Session E24: Many-Body Perturbation Theory for Electronic Excitations: Computational Advances

Plasmon Pole Approximations within a GW Sternheimer implementation

We use an implementation of the GW approximation that exploits a Sternheimer equation and a Lanczos procedure to circumvent the resource intensive sum over all bands and inversion of the dielectric matrix. I will present further improvement of the method that uses Plasmon Pole approximations to evaluate the integral over all frequencies analytically. A comparison study between the von Linden-Horsh and Engel-Farid approaches for energy levels of various molecules along with benchmarking of the computational ressources needed by the method will be discussed.   

Inclusion of the electron-phonon interaction in the BerkeleyGW computational package

The BerkeleyGW package is a highly optimized and efficient code for calculating, among others, the dielectric response, bandstructures, lifetimes, and optical absorption of materials from nanostructures and two-dimensional sheets to bulk materials. In the past the only interactions included in BerkeleyGW were electron-electron interactions, with other packages being used to include the effect of, say, electron-phonon interactions. One common approach is to use Wannier functions to interpolate all needed quantities to a very fine grids in energy and momentum, which leads to very accurate electron-phonon couplings and lifetimes. However, in materials with complex, even unknown, chemical environments the generation of Wannier functions can be quite time consuming and constitutes another step in an already difficult calculation. The BerkeleyGW package has a wavefunction-based interpolation scheme that is used in solving the Bethe-Salpeter equation and which is much more easily automated than Wannier interpolation. In this talk, we discuss results for the carrier lifetimes due to the electron-phonon interaction using this interpolation scheme. In particular, we discuss the computational efficiency and scalability, and the prospects for applying this method to a wide range of materials to get first principles lifetimes, and related quantities, such as mobilities and diffusion lengths.   

Large-scale GW software development

Electronic excitations are important in understanding and designing many functional materials. In terms of {\it ab initio} methods, the GW and Bethe-Saltpeter Equation (GW-BSE) beyond DFT methods have proved successful in describing excited states in many materials. However, the heavy computational loads and large memory requirements have hindered their routine applicability by the materials physics community. We summarize some of our collaborative efforts to develop a new software framework designed for GW calculations on massively parallel supercomputers. Our GW code is interfaced with the plane-wave pseudopotential {\it ab initio} molecular dynamics software ``OpenAtom'' which is based on the Charm++ parallel library [1]. The computation of the electronic polarizability is one of the most expensive parts of any GW calculation. We describe our strategy that uses a real-space representation to avoid the large number of fast Fourier transforms (FFTs) common to most GW methods. We also describe an eigendecomposition of the plasmon modes from the resulting dielectric matrix that enhances efficiency. [1] Bohm {\it et al.}, IBM J. RES. \& DEV. vol. 52 no. 1/2, 2008   

Towards highly scalable GW calculations

The GW and Bethe-Saltpeter Equation (GW-BSE) approach is an accurate and useful method beyond DFT to describe excited states of materials. However over the past few decades, most {\it ab initio} GW calculations used have been confined to small units of cells of bulk-like materials due to the extreme computational demands of the approach. We will present our collaborative efforts to develop new software that permits large scale GW calculations more efficiently: our GW software is interfaced with the ab initio plane wave pseudopotential OpenAtom software (http://charm.cs.uiuc.edu/OpenAtom/) that uses the Charm++ parallel framework. Here, we focus on describing our work on computing the static (so called ``COHSEX’’) GW self-energy. We describe the advantages of our real-space approach for quasi-particle calculations and provide information on scaling behavior of the resulting algorithms.   

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules: A Benchmark of GW Methods

The performance of different GW methods is assessed for a set of 24 organic acceptors. Errors are evaluated with respect to coupled cluster singles, doubles, perturbative triples [CCSD(T)] reference data for the vertical ionization potentials (IPs) and electron affinities (EAs), extrapolated to the complete basis set limit. Additional comparisons are made to experimental data, where available. We consider fully self-consistent GW (scGW), partial self-consistency in the Green's function (scGW$_{\mathrm{0}})$, non-self-consistent G$_{\mathrm{0}}$W$_{\mathrm{0}}$ based on several mean-field starting points, and a ``beyond GW'' second order screened exchange (SOSEX) correction to G$_{\mathrm{0}}$W$_{\mathrm{0}}$. The best performers overall are G$_{\mathrm{0}}$W$_{\mathrm{0}}+$SOSEX and G$_{\mathrm{0}}$W$_{\mathrm{0}}$ based on an IP-tuned long range corrected hybrid functional with the former being more accurate for EAs and the latter for IPs. Both provide a balanced treatment of localized vs. delocalized states and valence spectra in good agreement with photoemission spectroscopy (PES) experiments.   

