Within density functional theory we study the bulk band structure and surface states of bismuth oxychalcogenides Bi2O2Se and Bi2O2Te. We consider both polar and nonpolar surface terminations. On the basis of relativistic ab initio calculations, we show that both unreconstructed (polar) and reconstructed (nonpolar) surfaces possess the Rashba spin-split surface states. The metallic Rashba-split states on polar surfaces stem from huge potential bending, positive or negative, depending on surface polarity. On the nonpolar surfaces resulting from single-crystal cleavage the emerging Rashba-split states are nonmetallic. ; This work was supported by the Fundamental Research Program of the State Academies of Sciences, line of research III.23, and the Academic D. I. Mendeleev Fund Program of Tomsk State University (Project No. 8.1.01.2018). The support from the Saint Petersburg State University (Project No. 15.61.202.2015), Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), and the Spanish Ministry of Science and Innovation (Grant No. FIS2016-75862-P) is also acknowledged. Calculations were performed using computational resources provided by Resource Center "Computer Center of SPbU" and the SKIF-Cyberia supercomputer at the National Research Tomsk State University. S.V.E. thanks I. A. Nechaev for fruitful discussions.
To achieve climate protection goals set out by national governments and the United Nations, it is paramount to reduce society's dependence on fossil fuels and to introduce more sustainable energy solutions. Furthermore, to not only protect our climate but the natural environment in general, it is necessary to reduce humanity's waste production and to turn waste into a resource wherever possible. The solutions to both of these ambitions will heavily rely on new chemical processes being discovered and upscaled. Thus, with catalysis and photochemistry at its heart, the challenge to build a greener and more sustainable future is largely a materials discovery and design problem. In this work, I introduce a new way of aligning the electronic energy levels of semiconductors with respect to redox potentials which might facilitate in silico screening studies of materials suitable for photoelectrochemistry. In particular, I demonstrate how continuum solvation models can be used to replace computationally expensive atomistic descriptions of water when describing an electrode-electrolyte interface. I tested this approach on rutile (TiO2) showing that, when combined with a description of rutile's electronic structure within many-body perturbation theory, the proposed alignment procedure yields the correct positioning of rutile's band edges on the standard hydrogen electrode scale. My investigation surfaced and explained important differences between atomistic and continuum solvation models when describing the electric potential across interfaces. Furthermore, I present a detailed study of the electronic structure of osmium dioxide (OsO2) near its Fermi level. OsO2 is closely related to important catalysts such as IrO2 and RuO2, which also crystallise in the rutile structure. Specifically, by collaborating with colleagues specialised in experimental photoelectron spectroscopy (PES), we highlight the importance of computational insights for the correct interpretation of PES spectra. By going beyond a simple comparison between the experimentally measured PES spectrum and the computed single-particle electronic density of states, we reveal that the spectrum of OsO2 features a rare low-energy bulk plasmon satellite. ; Open Access
We have investigated the electronic structures of axially oxo functionalized titanylphthalocyanine (TiOPc) on Ag(111) by X-ray and ultraviolet photoelectron spectroscopies, two-photon photoemission, X-ray absorption spectroscopy, and X-ray magnetic circular dichroism. Furthermore, we use complementary data of TiOPc on graphite and planar copper phthalocyanine (CuPc) on Ag(111) for a comparative analysis. Both molecules adsorb on Ag(111) in a parallel orientation to the surface, for TiOPc with an oxygen-up configuration. The interaction of nitrogen and carbon atoms with the substrate is similar for both molecules, while the bonding of the titanium atom to Ag(111) in the monolayer is found to be slightly more pronounced than in the CuPc case. Ultraviolet photoemission spectroscopy reveals an occupation of the lowest unoccupied molecular orbital (LUMO) level in monolayer thick TiOPc on Ag(111) related to the interaction of the molecules and the silver substrate. This molecule-metal interaction also causes an upward shift of the Ag(111) Shockley state that is transformed into an unoccupied interface state with energies of 0.23 and 0.33 eV for the TiOPc monolayer and bilayer, respectively, at the Brillouin zone center. ; The authors acknowledge financial support from the Deutsche Forschungsgemeinschaft through SFB 1083 "Structure and Dynamics of Internal Interfaces", the Spanish CSIC I-Link programm, the Spanish Ministry of Economy and Competitiveness, MINECO (under Contract No. MAT2016-78293-C6-2-R, and Severo Ochoa No. SEV-2013-0295.), and by the Secretariat for Universities and Research, Knowledge Department of the Generalitat de Catalunya (2014 SGR 715). M. Paradinas thanks the Spanish Government for financial support through PTA2014-09788-I fellowships. ICN2 is funded by the CERCA Programme/Generalitat de Catalunya. ; Peer Reviewed
