Author Correction: Gate controlling of quantum interference and direct observation of anti-resonances in single molecule charge transport.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Origin of Ferroelectric Domain Wall Alignment with Surface Trenches in Ultrathin Films.

Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and superlattices promises control over the orientation and direction of FE domain walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST) parallel alignment, systems where DWs are known for becoming electrical conductors could now become useful nanocircuits using only standard lithographical techniques. Despite this clear application, the microscopic mechanism responsible for the alignment phenomenon has remained elusive. Using ultrathin PbTiO_{3} films as a model system, we explore this mechanism with large scale density functional theory simulations on as many as 5,136 atoms. Although we expect multiple contributing factors, we show that parallel DW-ST alignment can be well explained by this configuration giving rise to an arrangement of electric dipole moments which best restore polar continuity to the film. These moments preserve the polar texture of the pristine film, thus minimizing ST-induced depolarizing fields. Given the generality of this mechanism, we suggest that STs could be used to engineer other exotic polar textures in a variety of FE nanostructures as supported by the appearance of ST-induced polar cycloidal modulations in this Letter. Our simulations also support experimental observations of ST-induced negative strains which have been suggested to play a role in the alignment mechanism.

Blue moon ensemble simulation of aquation free energy profiles applied to mono and bifunctional platinum anticancer drugs.

Aquation free energy profiles of neutral cisplatin and cationic monofunctional derivatives, including triaminochloroplatinum(II) and cis-diammine(pyridine)chloroplatinum(II), were computed using state of the art thermodynamic integration, for which temperature and solvent were accounted for explicitly using density functional theory-based canonical molecular dynamics (DFT-MD). For all the systems, the "inverse-hydration" where the metal center acts as an acceptor of hydrogen bond has been observed. This has motivated to consider the inversely bonded solvent molecule in the definition of the reaction coordinate required to initiate the constrained DFT-MD trajectories. We found that there exists little difference in free enthalpies of activation, such that these platinum-based anticancer drugs are likely to behave the same way in aqueous media. Detailed analysis of the microsolvation structure of the square-planar complexes, along with the key steps of the aquation mechanism, is discussed.

Gate controlling of quantum interference and direct observation of anti-resonances in single molecule charge transport.

Quantum interference can profoundly affect charge transport in single molecules, but experiments can usually measure only the conductance at the Fermi energy. Because, in general, the most pronounced features of the quantum interference are not located at the Fermi energy, it is highly desirable to probe charge transport in a broader energy range. Here, by means of electrochemical gating, we measure the conductance and map the transmission functions of single molecules at and around the Fermi energy, and study signatures associated with constructive and destructive interference. With electrochemical gate control, we tune the quantum interference between the highest occupied molecular orbital and lowest unoccupied molecular orbital, and directly observe anti-resonance, a distinct feature of destructive interference. By tuning the molecule in and out of anti-resonance, we achieve continuous control of the conductance over two orders of magnitude with a subthreshold swing of ~17 mV dec-1, features relevant to high-speed and low-power electronics.

Notes on density matrix perturbation theory.

Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrödinger perturbation theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method.

Large scale and linear scaling DFT with the CONQUEST code.

We survey the underlying theory behind the large-scale and linear scaling density functional theory code, conquest, which shows excellent parallel scaling and can be applied to thousands of atoms with diagonalization and millions of atoms with linear scaling. We give details of the representation of the density matrix and the approach to finding the electronic ground state and discuss the implementation of molecular dynamics with linear scaling. We give an overview of the performance of the code, focusing in particular on the parallel scaling, and provide examples of recent developments and applications.

Communication: Generalized canonical purification for density matrix minimization.

A Lagrangian formulation for the constrained search for the N-representable one-particle density matrix based on the McWeeny idempotency error minimization is proposed, which converges systematically to the ground state. A closed form of the canonical purification is derived for which no a posteriori adjustment on the trace of the density matrix is needed. The relationship with comparable methods is discussed, showing their possible generalization through the hole-particle duality. The appealing simplicity of this self-consistent recursion relation along with its low computational complexity could prove useful as an alternative to diagonalization in solving dense and sparse matrix eigenvalue problems.

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

We introduce numerical optimization of multi-site support functions in the linear-scaling DFT code CONQUEST. Multi-site support functions, which are linear combinations of pseudo-atomic orbitals on a target atom and those neighbours within a cutoff, have been recently proposed to reduce the number of support functions to the minimal basis while keeping the accuracy of a large basis [J. Chem. Theory Comput., 2014, 10, 4813]. The coefficients were determined by using the local filter diagonalization (LFD) method [Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 205104]. We analyse the effect of numerical optimization of the coefficients produced by the LFD method. Tests on crystalline silicon, a benzene molecule and hydrated DNA systems show that the optimization improves the accuracy of the multi-site support functions with small cutoffs. It is also confirmed that the optimization guarantees the variational energy minimizations with multi-site support functions.

