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We report a phenomenological magneto-structural model based on competing free-energy terms that couple either polar or chiral distortions in cubic quadruple perovskites, depending on the global direction of magnetic moments. The model naturally explains why some compounds in this material system host magnetically-induced ferroelectricity at low temperature, while others such as CaMn$_3$(Cr$_3$Mn)O$_{12}$, which we characterise experimentally, do not. Importantly, our results suggest a new approach towards developing an applied multiferroic functionality, and can be generalised to other multi-sublattice systems where the magnetic interaction between sublattices is prohibited by spatial inversion., Comment: 6 pages, 3 figures

In this paper we use density-functional theory calculations to analyze both the stability and diffusion of Cu adatoms near and on the H-passivated Si(001) surface. Two different Cu sources are considered: depositing Cu from vacuum, and contaminating Cu outdiffusing from bulk Si. Deposited Cu from vacuum quickly moves subsurface to an interstitial site in the third Si layer (T2). Once there, Cu adatoms enter a subsurface zigzag migration route between T2 and another subsurface site, T2->HSL->T2, along the dimer row direction. Contaminating Cu outdiffusing from bulk is found to be a fast diffuser along both parallel and perpendicular directions to the dimer row when far from the surface. It is attracted to the layers close to the surface and becomes trapped at an interstitial site located at the sixth Si layer (T3). As the outdiffusing Cu atoms get closer to the surface, a channeling zigzag diffusion along the dimer row direction, similar to that one followed by deposited Cu from vacuum, is favoured over diffusion along the perpendicular direction. These results are consistent with previous experimental work done on similar systems and will motivate further experiments on the interesting interaction between Cu and Si surfaces.

CONQUEST is a DFT code which was designed from the beginning to enable extremely large-scale calculations on massively parallel platforms, implementing both exact and linear scaling solvers for the ground state. It uses local basis sets (both pseudo-atomic orbitals, PAOs, and systematically convergent B-splines) and sparse matrix storage and operations to ensure locality in all aspects of the calculation. Using exact diagonalisation approaches and a full PAO basis set, systems of up to 1,000 atoms can be modelled with relatively modest resources (200-500 cores), while use of multi-site support functions (MSSF) enable calculations of up to 10,000 atoms with similar resources. With linear scaling, the code demonstrates essentially perfect weak scaling (fixed atoms per process), and has been applied to over 1,000,000 atoms, scaling to nearly 200,000 cores; it has been run on both the K computer and Fugaku, among other computers. CONQUEST calculates the total energy, forces and stresses exactly, and allows structural optimisation of both ions and simulation cell. Molecular dynamics calculations within the NVE, NVT and NPT ensembles are possible with both exact diagonalisation and linear scaling[6]. The code interfaces with LibXC to implement LDA and GGA functionals, with metaGGA and hybrid functionals under development. Dispersion interactions can be included using semi-empirical methods (DFT-D2/3, TS) and vdW-DF. The polarisation can be calculated using Resta's approach., Comment: Submitted to Modell. Simul. Mat. Sci. Eng. as part of a roadmap on electronic structure methods for exascale computing

First principles density functional theory (DFT) simulations of antiferroelectric (AFE) PbZrO$_3$ and PbHfO$_3$ reveal a dynamical instability in the phonon spectra of their purported low temperature $Pbam$ ground states. This instability doubles the $c$-axis of $Pbam$ and condenses five new small amplitude phonon modes giving rise to an 80-atom $Pnam$ structure. Compared with $Pbam$, the stability of this structure is slightly enhanced and highly reproducible as demonstrated through using different DFT codes and different treatments of electronic exchange & correlation interactions. This suggests that $Pnam$ is a new candidate for the low temperature ground state of both materials. With this finding, we bring parity between the AFE archetypes and recent observations of a very similar AFE phase in doped or electrostatically engineered BiFeO$_3$., Comment: 14 pages, 3 figures and 4 tables

We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the scanning tunnelling microscope (STM) and surface problems, tracking the author's personal interest, though the general principles are widely applicable., Comment: 22 pages, 7 figures, accepted in Contemporary Physics