An investigation of the active site cofactors of the molybdenum and vanadium nitrogenases (FeMoco and FeVco) was performed using high-resolution X-ray spectroscopy. Synthetic heterometallic iron–sulfur cluster models and density functional theory calculations complement the study of the MoFe and VFe holoproteins using both non-resonant and resonant X-ray emission spectroscopy. Spectroscopic data show the presence of direct iron–heterometal bonds, which are found to be weaker in FeVco. Furthermore, the interstitial carbide is found to perturb the electronic structures of the cofactors through highly covalent Fe–C bonding. The implications of these conclusions are discussed in light of the differential reactivity of the molybdenum and vanadium nitrogenases towards various substrates. Possible functional roles for both the heterometal and the interstitial carbide are detailed. ; This work was supported by the European Research Council (ERC) under the European Union's Seventh Framework Programme (FP/2007–2013) ERC Grant Agreement number 615414 (S. D.) and the ERC N-ABLE project (O. E.). Funding was also provided by the Deutsche Forschungsgemeinschaft grants EI-520/7 and RTG1976 (O. E.), the NIH (R01-GM45881 to J. A. K.), and by the Max-Planck–Gesellschaft (S. D., R. B., J. K. K., and F. A. L.). J. A. R. was funded by a graduate study scholarship from the German Academic Exchange Service (DAAD). R. B. acknowledges support from the Icelandic Research Fund, Grant No. 141218051 and the University of Iceland Research Fund. Matthias Gschell and Florian Schneider are thanked for preparing the extracted FeMoco, and Tabea Hamann is thanked for providing samples of the molybdenum cubane. Stefan Hugenbruch, Benjamin Van Kuiken, Rebeca Gómez Castillo, and Anselm Hahn are thanked for assistance with data collection. The ESRF and CHESS are also acknowledged for providing beamtime, and Sara Lafuerza and Pieter Glatzel at beamline ID-26 (ESRF) and Kenneth D. Finkelstein at beamline C-1 (CHESS) are gratefully acknowledged for technical assistance with measurements. CHESS is supported by the National Science Foundation and the National Institutes of Health/National Institute of General Medical Sciences under NSF award DMR-133220. Open Access funding provided by the Max Planck Society. ; Peer Reviewed
The oxygen evolution reaction during the photosynthesis process performed in plants, algae and cyanobacteria is possibly one of the most important reactions on the planet that sustain most life on our planet. Understanding the structure and function of the "engine of life", the oxygen-evolving complex (OEC) in the active site of Photosystem II (PSII), has been one of the great and persistent challenges of modern science. Over the past decades, immense progress has been achieved in understanding the structure and mechanism of photosynthetic reactions. This progress is in large part due to the refinement of preparative protocols, X-Ray Diffractometry (XRD), site-directed mutagenesis, Electron Paramagnetic Resonance (EPR) spectroscopy, the coming of age of X-ray Free Electron Laser (XFEL) diffractometry and computational approaches in the investigation of PS II. Nevertheless, key mechanistic and electronic details of water oxidation still remain highly contentious. Elucidation of these details is complicated by the fact that the active site of PSII exists in four natural metastable oxidation states, as well as putative unnatural forms that are plausibly induced during experimental investigation. The leading motivation of the scientific community studying PSII is ultimately the development of new catalysts and even bio-inspired solar cells, that will produce clean and sustainable energy for the world. Over the last hundred years, approximately 80% of worldwide energy consumption has been based on fossil fuels, including coal, oil, and natural gas. However, humankind now has to face the consequences arising from this dependence on fossil fuels. Worldwide energy consumption is expected to increase by over 50% by the mid-2000s (see Fig. 0.1). Because fossil fuels are finite and regional around the world, it is greatly challenging to ensure that this demand can be met, in the face of possible political tensions and other potential problems with energy supplies. Due to the usage of fossil fuels, large quantities of emissions, e.g., CO2, SO2, and oxide particles, are the predominant reasons for global warming and severe pollution. Recent reports from the Intergovernmental Panel on Climate Change emphasized the necessity of decreasing CO2 emissions on a global scale to the zero level before the next century. These arguments make the development of sustainable and carbon-neutral energy technologies one of the most