Building bridges: matching density functional theory with experiment

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 Physic

Calculations on millions of atoms with DFT: Linear scaling shows its potential

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. Matte

A spin-polarised first principles study of short dangling bond wires on Si(001)

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 comment

An Efficient and Robust Technique for Achieving Self Consistency in Electronic Structure Calculations

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. Let

Density matrices in O(N) electronic structure calculations: theory and applications

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' comment

Parallel Sparse Matrix Multiplication for Linear Scaling Electronic Structure Calculations

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 Communication

Practical Methods for Ab Initio Calculations on Thousands of Atoms

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 Chemistr

Density-functional theory study of gramicidin A ion channel geometry and electronic properties

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. Interfac

Chemical accuracy for the van der Waals density functional

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 table

Demonstration of a dressed-state phase gate for trapped ions

We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.Comment: 5 pages, 4 figures, 1 tabl