The transition metal dichalcogenide $1T$-TiSe$_2$ is a quasi-two-dimensional layered material with a phase transition towards a commensurate charge density wave (CDW) at a critical temperature T$_{c}\approx 200$K. The relationship between the origin of the CDW instability and the semimetallic or semiconducting character of the normal state, i.e., with the non-reconstructed Fermi surface topology, remains elusive. By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations, we investigate $1T$-TiSe$_{2-x}$S$_x$ single crystals. Using STM, we first show that the long-range phase coherent CDW state is stable against S substitutions with concentrations at least up to $x=0.34$. The ARPES measurements then reveal a slow but continuous decrease of the overlap between the electron and hole ($e$-$h$) bands of the semimetallic normal-state well reproduced by DFT and related to slight reductions of both the CDW order parameter and $T_c$. Our DFT calculations further predict a semimetal-to-semiconductor transition of the normal state at a higher critical S concentration of $x_c$=0.9 $\pm$0.1, that coincides with a melted CDW state in TiSeS as measured with STM. Finally, we rationalize the $x$-dependence of the $e$-$h$ band overlap in terms of isovalent substitution-induced competing chemical pressure and charge localization effects. Our study highlights the key role of the $e$-$h$ band overlap for the CDW instability., Comment: 7 pages, 6 figures

Atomic nanolines are one dimensional systems realized by assembling many atoms on a substrate into long arrays. The electronic properties of the nanolines depend on those of the substrate. Here, we demonstrate that to fully understand the electronic properties of Bi nanolines on clean Si(001) several different contributions must be accounted for. Scanning tunneling microscopy reveals a variety of different patterns along the nanolines as the imaging bias is varied. We observe an electronic phase shift of the Bi dimers, associated with imaging atomic p-orbitals, and an electronic coupling between the Bi nanoline and neighbouring Si dimers, which influences the appearance of both. Understanding the interplay between the Bi nanolines and Si substrate could open a novel route to modifying the electronic properties of the nanolines., Comment: 6 pages (main), 2 pages (SI), accepted by Phys. Rev. B

The transition metal dichalcogenide 1$T$-TiSe$_2$ is a quasi-two-dimensional layered material undergoing a commensurate 2 $\times$ 2 $\times$ 2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below $\approx$ 200 K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows to go beyond the usual spatial resolution of STM and to intimately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric, achiral nature of the CDW in the $z$-direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds., Comment: 5 pages, 4 figures

Scanning tunneling microscopy (STM) reveals unusual sharp features in otherwise defect free bismuth nanolines self-assembled on Si(001). They appear as subatomic thin lines perpendicular to the bismuth nanoline at positive biases and as atomic size beads at negative biases. Density functional theory (DFT) simulations show that these features can be attributed to buckled Si dimers substituting for Bi dimers in the nanoline, where the sharp feature is the counterintuitive signature of these dimers flipping during scanning. The perfect correspondence between the STM data and the DFT simulation demonstrated in this study highlights the detailed understanding we have of the complex Bi-Si(001) Haiku system., Comment: Five pages, six figures, submitted to PRL

We study the impact of Cu intercalation on the charge density wave (CDW) in 1T-Cu$_{\text{x}}$TiSe$_{\text{2}}$ by scanning tunneling microscopy and spectroscopy. Cu atoms, identified through density functional theory modeling, are found to intercalate randomly on the octahedral site in the van der Waals gap and to dope delocalized electrons near the Fermi level. While the CDW modulation period does not depend on Cu content, we observe the formation of charge stripe domains at low Cu content (x$<$0.02) and a breaking up of the commensurate order into 2$\times$2 domains at higher Cu content. The latter shrink with increasing Cu concentration and tend to be phase-shifted. These findings invalidate a proposed excitonic pairing as the primary CDW formation mechanism in this material., Comment: 5 pages, 4 figures

In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it into phase-shifted domains. Here, we report scanning tunneling microscopy and spectroscopy experiments that reveal a dopant-site dependence of the CDW gap. Supported by density functional theory, we demonstrate that the loss of the longrange phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the $1T$-TiSe$_2$ CDW reveals a novel mechanism between CDW and defects in mutual influence., Comment: 5 pages, 4 figures

