Standard Density Functional Theory Research Articles

Single-particle-exact density functional theory

We introduce ‘single-particle-exact density functional theory’ (1pEx-DFT), a novel density functional approach that represents all single-particle contributions to the energy with exact functionals. Here, we parameterize interaction energy functionals by utilizing two new schemes for constructing density matrices from ‘participation numbers’ of the single-particle states of quantum many-body systems. These participation numbers play the role of the variational variables akin to the particle densities in standard orbital-free density functional theory. We minimize the total energies with the help of evolutionary algorithms and obtain ground-state energies that are typically accurate at the one-percent level for our proof-of-principle simulations that comprise interacting Fermi gases as well as the electronic structure of atoms and ions, with and without relativistic corrections. We thereby illustrate the ingredients and practical features of 1pEx-DFT and reveal its potential of becoming an accurate, scalable, and transferable technology for simulating mesoscopic quantum many-body systems.

What can lattice DFT teach us about real-space DFT?

In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density-density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn-Sham (KS) levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry.

Spherical densities and potentials in exactly solvable model molecules.

A recently initiated variant of density functional theory utilizes a set of spherically symmetric densities instead of the density. The exact functionals are unknown in the new theory akin to the standard density functional theory. In order to test approximate functionals exactly solvable models are introduced. A harmonic molecular ion, the analogue to the hydrogen molecule ion and a harmonic two-electron molecule showing analogy to the hydrogen molecule are proposed. It has been found that the wave function and the density can be given analytically. The exact spherical densities and the effective potentials of the Euler equations also have analytical form. It has been shown that the models can be easily extended to several "nuclei."

Structural and electronic properties of Ta2O5 with one formula unit

Based on particle swarm optimization (PSO) algorithm and density functional theory (DFT) calculations, we identify a stable triclinic crystal structure of Ta2O5 (named as γ1-Ta2O5) at atmospheric pressure whose unit cell contains one formula unit (Z = 1). Comparison with the Z = 1 Ta2O5 structures from the Materials Project [APL Mater. 1, 011,002 (2013)] reveals that γ1-Ta2O5 is energetically the most stable among the Z = 1 Ta2O5 phases, and is the second most stable among all the Ta2O5 phases. Characterization of γ1-Ta2O5 is carried out by analyzing the X-ray powder diffraction patterns, the elastic, vibrational, thermal and electronic properties. The electronic structures of γ1-Ta2O5 are calculated using standard DFT as well as many-body perturbation theory within the GW approximation. The results indicate that γ1-Ta2O5 is a wide band gap semiconductor with an indirect gap of ∼ 3.361 eV.

A Quantum-Chemical Bonding Database for Solid-State Materials

An in-depth insight into the chemistry and nature of the individual chemical bonds is essential for understanding materials. Bonding analysis is thus expected to provide important features for large-scale data analysis and machine learning of material properties. Such chemical bonding information can be computed using the LOBSTER software package, which post-processes modern density functional theory data by projecting the plane wave-based wave functions onto an atomic orbital basis. With the help of a fully automatic workflow, the VASP and LOBSTER software packages are used to generate the data. We then perform bonding analyses on 1520 compounds (insulators and semiconductors) and provide the results as a database. The projected densities of states and bonding indicators are benchmarked on standard density-functional theory computations and available heuristics, respectively. Lastly, we illustrate the predictive power of bonding descriptors by constructing a machine learning model for phononic properties, which shows an increase in prediction accuracies by 27% (mean absolute errors) compared to a benchmark model differing only by not relying on any quantum-chemical bonding features.

Preparation of low molecular weight chondroitin sulfate from different sources by H2O2/ascorbic acid degradation and its degradation mechanism

Low molecular weight chondroitin sulfate (LMCS) has attention for enhanced bioavailability and bioactivity compared to native CS. We optimized H2O2/ ascorbic acid (Vc) degradation conditions to prepare LMCS from chicken, bovine, and shark cartilages. Degradation kinetics models and chemical composition data of LMCS showed the GlcA residues of chondroitin-4-sulfate (CSA) may be preferentially attacked. Nuclear magnetic resonance (NMR) spectroscopy and high-performance liquid chromatography-electrospray mass spectrometry (HPLC-MS) indicated that the CH of GlcA in CS was broken through a hydrogen abstraction reaction to break the β-(1 → 3) bond and form the hexendioic acid product. Standard density functional theory (DFT) calculations indicated that the energy required for the hydrogen abstraction from the C1-H bond in GlcA was lower than that of GalNAc. Molecular dynamics (MD) showed that CSA was more likely to interact with hydroxyl radicals (·OH) than non-sulfated chondroitin (CSO) and chondroitin-6-sulfate (CSC). These results provide guidance for producing LMCS.

