arXiv subjects

Georg Kresse

Publications and source records attributed to Georg Kresse.

At least 55 records · Page 3Linked to original sources

arXiv2022

Approaching the basis-set limit of the dRPA correlation energy with explicitly correlated and Projector Augmented-wave methods

The direct random-phase approximation (dRPA) is used to calculate and compare atomization energies for the HEAT set and 10 selected molecules of the G2-1 set using both plane waves and Gaussian-type orbitals. We describe detailed procedures to obtain highly accurate and well converged results for the projector augmented-wave (PAW) method as implemented in the Vienna Ab-initio Simulation Package (VASP) as well as the explicitly correlated dRPA-F12 method as implemented in the TURBOMOLE package. The two approaches agree within chemical accuracy (1 kcal/mol) for the atomization energies of all considered molecules, both for the exact exchange as well as for the dRPA. The root mean-square deviation is 0.41 kcal/mol for the exact exchange (evaluated using density functional theory orbitals) and 0.33 kcal/mol for exact exchange plus the random-phase approximation.

physics.chem-ph↗

arXiv2022

Zero-point Renormalization of the Band Gap of Semiconductors and Insulators Using the PAW Method

We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fröhlich model, as discussed in Phys. Rev. Lett. 115, 176401 (2015) and Phys. Rev. B 92, 054307 (2015). The data are compared to recent calculations, npj Computational Materials 6, 167 (2020), and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find however that the pseudo version converges more rapidly with respect to the number of included unoccupied states.

cond-mat.mtrl-sci↗

arXiv2022

Core-hole excitations using the projector augmented-wave method and the Bethe-Salpeter equation

We present an implementation of the Bethe-Salpeter equation (BSE) for core-conduction band pairs within the framework of the projector augmented-wave method. For validation, the method is applied to the $K$-edges of diamond, graphite, hexagonal boron-nitride, as well as four lithium-halides (LiF, LiCl, LiI, LiBr). We compare our results with experiment, previous theoretical BSE results, and the density functional theory-based supercell core-hole method. In all considered cases, the agreement with experiment is excellent, in particular for the position of the peaks as well as the fine structure. Comparing BSE to supercell core-hole spectra we find that the latter often qualitatively reproduces the experimental spectrum, however, it sometimes lacks important details. This is shown for the $K$-edges of diamond and nitrogen in hexagonal boron-nitride, where we are capable to resolve within the BSE experimental features that are lacking in the core-hole method. Additionally, we show that in certain systems the supercell core-hole method performs better if the excited electron is added to the background charge. We attribute this improved performance to a reduced self-interaction.

cond-mat.mtrl-sci↗

arXiv2021

Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials

Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green-Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

cond-mat.mtrl-sci↗

arXiv2021

Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $Δ$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.

cond-mat.mtrl-sci↗

arXiv2021

Optical and excitonic properties of transition metal oxide perovskites by the Bethe-Salpeter equation

We present a systematic investigation of the role and importance of excitonic effects on the optical properties of transitions metal oxide perovskites. A representative set of fourteen compounds has been selected, including 3$d$ (SrTiO$_3$, LaScO$_3$, LaTiO$_3$, LaVO$_3$, LaCrO$_3$, LaMnO$_3$, LaFeO$_3$ and SrMnO$_3$), 4$d$ (SrZrO$_3$, SrTcO$_3$ and Ca$_2$RuO$_4$) and 5$d$ (SrHfO$_3$, KTaO$_3$ and NaOsO$_3$) perovskites, covering a band gap ranging from 0.1 eV to 6.1 eV and exhibiting different electronic, structural and magnetic properties. Optical conductivities and optical transitions including electron-hole interactions are calculated through the solution of the Bethe-Salpeter equation (BSE) with quasi-particle energies evaluated by single-shot $G_0W_0$ approximation. The exciton binding energies are computed by means of a model-BSE (mBSE), carefully benchmarked against the full BSE method, in order to obtain well-converged results in terms of k-point sampling. The predicted results are compared with available measured data, with an overall satisfactory agreement between theory and experiment.