The impact of variable Ti self-doping on the 1T-TiSe2 charge density wave (CDW) is studied by scanning tunneling microscopy. Supported by density functional theory we show that agglomeration of intercalated-Ti atoms acts as preferential nucleation centers for the CDW that breaks up in phaseshifted CDW domains whose size directly depends on the intercalated-Ti concentration and which are separated by atomically-sharp phase boundaries. The close relationship between the diminution of the CDW domain size and the disappearance of the anomalous peak in the temperature dependent resistivity allows to draw a coherent picture of the 1T-TiSe2 CDW phase transition and its relation to excitons., Comment: 5 pages, 4 figures

Mn has been found to self-assemble into atomic chains running perpendicular to the surface dimer reconstruction on Si(001). They differ from other atomic chains by a striking asymmetric appearance in filled state scanning tunneling microscopy (STM) images. This has prompted complicated structural models involving up to three Mn atoms per chain unit. Combining STM, atomic force microscopy and density functional theory we find that a simple necklace-like chain of single Mn atoms reproduces all their prominent features, including their asymmetry not captured by current models. The upshot is a remarkably simpler structure for modelling the electronic and magnetic properties of Mn atom chains on Si(001)., Comment: 5 pages, 4 figures

We present a detailed low temperature scanning tunneling microscopy study of the commensurate charge density wave (CDW) in 1$T$-TiSe$_2$ in the presence of single atom defects. We find no significant modification of the CDW lattice in single crystals with native defects concentrations where some bulk probes already measure substantial reductions in the CDW phase transition signature. Systematic analysis of STM micrographs combined with density functional theory modelling of atomic defect patterns indicate that the observed CDW modulation lies in the Se surface layer. The defect patterns clearly show there are no 2$H$-polytype inclusions in the CDW phase, as previously found at room temperature [Titov A.N. et al, Phys. Sol. State 53, 1073 (2011). They further provide an alternative explanation for the chiral Friedel oscillations recently reported in this compound [J. Ishioka et al., Phys. Rev. B 84, 245125, (2011)]., Comment: 5 pages, 4 figures

The transition metal dichalcogenide 1T-TiSe2 is a quasi two-dimensional layered material with a charge density wave (CDW) transition temperature of TCDW 200 K. Self-doping effects for crystals grown at different temperatures introduce structural defects, modify the temperature dependent resistivity and strongly perturbate the CDW phase. Here we study the structural and doping nature of such native defects combining scanning tunneling microscopy/spectroscopy and ab initio calculations. The dominant native single atom dopants we identify in our single crystals are intercalated Ti atoms, Se vacancies and Se substitutions by residual iodine and oxygen., Comment: 5 pages, 3 figures

The determining factor of the bulk properties of doped Si is the column rather than the row in the periodic table from which the dopants are drawn. It is unknown whether the basic properties of dopants at surfaces and interfaces, steadily growing in importance as microelectronic devices shrink, are also solely governed by their column of origin. The common light impurity P replaces individual Si atoms and maintains the integrity of the dimer superstructure of the Si(001) surface, but loses its valence electrons to surface states. Here we report that isolated heavy dopants are entirely different: Bi atoms form pairs with Si vacancies, retain their electrons and have highly localized, half-filled orbitals., Comment: 8 pages, 8 figures, to appear in Phys. Rev. B

Understanding the mechanisms underlying ion channel function from the atomic-scale requires accurate ab initio modelling as well as careful experiments. Here, we present a density functional theory (DFT) study of the ion channel gramicidin A, whose inner pore conducts only monovalent cations and whose conductance has been shown to depend on the side chains of the amino acids in the channel. We investigate the ground-state geometry and electronic properties of the channel in vacuum, focusing on their dependence on the side chains of the amino acids. We find that the side chains affect the ground state geometry, while the electrostatic potential of the pore is independent of the side chains. This study is also in preparation for a full, linear scaling DFT study of gramicidin A in a lipid bilayer with surrounding water. We demonstrate that linear scaling DFT methods can accurately model the system with reasonable computational cost. Linear scaling DFT allows ab initio calculations with 10,000 to 100,000 atoms and beyond, and will be an important new tool for biomolecular simulations., Comment: 15 pages, six figures, accepted for publication in J. Roy. Soc. Interface

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed., Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes)

