Exchange-correlation Energy Functionals Research Articles

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors.

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Investigation of structural and electronic properties of ZnO using first principle calculations

In this research, first-principle calculations have been performed to study the geometry structure and electronic properties of ZnO. All possible exchange-correlation energy functionals were used to perform geometry optimization of ZnO in order to find the efficient calculation conditions. Bandgap energy, density of states (DOS), projected DOS (PDOS); and other properties of ZnO were also calculated and discussed. The calculated band-gap value of ZnO is less than 1.0 eV, much smaller than experimental value of 3.37 eV; while the PDOS results indicate the important roles of O 2p and Zn 3d orbitals in ZnO band structures. The well-known limitation of band-gap value calculations using Density Functional Theory (DFT) was solved by applying Hubbard potential on Zn 3d and O 2p orbitals. A full investigation with Hubbard value varying from 0.5 to 10 eV has been performed and the selected value is 8.0 eV for both Zn 3d and O 2p electrons.

Partially deorbitalized meta-GGA

Mejia-Rodriguez and Trickey recently proposed a procedure for removing the explicit dependence of meta-GGA exchange-correlation energy functionals Exc on the kinetic energy density τ. We present a simple modification to this approach in which the exact Kohn-Sham τ is used as input for Exc but the functional derivative of τ with respect to the density ρ, required to calculate the potential term ∫d3r′δExc∕δτ(r′)∣ρ⋅δτ(r′)∕δρ(r), is evaluated using an approximate kinetic energy density functional. This ‘half-way’ strategy ensures that the Kohn-Sham potential is a local multiplicative function (as opposed to the non-local potential of a generalized Kohn-Sham approach) while preserving the inherent non-locality of the functional itself. Electronic structure codes can be easily modified to use the new method. We validate it by quantifying the accuracy of the predicted lattice parameters, bulk moduli, magnetic moments and cohesive energies of a large set of periodic solids. An unanticipated benefit of this method is to gauge the quality of approximate kinetic energy functionals by checking if the self-consistent solution is indeed at the variational minimum.

GradDFT. A software library for machine learning enhanced density functional theory.

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT: an endeavor with many open questions and technical challenges. In this work, we present GradDFT a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. GradDFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, GradDFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.

Investigating the Linear Response Function under Approximations Following the Coupled-Perturbed Approach for Atoms and Molecules.

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn-Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree-Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob's ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

TAO-DFT with the Polarizable Continuum Model.

For the ground-state properties of gas-phase nanomolecules with multi-reference character, thermally assisted occupation (TAO) density functional theory (DFT) has recently been found to outperform the widely used Kohn-Sham DFT when traditional exchange-correlation energy functionals are employed. Aiming to explore solvation effects on the ground-state properties of nanomolecules with multi-reference character at a minimal computational cost, we combined TAO-DFT with the PCM (polarizable continuum model). In order to show its usefulness, TAO-DFT-based PCM (TAO-PCM) was used to predict the electronic properties of linear acenes in three different solvents (toluene, chlorobenzene, and water). According to TAO-PCM, in the presence of these solvents, the smaller acenes should have nonradical character, and the larger ones should have increasing polyradical character, revealing striking similarities to the past findings in the gas phase.

Spin-crossover complexes: Self-interaction correction vs density correction.

Complexes containing a transition metal atom with a 3d4-3d7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem.

Recent experimental advances in strongly coupled light-matter systems have sparked the development of general abinitio methods capable of describing interacting light-matter systems from first principles. One of these methods, quantum-electrodynamical density-functional theory (QEDFT), promises computationally efficient calculations for large correlated light-matter systems with the quality of the calculation depending on the underlying approximation for the exchange-correlation functional. So far no true density-functional approximation has been introduced limiting the efficient application of the theory. In this Letter, we introduce the first gradient-based density functional for the QEDFT exchange-correlation energy derived from the adiabatic-connection fluctuation-dissipation theorem. We benchmark this simple-to-implement approximation on small systems in optical cavities and demonstrate its relatively low computational costs for fullerene molecules up to C_{180} coupled to 400 000 photon modes in a dissipative optical cavity. This Letter now makes first principle calculations of much larger systems possible within the QEDFT framework effectively combining quantum optics with large-scale electronic structure theory.

