All-electron Density Research Articles

The Stability of TiO2 Phases Studied Using r2SCAN in the Hubbard-Corrected Density Functional Theory

Titanium dioxide is a quintessential transition metal oxide with many technologically important applications. With its richness in phases, it has also been a testing ground for numerous theoretical studies including density functional theory. We investigated several phases of TiO2 using the all-electron density functional theory with a regularized–restored strongly constrained appropriately normed (r2SCAN) exchange–correlation functional, a popular choice of meta-generalized gradient approximation (meta-GGA). Specifically, the equilibrium lattice parameters were more accurate than those predicted by GGA and agreed well overall with the experimental data. With increasing pressure, the order of stability was determined as anatase < columbite < rutile < baddeleyite < orthorhombic I < cotunnite, as in the calculations using GGA. Including the Hubbard correction term, the correct ordering between rutile, anatase, and columbite can be achieved, consistent with experimental observations. The necessary U value using r2SCAN is much smaller than that using GGA+U. In addition, the Hubbard correction method using r2SCAN is substantially less sensitive to the size of the local projection space compared to the GGA+U study reported recently. We attribute these significantly improved results to the reduced self-interaction error in the r2SCAN functional.

Magnetically Induced Current-Density Susceptibility of Circum[n]coronenes.

We have calculated the magnetically induced current density (MICD) susceptibility at the all-electron density functional theory level for a series of coronoid molecules of increasing size and compared the MICD susceptibilities with those calculated using the pseudo-π (PP) model. The molecules sustain global diatropic magnetically induced ring currents (MIRCs), whereas paratropic MICD vortices mainly appear inside the benzene rings. The computationally cheaper PP calculations were also employed on circum[n]coronene molecules showing that the MICD pattern continues to alternate for odd and even n when increasing the size of the molecule. For even n, there is a local paratropic MIRC in the middle of the molecule, whereas when n is odd, the PP models do not sustain any paratropic MIRC pathways. The global diatropic MIRC flowing mainly along the outer edge of the molecule increases with increasing n suggesting that there is no size limit of the MIRC of circum[n]coronene molecules. There are seven weakly aromatic Clar rings in the middle of the PP model of the circum[n]coronene molecules with odd n, whereas circum[n]coronene molecules with even n have no Clar rings. There are no Clar rings in the outer part of the circum[n]coronene molecules with n > 1.

Exact nuclear cusps in all-electron orbital-free density functional theory

Exact nuclear cusps in all-electron orbital-free density functional theory

Periodic Bonding Behaviors of Actinide Atoms (An = Th-Cm) with Negatively Curved Nanographene.

The nanographene with negative curvature has been extensively studied due to its interesting properties and potential applications. In the present work, we have performed all-electron scalar relativistic density functional theory (DFT) calculations to understand the periodic interaction mechanisms of actinide atoms (An = Th, Cm) with the TB8C nanographene. The encapsulated complexes (An@TB8C) were formed due to the octagonal vacancy in the TB8C nanographene. TB8C shows fairly high affinity toward An atoms, especially for Th and Pa. AIMD simulations further confirmed the effective trapping of An atom with TB8C. The partial covalent characters of An-C bonds in An@TB8C were revealed through various bond analysis methods. The 6d electrons of An play an important role in the participation of chemical bonds. The delocalization index (DI) is proposed as a useful descriptor in the study of bond strength involving the actinides. Electronic absorption spectra were simulated for further identification in the experiments. The current work has expanded the potential molecular properties and applications of nanographene.

Towards chemical accuracy using a multi-mesh adaptive finite element method in all-electron density functional theory

Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn–Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn–Sham wavefunctions but also the Hartree potential, should be approximated accurately. Under the adaptive finite element framework, this can be implemented by constructing the a posteriori error indicator based on approximations of the aforementioned two quantities. However, this way results in a large amount of computational cost. To reduce the computational cost, we propose a novel solver for the Kohn–Sham equation by using the multi-mesh adaptive technique, in which the Kohn–Sham equation and the Poisson equation are solved in two different meshes on the same computational domain, respectively. With the proposed method, chemical accuracy can be achieved with less computational consumption compared with the adaptive method on a single mesh, as demonstrated in a number of numerical experiments.