urgent challenges facing humankind all over the world. Wind, ocean currents, tides, and waves are all potential sources of energy, but by far the most abundant renewable energy source on the planet is solar energy: solar illumination on Earth every hour is greater than the worldwide energy consumption for a whole year [35]. Therefore, the conversion and utilization of solar energy is a promising solution for energy problems. An intriguing potential solution to the expected shortfall in energy supplies is artificial photosynthesis [108], whereby light energy can be stored in chemical bonds and, hence, be made available as fuels [18, 200, 19, 364]. Synthetic molecular and heterogeneous manganese analogues still struggle to mimic the function and performance of the OEC. This is partly because these distinctive features are not intrinsic to the Mn4CaO5 core of the OEC but depend on its environment and result from elaborate gating and regulation mechanisms for coordinating the coupling of proton-electron transfer and the access, delivery, binding, positioning, activation, and coupling of substrate waters to form dioxygen. The high level of geometric and electronic control, both spatial and temporal, extends along the whole catalytic cycle and involves simultaneously the Mn4CaO5 cluster, its first coordination sphere, and the protein matrix that controls the flow of electrons, protons, substrates, and products. From the side of theoretical methods great progresses have been made in recent years. Due to the success of the density functional theory (DFT), not only in the field of solid state physics, but also on liquids and molecular compounds, it is possible to obtain the electronic structure of few hundreds atoms with an acceptable computational effort. Using the information provided by the experiments as starting point, it is possible to employ DFT to refine the geometries in relationship with the electron ground-state or different electronic states, to calculate the electron and spin density for a given system and to estimate spectroscopic properties. The coupling of DFT with molecular dynamics also allows us to perform ab-initio molecular dynamics of large systems at finite temperature to fully consider entropic contributions and low-energy conformational changes. Computational techniques can also provide considerable support in the analysis and interpretation of the complex IR spectra of such biological systems. In this thesis, the molecular and electronic structures of the multinuclear manganese containing bioinorganic system together with oxygen-evolving complex of PS II are investigated using DFT-based methods for the theoretical modeling of vibrational spectra in the gas phase by normal mode analysis and molecular dynamics simulations. Research on biological water oxidation traverses scientific fields and concentrates the efforts of a multitude of experimental and theoretical approaches. Different methods of investigation naturally lead to distinct views on the OEC. These are often complementary but at times are contradictory, and it is not always obvious whether the contradictions already exist in the data or arise from their suggested interpretations. Nevertheless, the overarching goals are common to all experimental and theoretical studies. These are not limited to the geometric and electronic structure of the cluster in each state of the cycle but encompass the role of the protein matrix, the channels, and secondary components of the second sphere of the cluster, such as the chloride ions. Chapter I of the thesis considers in detail the progress that have been done so far in structural and spectroscopic studies of OEC and its synthetic mimics given together with the general introduction on photosynthetic reactions occurring in the leaf. Theoretical background of the computational methods used in present work is given in detail in Chapter II. In this thesis, we explored the potentialities and the reliability of different state-of-the-art computational techniques for the investigation of the structural and vibrational properties of complex macromolecular materials of biochemical importance. The use of FTIR spectroscopy to probe the structure and function of the OEC complex in PS II has a long history. The synthesis of a very close structural mimic of the catalytic center has opened up the opportunity to perform a comprehensive and parallel study of both the natural and artificial compounds and of their vibrational modes. Chapter III is dedicated to the detailed assignment of the bands in the midand low-frequencies region by static and dynamic vibrational spectra calculations of the unique biomimetic complex. The detailed parallel analysis between the Natural and Synthetic complexes also provided a comprehensive characterization of the vibrational fingerprints in such class of cubane-like Mn-based compounds and is reported in Chapter IV. In Chapter V of the thesis we discussed the electronic and structural properties of the novel Mn4O4 synthetic compound mimicking the EPR spectroscopic nature of OEC in S2 state.