PCS/Bonds and PCS0: Pick your molecule and get its accurate structure and ground state rotational constants at DFT cost.

An unsupervised computational protocol is proposed with the aim of obtaining accurate structures of large molecules in the gas phase at the cost of standard density functional theory (DFT) computations. The whole workflow is fully automated and provides optimized equilibrium geometries and ground state rotational constants to be directly compared with experiments. The results for a panel of molecules of biological or medicinal interest show that the accuracy of the results delivered by the new tool at the cost of a single DFT geometry optimization is close to that delivered by state-of-the-art composite wavefunction methods for small semi-rigid molecules.

The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just one-body particle density. In this Part II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some nonstandard alternatives. For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, nondifferentiability of the density functional can be mitigated through Moreau-Yosida regularization. Interesting insights can be drawn from both Maxwell-Schrödinger DFT and quantum-electrodynamic DFT, which are also discussed here.

Electronic behavior of Ag-doped YBa2Cu3O7-δ using Hubbard-U correction method

The ability to accurately describe the electronic properties in the highly correlated materials YBa2-xAgxCu3O7-δ was queried. Previous calculations revealed that the electronic bandgap was estimated much lower than the established experimental value when standard density functional theory, DFT was used in the computation of pure YBa2Cu3O7-δ. The electronic properties of Ag-doped at Ba-site samples such as the bandgap, total and partial density of states, electron density, and Mulliken population, were computationally calculated using DFT with the Hubbard-U correction method, DFT+U and compared to the pure samples. The calculation was conducted using CASTEP code in Material Studio software applying both LDA and range of GGA exchange-correlation functionals. 2 × 2 × 1 supercell symmetry was applied to enlarge the single cell crystal structure to able the dopant concentration, x = 0.250 at the Ba-site. The calculated bandgap of pure YBa2Cu3O7-δ (Eg = 3.67 eV) shows 8.25% difference to the referred theoretical value using the GGA-PBE+U functional. Upon Ag-dopant, the bandgap was calculated to be Eg = 3.85 eV. The energy of the Ba 6p orbital on the valence band has shifted from − 10.49 eV to − 10.67 eV, away from the Fermi energy level, and the density of state has increased significantly by + 57.52%. The Ag dopant enhanced the electron density of Cu and O atoms along the CuO chain and CuO2 plane. The study enables the prediction of impurity dopant concentration prior to experimental work, hence promoting green research.

PBE-GGA predicts the B8↔B2 phase boundary of FeO at Earth’s core conditions

FeO is a crucial component of the Earth's core, and its thermodynamic properties are essential to developing more accurate core models. It is also a notorious correlated insulator in the NaCl-type (B1) phase at ambient conditions. It undergoes two polymorphic transitions at 300 K before it becomes metallic in the NiAs-type (B8) structure at ~100 GPa. Although its phase diagram is not fully mapped, it is well established that the B8 phase transforms to the CsCl-type (B2) phase at core pressures and temperatures. Here, we report a successful ab initio calculation of the B8↔B2 phase boundary in FeO at Earth's core pressures. We show that fully anharmonic free energies computed with the Perdew-Burke-Ernzerhof-generalized gradient approximation coupled with thermal electronic excitations reproduce the experimental phase boundary within uncertainties at P > 255 GPa, including the largely negative Clapeyron slope of -52 MPa/K. This study validates the applicability of a standard density functional theory functional to FeO under Earth's core conditions and demonstrates the theoretical framework that enables complex predictive studies of this region.