Electric field gradients at the nuclei from all-electron four-component relativistic density functional theory using Gaussian-type orbitals

Electric field gradients at the nuclei from all-electron four-component relativistic density functional theory using Gaussian-type orbitals

Correlations of the Electronic, Elastic and Thermo-Electric Properties of Alpha Copper Sulphide and Selenide

A full potential all-electron density functional method within generalized gradient approximation is used herein to investigate correlations of the electronic, elastic and thermo-electric transport properties of cubic copper sulphide and copper selenide. The electronic band structure and density of states suggest a metallic behaviour with a zero-energy band gap for both materials. Elastic property calculations suggest stiff materials, with bulk to shear modulus ratios of 0.35 and 0.44 for Cu2S and Cu2Se, respectively. Thermo-electric transport properties were estimated using the Boltzmann transport approach. The Seebeck coefficient, electrical conductivity, thermal conductivity and power factor all suggest a potential p-type conductivity for α-Cu2S and n-type conductivity for α-Cu2Se.

An efficient zero-order evolutionary method for solving the orbital-free density functional theory problem by direct minimization.

A differential evolution (DE) global optimization method for all-electron orbital-free density functional theory (OF-DFT) is presented. This optimization method does not need information about function derivatives to find extreme solutions. Results for a series of known orbital-free energy functionals are presented. Ground state energies of atoms (H to Ar) are obtained by direct minimization of the energy functional without using either Lagrange multipliers or damping procedures for reaching convergence. Our results are in agreement with previous OF-DFT calculations obtained using the standard Newton-Raphson and trust region methods. Being a zero-order method, the DE method can be applied to optimization problems dealing with non-differentiable functionals or functionals with non-closed forms.

Software implementation for calculating Chern and [formula omitted] topological invariants of crystalline solids with WIEN2k all-electron density functional package

We present two modules that expand functionalities of the all-electron full-potential density functional theory package WIEN2k for computation of the Chern and Z2 topological invariants. Characterization of topological properties relies on two methods: computing an evolution of hybrid Wannier charge centers for Z2 topological insulators (construction of maximally localized Wannier functions is not needed) and computing the Berry phase for a multitude of Wilson loops that discretize a 2D Brillouin zone for Chern insulators as well as for mapping the Berry curvature. The implementation is validated by testing on well-known materials that feature topologically non-trivial electronic states.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis.

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

Structure and charge analysis of a cyclic aluminium hydride: cyclo-1,5-bis-μ-dimethylamino-3,7-di-μ-hydrido-2,4,6,8-tetrakis(dimethylaluminium).

The title compound, [Al4(CH3)8(C2H7N)2H2], crystallizes as eight-membered rings with -(CH3)2Al-(CH3)2N-(CH3)2Al- moieties connected by single hydride bridges. In the X-ray structure, the ring has a chair conformation, with the hydride H atoms being close to the plane through the four Al atoms. An optimized structure was also calculated by all-electron density functional theory (DFT) methods, which agrees with the X-ray structure but gives a somewhat different geometry for the hydride bridge. Charges on the individual atoms were determined by valence shell occupancy refinements using MoPro and also by DFT calculations analyzed by several different methods. All methods agree in assigning a positive charge to the Al atoms, negative charges to the C, N, and hydride H atoms, and small positive charges to the methyl H atoms.

Deciphering the electrochemical sensing capability of novel Ga12As12 nanocluster towards chemical warfare phosgene gas: insights from DFT.

