Session H39: Electronic Structure: Calculations II

Variational investigations of the electronic structure and energy of finite hydrogen systems with the Gutzwiller wave function within local correlation matrix renormalization approximation

We introduce the correlation matrix renormalization Hartree-Fock (CMR-HF) method in which the many-body Hamiltonian of a multi-electronic system is solved using a variational Gutzwiller-type wave-function. The Gutzwiller approximation is generalized to renormalize the one-electron density matrix and two-electron correlation matrix of the system. To achieve a clear presentation of the concept and methodology, we describe the detailed formalisms for a finite hydrogen system with minimal basis set. The resulting expectation value of the Hamiltonian have clear parallels to terms in the standard uncorrelated Hartree-Fock method, allowing an iterative self-consistent field solution of the many-electron problem analogous to the Hartree-Fock solution. We have applied the method to a series of hydrogen clusters to compare with the results of several other quantum chemical calculation methods.   

Real-time time-correlation approach for x-ray absorption and emission spectra

We present a real-time approach for calculations of X-ray absorption (XAS) and emission spectra (XES) from deep core-levels, based on time-correlation functions. XAS and XES have traditionally been calculated using Fermi's golden rule in frequency space, and alternatively, using real-space Green's function (RSGF) methods. Recently, however, with the advent of very high brightness pulsed x-ray sources, calculations of time-dependent response have become a focus of attention. Here we obtain the time-correlation functions by propagating the initial, dipole-excited wavefunction with a Crank-Nicolson time-evolution operator.\footnote{Y. Takimoto \textit{et al.}, J. Chem. Phys. {\bf127}, 154114 (2007).} The initial state is obtained using projector augmented wave (PAW) transition matrix elements and, for XAS, the propagation is carried out in the presence of a core hole. The approach is implemented using an extension of SIESTA and can be applied both to molecular and extended systems. Illustrative examples are presented for several systems, and yield results in good agreement with RSGF and Fermi golden rule approaches using FEFF and StoBe respectively. Finally, we discuss improvements in order to include dynamic many-body effects.   

Calculation of Phonon Satellites in Electron Spectral Functions

We describe a first principles approach for calculations of phonon satellites in the electron self-energy and spectral function. The method is based on cumulant expansion techniques [1] applied to the self-energy model of Eiguren and Ambrosch-Draxl [2] with the dynamical matrix and electron-phonon couplings obtained from ABINIT [3]. In particular, the electron-phonon couplings are calculated from the Eliashberg functions as in [4], and the phonon DOS is obtained from a many-pole/Lanczos representation of the phonon Green's function [5]. The method is illustrated with results for a number of systems.\\[4pt] [1] F. Aryasetiawan et al., Phys. Rev. Lett. 77, 2268 (1996).\\[0pt] [2] A. Eiguren and C. Ambrosch-Draxl, Phys. Rev. Lett. 101, 036402 (2008).\\[0pt] [3] X. Gonze et al., Comput. Materials Science 25, 478 (2002).\\[0pt] [4] S. Y. Savrasov and D. Y. Savrasov Phys. Rev. B 54, 16487 (1996).\\[0pt] [5] F. Vila et al., Phys. Rev. B 76, 014301 (2007).   

Atomic Multiplets in X-ray spectroscopies revisited

Atomic multiplets are known since a long time to produce specific, crystal field dependent, fingerprints of open d- and f- shells in X-ray spectroscopies. Older computer programs originating from gas-phase optical spectroscopy of atoms tend to be difficult to apply to crystal field environments with lower symmetries. In order to study changes of X-ray absorption near edge spectra and resonant inelastic X-ray scattering (RIXS) across symmetry lowering phase transitions, a new multiplet program was developed. Starting from a Dirac-Slater spherical atom calculation we evaluate electron-electron interaction and crystal field in the Hilbert space spanned by the open shells by diagonalization. The crystal field can be simply defined by nominal charges and cartesian atomic positions relative to the core-hole atom. To overcome limitations of the model and for fitting known spectra, spin-orbit splitting, el-el interaction and crystal-field can be scaled independently. The nominal charges may be taken as further crystal field parameters. Various XAS and RIXS examples will be discussed, in particular in view of the polarisation dependence and symmetry of the crystal.   