cond-mat.mtrl-sci↗

arXiv2021

Electronic state unfolding for plane waves: energy bands, Fermi surfaces and spectral functions

Modern computing facilities grant access to first-principles density-functional theory study of complex physical and chemical phenomena in materials, that require large supercell to properly model the system. However, supercells are associated to small Brillouin zones in the reciprocal space, leading to folded electronic eigenstates that make the analysis and interpretation extremely challenging. Various techniques have been proposed and developed in order to reconstruct the electronic band structures of super cells, unfolded into the reciprocal space of an ideal primitive cell. Here, we propose an efficient unfolding scheme embedded directly in the Vienna Ab-initio Simulation Package (VASP), that requires modest computational resources and allows for an automatized mapping from the reciprocal space of the supercell to primitive cell Brillouin zone. This algorithm can computes band structures, Fermi surfaces and spectral functions, by using an integrated post-processing tool (bands4vasp). The method is here applied to a selected variety of complex physical situations: the effect of doping on the band dispersion in the BaFe$_{\rm 2(1-x)}$Ru$_{\rm 2x}$As$_2$ superconductor, the interaction between adsorbates and polaronic states on the TiO$_2$(110) surface, and the band splitting induced by non-collinear spin fluctuations in EuCd$_2$As$_2$.

cond-mat.mtrl-sci↗

arXiv2021

$α$-$β$ phase transition of zirconium predicted by on-the-fly machine-learned force field

The accurate prediction of solid-solid structural phase transitions at finite temperature is a challenging task, since the dynamics is so slow that direct simulations of the phase transitions by first-principles (FP) methods are typically not possible. Here, we study the $α$-$β$ phase transition of Zr at ambient pressure by means of on-the-fly machine-learned force fields. These are automatically generated during FP molecular dynamics (MD) simulations without the need of human intervention, while retaining almost FP accuracy. Our MD simulations successfully reproduce the first-order displacive nature of the phase transition, which is manifested by an abrupt jump of the volume and a cooperative displacement of atoms at the phase transition temperature. The phase transition is further identified by the simulated x-ray powder diffraction, and the predicted phase transition temperature is in reasonable agreement with experiment. Furthermore, we show that using a singular value decomposition and pseudo inversion of the design matrix generally improves the machine-learned force field compared to the usual inversion of the squared matrix in the regularized Bayesian regression.

cond-mat.mtrl-sci↗

arXiv2021

RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods

We present a method to approximate post-Hartree-Fock correlation energies by using approximate natural orbitals obtained by the random phase approximation (RPA). We demonstrate the method by applying it to the helium atom, the hydrogen and fluorine molecule, and to diamond as an example of a periodic system. For these benchmark systems, we show that RPA natural orbitals converge the MP2 correlation energy rapidly. Additionally, we calculated full configuration interaction energies for He and H$_2$, which are in excellent agreement with the literature and experimental values. We conclude that the proposed method may serve as a compromise to reach good approximations to correlation energies at moderate computational cost, and we expect the method to be especially useful for theoretical studies on surface chemistry by providing an efficient basis to correlated wave function based methods.

physics.chem-ph↗

arXiv2021

New insights into the 1D carbon chain through the RPA

We investigated the electronic and structural properties of the infinite linear carbon chain (carbyne) using density functional theory (DFT) and the random phase approximation (RPA) to the correlation energy. The studies are performed in vacuo and for carbyne inside a carbon nano tube (CNT). In the vacuum, semi-local DFT and RPA predict bond length alternations of about 0.04 Å and 0.13 Å, respectively. The frequency of the highest optical mode at the $Γ$ point is 1219 cm$^{-1}$ and about 2000 cm$^{-1}$ for DFT and the RPA. Agreement of the RPA to previous high level quantum chemistry and diffusion Monte-Carlo results is excellent. For the RPA we calculate the phonon-dispersion in the full Brillouine zone and find marked quantitative differences to DFT calculations not only at the $Γ$ point but also throughout the entire Brillouine zone. To model carbyne inside a carbon nanotube, we considered a (10,0) CNT. Here the DFT calculations are even qualitatively sensitive to the k-points sampling. At the limes of a very dense k-points sampling, semi-local DFT predicts no bond length alternation (BLA), whereas in the RPA a sizeable BLA of 0.09 Å prevails. The reduced BLA leads to a significant red shift of the vibrational frequencies of about 350 cm$^{-1}$, so that they are in good agreement with experimental estimates. Overall, the good agreement between the RPA and previously reported results from correlated wavefunction methods and experimental Raman data suggests that the RPA provides reliable results at moderate computational costs. It hence presents a useful addition to the repertoire of correlated wavefunction methods and its accuracy clearly prevails for low dimensional systems, where semi-local density functionals struggle to yield even qualitatively correct results.