Unraveling effects of electron correlation in two-dimensional FenGeTe2 (n = 3, 4, 5) by dynamical mean field theory

The FenGeTe2 systems are recently discovered two-dimensional van-der-Waals materials, exhibiting magnetism at room temperature. The sub-systems belonging to FenGeTe2 class are special because they show site-dependent magnetic behavior. We focus on the critical evaluation of magnetic properties and electron correlation effects in FenGeTe2 (n = 3, 4, 5) (FGT) systems performing first-principles calculations. Three different ab initio approaches have been used primarily, viz., (i) standard density functional theory (GGA), (ii) incorporating static electron correlation (GGA + U) and (iii) inclusion of dynamic electron correlation effect (GGA + DMFT). Our results show that GGA + DMFT is the more accurate technique to correctly reproduce the magnetic interactions, experimentally observed transition temperatures and electronic properties. The inaccurate values of magnetic moments, exchange interactions obtained from GGA + U make this method inapplicable for the FGT family. Correct determination of magnetic properties for this class of materials is important since they are promising candidates for spin transport and spintronic applications at room temperature.

Statistical analysis of the performance of a variety of first-principles schemes for accurate prediction of binary semiconductor band gaps.

Standard density functional theory (DFT) approximations tend to strongly underestimate band gaps, while the more accurate GW and hybrid functionals are much more computationally demanding and unsuitable for high-throughput screening. In this work, we have performed an extensive benchmark of several approximations with different computational complexity [G0W0@PBEsol, HSE06, PBEsol, modified Becke-Johnson potential (mBJ), DFT-1/2, and ACBN0] to evaluate and compare their performance in predicting the bandgap of semiconductors. The benchmark is based on 114 binary semiconductors of different compositions and crystal structures, for about half of which experimental band gaps are known. Surprisingly, we find that, compared with G0W0@PBEsol, which exhibits a noticeable underestimation of the band gaps by about 14%, the much computationally cheaper pseudohybrid ACBN0 functional shows a competitive performance in reproducing the experimental data. The mBJ functional also performs well relative to the experiment, even slightly better than G0W0@PBEsol in terms of mean absolute (percentage) error. The HSE06 and DFT-1/2 schemes perform overall worse than ACBN0 and mBJ schemes but much better than PBEsol. Comparing the calculated band gaps on the whole dataset (including the samples with no experimental bandgap), we find that HSE06 and mBJ have excellent agreement with respect to the reference G0W0@PBEsol band gaps. The linear and monotonic correlations between the selected theoretical schemes and experiment are analyzed in terms of the Pearson and Kendall rank coefficients. Our findings strongly suggest the ACBN0 and mBJ methods as very efficient replacements for the costly G0W0 scheme in high-throughput screening of the semiconductor band gaps.

Transport properties in liquids from first-principles: The case of liquid water and liquid argon.

Shear and bulk viscosities of liquid water and argon are evaluated from first-principles in the density functional theory (DFT) framework, by performing molecular dynamics simulations in the NVE ensemble and using the Kubo-Greenwood equilibrium approach. The standard DFT functional is corrected in such a way to allow for a reasonable description of van der Waals effects. For liquid argon, the thermal conductivity has been also calculated. Concerning liquid water, to our knowledge, this is the first estimate of the bulk viscosity and of the shear-viscosity/bulk-viscosity ratio from first-principles. By analyzing our results, we can conclude that our first-principles simulations, performed at a nominal average temperature of 366 to guarantee that the systems are liquid-like, actually describe the basic dynamical properties of liquid water at about 330K. In comparison with liquid water, the normal, monatomic liquid Ar is characterized by a much smaller bulk-viscosity/shear-viscosity ratio (close to unity) and this feature is well reproduced by our first-principles approach, which predicts a value of the ratio in better agreement with experimental reference data than that obtained using the empirical Lennard-Jones potential. The computed thermal conductivity of liquid argon is also in good agreement with the experimental value.

The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.

Comparative study of force-based classical density functional theory.

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.

