### Browsing by Author "Scheffler, Matthias"

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Item All-electron, real-space perturbation theory for homogeneous electric fields: Theory, implementation, and application within DFT(2018-07-01) Shang, Honghui; Raimbault, Nathaniel; Rinke, Patrick; Scheffler, Matthias; Rossi, Mariana; Carbogno, Christian; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-GesellschaftWithin density-functional theory, perturbation theory (PT) is the state-of-the-art formalism for assessing the response to homogeneous electric fields and the associated material properties, e.g., polarizabilities, dielectric constants, and Raman intensities. Here, we derive a real-space formulation of PT and present an implementation within the all-electron, numeric atom-centered orbitals electronic structure code FHI-aims that allows for massively parallel calculations. As demonstrated by extensive validation, we achieve a rapid computation of accurate response properties of molecules and solids. As an application showcase, we present harmonic and anharmonic Raman spectra, the latter obtained by combining hundreds of thousands of PT calculations with ab initio molecular dynamics. By using the PBE exchange-correlation functional with many-body van der Waals corrections, we obtain spectra in good agreement with experiment especially with respect to lineshapes for the isolated paracetamol molecule and two polymorphs of the paracetamol crystal.Item Density functional theory study of the α-γ phase transition in cerium: Role of electron correlation and f -orbital localization(2016-02-29) Casadei, Marco; Ren, Xinguo; Rinke, Patrick; Rubio, Angel; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-Gesellschaft; University of Science and Technology of ChinaThe long standing problem of the α-γ phase transition in cerium metal is approached by treating all electrons at the same quantum mechanical level, using both hybrid functionals (PBE0 and HSE06) and exact exchange plus correlation in the random-phase approximation (EX+cRPA). The exact-exchange contribution in PBE0 and HSE06 is crucial to produce two distinct solutions that can be associated with the α and γ phases. An analysis of the band structure and the electron density reveals a localization and delocalization behavior of the f electrons in the γ and α phases, respectively. However, a quantitative agreement with the extrapolated phase diagram to zero temperature is achieved only with EX+cRPA, based on the hybrid functional starting point. We predict that a pressure induced phase transition should exist at or close to T=0K. By adding entropic contributions we determine the pressure-temperature phase diagram, which is in reasonable agreement with experiment.Item Electron-phonon coupling in d-electron solids: A temperature-dependent study of rutile TiO2 by first-principles theory and two-photon photoemission(American Physical Society, 2019-12-05) Shang, Honghui; Argondizzo, Adam; Tan, Shijing; Zhao, Jin; Rinke, Patrick; Carbogno, Christian; Scheffler, Matthias; Petek, Hrvoje; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-Gesellschaft; University of Pittsburgh; University of Science and Technology of ChinaRutile TiO2 is a paradigmatic transition-metal oxide with applications in optics, electronics, photocatalysis, etc., that are subject to pervasive electron-phonon interaction. To understand how energies of its electronic bands, and in general semiconductors or metals where the frontier orbitals have a strong d-band character, depend on temperature, we perform a comprehensive theoretical and experimental study of the effects of electron-phonon (e-p) interactions. In a two-photon photoemission (2PP) spectroscopy study we observe an unusual temperature dependence of electronic band energies within the conduction band of reduced rutile TiO2, which is contrary to the well-understood sp-band semiconductors and points to a so far unexplained dichotomy in how the e-p interactions affect differently the materials where the frontier orbitals are derived from the sp- and d orbitals. To develop a broadly applicable model, we employ state-of-the-art first-principles calculations that explain how phonons promote interactions between the Ti-3d orbitals of the conduction band within the octahedral crystal field. The characteristic difference in e-p interactions experienced by the Ti-3d orbitals of rutile TiO2 crystal lattice are contrasted with the more familiar behavior of the Si-2s orbitals of stishovite SiO2 polymorph, in which the frontier 2s orbital experiences a similar crystal field with the opposite effect. The findings of this analysis of how e-p interactions affect the d- and sp-orbital derived bands can be generally applied to related materials in a crystal field. The calculated temperature dependence of d-orbital derived band energies agrees well with and explains the temperature-dependent inter-d-band transitions recorded in 2PP spectroscopy of TiO2. The general understanding of how e-p interactions affect d-orbital derived bands is likely to impact the understanding of temperature-dependent properties of highly correlated materials.Item Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation(2016-07-19) Atalla, Viktor; Zhang, Igor Ying; Hofmann, Oliver