Simulation of electron-energy-loss spectra including both diffraction and solid-state effects

Aberration-corrected scanning transmission electron microscopes yield probe-position-dependent electron-energy-loss spectra (EELS) that can potentially provide spatial mapping of the underlying electronic states. EELS calculations, however, typically describe excitations by a plane wave travelling in vacuum, neglecting diffraction and interference effects. Here we report the development and initial application of a methodology that combines a full electronic-structure calculation with beam propagation in a thin film. The simulations are based on PAW plane-wave calculations of the excitation spectrum of the material and Bloch wave simulations of the probe propagation.   

Precise all-electron response functions from a combined spectral sum and Sternheimer approach: application to EXX-OEP

The optimized-effective-potential (OEP) method is used to construct local potentials from non-local, orbital-dependent functionals, e.g., exact exchange (EXX). The method involves two response functions, which have to be converged to very high precision to obtain smooth and stable local potentials. Usually, this requires an exceptionally large orbital basis, leading to very costly calculations, especially for all-electron methods such as FLAPW [1]. In this work, we propose a scheme that combines the usual spectral sum from standard perturbation theory with a radial Sternheimer approach. It also comprises a, albeit small, Pulay-type correction, which refines the results especially for small basis sets. We demonstrate that with this new approach already the conventional minimal LAPW basis set is sufficient to yield precise response functions. Furthermore, very few unoccupied states are required, which reduces the computational cost considerably. The numerically important Sternheimer contribution arises from the potential dependence of the LAPW basis functions and is constructed by solving inexpensive radial differential equations. We show results for complex transition-metal oxides.\newline [1] M. Betzinger \emph{et al.}, Phys. Rev. B~{\bf 83}, 045105 (2011)   

Electronic band structure of lanthanum bromide and strontium iodide from many-body perturbation theory calculations

Rare-earth based scintillators represent a challenging class of scintillator materials due to pronounced spin-orbit coupling and subtle interactions between d and f states that cannot be reproduced by standard electronic structure methods such as density functional theory. In this contribution we present a detailed investigation of the electronic band structure of LaBr$_3$ using the quasi-particle self-consistent GW (QPscGW) method. This parameter-free approach is shown to yield an excellent description of the electronic structure of LaBr$_3$. Specifically we reproduce the correct level ordering and spacing of the 4f and 5d states, which are inverted with respect to the free La atom, the band gap as well as the spin-orbit splitting of La-derived states. We furthermore present electronic structure calculations using G$_0$W$_0$ for the important scintillator material SrI$_2$. We explicitly take into account spin-orbit coupling at all levels of the theory. Our results demonstrate the applicability and reliability of the GW approach for rare-earth halides and complex halides. They furthermore provide an excellent starting point for investigating the electronic structure of rare-earth dopants such as Ce and Er.   

First-principles studies of Ce and Eu doped inorganic materials as candidates for scintillator gamma ray detectors

We have performed high-throughput DFT based (GGA+U) band structure calculations for new Ce and Eu doped wide band gap inorganic materials to determine their potential as candidates for gamma ray scintillator detectors. These calculations are based on determining the 4f ground state level of the Ce and Eu relative to the valence band of the host as well as the position of the Ce and Eu 5d excited state relative to the conduction band of the host. We find many classes of candidate materials where the 5d is in the conduction band preventing scintillation. Even when the Eu and Ce 4f and 5d levels are placed well in the gap of the host, traps on the host can also prevent the energy of the gamma ray transferring to the Eu or Ce. We therefore also performed calculations for host hole traps and electron traps to compare their energies to the Ce and Eu 4f and 5d levels.   

