Generalized Gradient Approximation Functionals Research Articles

BSE@GW Prediction of Charge Transfer Exciton in Molecular Complexes: Assessment of Self-Energy and Exchange-Correlation Dependence.

The Bethe-Salpeter equation using the GW approximation to the self-energy (BSE@GW) is a computationally attractive method for studying electronic excitation from first principles within the many-body Green's function theory framework. We examine its dependence on the underlying exchange-correlation (XC) approximation as well as on the GW approximation for predicting the charge transfer exciton formation at representative type-II interfaces between molecular systems of tetrachloro-1,2-benzoquinone (TCBQ) and acene derivatives. For the XC approximation, we consider several widely used generalized gradient approximation (GGA) and hybrid GGA functionals. For the GW self-energy approximation, we examine the recently proposed renormalized singles approach by Yang and coauthors [J. Phys. Chem. Lett. 2019, 10 (3), 447-452; J. Chem. Theory Comput. 2022, 18, 7570-7585] in addition to other commonly employed approximated GW schemes. We demonstrate a reliable prediction of the charge transfer exciton within the BSE@GW level of theory.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States.

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

The structural, electronic, optical, and mechanical properties of carbon-based halides: An ab initio DFT approach

In the present work, we choose the carbon-based halides CX4 (X = Br, Cl) to conduct a study on the ground-state properties using first-principles calculations based on density functional theory. We provide a comparative study for bromide and chloride materials using standard generalized gradient approximation functionals. A total of 80 atoms have been simulated on a single unit cell. A direct bandgap energy of 3.28 (4.64) eV for X = Br (X = Cl) with Z–Z transition is found on the studied materials. According to our partial density of states plot, a hybridization of s orbitals on C and X atoms is observed. Metallic properties have also been identified. A low reflectivity of 6% (12%) has been measured, which presents excellent material absorption. Such a material is also determined to be brittle, based on the calculated Pugh’s ratio. The reflectivity (ductility) tends to increase as the X element increases down the Period Table. The negative Poisson’s ratio found also suggests that the materials could be used as an electrode for metal-ion (e.g., Li, K, and Na) batteries.

Analysing the suitability of CaTiO3/Ca1–xSrxTiO3/SrTiO3 perovskite for fabrication of optoelectronic devices using QuantumATK tool: a study for electronic and optical properties

Calcium Titanate (CaTiO3) as a material has been researched for various applications like those in capacitors, piezoelectric devices and ceramic applications. Same has been possible owing to the exhibition of various characteristics of this material like high melting point (1,625 °C) and dielectric properties. However, only limited studies have been conducted to understand the impact of Strontium (Sr) doping and possibility of adopting this material into any kind of optoelectronic applications. This paper carries on an in-depth analysis on CaTiO3 and study effect of Sr as a dopant on its properties. Analysis has been carried out using Quantum ATK tool based on DFT approximations. CaTiO3 perovskite properties were studied by using the GGA (Generalized Gradient Approximation) and PBE (Perdew–Burke–Ernzerhof) functionals, which are used with the LCAO calculator. As a result of the inclusion of Sr at the Ca site, the electronic band structure of CaTiO3 was changed by the introduction of a gamma point. Bandgap of CaTiO3 was analysed to be dependent on the Sr site concentration and increased from 2.3 eV (Direct bandgap) to 2.3612 eV (Indirect bandgap), when Sr and Ca site concentration were equal, but it decreased with further increase in Sr site concentration to 1.7155 eV. Pure CaTiO3’s projected density of states changed after doping, providing evidence for the effects of the dopant on the system. As a result of an examination of the optical properties of both systems, it is found that CaTiO3 at 380 nm (close to infrared) exhibits an effective extinction coefficient (k) value of 0.78, whereas at 600 nm, the attenuation of light decreases to zero. This makes Sr doping in CaTiO3 another attractive candidate for optical devices in addition to its ability to change optical properties.

Physical properties of newly synthesized noncentrosymmetric TaIr2B2 and NbIr2B2 superconductors: an extensive comparison of GGA and LDA functional investigations.

In recent years, noncentrosymmetric (NCS) structural compounds have received much attention from the scientific community in the exploration for the unconventional nature of superconductivity with exciting physical properties. This study uses the comprehensive generalized gradient approximation (GGA) and local density approximation (LDA) to gain insights into the physical properties of two recently synthesized Ir-based NCS superconductors, TaIr2B2 and NbIr2B2. The structural parameters, mechanical performance, electronic structure, Debye temperature, melting temperature, electronic specific heat, and electron-phonon coupling constant of TaIr2B2 and NbIr2B2 are explored and discussed in detail. Density functional theory (DFT) optimized structural parameters of both NCS phases agree well with experimental observation. Both GGA and LDA calculations show that the compounds are ductile, machinable, mechanically stable, and anisotropic in nature. The elastic moduli and hardness calculations reveal that TaIr2B2 is harder than NbIr2B2. The calculation of the melting temperature reveals that TaIr2B2 is more suitable for high temperature technology applications compared to NbIr2B2. Both GGA and LDA functionals reveal that the optical functions are very similar. Both compounds display a significant amount of reflectivity spectra over a wide range of photon energies. The GGA functional reveals a somewhat higher density of states value compared to that of LDA. The present calculated values of the electron-phonon coupling constant of both compounds are consistent with values previously reported from experimental studies.

