profile is observed in both quantities for binary alloys, in qualitative agreement with previous experimental findings. A range of optical and plasmonic figures of merit are discussed, and plotted for ordered [Formula: see text] at three representative solid-state laser wavelengths. On this basis, we predict that certain compositions may offer improved performance over elemental Au for particular application types. We predict that while the loss functions for both bulk and surface plasmons are typically diminished in strength through binary alloying, certain stoichiometric ratios may exhibit higher-quality (longer-lived) localized surface-plasmons and surface-plasmon polaritons, at technologically-relevant wavelengths, than those in elemental Au.

Equipartition of Energy Defines the Size-Thickness Relationship in Liquid-Exfoliated Nanosheets.

Liquid phase exfoliation is a commonly used method to produce 2D nanosheets from a range of layered crystals. However, such nanosheets display broad size and thickness distributions and correlations between area and thickness, issues that limit nanosheet application potential. To understand the factors controlling the exfoliation process, we have liquid-exfoliated 11 different layered materials, size-selecting each into fractions before using AFM to measure the nanosheet length, width, and thickness distributions for each fraction. The resultant data show a clear power-law scaling of nanosheet area with thickness for each material. We have developed a simple nonequilibrium thermodynamics-based model predicting that the power-law prefactor is proportional to both the ratios of in-plane-tearing/out-of-plane-peeling energies and in-plane/out-of-plane moduli. By comparing the experimental data with the modulus ratio calculated from first-principles, we find close agreement between experiment and theory. This supports our hypothesis that energy equipartition holds between nanosheet tearing and peeling during sonication-assisted exfoliation.

Liquid exfoliation of solvent-stabilized few-layer black phosphorus for applications beyond electronics.

Few-layer black phosphorus (BP) is a new two-dimensional material which is of great interest for applications, mainly in electronics. However, its lack of environmental stability severely limits its synthesis and processing. Here we demonstrate that high-quality, few-layer BP nanosheets, with controllable size and observable photoluminescence, can be produced in large quantities by liquid phase exfoliation under ambient conditions in solvents such as N-cyclohexyl-2-pyrrolidone (CHP). Nanosheets are surprisingly stable in CHP, probably due to the solvation shell protecting the nanosheets from reacting with water or oxygen. Experiments, supported by simulations, show reactions to occur only at the nanosheet edge, with the rate and extent of the reaction dependent on the water/oxygen content. We demonstrate that liquid-exfoliated BP nanosheets are potentially useful in a range of applications from ultrafast saturable absorbers to gas sensors to fillers for composite reinforcement.

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.