Extrapolation of G$_0$W$_0$ energy levels from small basis sets for elements from H to Cl

G$_0$W$_0$ calculations based on orbitals from a density-functional theory reference are widely used to predict carrier levels in molecular and inorganic materials. Their computational feasibility, however, is limited by the need to evaluate slow-converging sums over unoccupied states, requiring large basis sets paired with unfavorable scaling exponents to evaluate the self-energy. In the quantum chemistry literature, complete basis set (CBS) extrapolation strategies have been used successfully to overcome this problem for total energies. We here apply the principle of basis set extrapolation to G$_0$W$_0$ energy levels. For a set of 49 small molecules and clusters containing the elements H, Li through F, and Na through Cl, we test established extrapolation strategies based on Dunning's correlation-consistent (cc) basis sets (aug)-cc-pVNZ (N=2-5), as well as numeric atom-centered NAO-VCC-nZ (n=2-5) basis sets in the FHI-aims all-electron code. For the occupied and lowest unoccupied levels, different extrapolation strategies agree within $\pm$50 meV based on large 4Z and 5Z basis sets. We show that extrapolation based on much smaller 2Z and 3Z basis sets with largest errors $\pm$ 100 meV based on a refinement of the NAO-VCC-nZ basis sets.   

The Sternheimer-GW method and the spectral signatures of plasmonic polarons

During the past three decades the GW method has emerged among the most promising electronic structure techniques for predictive calculations of quasiparticle band structures. In order to simplify the GW work-flow while at the same time improving the calculation accuracy, we developed the Sternheimer-GW method [1]. In Sternheimer-GW both the screened Coulomb interaction and the electron Green's function are evaluated by using exclusively occupied Kohn-Sham states, as in density-functional perturbation theory. In this talk I will review the basics of Sternheimer-GW, and I will discuss two recent applications to semiconductors and superconductors. In the case of semiconductors we calculated complete energy- and momentum-resolved spectral functions by combining Sternheimer-GW with the cumulant expansion approach. This study revealed the existence of band structure replicas which arise from electron-plasmon interactions [2]. In the case of superconductors we calculated the Coulomb pseudo-potential from first principles, and combined this approach with the Eliashberg theory of the superconducting critical temperature [3]. [1] H. Lambert, F. Giustino, Phys. Rev. B 88, 075117 (2013). [2] F. Caruso, H. Lambert, F. Giustino, Phys. Rev. Lett. 114, 146404 (2015). [3] E. R. Margine, F. Giustino, Phys. Rev. B 87, 024505 (2013).   

Combination of Hedin's $GW$ and dynamical mean-field theory tested on H$_2$ molecule

We compare various flavors of ``$GW$+DMFT" approach with LDA+DMFT for the simplest strongly correlated system, the H$_2$ molecule. The following $GW$+DMFT methodologies are compared: (i) the fully self-consistent GW+DMFT, (ii) the quasi-particle self-consistent QS-GW+DMFT with dynamic double-counting, (iii) QS-GW+DMFT with static double-counting schemes. We found that fully self-consistent $GW$+DMFT with exact double-counting yields very precise spectra around equilibrium H-H distance, as well as reasonable total energy (comparable to LDA+DMFT). However, this scheme breaks down in the correlated regime due to causality violation. The QS-GW+DMFT approaches, which are not derivable from a functional, yield similar spectra as full GW+DMFT near equilibrium distance, and in static double-counting schemes, can also be extended into correlated regime. However, the total energy of these approaches is much worse than the total energy of LDA+DMFT. In summary, this toy model of correlated physics suggests that QS-GW+DMFT with constant double-counting should give accurate predictions of spectra, but not total energy, while LDA+DMFT gives very precise total energy, but somewhat less precise spectra.   

