arXiv subjects

Merzuk Kaltak

Publications and source records attributed to Merzuk Kaltak.

16 recordsLinked to original sources

arXiv2025

Constrained Random Phase Approximation: the spectral method

We present a constrained Random Phase Approximation (cRPA) method, termed spectral cRPA (s-cRPA), and compare it to established cRPA approaches for Scandium and Copper by varying the 3d shell filling. The s-cRPA method generally produces larger Hubbard U interaction values compared to conventional approaches. When applied to the realistic system CaFeO$_3$ , s-cRPA yields interaction parameters that align more closely with those required within DFT+U to reproduce the experimentally observed insulating state, addressing the metallic behaviour predicted by standard density functionals. We examine the issue of negative interaction values encountered in the projector cRPA method for filled d-shells. We show that s-cRPA provides improved numerical stability by preserving electron number conservation, a constraint that is violated in the projector cRPA method. The s-cRPA approach addresses some limitations of standard cRPA methods, particularly the tendency to underestimate U values, suggesting its potential utility for the community. Additionally, we have enhanced our implementation to include computation of multi-centre interactions for analysing spatial decay and developed an efficient low-scaling variant employing a compressed Matsubara grid to obtain full frequency-dependent interactions.

cond-mat.str-el↗

arXiv2025

Efficient periodic density functional theory calculations of charged molecules and surfaces using Coulomb kernel truncation

Density functional theory (DFT) calculations of charged molecules and surfaces are critical to applications in electro-catalysis, energy materials and related fields of materials science. DFT implementations such as the Vienna ab-initio Simulation Package (VASP) compute the electrostatic potential under 3D periodic boundary conditions, necessitating charge neutrality. In this work, we implement 0D and 2D periodic boundary conditions to facilitate DFT calculations of charged molecules and surfaces respectively. We implement these boundary conditions using the Coulomb kernel truncation method. Our implementation computes the potential under 0D and 2D boundary conditions by selectively subtracting unwanted long-range interactions in the potential computed under 3D boundary conditions. By combining the Coulomb kernel truncation method with a computationally efficient padding approach, we remove nonphysical potentials from vacuum in 0D and 2D systems. To illustrate the computational efficiency of our method, we perform large supercell calculations of the formation energy of a charged chlorine defect on a sodium chloride (001) surface and perform long time-scale molecular dynamics simulations on a stepped gold (211) | water electrode-electrolyte interface.

cond-mat.mtrl-sci↗

arXiv2024

Density-Based Long-Range Electrostatic Descriptors for Machine Learning Force Fields

This study presents a long-range descriptor for machine learning force fields (MLFFs) that maintains translational and rotational symmetry, similar to short-range descriptors while being able to incorporate long-range electrostatic interactions. The proposed descriptor is based on an atomic density representation and is structurally similar to classical short-range atom-centered descriptors, making it straightforward to integrate into machine learning schemes. The effectiveness of our model is demonstrated through comparative analysis with the long-distance equivariant (LODE) descriptor. In a toy model with purely electrostatic interactions, our model achieves errors below 0.1%, worse than LODE but still very good. For real materials, we perform tests for liquid NaCl, rock salt NaCl, and solid zirconia. For NaCl, the present descriptors improve on short-range density descriptors, reducing errors by a factor of two to three and coming close to message-passing networks. However, for solid zirconia, no improvements are observed with the present approach, while message-passing networks reduce the error by almost a factor of two to three. Possible shortcomings of the present model are briefly discussed.

cond-mat.mtrl-sci↗

arXiv2023

Machine learning density functionals from the random-phase approximation

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we construct a DFT substitute functional for the RPA using supervised and unsupervised machine learning (ML) techniques. Our ML-RPA model can be interpreted as a non-local extension to the standard gradient approximation. We train an ML-RPA functional for diamond surfaces and liquid water and show that ML-RPA can outperform the standard gradient functionals in terms of accuracy. Our work demonstrates how ML-RPA can extend the applicability of the RPA to larger system sizes, time scales and chemical spaces.

cond-mat.mtrl-sci↗

arXiv2021

Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation

The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase approximation (RPA) has played an important role ever since the conception of the OEP formalism. However, the solution of the OEP equation is computationally fairly expensive and has to be done in a self-consistent way. So far, large scale solid state applications have therefore been performed only using the quasiparticle approximation (QPA), neglecting certain dynamical screening effects. We obtain the exact RPA-OEP for 15 semiconductors and insulators by direct solution of the linearized Sham-Schl\"uter equation. We investigate the accuracy of the QPA on Kohn-Sham band gaps and dielectric constants, and comment on the issue of self-consistency.

