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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$_3$., 14 pages, 3 figures and 4 tables

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

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., 5 pages, 4 figures

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$, 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

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 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., 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes)

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

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., 7 pages, 2 figures, 3 tables, submitted to Surf. Sci. Lett Changed in response to referee's comments

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., 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., 13 pages, 4 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

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

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