The applications of 3D inorganic nanomaterials in environmental and agriculture monitoring have been exploited continuously; however, the utilization of semiconductor nanoclusters, especially for detecting warfare agents, has not been fully investigated yet. To fill this gap, the molecular modelling of novel inorganic semiconductor nanocluster Ga12As12 as a sensor for phosgene gas (highly toxic for living things and the environment) is accomplished employing benchmark DFT and TD-DFT investigations. Computational tools have been applied to explore different adsorption sites and the potential sensing capability of the Ga12As12 nanoclusters. The calculated adsorption energy (-21.34 ± 2.7 kcal mol-1) for ten selected complexes, namely, Pgn-Cl@4m-ring (MS1), Pgn-Cl@6m-ring (MS2), Pgn-Cl@XY66 (MS3), Pgn-O@4m-ring (MS4), Pgn-O@XY66 (MS5), Pgn-O@XY64 (MS6), Pgn-O@Y (MS7), Pgn-planar@Y (MS8), Pgn-planar@X (MS9), and Pgn-planar@4m-ring (MS10), manifest the remarkable and excessive adsorption response of the studied nanoclusters. The explored molecular electronic properties, such as interaction distance (3.05 ± 0.5 Å), energy gap (∼2.17 eV), softness (∼0.46 eV), hardness (1.10 ± 0.01 eV), electrophilicity index (10.27 ± 0.45 eV), electrical conductivity (∼1.98 × 109), and recovery time (∼3 × 10-12 s-1) values, ascertain the elevated reactivity and an imperishable sensitivity of the Ga12As12 nanocluster, particularly for its complex MS8. QTAIM analysis exhibits the presence of a strong electrostatic bond (positive ∇2ρ(r) values), electron delocalization (ELF < 0.5), and a strong chemical bond (because of high all-electron density values). In addition, NBO analysis explores the lone pair electron delocalization of phosgene to the nanocluster stabilized by intermolecular charge transfer (ICT) and different kinds of non-covalent interactions. Also, the green region existence expressed by NCI analysis (between the nanocluster and adsorbate) stipulate the energetic and dominant interactions. Furthermore, the UV-Vis, thermodynamic analysis, and density of state (DOS) demonstrate the maximum absorbance (562.11 nm) and least excitation energy (2.21 eV) by the complex MS8, the spontaneity of the interaction process, and the significant changes in HOMO and LUMO energies, respectively. Thus, the Ga12As12 nanocluster has proven to be a promising influential sensing material to monitor phosgene gas in the real world, and this study will emphasize the informative knowledge for experimental researchers to use Ga12As12 as a sensor for the warfare agent (phosgene).

Ionic forces and stress tensor in all-electron density functional theory calculations using an enriched finite-element basis

The enriched finite-element basis---wherein the finite-element basis is enriched with atom-centered numerical functions---has recently been shown to be a computationally efficient basis for systematically convergent all-electron density functional theory (DFT) ground-state calculations. In this work, we present the expressions to compute variationally consistent ionic forces and stress tensor for all-electron DFT calculations in the enriched finite-element basis. In particular, we extend the formulation of configurational forces [P. Motamarri and V. Gavini, Phys. Rev. B 97, 165132 (2018)] to the enriched finite-element basis and elucidate the additional contributions arising from the enrichment functions. We demonstrate the accuracy of the formulation by comparing the computed forces and stresses for various benchmark systems with those obtained from finite differencing the ground-state energy. Further, we also benchmark our calculations against the Gaussian basis for molecular systems and against the linearized augmented plane wave with local orbitals basis for periodic systems.

Photocatalytic Degradation of Rhodamine B Dye and Hydrogen Evolution by Hydrothermally Synthesized NaBH4-Spiked ZnS Nanostructures.

Metal sulphides, including zinc sulphide (ZnS), are semiconductor photocatalysts that have been investigated for the photocatalytic degradation of organic pollutants as well as their activity during the hydrogen evolution reaction and water splitting. However, devising ZnS photocatalysts with a high overall quantum efficiency has been a challenge due to the rapid recombination rates of charge carriers. Various strategies, including the control of size and morphology of ZnS nanoparticles, have been proposed to overcome these drawbacks. In this work, ZnS samples with different morphologies were prepared from zinc and sulphur powders via a facile hydrothermal method by varying the amount of sodium borohydride used as a reducing agent. The structural properties of the ZnS nanoparticles were analysed by X-ray diffraction (XRD), scanning electron microscopy (SEM), and X-ray photoelectron spectroscopy (XPS) techniques. All-electron hybrid density functional theory calculations were employed to elucidate the effect of sulphur and zinc vacancies occurring in the bulk as well as (220) surface on the overall electronic properties and absorption of ZnS. Considerable differences in the defect level positions were observed between the bulk and surface of ZnS while the adsorption of NaBH4 was found to be highly favourable but without any significant effect on the band gap of ZnS. The photocatalytic activity of ZnS was evaluated for the degradation of rhodamine B dye under UV irradiation and hydrogen generation from water. The ZnS nanoparticles photo-catalytically degraded Rhodamine B dye effectively, with the sample containing 0.01 mol NaBH4 being the most efficient. The samples also showed activity for hydrogen evolution, but with less H2 produced compared to when untreated samples of ZnS were used. These findings suggest that ZnS nanoparticles are effective photocatalysts for the degradation of rhodamine B dyes as well as the hydrogen evolution, but rapid recombination of charge carriers remains a factor that needs future optimization.