Linear scaling density matrix real time TDDFT: Propagator unitarity and matrix truncation.

Real time, density matrix based, time dependent density functional theory (TDDFT) proceeds through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals. It is possible to reduce the computational workload by imposing spatial cutoff radii on sparse matrices, and the propagation of the density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. Following a brief summary of our implementation, along with several benchmark tests illustrating the validity of the method, we present an exploration of the factors affecting the accuracy of the approach. In particular, we investigate the effect of basis set size and matrix truncation, the key approximation used in achieving linear scaling, on the propagator unitarity and optical spectra. Finally, we illustrate that, with an appropriate density matrix truncation range applied, the computational load scales linearly with the system size and discuss the limitations of the approach.

Single-Atom Control of Arsenic Incorporation in Silicon for High-Yield Artificial Lattice Fabrication.

Artificial lattices constructed from individual dopant atoms within a semiconductor crystal hold promise to provide novel materials with tailored electronic, magnetic, and optical properties. These custom-engineered lattices are anticipated to enable new, fundamental discoveries in condensed matter physics and lead to the creation of new semiconductor technologies including analog quantum simulators and universal solid-state quantum computers. This work reports precise and repeatable, substitutional incorporation of single arsenic atoms into a silicon lattice. A combination of scanning tunneling microscopy hydrogen resist lithography and a detailed statistical exploration of the chemistry of arsine on the hydrogen-terminated silicon (001) surface are employed to show that single arsenic dopants can be deterministically placed within four silicon lattice sites and incorporated with 97 ± 2% yield. These findings bring closer to the ultimate frontier in semiconductor technology: the deterministic assembly of atomically precise dopant and qubit arrays at arbitrarily large scales.

Understanding the role of ions and water molecules in the NaCl dissolution process.

The dissolution of NaCl in water is one of the most common everyday processes, yet it remains poorly understood at the molecular level. Here we report the results of an extensive density functional theory study in which the initial stages of NaCl dissolution have been examined at low water coverages. Our specific approach is to study how the energetic cost of moving an ion or a pair of ions to a less coordinated site at the surface of various NaCl crystals varies with the number of water molecules adsorbed on the surface. This "microsolvation" approach allows us to study the dependence of the defect energies on the number of water molecules in the cluster and thus to establish when and where dissolution becomes favorable. Moreover, this approach allows us to understand the roles of the individual ions and water molecules in the dissolution process. Consistent with previous work we identify a clear preference for dissolution of Cl ions over Na ions. However, the detailed information obtained here leads to the conclusion that the process is governed by the higher affinity of the water molecules to Na ions than to Cl ions. The Cl ions are released first as this exposes more Na ions at the surface creating favorable adsorption sites for water. We discuss how this mechanism is likely to be effective for other alkali halides.

H atom adsorption and diffusion on Si(110)-(1×1) and (2×1) surfaces.

We present a periodic density-functional study of hydrogen adsorption and diffusion on the Si(110)-(1×1) and (2×1) surfaces, and identify a local reconstruction that stabilizes the clean Si(110)-(1×1) by 0.51 eV. Hydrogen saturates the dangling bonds of surface Si atoms on both reconstructions and the different structures can be identified from their simulated scanning tunneling microscopy/current image tunneling spectroscopy (STM/CITS) images. Hydrogen diffusion on both reconstructions will proceed preferentially along zigzag rows, in between two adjacent rows. The mobility of the hydrogen atom is higher on the (2×1) reconstruction. Diffusion of a hydrogen vacancy on a monohydride Si(110) surface will proceed along one zigzag row and is slightly more difficult (0.2 eV and 0.6 eV on (1×1) and (2×1), respectively) than hydrogen atom diffusion on the clean surface.

DFT study of undoped and As-doped Si nanowires approaching the bulk limit.

The electronic properties of pure and As-doped Si nanowires (NWs) with radii up to 9.53 nm are studied using large scale density functional theory (DFT) calculations. We show that, for the undoped NWs, the DFT bandgap reduces with increasing diameter and converges to its bulk value, a trend in agreement with experimental data. Moreover, we show that the atoms closest to the surface of the nanowire (NW) contribute less to the states near the band edges, when compared with atoms close to the centre; this is shown to be due to differences in Si-Si atomic distances, as well as surface passivation effects. When considering As-doped Si NWs we show that dopant placement within the NW plays an important role in deciding electronic properties. We show that a low velocity band is introduced by As doping, in the gap, but close to the conduction band edge. The curvature of this low velocity band depends on the dopant location, with the curvature reducing when the dopant is placed closer to the center. We also show that asymmetry of dopant location with the NW leads to splitting of the valence band edge.

