Session A39: Electronic Structure: Theory and Numerical Methods

Ab initio calculation of atomic level stress in intermetallic compounds and glasses

The atomic level stress is largely unexplored as a characterization tool that is sensitive to the local atomic environment. Local quantities, such as magnetic moment and volume, are directly related to the local pressure. For example the local Voronoi volume and pressure have the expected inverse relationship and magnetic moments are reduced due to reduced volume associated with pressure. For a simple system with one atom per unit cell at equilibrium the local stresses are zero. An atom in a multicomponent system can find itself under pressure that results from its cage of surrounding atoms. The atomic level stress is calculated with the Locally Self-consistent Multiple scattering (LSMS) method for Al-Au and Cu-Zr compounds and glasses, and trends are compared to the results for simple B2 compounds with atoms of different sizes.   

Towards ab initio simulation of solid state materials at 10 nm scale

For the simulation of nanostructured materials and materials with structural defects, it is necessary to consider large size unit cells consisting of thousands or more atoms. It is especially true for our investigation of radiation damage effects on the structural materials. We found that for a reasonably high energy radiation, large unit cell samples at least at 10 nm scale are needed in order for allowing the thermal energy introduced into the sample by the radiation to have sufficient space to dissipate. In this presentation, we point out that, for ab initio electronic structure calculation of a system with a unit cell at such a large scale, it is essential to pay careful attention to numerical stability. We show some numerical pitfalls that will arise as a result of large number of atoms getting involved. The round-off errors accumulated in the calculation of long-range Coulomb interactions, in particular, can lead to divergence of self-consistent iterations. We discuss our approach for circumventing these numerical difficulties.   

Distributed Network-Based Verification and Validation of Electronic Structure Computations using ESTEST

ESTEST is a web-based framework for verification and validation of electronic structure computations [1,2]. It enables automatic comparison and post-processing of simulation data obtained using Abinit, Quantum-Espresso, Siesta, Exciting, Qbox and VASP. We present new features of ESTEST that extend its operation to a distributed network of servers. This capability enables sharing, verification, validation, comparison, and post-processing of simulations across a decentralized network of ESTEST servers hosted by different institutions. Examples of cross-server operations including multiple servers will be demonstrated. \\[4pt] [1] G. Yuan and F. Gygi, Computational Science \& Discovery 3, 015004 (2010) doi:10.1088/1749-4699/3/1/015004G\\[0pt] [2] http://estest.ucdavis.edu   

Calculation of quasi particle energies using a spectral decomposition of the static dielectric matrix: application to molecules and nanoparticles

We present a novel approach to evaluate quasi particle energies within many body perturbation theory, that substantially improves both the computational efficiency and the numerical accuracy of existing techniques.\footnote{Huy-Viet Nguyen, T. Anh Pham, D. Rocca and G. Galli (preprint).} We use a spectral decomposition of the static dielectric matrix as a basis for the frequency dependent density-density response function, and density functional perturbation theory to avoid the explicit calculation of empty electronic states. A Lanczos-chain algorithm is employed that allows for the evaluation of spectra over a wide frequency range. The numerical accuracy of computed quasi particle energies is controlled by a single parameter. The efficiency and accuracy of our approach are demonstrated by computing vertical ionization potentials and electron affinities of several molecules and diamondoids. Our results are in good agreement with experiment and those reported in the literature using Quantum Monte Carlo calculations.   

First-principles calculations of quasiparticle energies of open-shell condensed matter systems

We present a Green's function approach to quasiparticle excitations of open-shell systems within the GW approximation. It is shown that accurate calculations of the characteristic multiplet structure require a precise knowledge of the self energy and, in particular, its poles. We achieve this by constructing the self energy from appropriately chosen mean-field theories on a fine frequency grid. We present results for the nitrogen dioxide molecule and the negatively charged nitrogen-vacancy defect in diamond, which are in good agreement with experiment and other high-level theories.   