physics.chem-ph↗

arXiv2020

Local embedding of Coupled Cluster theory into the Random Phase Approximation using plane-waves

We present an embedding approach to treat local electron correlation effects in periodic environments. In a single, consistent framework, our plane-wave based scheme embeds a local high-level correlation calculation (here Coupled Cluster Theory, CC), employing localized orbitals, into a low-level correlation calculation (here the direct Random Phase Approximation, RPA). This choice allows for an accurate and effcient treatment of long-range dispersion effects. Accelerated convergence with respect to the local fragment size can be observed if the low-level and high-level long-range dispersion are quantitatively similar, as is the case for CC in RPA. To demonstrate the capabilities of the introduced embedding approach, we calculate adsorption energies of molecules on a surface and in a chabazite crystal cage, as well as the formation energy of a lattice impurity in a solid at the level of highly accurate many-electron perturbation theories. The absorption energy of a methane molecule in a zeolite chabazite, for instance, is converged with an error well below 20 meV at the CC level. As our largest periodic benchmark system, we apply our scheme to the adsorption of a water molecule on titania in a supercell containing more than 1000 electrons.

physics.chem-ph↗

arXiv2020

Nonrad: Computing Nonradiative Capture Coefficients from First Principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. [Phys. Rev. B 90, 075202 (2014)] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Lastly, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation.

cond-mat.mtrl-sci↗

arXiv2020

Accurate optical spectra through time-dependent density functional theory based on screening-dependent hybrid functionals

We investigate optical absorption spectra obtained through time-dependent density functional theory (TD-DFT) based on nonempirical hybrid functionals that are designed to correctly reproduce the dielectric function. The comparison with state-of-the-art $GW$ calculations followed by the solution of the Bethe-Sapeter equation (BSE-$GW$) shows close agreement for both the transition energies and the main features of the spectra. We confront TD-DFT with BSE-$GW$ by focusing on the model dielectric function and the local exchange-correlation kernel. The present TD-DFT approach achieves the accuracy of BSE-$GW$ at a fraction of the computational cost.

cond-mat.mtrl-sci↗

arXiv2020

Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory

We present a compressive sensing approach for the long standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary time and frequency grids that allow for extreme data compression of fermionic and bosonic functions in a broad temperature regime. The method is applied to the random phase and self-consistent $GW$ approximation of the grand potential. Integration and transformation errors are investigated for Si and SrVO$_3$.

cond-mat.mtrl-sci↗

arXiv2020

Comparative ab initio study of the structural, electronic, magnetic, and dynamical properties of LiOsO$_3$ and NaOsO$_3$

Despite similar chemical compositions, LiOsO$_3$ and NaOsO$_3$ exhibit remarkably distinct structural, electronic, magnetic, and spectroscopic properties. At low temperature, LiOsO$_3$ is a polar bad metal with a rhombohedral $R3c$ structure without the presence of long-range magnetic order, whereas NaOsO$_3$ is a $G$-type antiferromagnetic insulator with an orthorhombic $Pnma$ structure. By means of comparative first-principles DFT+$U$ calculations with the inclusion of the spin-orbit coupling, we ($i$) identify the origin of the different structural ($R3c$ vs. $Pnma$) properties using a symmetry-adapted soft mode analysis, ($ii$) provide evidence that all considered exchange-correlation functionals (LDA, PBE, PBEsol, SCAN, and HSE06) and the spin disordered polymorphous descriptions are unsatisfactory to accurately describe the electronic and magnetic properties of both systems simultaneously, and ($iii$) clarify that the distinct electronic (metallic vs. insulating) properties originates mainly from a cooperative steric and magnetic effect. Finally, we find that although at ambient pressure LiOsO$_3$ with a $Pnma$ symmetry and NaOsO$_3$ with a $R\bar{3}c$ symmetry are energetically unfavorable, they do not show soft phonons and therefore are dynamically stable. A pressure-induced structural phase transition from $R3c$ to $Pnma$ for LiOsO$_3$ is predicted, whereas for NaOsO$_3$ no symmetry change is discerned in the considered pressure range.

