The
approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the
...method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of
calculations in the past two decades has exploded with increased computing power and modern codes. The success of
can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing
calculations for the first time. We also give an introduction to the many-body theory behind
, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional
calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to
calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.
This article presents an overview on recent progress in the theory of nonequilibrium Green functions (NEGF). We discuss applications of NEGF simulations to describe the femtosecond dynamics of ...various finite fermionic systems following an excitation out of equilibrium. This includes the expansion dynamics of ultracold atoms in optical lattices following a confinement quench and the excitation of strongly correlated electrons in a solid by the impact of a charged particle. NEGF, presently, are the only ab initio quantum approach that is able to study the dynamics of correlations for long times in two and three dimensions. However, until recently, NEGF simulations have mostly been performed with rather simple selfenergy approximations such as the second-order Born approximation (SOA). While they correctly capture the qualitative trends of the relaxation towards equilibrium, the reliability and accuracy of these NEGF simulations has remained open, for a long time. Here we report on recent tests of NEGF simulations for finite lattice systems against exact-diagonalization and density-matrix-renormalization-group benchmark data. The results confirm the high accuracy and predictive capability of NEGF simulations-provided selfenergies are used that go beyond the SOA and adequately include strong correlation and dynamical-screening effects. With an extended arsenal of selfenergies that can be used effectively, the NEGF approach has the potential of becoming a powerful simulation tool with broad areas of new applications including strongly correlated solids and ultracold atoms. The present review aims at making such applications possible. To this end we present a selfcontained introduction to the theory of NEGF and give an overview on recent numerical applications to compute the ultrafast relaxation dynamics of correlated fermions. In the second part we give a detailed introduction to selfenergies beyond the SOA. Important examples are the third-order approximation, the approximation, the T-matrix approximation and the fluctuating-exchange approximation. We give a comprehensive summary of the explicit selfenergy expressions for a variety of systems of practical relevance, starting from the most general expressions (general basis) and the Feynman diagrams, and including also the important cases of diagonal basis sets, the Hubbard model and the differences occuring for bosons and fermions. With these details, and information on the computational effort and scaling with the basis size and propagation duration, readers will be able to choose the proper basis set and straightforwardly implement and apply advanced selfenergy approximations to a broad class of systems.
Abstract
This work presents the results of a theoretical study of the electronic structure of two actinide metals,
α
-U and
δ
-Pu. We compare our
ab-initio
results obtained with the recently ...developed self-consistent Vertex corrected GW approach with previously published experimental measurements such as photo-electron spectroscopy, for the occupied density of states, and bremsstralung isochromat spectroscopy (BIS) and inverse photo-electron spectroscopy (IPES), for the unoccupied density of states. Our
ab-initio
approach includes all important relativistic effects (it is based on Dirac’s equation) and it represents the first application of the Vertex corrected GW approach in the physics of actinides. Overall, our theoretical results are in good agreement with the experimental data, which supports the level of approximations which our theoretical method is based upon. By comparing our vertex corrected GW results with our results obtained with less sophisticated approaches (local density approximation and self-consistent GW) we differentiate the strength of correlation effects in Uranium and Plutonium. Also, our theoretical results allow us to elucidate the subtle differences between the previously published experimental BIS and IPES data on the unoccupied density of states in
α
-U.
We summarize the molgw code that implements density-functional theory and many-body perturbation theory in a Gaussian basis set. The code is dedicated to the calculation of the many-body self-energy ...within the GW approximation and the solution of the Bethe–Salpeter equation. These two types of calculations allow the user to evaluate physical quantities that can be compared to spectroscopic experiments. Quasiparticle energies, obtained through the calculation of the GW self-energy, can be compared to photoemission or transport experiments, and neutral excitation energies and oscillator strengths, obtained via solution of the Bethe–Salpeter equation, are measurable by optical absorption. The implementation choices outlined here have aimed at the accuracy and robustness of calculated quantities with respect to measurements. Furthermore, the algorithms implemented in molgw allow users to consider molecules or clusters containing up to 100 atoms with rather accurate basis sets, and to choose whether or not to apply the resolution-of-the-identity approximation. Finally, we demonstrate the parallelization efficacy of the molgw code over several hundreds of processors.
Program title: MOLGW
Catalogue identifier: AFAW_v1_0
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAW_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: GNU GPL v3
No. of lines in distributed program, including test data, etc.: 167871
No. of bytes in distributed program, including test data, etc.: 1309269
Distribution format: tar.gz
Programming language: Fortran 2003 with a few C subroutines, Python scripts.
Classification: 7.3, 16.6, 16.10.
External routines: libint 2, libxc 3, SCALAPACK 4 (optional)
Nature of problem:
Prediction of the electronic structure of atoms, molecules, clusters with a particular interest in their spectroscopic features, such as quasiparticle energies and optical spectra.