Hybrid exchange–correlation energy functionals for accurate prediction of the electronic and optical properties of alkaline-earth metal oxides

An essential issue in electro-optical applications is to design materials with appropriate band gaps. In the framework of density functional theory (DFT), the generalized gradient approximation (GGA) and local density approximation (LDA) generally underestimate band gaps for semiconductors. Hybrid functionals that include some exact Hartree–Fock exchange are known to be better. In this research, we applied hybrid functionals, which has the main factor of providing almost accurate exchange potential, for calculating structural, electronic and optical properties of alkaline earth metal oxides. Results show that the hybrid functionals have a tendency to improve the description of structural and electronic parameters with respect to LDA and GGA. We find that the PBE0 and B3PW91 are the best functional for estimating lattice constant. LDA-HF gives the better results for calculating the energy band gaps with respect to the experimental values, and B3PW91 and PBE0 improved the amount of dielectric constant. The calculated imaginary part of dielectric function and reflectivity spectra shows that B3PW91 and LDA-Fock α give the best accordance with experimental results. The present work has shown that applying hybrid functionals can lead to very accurate results, describing correctly the structural, electronic and optical properties of the alkaline earth metal oxides.

Improved transition metal surface energies from a generalized gradient approximation developed for quasi two-dimensional systems.

Nonuniform density scaling in the quasi-two-dimensional (quasi-2D) regime is an important and challenging aspect of the density functional theory. Semilocal exchange-correlation energy functionals, developed by solving the dimensional crossover criterion in the quasi-2D regime, have great theoretical and practical importance. However, the only semilocal generalized gradient approximation (GGA) that has been designed to satisfy this criterion is the Q2D-GGA [L. Chiodo et al., Phys. Rev. Lett. 108, 126402 (2012)]. Here, we establish the applicability, broadness, and accuracy of the Q2D-GGA functional by performing an extensive assessment of this functional for transition metal surface energies. The important characteristic of the surface density localization and oscillation due to the rearrangement of the d electrons is also shown for different metal surfaces.

A comparative study of structural, electronic and magnetic properties of DyOCl and HoOCl lanthanide oxychlorides: first-principles predictions of DFT, DFT + U and DFT + U + SOC methods

Apart from their fundamental interest, lanthanide compounds have potential implications as luminescent, catalytic, magnetic as well as biomedical materials for diverse applications. In this paper we report first time the electronic and magnetic properties of two members of lanthanide oxychloride family, namely- DyOCl and HoOCl from the first-principles calculations based on density functional theory (DFT). For the self-consistent DFT calculations, we incorporated the full-potential linearized augmented plane-wave (FP-LAPW) method using various DFT methods and DFT + U method without and with spin–orbit coupling (SOC). For the electronic structure calculations, the exchange-correlation energy functionals in Kohn–Sham equation are treated within local-spin-density-approximation (LSDA) and Generalized-Gradient-Approximation (GGA) in conjunction with Perdew-Bruke-Ernzerhof (PBE) and Wu-Cohen (WC) parameterization. In particular, a comparative analysis of electronic and magnetic properties is presented with LSDA, PBE-GGA, WC-GGA and GGA + U methods without and with SOC coupling. Both compounds are predicted to be half-metallic (HM) ferromagnetic (FM) within LSDA approximation, whereas within GGA + U approximation DoOCl is semiconducting while HoOCl is HMFM. On the other hand, the GGA + U scheme under FM and antiferromagnetic (AFM) ordering predicts that both DyOCl and HoOCl are metallic in AFM ordering while they show insulating nature in FM ordering.

Calculation of strained BaTiO3 with different exchange correlation functionals examined with criterion by Ginzburg-Landau theory, uncovering expressions by crystallographic parameters