Adensity functional theory study of NbSe2 single-layers in the normal non-modulated and the 3×3 CDWstates is reported.Weshow that, in the single layer, theCDWbarely affects the Fermi surface of the system, thus ruling out a nesting mechanism as the driving force for the modulation. TheCDW stabilizes levels lying around 1.35 eV below the Fermi level within the Se-based valence band but having a substantial Nb–Nb bonding character. The absence of interlayer interactions leads to the suppression of the pancake-like portion of the bulk Fermi surface in the single-layer.Weperform scanning tunneling microscopy simulations and find that the images noticeably change with the sign and magnitude of the voltage bias. The atomic corrugation of the Se sublayer induced by the modulation plays a primary role in leading to these images, but the electronic reorganization also has an important contribution. The analysis of the variation of these images with the bias voltage does not support a Fermi surface nesting mechanism for theCDW. It is also shown that underlying graphene layers (present in some of the recent experimental work) do not modify the conduction band, but do affect the shape of the valence band of NbSe2 single-layers. The relevance of these results in understanding recent physical measurements for NbSe2 single-layers is discussed. Introduction Transition metal dichalcogenides are layered materials, easily exfoliable due to the van der Waals forces linking their layers. They have been the focus of large attention in the past few years because they are ideal systems where to study the influence of the reduced electronic screening brought about by lowering the dimensionality from bulk to layers of different thickness. Among them, 2H-NbSe2 (from now on we will refer to it just as NbSe2) is metallic at room temperature, becomes superconducting (SC) at around 7 K [1, 2] and there are strong indications that it is a twogap superconductor [3–7]. Before reaching the SC state it undergoes a charge density wave (CDW) distortion at around 30 K [8, 9]. The bulk structure of NbSe2 is built from hexagonal layers containing Nb atoms in a trigonal prismatic coordination (see figure 1(a)) [10], but there are also relatively short interlayer Se–Se contacts providing a substantial interlayer coupling. Although ; This work has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) through the ERC Advanced Grant NOVGRAPHENE (GA 290846). Work in Bellaterra was supported by Spanish MINECO (Grant Nos. FIS2015-64886-C5-3-P and FIS2015-64886-C5-4-P, and the Severo Ochoa Centers of Excellence Program under Grants SEV-2013-0295 and SEV-2015-0496), and Generalitat de Catalunya (2014SGR301). We thank M. Ugeda for fruitful discussions. ; Peer reviewed
Under the terms of the Creative Commons Attribution License 3.0 (CC-BY). ; A combined experimental (superconductor-insulator-superconductor tunneling spectra) and theoretical (density functional theory) study of the two-gap superconductor MgB2 is reported. The calculations confirm that the small gap is associated with a π band mostly based on the boron pz orbitals leading to the three-dimensional band component of the Fermi surface. This channel almost completely dominates the tunneling images and spectra for c-axis-oriented samples and not the two-dimensional σ band. The origin of this effect is due to the faster decay of the electronic states associated with the boron px and py orbitals compared to those associated with the boron pz orbitals, together with the symmetry properties of the wave functions. The calculated tunneling channels and partial density of states for each band agree with the values deduced from precise fits of experimental tunneling spectra. The present approach provides a framework for the understanding of tunneling spectra and the nature of superconducting gaps of other multigap superconductors. ; Work in Bellaterra was supported by Spanish MINECO (Grants No. FIS2012-37549-C05-02 and No. FIS2012-37549-C05-05 with joint financing by FEDER Funds from the European Union, Grants No. CSD2007-00041 and No. CSD2007-00050) and Generalitat de Catalunya (2014SGR301). J.A.S.-G. and P.O. acknowledge support of the Spanish MINECO through the Severo Ochoa Centers of Excellence Program under Grant No. SEV-2013-0295. J.A.S.-G. was supported by an FPI Fellowship from MINECO. ; Peer Reviewed
The study of ytterbium halide crystals using the compound-tunable embedding potential (CTEP) method is carried out in the framework of the density functional theory. For subsequent calculations using the coupled-cluster methods, the optimization of atomic bases is carried out, and for this purpose stochiometric molecular systems were studied. The chemical shift of the lines of the X-ray emission spectrum, Kα1 and Kα2, in YbHal3 relative to YbHal2 was chosen as a criterion for verifying the computational accuracy of the properties localized on the nucleus of a heavy atom, Yb, since this method is a unique tool for analyzing partial electron densities near a heavy nucleus speci cally for compounds of d- and f-elements. In the study, ve main versions for the halogen basis set sizes were considered. The stability of the results was obtained using the CCSD and CCSD(T) coupled cluster methods for molecular systems YbF2, YbF3, YbCl2, YbCl3.
