Theory of quasiparticle energies in alkali metals

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Quasiparticle Self-Consistent GW Study of Simple Metals

The GW method is a standard method to calculate the electronic band structure from first principles. It has been applied to a large variety of semiconductors and insulators but less often to metallic systems, in particular, with respect to a self-consistent employment of the method. In this work, we take a look at all-electron quasiparticle self-consistent GW (QSGW) calculations for simple metals (alkali and alkaline earth metals) based on the full-potential linearized augmented-plane-wave approach and compare the results to single-shot (i.e., non-selfconsistent) G0W0 calculations, density-functional theory (DFT) calculations in the local-density approximation, and experimental measurements. We show that, while DFT overestimates the bandwidth of most of the materials, the GW quasiparticle renormalization corrects the bandwidths in the right direction, but a full self-consistent calculation is needed to consistently achieve good agreement with photoemission data. The results mainly confirm the common belief that simple metals can be regarded as nearly free electron gases with weak electronic correlation. The finding is particularly important in light of a recent debate in which this seemingly established view has been contested.

Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms

We investigate the performance of beyond-GW approaches in many-body perturbation theory by addressing atoms described within the spherical approximation via a dedicated numerical treatment based on B-splines and spherical harmonics. We consider the GW, second Born (2B), and GW + second order screened exchange (GW+SOSEX) self-energies and use them to obtain ionization potentials from the quasi-particle equation (QPE) solved perturbatively on top of independent-particle calculations. We also solve the linearized Sham–Schlüter equation (LSSE) and compare the resulting xc potentials against exact data. We find that the LSSE provides consistent starting points for the QPE but does not present any practical advantage in the present context. Still, the features of the xc potentials obtained with it shed light on possible strategies for the inclusion of beyond-GW diagrams in the many-body self-energy. Our findings show that solving the QPE with the GW+SOSEX self-energy on top of a PBE or PBE0 solution is a viable scheme to go beyond GW in finite systems, even in the atomic limit. However, GW shows a comparable performance if one agrees to use a hybrid starting point. We also obtain promising results with the 2B self-energy on top of Hartree–Fock, suggesting that the full time-dependent Hartree–Fock vertex may be another viable beyond-GW scheme for finite systems.

Single-particle excitations in the uniform electron gas by diagrammatic Monte Carlo

We calculate the single-particle excitation spectrum and the Landau liquid parameters for the archetypal model of solids, the three-dimensional uniform electron gas, with the variational diagrammatic Monte Carlo method, which gives numerically controlled results without systematic error. In the metallic range of density, we establish benchmark values for the wave-function renormalization factor Z, the effective mass \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m^*/m$$\end{document}m∗/m, and the Landau parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_0^s$$\end{document}F0s and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_0^a$$\end{document}F0a with unprecedented accuracy, and we resolve the long-standing puzzle of non-monotonic dependence of mass on density. We also exclude the possibility that experimentally measured large reduction of bandwidth in Na metal can originate from the charge and spin fluctuations contained in the model of the uniform electron gas.

Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW 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 GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW 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 GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Simple eigenvalue-self-consistent Δ ¯ G W 0

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ ¯ G W 0 , can be trivially implemented at zero additional cost for large scale one-shot G ₀ W ₀ calculations. The method significantly improves one-shot G ₀ W ₀ and for large systems is very accurate. Δ ¯ G W 0 is similar in spirit to evGW ₀ where the self-consistency is only applied on the eigenvalues entering Green's function, while both W and the eigenvectors of Green's function are held fixed. Δ ¯ G W 0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G ₀ W ₀ self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ ¯ G W 0 increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW ₀ to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW ₀ quite well and both methods are in good agreement with the experiment.

Vertex Corrections for Positive-Definite Spectral Functions of Simple Metals

We present a systematic study of vertex corrections in a homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as the generation of two plasmon excitations or the decay of the one-particle state into a two-particle-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for a reduction of the bandwidth, the appearance of a secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed.

Valence band x-ray emission spectra of compressed germanium

We report measurements of the valence band width in compressed Ge determined from x-ray emission spectra below the Ge K edge. The width of the valence band does not show any pressure dependence in the semiconducting diamond-type structure of Ge below 10 GPa. On the other hand, in the metallic beta-Sn phase above 10 GPa the valence band width increases under compression. Density-functional calculations show an increasing valence band width under compression both in the semiconducting phase (contrary to experiment) and in the metallic beta-Sn phase of Ge (in agreement with observed pressure-induced broadening). The pressure-independent valence band width in the semiconducting phase of Ge appears to require theoretical advances beyond the density-functional theory or the GW approximation.

Nonequilibrium superoperator GW equations

Hedin's equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green's function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green's function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.