In the calculations of tetragonal BaTiO3, some exchange-correlation (XC) energy functionals such as local density approximation (LDA) have shown good agreement with experiments at room temperature (RT), e.g., spontaneous polarization (P S), and superiority compared with other XC functionals. This is due to the error compensation of the RT effect and, hence, will be ineffective in the heavily strained case such as domain boundaries. Here, ferroelectrics under large strain at RT are approximated as those at 0 K because the strain effect surpasses the RT effects. To find effective XC energy functionals for strained BaTiO3, we propose a new comparison, i.e., a criterion. This criterion is the properties at 0 K given by the Ginzburg-Landau (GL) theory because GL theory is a thermodynamic description of experiments working under the same symmetry-constraints as ab initio calculations. With this criterion, we examine LDA, generalized gradient approximations (GGA), meta-GGA, meta-GGA + local correlation potential (U), and hybrid functionals, which reveals the high accuracy of some XC functionals superior to XC functionals that have been regarded as accurate. This result is examined directly by the calculations of homogenously strained tetragonal BaTiO3, confirming the validity of the new criterion. In addition, the data points of theoretical P S vs. certain crystallographic parameters calculated with different XC functionals are found to lie on a single curve, despite their wide variations. Regarding these theoretical data points as corresponding to the experimental results, analytical expressions of the local P S using crystallographic parameters are uncovered. These expressions show the primary origin of BaTiO3 ferroelectricity as oxygen displacements. Elastic compliance and electrostrictive coefficients are estimated. For the comparison of strained results, we show that the effective critical temperature T C under strain <-0.01 is >1000 K from an approximate method combining ab initio results with GL theory. In addition, in a definite manner, the present results show much more enhanced ferroelectricity at large strain than the previous reports.

Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory.

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: Exc[ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: Exc[ρ,∇ × m]. The exchange-correlation magnetic field, Bxc, then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. This source-free method is simple to implement in all existing density functional theory codes.

A study of accurate exchange-correlation functionals through adiabatic connection.

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial generalized gradient approximation (GGA) functionals, this has culminated into the recently proposed SCAN (strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals-the GGA hybrid functionals B3LYP and PBE0 and the meta-GGA functional SCAN-from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as αVee with α varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density.

The effects of strong correlations on the band structure of Ag8SnSe6 argyrodite

The electronic energy band spectra, as well as partial and total density of electronic states of the crystal argyrodite Ag$_{8}$SnSe$_{6}$ have been evaluated within the projector augmented waves (PAW) approach by means of the ABINIT code. The one-electron energies have been evaluated using two functionals for exchange-correlation energy. The first one is the generalized gradient approximation (GGA) approach. The second one is the hybrid functional PBE0 composed of the semilocal GGA part and Hartree-Fock exact exchange non-local energy for strongly correlated $4d$ electrons of Ag atom. The second approach eliminates the Coulomb self-interaction of the Ag $4d$ electrons. This leads to a significant restructuring of the energy bands in the filled valence part and to an improved location of the Ag $4d$-states on the energy scale, and the resulting value of the band gap is well compared with experiment. The effects of strong correlation on the electronic structure of the crystal argyrodite are considered here for the first time.

Electronic structure of layered quaternary chalcogenide materials for band-gap engineering: The example ofCs2MIIM3IVQ8

Quaternary chalcogenide materials offer a wide variety of chemical and physical properties, and hence, those compounds have been widely studied for several technological applications. Recently, experimental studies have found that the chalcogenide ${\mathrm{Cs}}_{2}{\mathrm{M}}^{\mathrm{II}}{\mathrm{M}}_{3}^{\mathrm{IV}}{\mathrm{Q}}_{8}$ family (${\mathrm{M}}^{\mathrm{II}}$ = $\mathrm{Mg}, \mathrm{Zn}, \mathrm{Cd}, \mathrm{Hg}, {\mathrm{M}}^{\mathrm{IV}}$ = $\mathrm{Ge}, \mathrm{Sn}$ and $\mathrm{Q}$ = $\mathrm{S}, \mathrm{Se}, \mathrm{Te}$), which includes 24 compounds, yields a wide range of band gaps, namely, from 1.07 to 3.4 eV, and hence, they have attracted great interest. To obtain an improved atomistic understanding of the role of the cations and anions on the physical properties, we performed a first-principles investigation of the 24 ${\mathrm{Cs}}_{2}{\mathrm{M}}^{\mathrm{II}}{\mathrm{M}}_{3}^{\mathrm{IV}}{\mathrm{Q}}_{8}$ compounds employing density functional theory within semilocal and hybrid exchange-correlation energy functionals and the addition of van der Waals corrections to improve the description of the weakly interacting layers. Our lattice parameters are in good agreement with the available experimental data (i.e., 11 compounds), and the equilibrium volume increases linearly by increasing the atomic number of the chalcogen, which can be explained by the increased atomic radius of the chalcogen atoms from $\mathrm{S}$ to $\mathrm{Te}$. We found that van der Waals corrections play a crucial role in the lattice parameter in the stacking direction of the ${\mathrm{Cs}}_{2}{\mathrm{M}}^{\mathrm{II}}{\mathrm{M}}_{3}^{\mathrm{IV}}{\mathrm{Q}}_{8}$ layers, while the binding energy per unit area has similar magnitude as obtained for different layered materials. We obtained that the band gaps follow a linear relation as a function of the unit cell volume, which can be explained by the atomic size of the chalcogen atom and the relative position of the $\mathrm{Q} p$ states within the band structure. The fundamental and optical band gaps differ by less than 0.1 eV. The band gaps obtained with the hybrid functional are in good agreement with the available experimental data. Furthermore, we found from the Bader analysis, that the Coulomb interations among the cations and anions play a crucial role on the energetic properties.