Se reportan las propiedades estructurales y electrónicas de la perovskita en la fase cristalográfica tetragonal. Este material tiene un carácter superconductor con una temperatura crítica alrededor de 80 K. En el compuesto , la transición tetragonal a ortorrómbico no aparece cuando se disminuye el contenido de oxígeno, como ocurre en el caso del . A pesar de su importancia, son pocos los cálculos teóricos de la estructura electrónica y de bandas de energía para esta familia de perovskitas. Se presentan los posibles mecanismos superconductores en el plano de y cadenas O, en este tipo de material. Los cálculos se realizaron para el compuesto en el estado normal por medio del método FP-LAPW, en la aproximación GGA, siempre dentro del formalismo de la teoría del funcional de densidad (DFT). En primer lugar, el estudio consistió en encontrar la energía del compuesto, el volumen óptimo y el módulo de volumen. También se optimizó la relación c/a, donde a y c son los parámetros de red de la celda cristalográfica tetragonal. A partir de estos resultados, se llevó a cabo un estudio detallado de las propiedades electrónicas para este material. El objetivo de esta investigación es la determinación de las relaciones de dispersión y el cálculo de la densidad de los estados (DOS). También se determinó la proyección de la DOS en los orbitales atómicos. Se concluye que el orden de Cu y los átomos de oxígeno en los planos estructurales son importantes para el comportamiento superconductor del .Palabras clave: DFT, estructura electrónica, superconductor de alta temperatura, CaLaBaCu3O7.
PACS number s : 71.10. w.-- et al. ; We propose graphite intercalation compounds GICs as a material system with precisely the same electronic properties as doped few layer graphene. Despite the fact that GICs have been around for the last four decades, this fact has gone unnoticed so far. Especially, we focus on the electronic energy bands of KC8 which correspond to a doped graphene monolayer. We provide extensive theoretical and experimental evidence for this claim employing a combined angle-resolved photoemission and theory approach using tight-binding, standard density-functional theory and including electron-electron correlation on a GW level. We observe a strong momentum-dependent kink in the quasiparticle dispersion at 166 meV highlighting electron-phonon coupling to an in-plane transversal optical phonon. These results are key for understanding both the unique electronic properties of doped graphene layers and superconductivity in KC8. ; A.G. acknowledges an APART Fellowship from the Austrian Academy of Sciences and a Marie Curie Individual Fellowship COMTRANS from the European Union. T.P. acknowledges DFG under Project No. PI 440/3/4/5. C.A. and A.R. acknowledge funding by the Spanish MEC Grant No. FIS2007-65702-C02-01 , "Grupos Consolidados UPV/EHU del Gobierno Vasco" Grant No. IT-319-07 , and the European Community through NoE Nanoquanta Grant No. NMP4-CT-2004-500198 , e-I3 ETSF Project INFRA-2007-1.2.2: Grant No. 211956 , and SANES Grant No. NMP4-CT-2006-017310 . The computer resources were provided by the Barcelona Supercomputing Center and the Basque Country University UPV/EHU SGIker Arina and ETSF. D.V. acknowledges DFG under Project No. VY64/1-1. J.F. acknowledges and appreciates financial support by the DFG Forschergruppe No. FOR 538). ; Peer reviewed
This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes ; Recent advances in graphene-nanoribbon-based research have demonstrated the controlled synthesis of chiral graphene nanoribbons (chGNRs) with atomic precision using strategies of on-surface chemistry. However, their electronic characterization, including typical figures of merit like band gap or frontier band's effective mass, has not yet been reported. We provide a detailed characterization of (3,1)-chGNRs on Au(111). The structure and epitaxy, as well as the electronic band structure of the ribbons, are analyzed by means of scanning tunneling microscopy and spectroscopy, angle-resolved photoemission, and density functional theory ; The project leading to this publication has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 635919), from the Spanish Ministry of Economy, Industry and Competitiveness (MINECO, grant nos. MAT2016-78293-C6, FIS2015-62538-ERC), from the Basque Government (grant nos. IT-621-13, PI-2015-1-42, PI-2016-1-0027), from the European Commission in FP7 FET-ICT "Planar Atomic and Molecular Scale Devices" (PAMS) project (contract no. 610446), from the Xunta de Galicia (Centro singular de investigación de Galicia accreditation 2016−2019, ED431G/09), and from the European Regional Development Fund (ERDF)