First Principle Investigations on Structural, Mechanical, Electronic, And Thermoelectric Properties of XCoP (XTi, Zr, Hf) Half Heusler Alloys for Energy Recovery Application

AbstractXCoP (XTi, Zr, Hf) half Heusler alloys are investigated through density functional theory in stable non‐magnetic phase. The exchange‐correlation functional Generalized Gradient Approximation (GGA) is used to study these alloys. The equilibrium lattice constants and corresponding ground state energies of the studied alloys are calculated in stable γ‐phase. All these three reported alloys exhibit semiconducting behavior with corresponding bandgap values of 1.40, 1.29, and 1.38 eV for TiCoP, ZrCoP, and HfCoP, respectively. The studied alloys are mechanically stable and ductile in nature. The obtained thermoelectric figure of merit for p‐type TiCoP, ZrCoP and HfCoP are 0.5, 0.6, and 0.7 at 1200 K. Similarly, the figure of merit obtained for n‐type TiCoP, ZrCoP, HfCoP are 0.54, 0.37, and 0.31, respectively, at the same temperature. The investigated favorable transport properties of these alloys show that they are the potential candidates for waste heat energy harvesting application.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat.

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

Multiconfigurational Pair-Density Functional Theory Is More Complex than You May Think.

Multiconfigurational pair-density functional theory (MC-PDFT) is a promising way to describe both strong and dynamic correlations in an inexpensive way. The functionals in MC-PDFT are often "translated" from standard spin density functionals. However, these translated functionals can in principle lead to "translated spin densities" with a nonzero imaginary component. Current developments so far neglect this imaginary part by simply setting it to zero. In this work, we show how this imaginary component is actually needed to reproduce the correct physical behavior in a range of cases, especially low-spin open shells. We showcase the resulting formalism on both local density approximation and generalized gradient approximation functionals and illustrate the numerical behavior by benchmarking a number of singlet-triplet splittings (ST gaps) of organic diradicals and low-lying excited states of some common organic molecules. The results demonstrate that this scheme improves existing translated functionals and gives more accurate results, even with minimal active spaces.

Different look at S-p bonding orbital in CdS, with Zn and Se series gap investigations

The electronic characteristics of Cadmium sulfide (CdS) series Zn x Cd16−x S8Se8 and Cd16Se16−x S x are investigated. According to the calculations, barely 12% Zn (X = 2) in the form Zn2Cd14Se16 is required to maximize the gap. To properly evaluate the excited states, the generalized gradient approximation (GGA) and modified Becke-Johnson (mBJ) potentials are utilized in the computations. The parent compound CdS exhibits three distinct forms of crystal structures, with the hexagonal structure being remarkably stable under the GGA and mBJ functionals. The partial density of states around the Fermi level demonstrates that the system’s electronic characteristics are determined by the interaction of S-p and Cd-s,p states. A substantial splitting of the valence band, shown by band structure analysis, suggests a greater polarization crystal field in the hexagonal CdS structure. The stereochemical activity of the S atom stimulated the CdS compound for extremely tiny displacements of 0.0014 Å and 0.043 Å for the Cd and S atoms in the [001] direction, respectively, as well as tilting of the Cd-S-Cd link. This compound exhibits lone pair properties, with three valance electrons of the p-orbital participating in covalent bonding and S-s electrons fully occupied. Furthermore, Van Hove singularities are discovered in the electron density of states due to the Cd-d atoms that support in the analysis of optical absorption spectra. Finally, the results suggest that CdS has potential for solar cells applications due to its direct wide band gap semiconductor features,

The application of the SCAN density functional to color centers in diamond.

