Simulating STM transport in alkanes from first principles

Simulations of scanning tunneling microscopy measurements for molecules on surfaces are traditionally based on a perturbative approach, most typically employing the Tersoff-Hamann method. This assumes that the STM tip is far from the sample so that the two do not interact with each other. However, when the tip gets close to the molecule to perform measurements, the electrostatic interplay between the tip and substrate may generate non-trivial potential distribution, charge transfer and forces, all of which may alter the electronic and physical structure of the molecule. These effects are investigated with the ab initio quantum transport code SMEAGOL, combining non-equilibrium Green's functions formalism with density functional theory. In particular, we investigate alkanethiol molecules terminated with either CH3 or CF3 end-groups on gold surfaces, for which recent experimental data are available. We discuss the effects connected to the interaction between the STM tip and the molecule, as well as the asymmetric charge transfer between the molecule and the electrodes.Comment: 10 pages, 18 figure

Investigating correlations in time delay interferometry combinations of LISA data

The detection of Gravitational Waves using the Laser Interferometer Space Antenna (LISA) will open whole new areas of physics and astrophysics for exploration. The lower frequency signals detected by the antenna will allow us to probe gravitational wave sources that are inaccessible with current and future ground based detectors. However, the ability of LISA to detect gravitational wave signals is dependent on the removal of the laser frequency noise realisations from the optical bench measurements, that would otherwise dominate the signal data streams. Time Delay Interferometry (TDI) provides a method for removing the laser noise contributions by time shifting the individual optical bench measurements. The cancellation of the noise is achieved by identifying the individual optical bench measurements that contain equal numbers of identical realisations of the laser noise but with opposing signs. Although the TDI combinations produce signal datastreams that are free from the laser frequency noise contributions, the time shifting of the optical bench measurements means that the TDI combination data streams defined at different time stamps will nevertheless contain identical realisations of the remaining detector noise terms. Independent TDI combinations (denoted A, E and T) can be constructed from the simpler laser-noise cancelling combinations by diagonalising the correlation matrix of the combination data streams at any given timestamp. This ensures that the optimal combinations are independent with respect to each other at this particular timestamp, but this result does not apply when the optimal combinations are compared at different timestamps. As the time shifting of the optical bench measurements introduces within them identically equal realisations of the remaining detector noise terms, the A, E and T data streams could therefore be correlated in time. The presence, and potential impact, of these time correlations has been investigated for the first time within this thesis. This work has been carried out by identifying the time stamps and optical bench designations of the individual optical bench terms in the algebraic expression for each TDI combination. The resultant configuration of non-zero off-diagonal terms in the covariance matrix for the TDI combination data streams has been investigated for simplified models of the LISA constellation. The presence of non-zero correlations between the combination datastreams could pose a serious problem to a number of signal parameter search methods that rely on the datastreams being independent. The effects on the parameter recovery for a gravitational wave signal containing two sinusoids has been investigated for a simplified LISA model and for the combination datastreams produced using the data from the second Mock LISA Data Challenge. In both cases, the presence of identically equal detector noise realisations in different time stamps of the signal data streams introduces auto and cross correlations between the combinations. When the non-zero covariances were explicitly accounted for within the likelihood function, the confidence intervals, reflecting the uncertainty in our inference of the unknown parameters, were found to be significantly smaller - indicating significantly tighter constraints on the true signal parameters, in comparison to the results obtained with a likelihood function that assumed the data streams to be independent in time

Help! Is my sample big enough?

© 2017 The Royal Statistical Society Anne Beeston writes: I am planning a study to evaluate the efficacy of a treatment to reduce the microbial load in dried flowers, and need some advice on sample size to allow the determination of statistically significant differences in two groups

Mathematics, statistics and operational research project B: Book of Abstracts 2014-2016

This collection of abstracts represents student work over the course of two academic years. It highlights the wide variety of project topics that are run under the banner of MSOR (b) projects.The motivation behind the research topics chosen by students doing this project module is varied. It can arise from personal interests, from placement experience, or research topics can be driven by collaborations with partners both inside and outside of UWE.Some projects presented here using real data collaborating with partners have associated reporting restrictions. The others, either based on using simulations or publically available data, or based on theoretical work, have no such restrictions.Each year has a separate table of contents. The advisors names have been included beside each project title to help inform potential students about the type of topics that staff members have previously advised upon.We want to congratulate those graduates whose research is included in this collection and thank them for the time and effort they have given in undertaking their projects. I am honoured to share in our graduates’ success and delighted to have this opportunity to open up their work to a wider audience. We wish all our graduates every success in their future

Scrambled statistics: What are the chances of finding multi-yolk eggs?

