The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

https://iopscience.iop.org/article/10.1088/0953-8984/9/4/002/pdf

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method

Semiconductor photocatalysis has received much attention as a potential solution to the worldwide energy shortage and for counteracting environmental degradation. This article reviews state-of-the-art research activities in the field, focusing on the scientific and technological possibilities offered by photocatalytic materials. We begin with a survey of efforts to explore suitable materials and to optimize their energy band configurations for specific applications. We then examine the design and fabrication of advanced photocatalytic materials in the framework of nanotechnology. Many of the most recent advances in photocatalysis have been realized by selective control of the morphology of nanomaterials or by utilizing the collective properties of nano-assembly systems. Finally, we discuss the current theoretical understanding of key aspects of photocatalytic materials. This review also highlights crucial issues that should be addressed in future research activities.

Nano‐photocatalytic Materials: Possibilities and Challenges

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

https://perssongroup.lbl.gov/papers/compmatsci2013-pymatgen.pdf

Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

An approach to first-principles simulations that incorporates dynamically screened Coulomb interactions between iron d electrons enables the low-energy electronic structure and angle-resolved photoemission spectroscopy spectra of iron-based superconductors to be modelled with unprecedented accuracy.

Satellites and large doping and temperature dependence of electronic properties in hole-doped BaFe2As2

he valence photoemission spectra of alkali metals exhibit multiple plasmon satellite structure. The calculated spectral functions within the GW approximation show only one plasmon satellite at too large binding energy. In this Letter we use the cumulant expansion approach to obtain the spectral functions of Na and Al from ab initio calculations including the effects of band structure. The GW spectral functions are dramatically improved and the positions of the multiple plasmon satellites are in very good agreement with experiment while their intensities cannot be explained from intrinsic effects only.

Multiple Plasmon Satellites in Na and Al Spectral Functions from Ab Initio Cumulant Expansion.

The one-electron excitation spectra of ferromagnetic nickel have been obtained from a first-principles calculation of the self-energy operator within the so-called GW approximation. The dielectric matrix, needed to form the screened potential W, is computed within the random-phase approximation. The quasiparticle energies are in very good agreement with angle-resolved photoemission data. The bottom of the d band is raised by about 1 eV resulting in band narrowing as observed experimentally and the quasiparticle widths are also in favorable agreement with experiment. The exchange splittings, however, are the same for most cases as those given by the local-density approximation in density-functional theory. The satellite at 6 eV is not reproduced. Instead, we found a significant contribution to the spectral weight from quasiparticle peaks around that energy. We discuss the success and the shortcomings of the GW approximation in the light of our results.

Ferdi Aryasetiawan

Papers

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method

The GW method

Satellites and large doping and temperature dependence of electronic properties in hole-doped BaFe2As2

Multiple Plasmon Satellites in Na and Al Spectral Functions from Ab Initio Cumulant Expansion.

Self-energy of ferromagnetic nickel in the GW approximation.