arXiv subjects

Fabien Tran

Publications and source records attributed to Fabien Tran.

At least 19 recordsLinked to original sources

arXiv2026

A test drive for exchange-correlation functionals on noncollinear magnets: Mn$_3$Ir, Mn$_3$Ge, NiS$_2$, and YMnO$_3$

A first-principles description of noncollinear magnets is challenging, and the practical behavior of genuinely noncollinear exchange-correlation approximations is largely untested. Spin-current density-functional theory (SCDFT) admits noncollinear approximations constrained by local U(1)$\times$SU(2) gauge invariance, an exact condition unavailable in the more restrictive framework of spin-DFT (SDFT). Using the Vienna ab initio simulation package (VASP), we compare two recently developed noncollinear SCDFT functionals, NCMSCAN and LFNCBR89-NCCS, against locally collinear SDFT extensions of four common functionals (PZ, PW92, PBE, and SCAN) for several noncollinear $d$-electron systems. The key finding is that among all tested functionals, only the SCDFT functionals recover the spin texture of the experimental ground state of NiS$_2$, and they do so at a cost comparable to standard semi-local approximations. Yet the two SCDFT functionals differ in equilibrium volumes, band gaps, and on-site magnetic moments. Overall, this survey illustrates the usefulness of SCDFT in capturing noncollinear physics with the tested approximations.

cond-mat.mtrl-sci↗

arXiv2026

Semi-Local Exchange-Correlation Approximations in Density Functional Theory

Density functional theory has become the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, biochemistry, etc. At its heart lies the exchange-correlation functional, a quantity which exactly encapsulates the many-body effects stemming from the quantum mechanical interactions between the electrons. Yet, the exact functional is unknown, and computationally tractable approximations are therefore necessary for practical applications. Over the past six decades, hundreds of density functional approximations have been proposed with varying accuracy and computational efficiency. This review surveys the theoretical foundations of semi-local functionals, including local density approximations, generalized gradient approximations, and meta-generalized gradient approximations. We provide a comprehensive, consistently organized discussion that consolidates both historical developments and recent advances in this field. Beginning with the essentials of Kohn-Sham density functional theory, we present the construction principles of semi-local exchange-correlation functionals. Special attention is given to the physical motivations underlying functional development, the mathematical properties that guide their construction, and the practical considerations that determine their applicability across different chemical and physical systems. This work is intended to serve as both an introduction for newcomers to the field and a comprehensive reference for practitioners. By consolidating the extensive literature on semi-local functionals and providing a unified framework for their construction and application, we aim to facilitate further developments in density functional approximations and their use in tackling the diverse challenges of modern computational chemistry and condensed matter physics.

physics.chem-ph↗

arXiv2025

Capturing exchange-correlation spin-torque effects with a semilocal functional

We cure the lack of exchange-correlation (XC) spin torque in semilocal XC functionals by treating XC effects in the framework of spin-current-density-functional theory (SCDFT), and present the implementation of the first kind of this novel family of XC functionals in the Vienna ab-initio simulation package (VASP): An U(1)$\times$SU(2) gauge-invariant SCDFT functional featuring a $2\times 2$ XC potential. While the framework can be applied to other XC functionals, the presented flavor of the SCDFT functional is based on Becke-Roussel exchange and Colle-Salvetti correlation. In addition to the $2\times 2$ spin density and kinetic-energy density, the XC functional depends on the $2\times 2$ spin-current density. The implementation requires the computation of the spin-current density within the projector-augmented-wave method and the variation of the XC energy with respect to it. The application to a Cr$_3$ molecule and bulk MnO reveals (i) XC spin torque of the same order as obtained by methods including exact exchange, (ii) a counterintuitive contribution to the energy even in collinear ferromagnetic systems without spin-orbit coupling due to the semilocality of the magnetization, and (iii) a similar computational cost per electronic step as calculations that depend on, inter alia, the kinetic-energy density, but convergence within fewer electronic steps.

cond-mat.mtrl-sci↗

arXiv2022

Efficient and improved prediction of the band offsets at semiconductor heterojunctions from meta-GGA density functionals

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations and efficient and accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk band gaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (revised strongly-constrained and appropriately-normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and K\"ummel meta-GGA functional), and LMBJ (local modified Becke-Johnson) exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the DFT framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy.