Electron-phonon coupling using many-body GW theory

Electron-phonon coupling drives a plethora of phenomena, such as superconductivity in metals, or the temperature dependence of optical properties in semiconductors. There is increasing evidence that semi-local density functional theory (DFT) is not adequate for the description of electron-phonon coupling, and instead effects such as electronic correlation need to be included. Unfortunately, methods beyond semi-local DFT are computationally demanding, limiting the study of these phenomena. In this talk we will introduce the idea of ``thermal lines'', which can be used to explore the vibrational phase space of solids and molecules at small computational cost. In particular, we will describe how thermal lines can be exploited to calculate the temperature dependence of band structures beyond semi-local DFT, by using many-body GW theory, or by including the effects of spin-orbit coupling. We will present first-principles results showing the effects of electron correlation on the strength of electron-phonon coupling, and the effects of electron-phonon coupling on topological states of matter.   

Plane wave based selfconsistent solution of the GW Dyson equation

We have developed a selfconsistent procedure to calculate the full Dyson equation based on plane wave basis set. The whole formalism is based on the Greens function matrix of the plane wave G-vector. There is no truncation of the conduction band when the dielectric function is calculated. The Dyson equation is the variational minimum solution of the total energy in terms of the Greens function. The calculation uses the "space-time" method, with special algorithm for imaginary time integration and Fourier transformation. We have tested isolated molecules and periodic systems. The effects of selfconsistency compared to the G0W0 results will be presented. We will also discuss some special techniques used in the k-point summation for the periodic system. Massive parallelization is used to carry out such calculations.   

Post-GW energies from an extended Bethe-Salpeter scheme

Hedin's breakthrough in many-body physics is a computationally manageable scheme to implicitly account for many-body effects thanks to the introduction of a self-energy, whose expression is known but in practice approximated by truncation at some order in the inter-particle interaction. \\ Hedin's scheme allows the computation of quasi-particle addition and removal energies. The introduction of an added particle (or hole) to the system will trigger the formation of higher order neutral excitations (particle/hole pairs formation). The widespread GW approximation only partially accounts for these effects by replacing the bare interparticle interaction with a dressed one. Other effects are contained in the vertex function and are typically disregarded.\\ In the present work, we move beyond the GW level by including vertex effects in the self-energy. This is implemented by expressing the self-energy in terms of the reducible two-particle scattering amplitude. The latter is related to the kernel of the Bethe-Salpeter equation and to the corresponding polarisation propagator. The proposed implementation allows us to evaluate the quality of quasi-particle spectra for a range of realistic solids and molecular systems.   

GW Calculations of Materials on the Intel Xeon-Phi Architecture

Intel Xeon-Phi processors are expected to power a large number of High-Performance Computing (HPC) systems around the United States and the world in the near future. We evaluate the ability of GW and pre-requisite Density Functional Theory (DFT) calculations for materials on utilizing the Xeon-Phi architecture. We describe the optimization process and performance improvements achieved. We find that the GW method, like other higher level Many-Body methods beyond standard local/semilocal approximations to Kohn-Sham DFT, is particularly well suited for many-core architectures due to the ability to exploit a large amount of parallelism over plane-waves, band-pairs and frequencies.   

Recent Advances in Modeling Transition Metal Oxides for Photo-electrochemistry

Computational research offers a wide range of opportunities for materials science and engineering, especially in the energy arena where there is a need for understanding how material composition and structure control energy conversion, and for designing materials that could improve conversion efficiency. Potential inexpensive materials for energy conversion devices are metal oxides. However, their conversion efficiency is limited by at least one of several factors: a too large band gap for efficiently absorbing solar energy, similar conduction and valence band edge characters that may lead to unfavorably high electron-hole recombination rates, a valence band edge that is not positioned well for oxidizing water, low stability, low electronic conductivity, and low surface reactivity. I will show how we model metal oxides with ab-initio methods, primarily DFT$+$U. Our previous results show that doping with lithium, sodium, or hydrogen could improve iron (II) oxide's electronic properties, and alloying with zinc or nickel could improve iron (II) oxide's optical properties. Furthermore, doping nickel (II) oxide with lithium could improve several key properties including solar energy absorption. In this talk I will highlight new results on our understanding of the mechanism of iron (III) oxide's surface reactivity. Our theoretical insights bring us a step closer towards understanding how to design better materials for photo-electrochemistry. References: 1. O. Neufeld and M. Caspary Toroker, ``Pt-doped Fe2O3 for enhanced water splitting efficiency: a DFT$+$U study'', J. Phys. Chem. C 119, 5836 (2015). 2. M. Caspary Toroker, ``Theoretical Insights into the Mechanism of Water Oxidation on Non-stoichiometric and Ti -- doped Fe$_{\mathrm{2}}$O$_{\mathrm{3}}$(0001)'', J. Phys. Chem. C, 118, 23162 (2014).