Nuclear quantum effects on zeolite proton hopping kinetics explored with machine learning potentials and path integral molecular dynamics

Proton hopping is a key reactive process within zeolite catalysis. However, the accurate determination of its kinetics poses major challenges both for theoreticians and experimentalists. Nuclear quantum effects (NQEs) are known to influence the structure and dynamics of protons, but their rigorous inclusion through the path integral molecular dynamics (PIMD) formalism was so far beyond reach for zeolite catalyzed processes due to the excessive computational cost of evaluating all forces and energies at the Density Functional Theory (DFT) level. Herein, we overcome this limitation by training first a reactive machine learning potential (MLP) that can reproduce with high fidelity the DFT potential energy surface of proton hopping around the first Al coordination sphere in the H-CHA zeolite. The MLP offers an immense computational speedup, enabling us to derive accurate reaction kinetics beyond standard transition state theory for the proton hopping reaction. Overall, more than 0.6 μs of simulation time was needed, which is far beyond reach of any standard DFT approach. NQEs are found to significantly impact the proton hopping kinetics up to ~473 K. Moreover, PIMD simulations with deuterium can be performed without any additional training to compute kinetic isotope effects over a broad range of temperatures.

Effects of dispersion corrections on the theoretical description of bulk metals

The addition of a London dispersion correction to standard Kohn-Sham density-functional theory is essential for an accurate description of noncovalent interactions. While several dispersion-corrected density functionals (DC-DFs) have shown excellent performance for hard solids at ambient conditions, their transferability to metallic systems at ambient conditions or under isotropic compression has not been systematically examined. In this study, we assess the ability of selected DC-DFs to describe the equations of state (EOSs) of selected elemental metals and intermetallic compounds up to several gigapascals of pressure. EOS-derived properties, such as the unit-cell volume, the bulk modulus, and its pressure derivative, were then evaluated with and without thermal effects and the results compared with experimental reference data. We also assess the ability of the DC-DFs to predict the phase-transition pressures for a set of intermetallic compounds. The results of this study establish that London dispersion physics, and even dispersion contributions from the core electrons, is important in the description of bulk metals.

Efficient implementation of time-dependent auxiliary density functional theory.

The random phase approximation of time-dependent auxiliary density functional theory (TDADFT) is rederived from auxiliary density perturbation theory. Our exhaustive validation of TDADFT reveals an upshift of the excitation energies by ∼0.1eV with respect to standard time-dependent density functional theory. For the computationally efficient implementation of TDADFT, floating point operation optimized three-center electron repulsion integral recurrence relations and their double asymptotic expansions are implemented into the Davidson solver. The computational efficiency of TDADFT is benchmarked with four sets of molecules comprising alkanes, fullerenes, DNA fragments, and zeolites. The results show that TDADFT has a computational scaling between 1.3 and 1.9 with respect to the number of basis functions, which is lower than the scaling of standard time-dependent density functional theory. Due to its computational simplifications, TDADFT is particularly well suited for Born-Oppenheimer molecular dynamics simulations. As illustrative examples, we present the temperature effects on the gas-phase absorption spectra of benzene, naphthalene, and anthracene.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set.

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Ab-initio calculations of temperature dependent electronic structures of inorganic halide perovskite materials.

Despite wide interest in halide perovskite materials, it is still challenging to accurately calculate their electronic structure and its temperature dependence. In this work, we present ab-initio calculations of the temperature dependence of the electronic structure of CsPbX3 materials (X = Cl, Br or I) in the cubic form and of the zero temperature electronic structure of the orthorhombic phase of these materials. Phonon-induced temperature dependent band energy renormalization was calculated within the framework of Allen-Heine-Cardona theory, where we exploited the self-consistent procedure to determine both the energy level shifts and their broadenings. The phonon spectrum of the materials was obtained using the self-consistent phonon method since standard density functional perturbation theory calculations in harmonic approximation yield phonon modes with imaginary frequencies due to the fact that the cubic structure is not stable at zero temperature. Our results suggest that low energy phonon modes mostly contribute to phonon-induced band energy renormalization. The calculated values of the band gaps at lowest temperature where the material exhibits a cubic structure are in good agreement with experimental results from the literature. The same is the case for the slope of the temperature dependence of the band gap for the CsPbI3 material where reliable experimental data are available in the literature. We also found that phonon-induced temperature dependence of the band gap is most pronounced for the conduction band minimum and valence band maximum, while other bands exhibit a weaker dependence.