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

Plane wave basis set correction methods for RPA correlation energies

Electronic correlation energies from the random-phase approximation converge slowly with respect to the plane wave basis set size. We study the conditions, under which a short-range local density functional can be used to account for the basis set incompleteness error. Furthermore, we propose a one-shot extrapolation scheme based on the Lindhard response function of the homogeneous electron gas. The different basis set correction methods are used to calculate equilibrium lattice constants for prototypical solids of different bonding types.

cond-mat.mtrl-sci↗

arXiv2018

Beyond the quasiparticle approximation: Fully self-consistent $GW$ calculations

We present quasiparticle (QP) energies from fully self-consistent $GW$ (sc$GW$) calculations for a set of prototypical semiconductors and insulators within the framework of the projector-augmented wave methodology. To obtain converged results, both finite basis-set corrections and $k$-point corrections are included, and a simple procedure is suggested to deal with the singularity of the Coulomb kernel in the long-wavelength limit, the so called head correction. It is shown that the inclusion of the head corrections in the sc$GW$ calculations is critical to obtain accurate QP energies with a reasonable $k$-point set. We first validate our implementation by presenting detailed results for the selected case of diamond, and then we discuss the converged QP energies, in particular the band gaps, for a set of gapped compounds and compare them to single-shot $G_0W_0$, QP self-consistent $GW$, and previously available sc$GW$ results as well as experimental results.

cond-mat.mtrl-sci↗

arXiv2017

Charge Localization and Ordering in A$_2$Mn$_8$O$_{16}$ Hollandite Group Oxides: Impact of Density Functional Theory Approaches

The phases of A$_2$Mn$_8$O$_{16}$ hollandite group oxides emerge from the competition between ionic interactions, Jahn-Teller effects, charge ordering, and magnetic interactions. Their balanced treatment with feasible computational approaches can be challenging for commonly used approximations in Density Functional Theory. Three examples (A = Ag, Li and K) are studied with a sequence of different approximate exchange-correlation functionals. Starting from a generalized gradient approximation (GGA), an extension to include van der Waals interactions and a recently proposed meta-GGA are considered. Then local Coulomb interactions for the Mn $3d$ electrons are more explicitly considered with the DFT+$U$ approach. Finally selected results from a hybrid functional approach provide a reference. Results for the binding energy of the A species in the parent oxide highlight the role of van der Waals interactions. Relatively accurate results for insertion energies can be achieved with a low $U$ and a high $U$ approach. In the low $U$ case, the materials are described as band metals with a high symmetry, tetragonal crystal structure. In the high $U$ case, the electrons donated by A result in formation of local Mn$^{3+}$ centers and corresponding Jahn-Teller distortions characterized by a local order parameter. The resulting degree of monoclinic distortion depends on charge ordering and magnetic interactions in the phase formed. The reference hybrid functional results show charge localization and ordering. Comparison to low temperature experiments of related compounds suggests that charge localization is the physically correct result for the hollandite group oxides studied here. . . .

cond-mat.mtrl-sci↗

arXiv2016

Cubic scaling $GW$: towards fast quasiparticle calculations

Within the framework of the full potential projector-augmented wave methodology, we present a promising low-scaling $GW$ implementation. It allows for quasiparticle calculations with a scaling that is cubic in the system size and linear in the number of $k$ points used to sample the Brillouin zone. This is achieved by calculating the polarizability and self-energy in the real space and imaginary time domain. The transformation from the imaginary time to the frequency domain is done by an efficient discrete Fourier transformation with only a few nonuniform grid points. Fast Fourier transformations are used to go from real space to reciprocal space and vice versa. The analytic continuation from the imaginary to the real frequency axis is performed by exploiting Thiele's reciprocal difference approach. Finally, the method is applied successfully to predict the quasiparticle energies and spectral functions of typical semiconductors (Si, GaAs, SiC, and ZnO), insulators (C, BN, MgO, and LiF), and metals (Cu and SrVO$_3$). The results are compared with conventional $GW$ calculations. Good agreement is achieved, highlighting the strength of the present method.