On the accuracy of the G$^0$W$^0$ method: From Si to ZnO

The \textit{ab initio} GW method has been recognized as one of the most powerful theories in predicting quasiparticle excitations in solids. Due to computational limitations, earlier GW calculations usually made use of certain generalized plasmon-pole approximations to carry out frequency integration of the electron self-energy. In addition, often the convergence of the calculated results with respect to various cutoff parameters (such as the number of conduction bands and the size of the dielectric matrix) was not investigated in details. With advances in computational methodology and technology, fully converged GW calculations with explicit frequency integration become possible. In this talk, we will discuss fully converged G$^0$W$^0$ results for a range of materials, ranging from the most ``theory friendly'' system Si to the widely discussed and controversial system ZnO. We will compare explicit frequency integration vs various generalized plasmon-pole models. We will also discuss effects of various cutoff parameters used in GW calculations.   

A Comparison of Different Treatments of Spin-Orbit Coupling within the GW Approach

Spin-orbit coupling is responsible for the unique electronic properties of many fascinating materials such as topological insulators. We have developed and implemented an approach in which the effects of spin-orbit interactions to the quasiparticle band structure are incorporated within the GW approach, employing spinor wavefunctions computed at the DFT level with fully relativistic pseudopotentials. We compare these results to separate calculations where spin-orbit coupling is applied as a perturbation either before or after the GW calculation of the band structure. We apply these methods to the properties of materials with heavy ion cores to determine possible differences from the different schemes.   

Dielectric screening : Effects of Core Polarization on Phonons and Quasiparticle Bands

We investigate the influence of core polarization on the dielectric screening of atoms, molecules and solids with focus on non metallic systems. We compare results for dielectric band structures and for the eigenvalues of the dielectric matrix obtained by varying the number of valence electrons included in our calculations. We show that (semi)-core electronic states may substantially influence the dielectric screening, even if they lie very deep in energy compared to the outermost valence electrons. We then discuss how the changes in dielectric screening observed when including (semi)-core electrons affect computed quasi particle energies at the GW level, and phonon frequencies, e.g. the LO-TO splitting. We focus on closed shell atoms, including Be,Mg, Ca, Ar, Zn, simple diatomic molecules and simple ionic solids, e.g. LiH and NaH.   

Novel approach to electron partitioning and definitive oxidation state assignment in solids

Oxidation state of a atom is usually defined by partitioning electrons to the nucleus based on charge density distribution, which inherits uncertainty from the probabilistic nature of wavefunctions. Here we propose a first principle approach to electron partitioning in insulating solids based on wavefunction topology. By calculating polarization change upon shifting an atomic sublattice to its periodic image, the charge transferred during nuclei displacement can be derived. To rationalize, in Wannier representation the Berry's phase polarization is directly related to the position of Wannier Center (WC) of each band, therefore a quantized charge flow is determined by the number of WCs that move together with (\textit{i.\ e.} belong to ) the nucleus. We provide both rigorous mathematical definition of oxidation states in this scheme and results from calculations of various sample systems that corroborate with oxidation states assigned by conventional chemical insight.   

On the Formation of XLi$_{3}$N$_{2}$ Compounds (X = Sc-Zn)

Ternary lithium nitrides XLi$_{3}$N$_{2}$ are known to form for the 3d transition elements X = Sc, Fe. We explore the formation of such compounds for other 3d elements by means of density functional theory using the crystal structures of ScLi$_{3}$N$_{2}$ and FeLi$_{3}$N$_{2}$ as templates. Enthalpies of formation including electronic and phonon contributions are calculated for the most stable structures. Thermodynamic stability with respect to known binary and ternary compounds is investigated in order to assess prospects for phase formation. In the case of FeLi$_{3}$N$_{2}$ we find an antiferromagnetic state lower in energy than the ferromagnetic state previously identified.   