Test of Variational Methods for Molecular and Solid State Properties by Application to Hyperfine Interaction in Phosphorous Atom

As part of our program for testing the accuracy of variational methods for studying energy and wave-function dependent molecular and solid state properties, namely the Variational Hartree-Fock Many Body Perturbation Theory (VHFMBPT) and Variational Density Functional Theory (VDFT), we have studied the magnetic hyperfine interaction for $^{31}$P nucleus in the ground state. Our investigations provide hyperfine constants of +35.2MHz by the VHFMBPT and -11.2 MHz by VDFT procedures as compared to +55.055 MHz from experiment [1]. The VHFMBPT procedure provides the same signs for one-electron and many-body contributions as obtained earlier [2] by the HFMBPT procedure which uses the needed one-electron atomic wave-functions for the occupied and unoccupied states obtained by solving the Hartree-Fock equations through numerical integration, and not variationally as in the VHFMBPT procedure. Possible avenues for improved agreement by both variational procedures will be suggested. [1] N.C. Dutta, C. Matsubara, R.T. Pu and T.P. Das, Phys. Rev. Lett. 21, 1139 (1963) and references therein, [2] T.P. Das Hyperfine Interactions 34, 149 (1987) and reference therein to the experimental result for phosphorous atom. [3] Alfred Owusu, R.W. Dougherty, G. Gowri, J. Andriessen, T.P. Das, Phys. Rev. A 56, 305 (1997) and references therein.   

Sharp transition for single polarons in one-dimensional models with non-diagonal Su-Schrieffer-Heeger coupling

Ever since Landau pointed out the possibility of an electron becoming self-trapped in its own lattice distortion, people have looked for sharp transitions in polaronic states. Gerlach and L\"owen [1] proved the absence of such a transition in the case of a gapped (i.e. optical) phonon branch and an electron-phonon coupling $g(q)$ depending only on the phonon momentum $q$. Whether a sharp transition could be found in other models remained an open question for the last twenty years. By presenting both unbiased Diagrammatic Monte Carlo results for the single polaron with Su-Schrieffer-Heeger (SSH) coupling to optical phonons, and supporting results from no less than three other numerical and analytical approximations, we believe our previous work and that of our collaborators [2] to be the first unequivocal demonstration of a sharp transition in a polaronic system. Here we expand this work to more general models that include either an additional diagonal Holstein coupling to optical phonons, or a SSH coupling to acoustic phonons. The survival of the sharp transition in these models is investigated using the Bold Diagrammatic Monte Carlo method and the Momentum Average approximation. References: [1] Rev. Mod. Phys. 63, 63 (1991) [2] Phys. Rev. Lett. 105, 266605 (2010)   

Many-Pole Model Calculations of Inelastic Losses in XPS

Inelastic losses such as satellites in x-ray photo-emission spectra (XPS) are difficult to treat theoretically due to the importance of many-body effects beyond the quasi-particle approximation. Here we present an approach based on an exponential (i.e., cumulant) representation\footnote{M. Guzzo et al., Phys. Rev. Lett. {\bf 107}, 166401 (2011)} of the one-particle Green's function, together with\footnote{J. Kas et al., Phys. Rev. B {\bf 76}, 195116 (2007)} a many-pole model of the dielectric function, which incorporates dynamic effects beyond the GW approximation. In this method the photo-electron is treated as in inverted LEED state which couples to the system via neutral, quasi-boson excitations. The approach yields an approximation to the XPS in terms of a convolution of a quasi-particle calculation and a spectral function that includes contributions from both intrinsic and extrinsic excitations,\footnote{L. Hedin et al., Phys. Rev. B {\bf 58}, 15565 (1998)} as well as interference between them. The method is illustrated with recent experimental results.\footnote{Guzzo, op. cit.}   