First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community ; The authors would like to thank CECAM for launching and pushing the ESL, as well as hosting part of its infrastructure, and partly funding the extended workshops where most of the coding was done, both in the Lausanne headquarters and in the Dublin, Trieste, and Zaragoza nodes. Within CECAM, the authors particularly thank Sara Bonella, Bogdan Nichita, and Ignacio Pagonabarraga. The authors also acknowledge all the people who have supported and contributed to the ESL in different ways, including Luis Agapito, Xavier Andrade, Balint Aradi, Emanuele Bosoni, Lori A. Burns, Christian Carbogno, Ivan Carnimeo, Abel Carreras Conill, Alberto Castro, Michele Ceriotti, Anoop Chandran, Wibe de Jong, Pietro Delugas, Thierry Deutsch, Hubert Ebert, Aleksandr Fonari, Luca Ghiringhelli, Paolo Giannozzi, Matteo Giantomassi, Judit Gimenez, Ivan Girotto, Xavier Gonze, Benjamin Hourahine, Jürg Hutter, Thomas Keal, Jan Kloppenburg, Hyungjun Lee, Liang Liang, Lin Lin, Jianfeng Lu, Nicola Marzari, Donal MacKernan, Layla Martin-Samos, Paolo Medeiros, Fawzi Mohamed, Jens Jørgen Mortensen, Sebastian Ohlmann, David O'Regan, Charles Patterson, Etienne Plésiat, Markus Rampp, Laura Ratcliff, Stefano Sanvito, Paul Saxe, Matthias Scheffler, Didier Sebilleau, Søren Smidstrup, James Spencer, Atsushi Togo, Joost Vandevondele, Matthieu Verstraete, and Brian Wylie. The authors would also like to thank the Psi-k network for having partially funded several of the ESL workshops. A.O., E.A., D.L.-D., S.G., E.K., A.A.M., and M.C.P. received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 676531 (Centre of Excellence project E-CAM). The same project has partly funded the extended software development workshops in which most of the ESL coding effort has happened. A.G., S.M., and E.A. acknowledge support from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 824143 (Centre of Excellence project MaX). M.A.L.M. acknowledges partial support from the DFG through Project No. MA-6786/1. D.G.A.S. was supported by the U.S. National Science Foundation (NSF) (Grant No. ACI-1547580). M.C.P. acknowledges support from the EPSRC under Grant No. EP/P034616/1. A.A.M. acknowledges support from the Thomas Young Centre under Grant No. TYC-101, the Wannier Developers Group, and all of the authors and contributors of the wannier90 code (see Ref. 115 for a complete list). A.M.E. acknowledges support from CoSeC, the Computational Science Centre for Research Communities, through CCP5: The Computer Simulation of Condensed Phases (EPSRC Grant Nos. EP/M022617/1 and EP/P022308/1). A.G. and J.M.S. acknowledge Spain's Ministry of Science (Grant No. PGC2018-096955-B-C42). E.A., A.G., and J.M.S. acknowledge Spain's Ministry of Science (Grant No. FIS2015-64886-C5). Y.P., D.L.-D., and E.A. acknowledge support from the Spanish MINECO and EU Structural Investment Funds (Grant No. RTC-2016-5681-7). M.L. acknowledges support from the EPRSC under Grant No. EP/M022668/1. M.L., M.J.T.O., and Y.P. acknowledge support from the EU COST action (Grant No. MP1306). J.M. was supported by the European Regional Development Fund (ERDF), project CEDAMNF (Reg. No. CZ.02.1.01/0.0/0.0/15-003/0000358). V.W.-Z.Y., W.P.H., Y.L., and V.B. acknowledge support from the National Science Foundation under Award No. ACI-1450280 (the ELSI project). V.W.-Z.Y. also acknowledges a MolSSI fellowship (NSF Award No. ACI-1547580). Simune Atomistics S.L. is thanked for allowing A.H.L. and Y.P. to contribute to the ESL, as is Synopsys, Inc., for the partial availability of F.C ; Peer Reviewed ; Postprint (author's final draft)