cond-mat.mtrl-sci↗

arXiv2016

Screened moments and absence of ferromagnetism in FeAl

While the stoichiometric intermetallic compound FeAl is found to be paramagnetic in experiment, standard band-theory approaches predict the material to be ferromagnetic. We show that this discrepancy can be overcome by a better treatment of electronic correlations with density functional plus dynamical mean field theory. Our results show no ferromagnetism down to 100 K and since the susceptibility is decreasing at the lowest temperatures studied we also do not expect ferromagnetism at even lower temperatures. This behavior is found to originate from temporal quantum fluctuations that screen short-lived local magnetic moments of 1.6 $μ_B$ on Fe.

cond-mat.str-el↗

arXiv2015

Singles correlation energy contributions in solids

The random phase approximation to the correlation energy often yields highly accurate results for condensed matter systems. However, ways how to improve its accuracy are being sought and here we explore the relevance of singles contributions for prototypical solid state systems. We set out with a derivation of the random phase approximation using the adiabatic connection and fluctuation dissipation theorem, but contrary to the most commonly used derivation, the density is allowed to vary along the coupling constant integral. This yields results closely paralleling standard perturbation theory. We re-derive the standard singles of Görling-Levy perturbation theory [Görling and Levy, Phys. Rev. A {\bf 50}, 196 (1994)], highlight the analogy of our expression to the renormalized singles introduced by Ren and coworkers [Ren, Tkatchenko, Rinke, and Scheffler, Phys. Rev. Lett. {\bf 106}, 153003 (2011)], and introduce a new approximation for the singles using the density matrix in the random phase approximation. We discuss the physical relevance and importance of singles alongside illustrative examples of simple weakly bonded systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on NaCl, and solid benzene. The effect of singles on covalently and metallically bonded systems is also discussed.

cond-mat.mtrl-sci↗

arXiv2014

A direct view at excess electrons in TiO$_2$ rutile and anatase

A combination of Scanning Tunneling Microscopy/Spectroscopy and Density Functional Theory (DFT+U) is used to characterize excess electrons in TiO$_2$ rutile and anatase, two prototypical materials with identical chemical composition but different crystal lattices. In rutile, excess electrons can localize at any lattice Ti atom, forming a small polaron, which can easily hop to neighboring sites. In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen vacancies or form shallow donor states bound to Nb dopants. The present study conclusively explains the differences between the two polymorphs and indicates that even small structural variations in the crystal lattice can lead to a very different behavior.

cond-mat.str-el↗

arXiv2014

Predictive GW calculations using plane waves and pseudopotentials

We show that quasiparticle (QP) energies as calculated in the $GW$ approximation converge to the wrong value using the projector augmented wave (PAW) method, since the overlap integrals between occupied orbitals and high energy, plane wave like orbitals, are incorrectly described. The error is shown to be related to the incompleteness of the partial wave basis set inside the atomic spheres. It can be avoided by adopting norm-conserving partial waves, as shown by analytic expressions for the contribution from unoccupied orbitals with high kinetic energy. Furthermore, $G_0W_0$ results based on norm-conserving PAW potentials are presented for a large set of semiconductors and insulators. Accurate extrapolation procedures to the infinite basis set limit and infinite k-point limit are discussed in detail.

cond-mat.mtrl-sci↗

arXiv2012

Comparing $GW$+DMFT and LDA+DMFT for the testbed material SrVO$_3$

We have implemented the $GW$+dynamical mean field theory (DMFT) approach in the Vienna ab initio simulation package. Employing the interaction values obtained from the locally unscreened random phase approximation (RPA), we compare $GW$+DMFT and LDA+DMFT against each other and against experiment for SrVO$_3$. We observed a partial compensation of stronger electronic correlations due to the reduced $GW$ bandwidth and weaker correlations due to a larger screening of the RPA interaction, so that the obtained spectra are quite similar and well agree with experiment. Noteworthily, the $GW$+DMFT better reproduces the position of the lower Hubbard side band.

cond-mat.str-el↗

arXiv2012

Effective Onsite Interaction for Dynamical Mean-Field Theory

A scheme to incorporate non-local polarizations into the dynamical mean-field theory (DMFT) and a tailor-made way to determine the effective interaction for the DMFT are systematically investigated. Applying it to the two-dimensional Hubbard model, we find that non-local polarizations induce a non-trivial filling-dependent anti-screening effect for the effective interaction. The present scheme combined with density functional theory offers an ab initio way to derive effective onsite interactions for the impurity problem in DMFT. We apply it to SrVO3 and find that the anti-screening competes with the screening caused by the off-site interaction.

cond-mat.str-el↗