cond-mat.mtrl-sci↗

arXiv2022

Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals

The density functional theory (DFT) approximations that are the most accurate for the calculation of band gap of bulk materials are hybrid functionals like HSE06, the MBJ potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGA), like HLE16, or meta-GGAs, like (m)TASK, have proven to be also quite accurate for the band gap. Here, the focus is on 2D materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [Rauch et al., Phys. Rev. B 101, 245163 (2020) and Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the band gap of 2D systems, $G_{0}W_{0}$ results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the band gaps that are the closest to $G_{0}W_{0}$. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.

cond-mat.mtrl-sci↗

arXiv2021

Implementation of self-consistent MGGA functionals in augmented plane wave based methods

Functionals of the meta-generalized gradient approximation (MGGA) are nowadays widely used in chemistry and solid-state physics for the simulation of electronic systems like molecules, solids, or surfaces. Due to their dependency on the kinetic energy density, they are in principle more accurate than GGA functionals for various properties (geometry, binding energy, electronic structure, etc.), while being nearly as fast since they are still of the semilocal form. Thus, when an accuracy better than GGA is required, one may consider using a MGGA instead of the much more costly hybrid functionals or methods like the random-phase approximation or $GW$. In this work, the self-consistent implementation of MGGA functionals in APW based methods is presented. Technical aspects of the implementation are discussed, and calculations of band gaps, lattice constants, and magnetic moments are presented in order to validate our implementation. To test the changes of the electron density due to a MGGA, the electric field gradient on transition-metal atoms is calculated.

cond-mat.mtrl-sci↗

arXiv2021

Correct and accurate polymorphic energy ordering of transition-metal monoxides obtained from semilocal and onsite-hybrid exchange-correlation approximations

The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct ground state of MnO. The relative energy differences of zinc-blende (zb) and rock-salt (rs) structures as computed using MGGAC are found to be in nice agreement with those obtained from high-level correlation methods like the random phase approximation or quantum Monte Carlo techniques. Besides, we have also applied the onsite hybrid functionals (closely related to DFT+U ) based on GGA and meta-GGA functionals, and it is shown that a relatively high amount of Hartree-Fock exchange is necessary to obtain the correct ground-state structure. Our present investigation suggests that the semilocal MGGAC and onsite hybrids, both being computationally cheap, as methods of choice for the calculation of the relative stability of antiferromagnetic transition-metal oxides having potential applications in solid-state physics and structural chemistry.

cond-mat.mtrl-sci↗

arXiv2021

Density analysis for estimating the degree of on-site correlation on transition-metal atoms in extended systems

In the context of the modified Becke-Johnson (mBJ) potential, we recently underlined that $\bar{g}$, the average of $\left\vert\nablaρ\right\vert/ρ$ in the unit cell, has markedly different values in transition-metal oxides and pure transition metals [Tran et al., J. Appl. Phys. 126, 110902 (2019)]. However, since $\bar{g}$ is a constant it is not able to provide local information about a particular atom in the system. Furthermore, while $\overline{g}$ can be used only for periodic bulk solids, a local (i.e., position-dependent) version would allow us to consider also low-dimensional systems and interfaces. Such a local function has been proposed by Rauch et al. [J. Chem. Theory Comput. 16, 2654 (2020)] for the local mBJ potential. Actually, a local version of $\overline{g}$, or of another similar quantity like the reduced density gradient $\overline{s}$, could also be used in the framework of other methods. Here, we explored the idea to use such a local function $\tilde{g}$ (or $\tilde{s}$), defined as the average of $g$ (or $s$) over a certain region around a transition-metal atom, to estimate the degree of on-site correlation on this atom. We found a large difference in our correlation estimators between non-correlated and correlated materials, proving its usefulness and reliability. Our estimators can subsequently be used to determine whether or not a Hubbard $U$ on-site correction in the DFT+$U$ method should be applied to a particular atom. This is particularly interesting in cases where the degree of correlation of the transition-metal atoms is not clear, like interfaces between correlated and non-correlated materials or oxygen-covered metal surfaces. In such cases, our estimators could also be used for an interpolation of $U$ between correlated and non-correlated atoms.