First-principles calculation on electronic properties of zinc oxide by zinc–air system

First-principles calculations are performed to study the electronic properties of zinc oxide (ZnO) formed on an anode after discharging a Zn–air system. Prior to calculation, the ZnO is characterised by X-ray diffraction using Rietveld refinement. Diffracted patterns proved the formation of single phase ZnO, while Rietveld analysis shows that the ZnO has a hexagonal wurtzite structure with lattice parameters, a=3.244 and c=5.199Å. Geometry optimisation of the hexagonal wurtzite structure of the ZnO is performed using various exchange–correlation energy functionals. The local density approximation functional method is used to explain the structure, electronic band structure and density of state properties of hexagonal ZnO. The calculated energy band gap was 0.75eV while the density of states reveals that the O 2p (the top valence band) and Zn 4s (the bottom conduction band) states domination.

Highly accurate local pseudopotentials of Li, Na, and Mg for orbital free density functional theory

We present a method to make highly accurate pseudopotentials for use with orbital-free density functional theory (OF-DFT) with given exchange-correlation and kinetic energy functionals, which avoids the compounding of errors of Kohn–Sham DFT and OF-DFT. The pseudopotentials are fitted to reference (experimental or highly accurate quantum chemistry) values of interaction energies, geometries, and mechanical properties, using a genetic algorithm. This can enable routine large-scale ab initio simulations of many practically relevant materials. Pseudopotentials for Li, Na, and Mg resulting in accurate geometries and energies of different phases as well as of vacancy formation and bulk moduli are presented as examples.

Augmented methane adsorption at Ca decorated carbon nanotubes—a DFT study

Methane adsorption at Ca decorated single wall carbon nanotubes has been studied by ab initio total energy calculations based on the density functional theory. The adsorption configurations have been studied by using various exchange-correlation energy functionals also including two possible long-range interaction correction schemes. Our calculations show that methane adsorption at Ca decorated carbon nanotubes is markedly enhanced when impurity atoms are considered as individual adsorption sites. We demonstrate that up to six CH4 molecules can bind at a single Ca impurity at room temperature. The phenomenon responsible for the measured adsorption energy is recognized as a Kubas-type interaction that involves the orbital overlap between the Ca d state and the methane σ molecular orbitals. The adsorption values obtained with the different energy functionals used are discussed showing that local density approximation, often employed in the recent literature for similar adsorption problems, is affected by severe limitations when orbital overlap and physisorption co-exist. Lastly the well-known problem of Ca clustering is studied and discussed showing that, different from the hydrogen case, it does not induce any molecular dissociation.

Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas.

Nonlocal exchange-correlation energy functionals are constructed using the accurate model exchange-correlation hole for the uniform electron gas developed by Gori-Giorgi and Perdew. The exchange-correlation hole is constrained to be symmetric and normalized, so the resulting functionals can be viewed as symmetrized versions of the weighted density approximation; we call them two-point weighted density approximations. Even without optimization of parameters or functional forms, the exchange-correlation energies for small molecules are competitive with those of the best generalized gradient approximation functionals. Two-point weighted density approximations seem to be an interesting new direction for functional development. A more general version of the conditions that define the energy for fractional electron number and fractional spin are presented. These "generalized flat-planes" conditions are closely linked to the normalization of the spin-resolved exchange-correlation hole at noninteger electron number. This and many other properties of the exact exchange-correlation functional can be imposed straightforwardly and directly in symmetrized weighted density approximation.