Solution method:
Using the GW approximation to many-body perturbation theory, MOLGW calculates total-energies, quasiparticle energies, and optical excitations.
Additional comments:
Python3 is required to run the test suite provided.
Running time:
From 30 s to a few hours
References: 1http://www.gnu.org/copyleft/gpl.txt2https://github.com/evaleev/libint3http://www.tddft.org/programs/octopus/wiki/index.php/Libxc4http://www.netlib.org/scalapack
The magnitude of the renormalization of the band gaps due to zero-point motions of the lattice is calculated for 18 semiconductors, including diamond and silicon. This particular collection of ...semiconductors constitute a wide range of band gaps and atomic masses. The renormalized electronic structures are obtained using stochastic methods to sample the displacement related to the vibrations in the lattice. Specifically, a recently developed one-shot method is utilized where only a single calculation is needed to get similar results as the one obtained by standard Monte-Carlo sampling. In addition, a fast real-space GW method is employed and the effects of G0W0 corrections on the renormalization are also investigated. We find that the band-gap renormalizations inversely depend on the mass of the constituting ions, and that for the majority of investigated compounds the G0W0 corrections to the renormalization are very small and thus not significant.
We implement stochastic many-body perturbation theory for systems with 2D periodic boundary conditions. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. ...Excitation energies are studied using stochastic Formula: see text and partially self-consistent Formula: see text approaches. The approach is inexpensive; it is used to study twisted systems with unit cells containing >2700 atoms (>13 500 valence electrons), which corresponds to a minimum twisting angle of Formula: see text Formula: see text. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moiré impurity states, as documented by band-structure unfolding. Structural changes in twisted structures lift band degeneracies. Energies of the impurity states vary with the twisting angle due to an interplay between non-local exchange and polarization effects. The mechanisms of quasiparticle energy (de)stabilization due to twisting are likely applicable to a wide range of low-dimensional Moiré superstructures.
Recently, SnTe has gained attention due to its non-trivial topological nature and eco-friendly thermoelectric applications. We report a detailed temperature dependent electronic structure of this ...compound using DFT and
methods. The calculated values of bandgaps by using PBEsol and
methods are found to be in good agreement with the experiment, whereas mBJ underestimates the bandgap. The averaged value of diagonal matrix elements of fully screened Coulomb interaction (W̄) at
= 0 eV for Sn (Te) 5
orbitals is ∼1.39 (∼1.70) eV. The nature of frequency dependentW̄(ω)reveals that the correlation strength of this compound is relatively weaker and hence the excited electronic state can be properly studied by full-
many-body technique. The plasmon excitation is found to be important in understanding this frequency dependentW̄(ω). The temperature dependent electron-electron interactions (EEI) reduces the bandgaps with increasing temperature. The value of bandgap at 300 K is obtained to be ∼161 meV. The temperature dependent lifetimes of electronic state along
-
-Γ direction are also estimated. This work suggests that EEI is important to explain the high temperature transport behaviour of SnTe.
Abstract
Finite size armchair graphene nanoribbons (GNRs) of different families are theoretically studied using the Hubbard model in both mean-field and GW approximations, including spin correlation ...effects. It is shown that correlation primarily affect the properties of topological end states of the nanoribbons. A representative structure of each of the three GNR families is considered but the seven-atom width nanoribbon is studied in detail and compared to previously published experimental results, showing a clear improvement when correlations are included. Using isolated spin contributions to scanning tunneling microscopy (STM) simulations, spin-polarized measurements in STM are also suggested to help distinguish and highlight correlation effects.
The question of spatial locality of electronic correlations beyond GW approximation is one of the central issues of the famous combination of GW and dynamical mean field theory, GW+DMFT. In this ...study, the above question is addressed directly (for the first time) by performing calculations with and without assumption of locality of the corresponding diagrams. For this purpose we use sc(GW+G3W2) approach where the higher order part (G3W2) is evaluated with fully momentum dependent Green's function G and screened interaction W and with "local" variant, where the single site approximation is assumed for both G and W. For all three materials studied in this work (NiO, α-Ce, LiFeAs), we have found the spatial non-locality effects to be strong. For NiO and LiFeAs they, in fact, are decisive for the proper evaluation of vertex corrections. The results of this study have direct impact on our understanding of approximations made in practical implementations of GW+DMFT method, where all diagrams beyond GW (DMFT part) are assumed to be local. Taking into account the fact that the first diagrams beyond GW represent the most important contribution also in GW+DMFT calculations, we conclude that the basic assumption of GW+DMFT, namely the locality of diagrams evaluated in the DMFT part, is not as good as it is believed to be.
PDF