We present a detailed study of the structural and electronic properties of a self-assembled silicon nanoline embedded in the H-terminated silicon (001) surface, known as the Haiku stripe. The nanoline is a perfectly straight and defect free endotaxial structure of huge aspect ratio; it can grow micrometre long at a constant width of exactly four Si dimers (1.54nm). Another remarkable property is its capacity to be exposed to air without suffering any degradation. The nanoline grows independently of any step edges at tunable densities, from isolated nanolines to a dense array of nanolines. In addition to these unique structural characteristics, scanning tunnelling microscopy and density functional theory reveal a one-dimensional state confined along the Haiku core. This nanoline is a promising candidate for the long sought after electronic solid-state one-dimensional model system to explore the fascinating quantum properties emerging in such reduced dimensionality., Comment: 8 pages, 6 figures

Single atom metallic wires of arbitrary length are of immense technological and scientific interest. We describe a novel silicon-only template enabling the self-organised growth of isolated micrometer long surface and subsurface single-atom chains. It consists of a one dimensional, defect-free reconstruction - the Haiku core, here revealed for the first time in details - self-assembled on hydrogenated Si(001) terraces, independent of any step edges. We discuss the potential of this Si-in-Si template as an appealing alternative to vicinal surfaces for nanoscale patterning., Comment: 3 pages, 2 figures

An overview of the Conquest linear scaling density functional theory (DFT) code is given, focussing particularly on the scaling behaviour on modern high- performance computing (HPC) platforms. We demonstrate that essentially perfect linear scaling and weak parallel scaling (with fixed atoms per processor core) can be achieved, and that DFT calculations on millions of atoms are now possible., Comment: 11 pages, three figures, in press with J. Phys.:Condens. Matter

The non-local van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be dramatically improved both for dispersion and hydrogen bonded complexes through the judicious selection of its underlying exchange functional. New and published exchange functionals are identified that deliver much better than chemical accuracy from vdW-DF for the S22 benchmark set of weakly interacting dimers and for water clusters. Improved performance for the adsorption of water on salt is also obtained., Comment: 5 pages, 2 figures, 2 tables

In this review we consider those processes in condensed matter that involve the irreversible flow of energy between electrons and nuclei that follows from a system being taken out of equilibrium. We survey some of the more important experimental phenomena associated with these processes, followed by a number of theoretical techniques for studying them. The techniques considered are those that can be applied to systems containing many non-equivalent atoms. They include both perturbative approaches (Fermi's Golden Rule, and non-equilibrium Green's functions) and molecular dynamics based (the Ehrenfest approximation, surface hopping, semi-classical gaussian wavefunction methods and correlated electron-ion dynamics). These methods are described and characterised, with indications of their relative merits., Comment: LaTeX with IoP style files, 43 pages, 3 figures

While the success of density functional theory (DFT) has led to its use in a wide variety of fields such as physics, chemistry, materials science and biochemistry, it has long been recognised that conventional methods are very inefficient for large complex systems, because the memory requirements scale as $N^2$ and the cpu requirements as $N^3$ (where $N$ is the number of atoms). The principles necessary to develop methods with linear scaling of the cpu and memory requirements with system size ($\mathcal{O}(N)$ methods) have been established for more than ten years, but only recently have practical codes showing this scaling for DFT started to appear. We report recent progress in the development of the \textsc{Conquest} code, which performs $\mathcal{O}(N)$ DFT calculations on parallel computers, and has a demonstrated ability to handle systems of over 10,000 atoms. The code can be run at different levels of precision, ranging from empirical tight-binding, through \textit{ab initio} tight-binding, to full \textit{ab initio}, and techniques for calculating ionic forces in a consistent way at all levels of precision will be presented. Illustrations are given of practical \textsc{Conquest} calculations in the strained Ge/Si(001) system., Comment: 12 pages, 7 figures, accepted by phys. stat. sol. b

A number of different families of nanowires which self-assemble on semiconductor surfaces have been identified in recent years. They are particularly interesting from the standpoint of nanoelectronics, which seeks non-lithographic ways of creating interconnects at the nanometre scale (though possibly for carrying signal rather than current), as well as from the standpoint of traditional materials science and surface science. We survey these families and consider their physical and electronic structure, as well as their formation and reactivity. Particular attention is paid to rare earth nanowires and the Bi nanoline, both of which self-assemble on Si(001)., Comment: 32 pages, 30 figures