Low Energy Positron Interactions with Biological Molecules

There is some experimental evidence that positrons can produce distinctive molecular fragmentation patterns. It is known that tuning the incident positron energy to near resonance with molecule vibrations can strongly enhance the positron annihilation probability for a molecule.\footnote{Gribakin, Young, and Surko, Rev. Mod. Phys. 82 (2010) 2577} This suggests that fragmentation induced by slow positrons may provide valuable complementary information to existing techniques for identification and study of proteins. In order to study this concept, we are developing a general quantum method for reliably calculating the density distribution for positrons bound to large biological molecules using NEO/GAMESS. We developed transferrable atom-centered positron basis sets for first-principles calculations for molecules containing O, N, C, and H. The positron density in the bound state is concentrated near the most electronegative atomic sites so that e$^{-}$e$^{+}$ annihilation will be most likely to occur in these regions for low incident positron energies leading to positron trapping in the bound state. Using the basis sets and approximations we have tested to predict where annihilation occurs can ultimately help us understand the resulting fragmentation patterns of larger biological molecules.   

Atomic Probing Structures of Electrolytes at Graphene Surface:~Insights from X-ray Scattering and Molecular Dynamics

The interactions of electrolyte fluids with carbon-based electrodes control many complex interfacial processes encountered in electrochemical energy storage systems. However, our knowledge of the atomic/nanoscale reactivity at interfaces of electrolytes with electrodes remain scares due to the incomplete understanding of interfacial structures and processes in-situ and real-time encountered in real operation conditions. In this talk, we will present our efforts to obtain a molecular-scale perspective of the interactions of electrolytes with carbon surfaces near ``real world'' conditions. Structures of various electrolytes including slat aqueous and ionic liquids on atomically flat graphene (epitaxially grown on a SiC substrate), an ideal model fluid-solid interface system, were investigated by coupling high-resolution interface X-ray scattering techniques with molecular modeling-simulation approaches. These results provide a base-line for understanding relevant electrolyte/carbon interactions and will lead to fundamentally new insights and provide unique tests of atomistic fluid-solid interface models for energy storage systems.   

Charge Transfer Resistance of a Pristine Graphitic Carbon Interface

Electron transfer to and from graphitic carbons is highly sensitive to the chemistry of the graphitic carbon surface. It is known that pristine graphitic carbon has a much higher interfacial resistance than defective carbon; however, a quantitative measure of the difference is limited by the difficulty of preparing truly pristine, defect-free surfaces. Here, we use an individual single-walled carbon nanotube (SWNT) and its single defect sensitivity to ensure that the graphitic carbon surface is pristine. The interfacial charge transfer resistance is measured in the context of a MnO2-coated SWNT, a psuedocapacitor device whose charge cycling performance is found to be limited by the chemistry of the carbon interface. In our devices, the SWNT is uniformly coated with 250-350 nm of MnO2 and cyclic voltammetry is analyzed using an equivalent circuit model to determine the charge transfer resistance. We prove that the defect-free carbon interface is less active than disordered interfaces of carbon or of metallic electrodes. This research is supported by the NEES Energy Frontier Research Center of the U.S. DOE Office of Basic Energy Sciences ({\#}DESC0001160).   

Applications of Light Element X-ray Raman Spectroscopy and Hard X-ray Emission Spectroscopy to the Electronic Structure of Energy Storage Materials: Prospects and Initial Results from the Spectroscopy Program at SSRL

We present the applicability of x-ray raman spectroscopy of light elements and hard x-ray emission to probe the electronic structure of energy storage materials under in-situ conditions. In particular, recent advances in resolution and throughput of x-ray raman spectroscopy (XRS) offer the capability to measure 1s x-ray absorption profiles of light elements such as lithium, boron, carbon, nitrogen and oxygen with less than 0.3eV resolution in the order of 10s of minutes. Initial results from the Spectroscopy program at SSRL and collaborations with groups in various energy storage fields will be presented, with an emphasis on Lithium Batteries and Hydrogen Storage applications.