Theory of Scanning Tunneling Microscopy

This lecture has been given at the 45th Spring School: Computing Solids: Models, Ab-initio Methods and Supercomputing organized at the Forschungszentrum J\"ulich. The goal of this manuscript is to review the basics behind the theory accompanying Scanning Tunneling Microscopy.Comment: 38 pages, 45th IFF Spring School: Computing Solids: Models, Ab-initio Methods and Supercomputing organized at the research center of Juelic

New Algebraic Formulation of Density Functional Calculation

This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for the construction of such for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures

Ab initio based thermal property predictions at a low cost : an error analysis

Ab initio calculations often do not straightforwardly yield the thermal properties of a material yet. It requires considerable computational efforts, for example, to predict the volumetric thermal expansion coefficient alpha(V) or the melting temperature T-m from first principles. An alternative is to use semiempirical approaches. They relate the experimental values to first-principles predictors via fits or approximative models. Before applying such methods, however, it is of paramount importance to be aware of the expected errors. We therefore quantify these errors at the density-functional theory level using the Perdew-Burke-Ernzerhof functional for several semiempirical approximations of alpha(V) and T-m, and compare them to the errors from fully ab initio methods, which are computationally more intensive. We base our conclusions on a benchmark set of 71 ground-state elemental crystals. For the thermal expansion coefficient, it appears that simple quasiharmonic theory, in combination with different approximations to the Gruneisen parameter, provides a similar overall accuracy as exhaustive first-principles phonon calculations. For the melting temperature, expensive ab initio molecular-dynamics simulations still outperform semiempirical methods

Recent achievements in ab initio modelling of liquid water

The application of newly developed first-principle modeling techniques to liquid water deepens our understanding of the microscopic origins of its unusual macroscopic properties and behaviour. Here, we review two novel ab initio computational methods: second-generation Car-Parrinello molecular dynamics and decomposition analysis based on absolutely localized molecular orbitals. We show that these two methods in combination not only enable ab initio molecular dynamics simulations on previously inaccessible time and length scales, but also provide unprecedented insights into the nature of hydrogen bonding between water molecules. We discuss recent applications of these methods to water clusters and bulk water.Comment: 23 pages, 17 figure

First-principles investigation of the Ni-Fe-Al system

By combining ab-initio electron theory and statistical mechanics, the physical properties of the ternary intermetallic system Ni-Fe-Al in the ground state and at finite temperatures were investigated. The Ni-Fe-Al system is not only of high technological interest, but exhibits also rich physics, e.g., a delicate interplay between structure and magnetism over a wide composition range and substantial electronic correlations which is challenging for modern electronic structure methods. The new Stuttgart ab-initio mixed-basis pseudopotential code in the generalized gradient approximation (GGA) was used to determine the energetics in the ground state. Therewith, in combination with the cluster expansion (CE) method a representation of the energy landscape at $T$=0 over the whole Gibbs triangle was elaborated. At finite temperatures, the cluster variation method (CVM) in tetrahedron approximation was employed in order to calculate the ab-initio ternary phase diagram on the bcc and fcc lattice. Thereby, a miscibility gap in the ternary B2 phase was theoretically verified.Comment: 27 page

Merging GW with DMFT and non-local correlations beyond

We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna {\it ab initio} simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (D$\Gamma$A). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the three methods with a focus on the benchmark material SrVO$_3$.Comment: tutorial review submitted to EPJ-ST (scientific report of research unit FOR 1346); 11 figures 27 page