Surface Studies with Combined Free Energy Functionals of Electronic and Liquid Densities

The microscopic structure of both a solid surface and a contacting liquid can be dramatically affected by the interaction between the two systems, particularly at the interface between a polar surface and a polar liquid. We present a study of oxide and metallic surfaces in an aqueous electrolyte environment with Joint Density Functional Theory (JDFT), a computationally efficient alternative to molecular dynamics simulations which replaces thermal sampling with a single variational principle for the free energy of the full system. Within the rigorous framework of JDFT, we introduce classical density-functionals for ionic species and describe how to couple them with existing functionals for liquid water and traditional electronic density-functionals. Calculations employ a liquid water functional, which captures bulk properties and microscopic structure over the entire phase diagram of the liquid, and a density-only coupling functional between the electronic and liquid systems, which can reproduce solvation free energies of small molecules to within chemical accuracy. With this microscopically accurate description of the liquid-solid interface structure, we gain physical insight which could direct future studies of catalysis and electrode stability in electrochemical systems.   

Origin of magnetic interactions and their influence on the structural properties of Ni2MnGa and related compounds

In this work, we perform first principles DFT calculations to investigate the interplay between magnetic and structural properties in Ni$_2$MnGa. We demonstrate that the relative stability of austenite (cubic) and non-modulated martensite (tetragonal) phases depend critically on magnetic interactions between Mn atoms. While standard approximate DFT functionals stabilize the latter phase, a more accurate treatment of electronic localization and magnetism obtained with DFT+U suppresses the non-modulated tetragonal structure for the stoichiometric compound, in better agreement with the experiments. This observation can be explained using the Anderson impurity model, where Mn atoms are treated as periodic magnetic impurities embedded in Ga $p$ and Ni $d$ conduction electrons that mediate RKKY type magnetic interactions between Mn $d$ electrons. Using this picture we show that the structural properties of the material are determined by the competition between super-exchange interactions mediated through Ni $d$ and Ga $p$ states. Finally, we show that off-stoichiometric compositions with excess Mn promote transition to a non-modulated tetragonal structure, in agreement with experiments.   

Redshift of excitons in carbon nanotubes caused by the environment polarizability: A BSE study

Optical excitations of molecular systems can be modified by their physical environment. We analyze the underlying mechanisms within many-body perturbation theory (GW approximation and Bethe-Salpeter equation, BSE), which is particularly suited to study non-local polarizability effects on the electronic structure. Here we focus on the example of a semiconducting carbon nanotube, which observes redshifts of its excitons when the tube is touched by another nanotube or other physisorbates. We show that the redshifts mostly result from the polarizability of the attached ad-system. Electronic coupling may enhance the redshifts, but depends very sensitively on the structural details of the contact.   

Vibrational properties of correlated systems from ab-initio calculations

In this talk I will present a recent extension of Density Functional Perturbation Theory to the DFT+U energy functional that allows to compute the vibrational properties of materials from their correlated ground state. The new computational tool, named DFPT+U, is used to investigate the phonon spectrum of MnO and NiO. The more accurate account of electronic correlation through the Hubbard-corrected functional results in a significant improvement in the agreement between the computed phonon frequencies and available experiments. In particular, we obtain a significant reduction in the splitting between the center-zone optical modes (due to the antiferromagnetic order) that confirms the importance of electronic localization in the description of magnetic couplings between metal ions. The order of the split optical modes is also shown to correlate with the occupation of the d states of the transition metal atoms opening for the possibility to use measurements of the vibrational frequencies to investigate certain aspects of the electronic structure of these compounds. In the last part of the talk I will also present the application of DFPT+U to Cu compounds and will discuss the possibility to use it to compute the electron-phonon coupling of high T$_c$ superconductors.   

Effect of strong correlations on the electronic and transport properties of porphyrin wires

Recent transport experiments performed on porphyrin molecules show that wires based on these molecules could be used to design future nanoscale elements with low attenunation as a function of distance and able to work at room temperature. Apart from their rather good transport properties, which come from the conjugation of their molecular backbone, porphyrins are also very interesting due to the fact that they have a metallic element in the middle that affects their electronic properties and could also introduce magnetic effects. In this talk I will show first-principles simulations based on density functional on the electronic and transport properties of porphyrin wires between gold leads, paying special attention to the effect of using different metallic elements in the central part of the molecule (Fe, Co, Ni, Zn and Cu). Strong correlations are introduced in the form of LDA+U. The results show that the metallic element plays a crucial role in the electronic structure of the molecule around the HOMO and LUMO orbitals and introduces magnetic effects that affect the transport properties.