Detailed characterization of deep-level color centers requires understanding their electronic and atomic structure, which is most commonly investigated utilizing the Kohn-Sham density functional theory. Standard semilocal functionals based on the generalized gradient approximation (GGA) are inclined toward an imprecise quantitative description of defects' electronic structure. Hybrid functionals provide an improved prediction of electronic properties, albeit at a much higher computational cost. In this work, we test the newly developed Strongly Constrained and Appropriately Normed (SCAN) family of meta-GGA density functionals for selected color centers in diamond. In particular, we study nitrogen-, silicon-, germanium-, and tin-vacancy centers that have been recently investigated for their use in quantum technological applications. We show that SCAN and its derivatives, the rSCAN and r2SCAN functionals, significantly improve the calculated energies of optical transitions within the delta-self-consistent-field approach, almost reaching the accuracy of the hybrid Heyd-Scuseria-Ernzerhof (HSE) functional. In the case of the NV- center, we also show that the SCAN family of functionals improves the description of the adiabatic potential energy surfaces compared to both GGA and hybrid functionals, improving calculated luminescence lineshapes. As a result of these findings, we recommend using the SCAN family of functionals as a promising alternative for studying color centers in solids.

Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations

Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 511 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely {}^{3}A_2 < {}^{1}E < {}^{1}A_1 < {}^{3}E3A2<1E<1A1<3E. Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.

How graphenic are graphynes? Evidence for low-lying correlated gapped states in graphynes.

Graphynes can be structurally envisioned as 2D extensions to graphene, whereby linearly bonded carbon linkages increase the distance between trigonal carbon nodes. Many graphynes have been predicted to exhibit a Dirac-like semimetallic (SEM) graphenic electronic structure, which could potentially make them competitive with graphene for applications. Currently, most graphynes remain as attractive synthetic targets, and their properties are still unconfirmed. Here, we demonstrate that the electronic structure of hexagonal α-graphyne is analogous to that of biaxially strained graphene. By comparison with accurate quantum Monte Carlo results on strained graphene, we show that the relative energetic stability of electronic states in this correlated 2D system can be captured by density functional theory (DFT) calculations using carefully tailored hybrid functionals. Our tuned hybrid DFT approach confirms that α-graphyne has a low energy correlated Mott-like antiferromagnetic insulating (AFI) state, which competes with the SEM state. Our work shows that the AFI-SEM crossover in α-graphyne could be tunable by in-plane biaxial strain. Applying our approach to other graphynes shows that they should also exhibit correlated AFI states, which could be dominant even at zero strain. Calculations using an onsite Coulombic repulsive term (i.e., DFT + U) also confirm the predictions of our hybrid DFT calculations. Overall, our work strongly suggests that graphynes are not as graphenic (i.e., Dirac-like) as often previously predicted by DFT calculations using standard generalized gradient approximation functionals. However, due to the greater electronic versatility (e.g., tunable semiconducting bandgaps and accessible spin polarized states) implied by our study, graphynes could have novel device applications that are complementary to those of graphene.

Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe2+ /Fe3+ Redox Reaction.

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe2+ /Fe3+ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe2+ /Fe3+ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe2+ /Fe3+ system computed from these simulations are compared with the available experimental data for validation.

Energetic Order of Nb 2 O 5 and Ta 2 O 5 Polymorphs

Nb2O5 and Ta2O5 are materials with important technical applications, e.g., in electrochemistry as anode materials for Li or Na storage, or as selective oxidation catalysts. The properties of both oxides largely depend on their various polymorphs with different crystal structures. So far, the literature does not agree on which polymorphs of Nb2O5 and Ta2O5 are most stable under standard conditions. Herein, the relative stability of all relevant polymorphs of Nb2O5 and Ta2O5 is calculated using density-functional theory and the recently developed rev2-POB basis sets. First, a benchmark of the atomization-free enthalpies of Nb2O5 is performed with selected generalized gradient approximation and hybrid functionals. The effect of London dispersion on structural and energetic properties is explicitly investigated. A large scattering of atomization energies is observed for the various functionals. The range-separated hybrid functional RSHXLDA without dispersion correction proves to be the method of choice for the systems under investigation. For this reason, the stability order obtained with RSHXLDA is consisdered as most reliable.

First-principles calculations to investigate structural, electronic and phonon properties of sodium bromide (NaBr) and sodium iodide (NaI) crystals

In this paper, the first-principles study is performed to calculate the structural, electronic and phonon properties of alkali halides NaBr and NaI. The calculations for structural and electronic properties have been carried out using the full-potential linearized augmented plane-wave (FP-LAPW) method that is employed in the WIEN2k code, whereas the phonon properties are studied using the Quantum Espresso program based on density-functional theory within plane-wave fundamental sets and pseudo-potentials approaches. The calculation of structural, electronic band properties were carried out using generalized gradient approximation (GGA), local-density approximation (LDA) and a combination of modified Becke-Johnson exchange potential with LDA and GGA (TB-mBJ-GGA/LDA) for exchange-correlation potential. The calculated structural parameters are in good agreement with experimental results. In our electronic calculations, the obtained bandgaps are underestimated by LDA and GGA functionals compared to empirically derived results, which is an expected result. However, the calculated bandgaps by the modified Becke-Johnson exchange potential are in perfect agreement with the experiment. Finally, the dynamic properties of NaBr and NaI compounds were investigated. Both phonon dispersion and phonon density of states curves were calculated for compounds along with the high symmetry directions in the Brillouin region. The dynamical properties of NaBr and NaI crystals are analyzed and discussed.