Reaction paths of alane dissociation on the Si(0 0 1) surface.

Building on our earlier study, we examine the kinetic barriers to decomposition of alane, AlH3, on the Si(0 0 1) surface, using the nudged elastic band approach within density functional theory. We find that the initial decomposition to AlH with two H atoms on the surface proceeds without a significant barrier. There are several pathways available to lose the final hydrogen, though these present barriers of up to 1 eV. Incorporation is more challenging, with the initial structures less stable in several cases than the starting structures, just as was found for phosphorus. We identify a stable route for Al incorporation following selective surface hydrogen desorption (e.g. by scanning tunneling microscope tip). The overall process parallels PH3, and indicates that atomically precise acceptor doping should be possible.

Structural properties of silicon-germanium and germanium-silicon core-shell nanowires.

Core-shell nanowires made of Si and Ge can be grown experimentally with excellent control for different sizes of both core and shell. We have studied the structural properties of Si/Ge and Ge/Si core-shell nanowires aligned along the [Formula: see text] direction, with diameters up to 10.2 nm and varying core to shell ratios, using linear scaling density functional theory. We show that Vegard's law, which is often used to predict the axial lattice constant, can lead to an error of up to 1%, underlining the need for a detailed ab initio atomistic treatment of the nanowire structure. We analyse the character of the intrinsic strain distribution and show that, regardless of the composition or bond direction, the Si core or shell always expands. In contrast, the strain patterns in the Ge shell or core are highly sensitive to the location, composition and bond direction. The highest strains are found at heterojunction interfaces and the surfaces of the nanowires. This detailed understanding of the atomistic structure and strain paves the way for studies of the electronic properties of core-shell nanowires and investigations of doping and structure defects.

High-accuracy large-scale DFT calculations using localized orbitals in complex electronic systems: the case of graphene-metal interfaces.

Over many years, computational simulations based on density functional theory (DFT) have been used extensively to study many different materials at the atomic scale. However, its application is restricted by system size, leaving a number of interesting systems without a high-accuracy quantum description. In this work, we calculate the electronic and structural properties of a graphene-metal system significantly larger than in previous plane-wave calculations with the same accuracy. For this task we use a localised basis set with the Conquest code, both in their primitive, pseudo-atomic orbital form, and using a recent multi-site approach. This multi-site scheme allows us to maintain accuracy while saving computational time and memory requirements, even in our exemplar complex system of graphene grown on Rh(1 1 1) with and without intercalated atomic oxygen. This system offers a rich scenario that will serve as a benchmark, demonstrating that highly accurate simulations in cells with over 3000 atoms are feasible with modest computational resources.

Effects of the Hubbard U on density functional-based predictions of BiFeO3 properties.

First principles studies of multiferroic materials, such as bismuth ferrite (BFO), require methods that extend beyond standard density functional theory (DFT). The DFT + U method is one such extension that is widely used in the study of BFO. We present a systematic study of the effects of the U parameter on the structural, ferroelectric and electronic properties of BFO. We find that the structural and ferroelectric properties change negligibly in the range of U typically considered for BFO (3-5 eV). In contrast, the electronic structure varies significantly with U. In particular, we see large changes to the character and curvature of the valence band maximum and conduction band minimum, in addition to the expected increase in band gap, as U increases. Most significantly, we find that the [Formula: see text]/[Formula: see text] ordering at the conduction band minimum inverts for U values larger than 4 eV. We therefore recommend a U value of at most 4 eV to be applied to the Fe d orbitals in BFO. More generally, this study emphasises the need for systematic investigations of the effects of the U parameter not merely on band gaps but on the electronic structure as a whole, especially for strongly correlated materials.

Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.

We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.

Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments.

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F68, 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult's law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult's law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult's law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.

Efficient Calculation of Electronic Structure Using O(N) Density Functional Theory.

We propose an efficient way to calculate the electronic structure of large systems by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura method. The electronic Hamiltonian and charge density of large systems are obtained by Conquest, and the eigenstates of the Hamiltonians are then obtained by the Sakurai-Sugiura method. Applications to a hydrated DNA system and adsorbed P2 molecules and Ge hut clusters on large Si substrates demonstrate the applicability of this combination on systems with 10,000+ atoms with high accuracy and efficiency.