cond-mat.mtrl-sci↗

arXiv2020

Electron-Phonon Interactions Using the PAW Method and Wannier Functions

We present an ab-initio density-functional-theory approach for calculating electron-phonon interactions within the projector augmented-wave method. The required electron-phonon matrix elements are defined as the second derivative of the one-electron energies in the PAW method. As the PAW method leads to a generalized eigenvalue problem, the resulting electron-phonon matrix elements lack some symmetries that are usually present for simple eigenvalue problems and all-electron formulations. We discuss the relation between our definition of the electron-phonon matrix element and other formulations. To allow for efficient evaluation of physical properties, we introduce a Wannier-interpolation scheme, again adapted to generalized eigenvalue problems. To explore the method's numerical characteristics, the temperature-dependent band-gap renormalization of diamond is calculated and compared with previous publications. Furthermore, we apply the method to selected binary compounds and show that the obtained zero-point renormalizations agree well with other values found in literature and experiments.

cond-mat.mtrl-sci↗

arXiv2019

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

Recently, two nonempirical hybrid functionals, dielectric-dependent range-separated hybrid functional based on the Coulomb-attenuating method (DD-RSH-CAM) and doubly screened hybrid functional (DSH), have been suggested by [Chen et al, Phys. Rev. Mater. 2, 073803 (2018)] and [Cui et al, J. Phys. Chem. Lett. 9, 2338 (2018)], respectively. These two hybrid functionals are both based on a common model dielectric function approach, but differ in the way how to non-empirically obtain the range-separation parameter. By retaining the full short-range Fock exchange and a fraction of the long-range Fock exchange that equals the inverse of the dielectric constant, both DD-RSH-CAM and DSH turn out to perform very well in predicting the band gaps for a large variety of semiconductors and insulators. Here, we assess how these two hybrid functionals perform on challenging antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO by comparing them to other conventional hybrid functionals and the $GW$ method. We find that single-shot DD0-RSH-CAM and DSH0 improve the band gaps towards experiments as compared to conventional hybrid functionals. The magnetic moments are slightly increased, but the predicted dielectric constants are decreased. The valence band density of states (DOS) predicted by DD0-RSH-CAM and DSH0 are as satisfactory as HSE03 in comparison to experimental spectra, however, the conduction band DOS are shifted to higher energies by about 2 eV compared to HSE03. Self-consistent DD-RSH-CAM and DSH deteriorate the results with a significant overestimation of band gaps.

cond-mat.mtrl-sci↗

arXiv2019

On-the-fly machine learning force field generation: Application to melting points

An efficient and robust on-the-fly machine learning force field method is developed and integrated into an electronic-structure code. This method realizes automatic generation of machine learning force fields on the basis of Bayesian inference during molecular dynamics simulations, where the first principles calculations are only executed, when new configurations out of already sampled datasets appear. The developed method is applied to the calculation of melting points of Al, Si, Ge, Sn and MgO. The applications indicate that more than 99 \% of the first principles calculations are bypassed during the force field generation. This allows the machine to quickly construct first principles datasets over wide phase spaces. Furthermore, with the help of the generated machine learning force fields, simulations are accelerated by a factor of thousand compared with first principles calculations. Accuracies of the melting points calculated by the force fields are examined by thermodynamic perturbation theory, and the examination indicates that the machine learning force fields can quantitatively reproduce the first principles melting points.

cond-mat.mtrl-sci↗