Effects of pseudopotentials and exchange-correlation functionals on phase transition of LaH10

To assess the effects of pseudopotentials and exchange-correlation functionals on trigonal to face-centered cubic phase transition of LaH10, we performed density functional theory based first-principles calculations by employing three-types of pseudopotentials with LDA (local density approximation) and GGA (generalized gradient approximation) exchange-correlation functionals. We found that the lattice parameters such as cell angle or cell volume and phase transition pressure exhibit a significant variation with LDA and GGA functionals whereas they exhibit a weak dependence on the pseudopotentials. In general, LDA calculations result in a lower phase transition pressure than GGA calculations. We also investigated the effects of pseudopotentials and exchange-correlation functionals on the electronic properties by calculating the total and partial density of state functions for face-centered cubic phase of LaH10 at 150 GPa. Computed electronic densities of states at the Fermi level are found to exhibit a weak dependence on the exchange-correlation functionals.

Assessment of the Accuracy of Density Functionals for Calculating Oxygen Reduction Reaction on Nitrogen-Doped Graphene.

Experimental studies of the oxygen reduction reaction (ORR) at nitrogen-doped graphene electrodes have reported a remarkably low overpotential, on the order of 0.5 V, similar to Pt-based electrodes. Theoretical calculations using density functional theory have lent support to this claim. However, other measurements have indicated that transition metal impurities are actually responsible for the ORR activity, thereby raising questions about the reliability of both the experiments and the calculations. To assess the accuracy of the theoretical calculations, various generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are employed here and calibrated against high-level wave-function-based coupled-cluster calculations (CCSD(T)) of the overpotential as well as self-interaction corrected density functional calculations and published quantum Monte Carlo calculations of O adatom binding to graphene. The PBE0 and HSE06 hybrid functionals are found to give more accurate results than the GGA and meta-GGA functionals, as would be expected, and for a low dopant concentration, 3.1%, the overpotential is calculated to be 1.0 V. The GGA and meta-GGA functionals give a lower estimate by as much as 0.4 V. When the dopant concentration is doubled, the overpotential calculated with hybrid functionals decreases, while it increases in GGA functional calculations. The opposite trends result from different potential-determining steps, the *OOH species being of central importance in the hybrid functional calculations, while the reduction of *O determines the overpotential obtained in GGA and meta-GGA calculations. The results presented here are mainly based on calculations of periodic representations of the system, but a comparison is also made with molecular flake models that are found to give erratic results due to finite size effects and geometric distortions during energy minimization. The presence of the electrolyte has not been taken into account explicitly in the calculations presented here but is estimated to be important for definitive calculations of the overpotential.

Comparison of the accuracy of DFT methods for reactions with relevance to nitrogenase

We have studied the accuracy of 16 different density functional theory methods to reproduce experimental data for bond lengths, angles, vibrational frequencies, as well as enthalpies and entropies for the binding of N2, H2, CO and hydride ions to various transition-metal complexes (with Fe, Ni, Cr, Mo and W) with relation to nitrogenase. We show that generalized gradient approximation functionals give better structure-related parameters, whereas hybrid functionals often give better energies. However, the BLYP and B97D functionals seem to give reasonably accurate results for both types of properties. Geometries and entropies are converged with split-valence basis sets, but energies and vibrational frequencies (and therefore also thermal corrections) in general require a basis set of triple-zeta quality. Dispersion corrections are important to obtain accurate energies (contributing by up to 57 kJ mol−1), as well as structures.

General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study.

We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Spin-orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories.

We revise formal and numerical aspects of collinear and non-collinear density functional theories in the context of a two-component self-consistent treatment of spin-orbit coupling. Theoretical and numerical analyses of the non-collinear approaches confirm their ability to yield the proper collinear limit and provide rotational invariance of the total energy for functionals in the local-density or generalized-gradient approximations (GGAs). Calculations on simple molecules corroborate the formal considerations and highlight the importance of an effective screening algorithm to provide the sufficient level of numerical stability required for a rotationally invariant implementation of non-collinear GGA functionals. The illustrative calculations provide a first numerical comparison of both previously proposed non-collinear formulations for GGA functionals. The proposed screening procedure allows us to effectively deal with points of small magnetization, which would otherwise be problematic for the evaluation of the exchange-correlation energy and/or potential for non-collinear GGA functionals. Both previously suggested formulations for the non-collinear GGA are confirmed to be adequate for total energy calculations, provided that the screening is achieved on a sufficiently fine grid. All methods are implemented in the Crystal program.