cond-mat.mtrl-sci↗

arXiv2020

Perturbation approach to ab initio effective mass calculations

A degenerate perturbation $k\cdot p$ approach for effective mass calculations is implemented in the all-electron density functional theory (DFT) package WIEN2k. The accuracy is tested on major group IVA, IIIA-VA, and IIB-VIA semiconductor materials. Then, the effective mass in graphene and CuI with defects is presented as illustrative applications. For states with significant Cu-d character additional local orbitals with higher principal quantum numbers (more radial nodes) have to be added to the basis set in order to converge the results of the perturbation theory. Caveats related to a difference between velocity and momentum matrix elements are discussed in the context of application of the method to non-local potentials, such as Hartree-Fock/DFT hybrid functionals and DFT+U.

cond-mat.mtrl-sci↗

arXiv2020

Shortcomings of meta-GGA functionals when describing magnetism

Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGA functionals for magnetism, we extend the assessment to more functionals, but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice-versa. We also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.

cond-mat.mtrl-sci↗

arXiv2020

Validation of pseudopotential calculations for the electronic band gap of solids

Nowadays pseudopotential density-functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed pseudopotential tables that were built from all-electron atomic calculations using few popular semi-local exchange-correlation functionals, while pseudopotentials based on more modern functionals, like meta-GGA and hybrid functionals, or for many-body methods, such as $GW$, are often not available. Because of this, employing pseudopotentials created with inconsistent exchange-correlation functionals has become a common practice. Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional pseudopotential calculations are performed. To this end we compare band gaps obtained with norm-conserving pseudopotentials or the projector-augmented wave method with all-electron calculations for a large dataset of 473 solids. We focus in particular on density functionals that were designed specifically for band-gap calculations. On average, the absolute error is about 0.1 eV, yielding absolute relative errors in the 5-10\% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent pseudopotential is rather harmless for most applications. However, we find specific cases where absolute errors can be larger than 1 eV, or others where relative errors can amount to a large fraction of the band gap.

physics.comp-ph↗

arXiv2019

On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy

During the last few years, it has become more and more clear that functionals of the meta generalized gradient approximation (MGGA) are more accurate than GGA functionals for the geometry and energetics of electronic systems. However, MGGA functionals are also potentially more interesting for the electronic structure, in particular when the potential is non-multiplicative (i.e., when MGGAs are implemented in the generalized Kohn-Sham framework), which may help to get more accurate bandgaps. Here, we show that the calculation of bandgap of solids with MGGA functionals can be done very accurately also in a non-self-consistent manner. This scheme uses only the total energy and can, therefore, be very useful when the self-consistent implementation of a particular MGGA functional is not available. Since self-consistent MGGA calculations may be difficult to converge, the non-self-consistent scheme may also help to speed-up the calculations. Furthermore, it can be applied to any other types of functionals, for which the implementation of the corresponding potential is not trivial.

cond-mat.mtrl-sci↗

arXiv2019

Semilocal exchange-correlation potentials for solid-state calculations: Current status and future directions

Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional $E_{\text{xc}}$ and/or potential $v_{\text{xc}}$. Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and allow to treat systems containing up to thousands of atoms. Among them, there is the modified Becke-Johnson potential that is widely used to calculate the fundamental band gap of semiconductors and insulators. The accuracy for other properties like the magnetic moment or the electron density, that are also determined directly by $v_{\text{xc}}$, is also discussed.

cond-mat.mtrl-sci↗

arXiv2019

Nonlocal van der Waals functionals for solids: Choosing an appropriate one

The nonlocal van der Waals (NL-vdW) functionals [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] are being applied more and more frequently in solid-state physics, since they have shown to be much more reliable than the traditional semilocal functionals for systems where weak interactions play a major role. However, a certain number of NL-vdW functionals have been proposed during the last few years, such that it is not always clear which one should be used. In this work, an assessment of NL-vdW functionals is presented. Our test set consists of weakly bound solids, namely rare gases, layered systems like graphite, and molecular solids, but also strongly bound solids in order to provide a more general conclusion about the accuracy of NL-vdW functionals for extended systems. We found that among the tested functionals, rev-vdW-DF2 [Hamada, Phys. Rev. B 89, 121103(R) (2014)] is very accurate for weakly bound solids, but also quite reliable for strongly bound solids.