Short dangling bond wires (DB wires), fabricated on H-terminated Si(001) surfaces, show patterns of displacement that depend on their length. We have performed density function calculations, with and without spin-polarisation, designed to investigate the atomic and electronic structure of these wires. As expected, we find that even length wires are accurately modelled by non-spin polarised calculations, whilst odd length wires must be modelled using spin-polarised calculations. In particular, the use of spin-polarisation provides quantative agreement with STM observations, rather than the qualitative agreement reported elsewhere., Comment: 7 pages, 2 figures, 3 tables, submitted to Surf. Sci. Lett Changed in response to referee's comments

Dangling bond wires on Si(001) are prototypical one dimensional wires, which are expected to show polaronic and solitonic effects. We present electronic structure calculations, using the tight binding model, of solitons in dangling-bond wires, and demonstrate that these defects are stable in even-length wires, although approximately 0.1 eV higher in energy than a perfect wire. We also note that in contrast to conjugated polymer systems, there are two types of soliton and that the type of soliton has strong effects on the energetics of the bandgap edges, with formation of intra-gap states between 0.1 eV and 0.2 eV from the band edges. These intra-gap states are localised on the atoms comprising the soliton., Comment: 6 pages, 3 figures, 3 tables, submitted to Phys. Rev. B

Heteroepitaxial strain can be a controlling factor in the lateral dimensions of 1-D nanostructures. Bi nanolines on Si(001) have an atomic structure which involves a large sub-surface reconstruction, resulting in a strong elastic coupling to the surrounding silicon. We present variable-bias STM and first principles electronic structure calculations of the Bi nanolines, which investigates this interaction. We show that the strain associated with the nanolines affects the atomic and electronic structure of at least two neighbouring Si dimers, and identify the mechanism behind this. We also present partial charge densities (projected by energy) for the nanoline with clean and hydrogenated surroundings and contrast it to the clean Si(001) surface., Comment: 10 pages, 3 figures, submitted to Surface Science

Injecting charge into dangling bond wires on Si(001) has been shown to induce polarons, which are weakly coupled to the underlying bulk phonons. We present elevated temperature tight binding molecular dynamics simulations designed to obtain a diffusion barrier for the diffusive motion of these polarons. The results indicate that diffusion of the polarons would be observable at room temperature, and that the polarons remain localised even at high temperatures., Comment: 8 pages, 4 figures, accepted as a letter in J.Phys.:Condens. Matter

Elevated temperature STM measurements have shown that one key phase during gas-source homoepitaxy of Si(001) is the formation of clean Si ad-dimers from hydrogenated ad-dimers, though the mechanism for this formation is unknown. We present ab initio density functional calculations designed to explore this mechanism. The calculations show that there is a pathway consistent with the experimentally observed reaction rates, which proceeds via a meta-stable intermediate, and is effectively irreversible. This result fills a vital gap in our understanding of the atomic-scale details of gas-source growth of Si(001)., Comment: 6 pages, 8 figures, submitted to Phys. Rev. B

Experimental observations of the growth of more than one monolayer of Ge on Si(001) show a progression of effects beyond the (2xN) reconstruction which is seen at submonolayer coverages: a reduction in the value of N with coverage; formation of straight trenches of missing dimer vacancies; and formation of the (MxN) ``patch'' structure. We present tight binding calculations which investigate the energetics and geometries associated with these effects, and extend our earlier treatment of formation energies for reconstructions with different stoichiometries to the case of several layers of Ge. The results provide explanations for the various effects seen, and are in good agreement with experimental observations., Comment: 16 pages, 4 figures, submitted to Surface Science

Experimental observations of heteroepitaxial growth of Ge on Si(001) show a (2xn) reconstruction for sub-monolayer coverages, with dimer rows crossed by missing-dimer trenches. We present first-principles density-functional calculations designed to elucidate the energetics and relaxed geometries associated with this reconstruction. We also address the problem of how the formation energies of reconstructions having different stoichiometries should be compared. The calculations reveal a strong dependence of the formation energy of the missing-dimer trenches on spacing n, and demonstrate that this dependence stems almost entirely from elastic relaxation. The results provide a natural explanation for the experimentally observed spacings in the region of n \~ 8., Comment: 13 pages, 4 figures, submitted to Surface Science