T.; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Qudosoft; Fritz-Haber-Institut der Max-Planck-Gesellschaft; Graz University of Technology; University of Science and Technology of ChinaWe obtain the exchange parameter of hybrid functionals by imposing the fundamental condition of a piecewise linear total energy with respect to electron number. For the Perdew-Burke-Ernzerhof (PBE) hybrid family of exchange-correlation functionals (i.e., for an approximate generalized Kohn-Sham theory) this implies that (i) the highest occupied molecular orbital corresponds to the ionization potential (I), (ii) the energy of the lowest unoccupied molecular orbital corresponds to the electron affinity (A), and (iii) the energies of the frontier orbitals are constant as a function of their occupation. In agreement with a previous study [N. Sai, Phys. Rev. Lett. 106, 226403 (2011)10.1103/PhysRevLett.106.226403], we find that these conditions are met for high values of the exact exchange admixture α and illustrate their importance for the tetrathiafulvalene-tetracyanoquinodimethane complex for which standard density functional theory functionals predict artificial electron transfer. We further assess the performance for atomization energies and weak interaction energies. We find that atomization energies are significantly underestimated compared to PBE or PBE0, whereas the description of weak interaction energies improves significantly if a 1/R6 van der Waals correction scheme is employed.Item First-principles supercell calculations of small polarons with proper account for long-range polarization effects(2018-03-01) Kokott, Sebastian; Levchenko, Sergey V.; Rinke, Patrick; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Fritz Haber Institute of the Max Planck SocietyWe present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron-phonon (el-ph) interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces the dependence of polaron properties on the DFT exchange-correlation functional and the size of the supercell in the limit of strong el-ph coupling. Using our correction approach, we present accurate all-electron full-potential DFT results for small polarons in rocksalt MgO and rutile TiO2.Item GW100: Benchmarking G0W0 for Molecular Systems(AMERICAN CHEMICAL SOCIETY, 2015) van Setten, Michiel J.; Caruso, Fabio; Sharifzadeh, S.; Ren, Xinguo; Scheffler, Matthias; Liu, Fang; Lischner, J.; Lin, Lin; Deslippe, J.R.; Louie, S.G.; Yang, Chao; Weigend, Florian; Neaton, J.B.; Evers, F.; Rinke, Patrick; Department of Applied Physics; Computational Electronic Structure TheoryItem Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron density functional theory(2010) Havu, Paula; Blum, Volker; Havu, Ville; Rinke, Patrick; Scheffler, Matthias; Department of Applied Physics; Electronic Properties of MaterialsThe low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies remain even today, specifically for the large-scale quasihexagonally reconstructed (100) surfaces: rather dissimilar reconstruction energies for Au and Pt in available experiments and experiment and theory do not match for Pt. We here show by all-electron density functional theory that only large enough “(5×N)” approximant supercells capture the qualitative reconstruction energy trend between Au(100) and Pt(100), in contrast to what is often done in the theoretical literature. Their magnitudes are then in fact similar and closer to the measured value for Pt(100); our calculations achieve excellent agreement with known geometric characteristics and provide direct evidence for the electronic reconstruction driving force.Item Lattice dynamics calculations based on density-functional perturbation theory in real space(2017) Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-GesellschaftA real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.Item Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept(2016-04-06) Chibani, Wael; Ren, Xinguo; Scheffler, Matthias; Rinke, Patrick; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-GesellschaftWe present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.Item Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation(2016-09-21) Zhang, Igor Ying; Rinke, Patrick; Perdew, John P.; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-Gesellschaft; Temple University; University of California, Santa BarbaraWe present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H2 and H2+, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H2 and H2+, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.Item Wave-function inspired density functional applied to the H2/H2 + challenge(2016-07-01) Zhang, Igor Ying; Rinke, Patrick; Scheffler, Matthias; Department of Applied Physics; Computational Electronic Structure Theory; Fritz-Haber-Institut der Max-Planck-Gesellschaft; University of California, Santa BarbaraWe start from the Bethe-Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional - BGE2 - which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair correlations. We demonstrate that BGE2 is size consistent and one-electron 'self-correlation' free. The electron-pair correlation coupling ensures the correct H2 dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H2 and dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H2 in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.