cond-mat.mtrl-sci↗

arXiv2019

Limitations of the DFT-1/2 method for covalent semiconductors and transition-metal oxides

The DFT-1/2 method in density functional theory [L. G. Ferreira et al., Phys. Rev. B 78, 125116 (2008)] aims to provide accurate band gaps at the computational cost of semilocal calculations. The method has shown promise in a large number of cases, however some of its limitations or ambiguities on how to apply it to covalent semiconductors have been pointed out recently [K.-H. Xue et al., Comput. Mater. Science 153, 493 (2018)]. In this work, we investigate in detail some of the problems of the DFT-1/2 method with a focus on two classes of materials: covalently bonded semiconductors and transition-metal oxides. We argue for caution in the application of DFT-1/2 to these materials, and the condition to get an improved band gap is a spatial separation of the orbitals at the valence band maximum and conduction band minimum.

cond-mat.mtrl-sci↗

arXiv2018

Density-gradient-free variable in exchange-correlation functionals for detecting inhomogeneities in the electron density

An alternative type of approximation for the exchange and correlation functional in density functional theory is proposed. This approximation depends on a variable $u$ that is able to detect inhomogeneities in the electron density $ρ$ without using derivatives of $ρ$. Instead, $u$ depends on the orbital energies which can also be used to measure how a system differs from the homogeneous electron gas. Starting from the functional of Perdew, Burke, and Ernzerhof (PBE) [Phys. Rev. Lett. 77, 3865 (1996)], a functional depending on $u$ is constructed. Tests on the lattice constant, bulk modulus, and cohesive energy of solids show that this $u$-dependent PBE-like functional is on average as accurate as the original PBE or its solid-state version PBEsol. Since $u$ carries more nonlocality than the reduced density gradient $s$ used in functionals of the generalized gradient approximation (GGA) like PBE and $α$ used in meta-GGAs, it will be certainly useful for the future development of more accurate exchange-correlation functionals.

cond-mat.mtrl-sci↗

arXiv2018

Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: tests on solids

A recent study of Mejia-Rodriguez and Trickey [Phys. Rev. A 96, 052512 (2017)] showed that the deorbitalization procedure (replacing the exact Kohn-Sham kinetic-energy density by an approximate orbital-free expression) applied to exchange-correlation functionals of the meta-generalized gradient approximation (MGGA) can lead to important changes in the results for molecular properties. For the present work, the deorbitalization of MGGA functionals is further investigated by considering various properties of solids. It is shown that depending on the MGGA, common orbital-free approximations to the kinetic-energy density can be sufficiently accurate for the lattice constant, bulk modulus, and cohesive energy. For the band gap, calculated with the modified Becke-Johnson MGGA potential, the deorbitalization has a larger impact on the results.

cond-mat.mtrl-sci↗

arXiv2017

Assessment of the GLLB-SC potential for solid-state properties and attempts for improvement

Based on the work of Gritsenko et al. (GLLB) [Phys. Rev. A 51, 1944 (1995)], the method of Kuisma et al. [Phys. Rev. B 82, 115106 (2010)] to calculate the band gap in solids was shown to be much more accurate than the common local density approximation (LDA) and generalized gradient approximation (GGA). The main feature of the GLLB-SC potential (SC stands for solid and correlation) is to lead to a nonzero derivative discontinuity that can be conveniently calculated and then added to the Kohn-Sham band gap for a comparison with the experimental band gap. In this work, a thorough comparison of GLLB-SC with other methods, e.g., the modified Becke-Johnson (mBJ) potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)], for electronic, magnetic, and density-related properties is presented. It is shown that for the band gap, GLLB-SC does not perform as well as mBJ for systems with a small band gap and strongly correlated systems, but is on average of similar accuracy as hybrid functionals. The results on itinerant metals indicate that GLLB-SC overestimates significantly the magnetic moment (much more than mBJ does), but leads to excellent results for the electric field gradient, for which mBJ is in general not recommended. In the aim of improving the results, variants of the GLLB-SC potential are also tested.

cond-mat.mtrl-sci↗