We describe how we have used tight binding calculations as a quick, efficient tool to search for possible structures of Bi nanolines on Si(001). After identifying promising candidate structures, we have concentrated on these with \textit{ab initio} electronic structure techniques. The energetics of the tight binding are shown to be in good agreement with the density functional calculations and with experimental observations, and have proved invaluable in the search for a structure, validating the use of tightbinding as a search tool., Comment: 6 pages, 3 figures, submitted to Phys. Rev. B

Stress resulting from mismatch between a substrate and an adsorbed material has often been thought to be the driving force for the self-assembly of nanoscale structures. Bi nanolines self-assemble on Si(001), and are remarkable for their straightness and length -- they are often more than 400 nm long, and a kink in a nanoline has never been observed. Through electronic structure calculations, we have found an energetically favourable structure for these nanolines that agrees with our scanning tunneling microscopy and photoemission experiments; the structure has an extremely unusual subsurface structure, comprising a double core of 7-membered rings of silicon. Our proposed structure explains all the observed features of the nanolines, and shows that surface stress resulting from the mismatch between the Bi and the Si substrate are responsible for their self-assembly. This has wider implications for the controlled growth of nanostructures on semiconductor surfaces., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must be run on parallel computers. We analyse the problem of parallelising the multiplication of sparse matrices with the sparsity pattern required by linear-scaling techniques. We show that the management of inter-node communications and the effective use of on-node cache are helped by organising the atoms into compact groups. We also discuss how to identify a key part of the code called the `multiplication kernel', which is repeatedly invoked to build up the matrix product, and explicit code is presented for this kernel. Numerical tests of the resulting multiplication code are reported for cases of practical interest, and it is shown that their scaling properties for systems containing up to 20,000 atoms on machines having up to 512 processors are excellent. The tests also show that the cpu efficiency of our code is satisfactory., Comment: 20 pages, 6 figures, submitted to Computer Physics Communications

Pulay's Residual Metric Minimization (RMM) method is one of the standard techniques for achieving self consistency in ab initio electronic structure calculations. We describe a reformulation of Pulay's RMM which guarantees reduction of the residual at each step. The new version avoids the use of empirical mixing parameters, and is expected to be more robust than the original version. We present practical tests of the new method implemented in a standard code based on density-functional theory (DFT), pseudopotentials, and plane-wave basis sets. The tests show improved speed in achieving self consistency for a variety of condensed-matter systems., Comment: Six pages, one table, no figures. Accepted by Chem. Phys. Lett

From electronic structure calculations, we find that carriers injected into dangling-bond atomic wires on the Si(001) surface will self-trap to form localised polaron states. The self-trapping distortion takes the form of a local suppression of the buckling of the dimers in the wire, and is qualitatively different for the electron and hole polarons. This result points to the importance of polaronic effects in understanding electronic motion in such nanostructures., Comment: LaTeX with APS RevTeX macros; 14 pages including 4 figures in EPS format

We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then describe our scheme, which operates within density functional theory. Efficient methods for reaching the electronic ground state are summarised, both for finding the density matrix, and in varying the localised orbitals., Comment: 11 pages, 5 figures. Submitted to the International Journal of Quantum Chemistry

We analyze the problem of determining the electronic ground state within O(N) schemes, focusing on methods in which the total energy is minimized with respect to the density matrix. We note that in such methods a crucially important constraint is that the density matrix must be idempotent (i.e. its eigenvalues must all be zero or unity). Working within orthogonal tight-binding theory, we analyze two related methods for imposing this constraint: the iterative purification strategy of McWeeny, as modified by Palser and Manolopoulos; and the minimization technique of Li, Nunes and Vanderbilt. Our analysis indicates that the two methods have complementary strengths and weaknesses, and leads us to propose that a hybrid of the two methods should be more effective than either method by itself. This idea is tested by using tight-binding theory to apply the proposed hybrid method to a set of condensed matter systems of increasing difficulty, ranging from bulk crystalline C and Si to liquid Si, and the effectiveness of the method is confirmed. The implications of our findings for O(N) implementations of non-orthogonal tight-binding theory and density functional theory are discussed., Comment: ReVTeX, 12 pages, 5 figures. Submitted to PRB Changed in response to referees' comments