© 2016 The Royal Statistical Society Journalists ask a lot of questions of statisticians, but some are more bizarre than others. Statistical ambassador Deirdre Toher recounts one such experience

Efficient atomic self-interaction correction scheme for non-equilibrium quantum transport

Density functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. These originate from the interaction of an electron with the potential generated by itself and may be significant in metal-molecule-metal junctions due to the localized nature of the molecular orbitals. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions, a failure similar to the inability of local functionals of describing Mott-Hubbard insulators. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the Green's function non-equilibrium transport code Smeagol and applied to the prototypical cases of benzene molecules sandwiched between gold electrodes. The self-interaction corrected Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low bias current in much better agreement with experiments.Comment: 4 pages, 5 figure

AFLOW for alloys

Many different types of phases can form within alloys, from highly-ordered intermetallic compounds, to structurally-ordered but chemically-disordered solid solutions, and structurally-disordered (i.e. amorphous) metallic glasses. The different types of phases display very different properties, so predicting phase formation is important for understanding how materials will behave. Here, we review how first-principles data from the AFLOW repository and the aflow++ software can be used to predict phase formation in alloys, and describe some general trends that can be deduced from the data, particularly with respect to the importance of disorder and entropy in multicomponent systems.Comment: Small AFLOW review submitted to special issue. 6 pages, 4 picture

AFLOW-QHA3P: Robust and automated method to compute thermodynamic properties of solids

Accelerating the calculations of finite-temperature thermodynamic properties is a major challenge for rational materials design. Reliable methods can be quite expensive, limiting their applicability in autonomous high-throughput workflows. Here, the three-phonon quasiharmonic approximation (QHA) method is introduced, requiring only three phonon calculations to obtain a thorough characterization of the material. Leveraging a Taylor expansion of the phonon frequencies around the equilibrium volume, the method efficiently resolves the volumetric thermal expansion coefficient, specific heat at constant pressure, the enthalpy, and bulk modulus. Results from the standard QHA and experiments corroborate the procedure, and additional comparisons are made with the recently developed self-consistent QHA. The three approaches—three-phonon, standard, and self-consistent QHAs—are all included within the open-source ab initio framework aflow, allowing the automated determination of properties with various implementations within the same framework

Electrical transport through a mechanically gated molecular wire

A surface-adsorbed molecule is contacted with the tip of a scanning tunneling microscope (STM) at a pre-defined atom. On tip retraction, the molecule is peeled off the surface. During this experiment, a two-dimensional differential conductance map is measured on the plane spanned by the bias voltage and the tip-surface distance. The conductance map demonstrates that tip retraction leads to mechanical gating of the molecular wire in the STM junction. The experiments are compared with a detailed ab initio simulation. We find that density functional theory (DFT) in the local density approximation (LDA) describes the tip-molecule contact formation and the geometry of the molecular junction throughout the peeling process with predictive power. However, a DFT-LDA-based transport simulation following the non-equilibrium Green's functions (NEGF) formalism fails to describe the behavior of the differential conductance as found in experiment. Further analysis reveals that this failure is due to the mean-field description of electron correlation in the local density approximation. The results presented here are expected to be of general validity and show that, for a wide range of common wire configurations, simulations which go beyond the mean-field level are required to accurately describe current conduction through molecules. Finally, the results of the present study illustrate that well-controlled experiments and concurrent ab initio transport simulations that systematically sample a large configuration space of molecule-electrode couplings allow the unambiguous identification of correlation signatures in experiment.Comment: 31 pages, 10 figure