Modeling oxidised polypyrrole in the condensed phase with a novel force field

A novel model potential is developed for simulating oxidised oligopyrroles in condensed phases. The force field is a coarse grained model that represents the pyrrole monomers as planar rigid bodies with fixed charge and dipole moment and the chlorine dopants as point atomic charges. The analytic function contains 17 adjustable parameters that are initially fitted on a database of small structures calculated within all-electron density functional theory. A subsequent potential function refinement is pursued with a battery of condensed phase isothermal–isobaric Metropolis Monte Carlo in-silico simulations at ambient conditions with the goal of implementing a hybrid parametrization protocol enabling agreement with experimentally known thermodynamic properties of oxidised polypyrrole. The condensed system is composed of oligomers containing 12 monomers with a 1:3 dopant-to-monomer concentration. The final set of force field optimised parameters yields an equilibrium density of the condensed system at ambient conditions in excellent agreement with oxidised polypyrrole samples synthesised in wet-laboratories.

The strong interaction of actinyl ions with fullerenol driven by multiple hydrogen bonds.

The removal of actinides from radioactive wastewater is an important subject with the continuous application of nuclear energy. All-electron density functional theory (DFT) calculations were carried out to understand the adsorption behaviors of actinyl ions on C60(OH)24 fullerenol in this work. The outer-sphere (OS) bonding mode is more stable than the inner-sphere one because of the formation of multiple hydrogen bonds in the OS mode. The actinyl(VI) ions can be more efficiently absorbed by fullerenol than actinyl(V) ones. The bonding nature of actinyl ions with C60(OH)24 was revealed by various electron density topological analyses. Multiple hydrogen bonds formed in the OS complexes show moderate bond strength with partial covalent nature and are responsible for their high stability. IR spectra were fingerprinted to distinguish the interaction modes of actinyl ions with C60(OH)24.

Carbon-doped anatase titania nanoparticles: similarities and differences with respect to bulk and extended surface models.

C-Doping of titania nanoparticles is analyzed by using all-electron density functional theory-based calculations considering the (TiO2)84 nanoparticle as a realistic representative of nanoparticles in the scalable regime. Several sites are evaluated including substituting oxygen (CO) and titanium (CTi) sites as well as interstitial (Ci) situations. The formation energy of such a doped structure is studied as a function of the oxygen chemical potential (or oxygen partial pressure). Our calculations predict that low partial oxygen pressure favors the formation of C-doped (TiO2)84 NPs at oxygen and interstitial sites. For the former, the most stable situation is for O sites at the inner part of the nanoparticle. Interestingly, the substitution of O by C at facet sites requires formation energies as those reported in previous studies where the bulk anatase and surfaces models were considered. However, C-doping - at other low coordinated sites not presented in extended models - is even more favorable which shows the need to employ more realistic models for nanostructures involved in photocatalytic processes.

Flexible boundary layer using exchange for embedding theories. II. QM/MM dynamics of the hydrated electron.

The FlexiBLE embedding method introduced in Paper I [Z. Shen and W. J. Glover, J. Chem. Phys. 155, 224112 (2021)] is applied to explore the structure and dynamics of the aqueous solvated electron at an all-electron density functional theory Quantum Mechanics/Molecular Mechanics level. Compared to a one-electron mixed quantum/classical description, we find the dynamics of the many-electron model of the hydrated electron exhibits enhanced coupling to water OH stretch modes. Natural bond orbital analysis reveals this coupling is due to significant population of water OH σ* orbitals, reaching 20%. Based on this, we develop a minimal frontier orbital picture of the hydrated electron involving a cavity orbital and important coupling to 4-5 coordinating OH σ* orbitals. Implications for the interpretation of the spectroscopy of this interesting species are discussed.

Pressure induced structural, electronic and optical properties of wurtzite beryllium monoxide (w-BeO) from first-principle calculations

All-electron density functional calculations of structural, electronic and optical properties of wutrzite beryllium oxide (w-BeO) are carried out at different applied hydrostatic pressure. Calculated lattice constants decrease (a, c), while bulk modulus increases with increasing pressure. Direct fundamental band-gap (Eg) of w-BeO increases with increasing pressure and vice versa and the variation provides first and second order pressure coefficient of band-gap. The calculated volume deformation potential of band-gap of w-BeO is −11.5972 eV. Optical properties of w-BeO at zero and high pressures have been studied in terms of dielectric function ε(ω) and related ancillary optical parameters. Each optical parameter is marginally anisotropic. Calculated components of refractive index at each pressure signify uniaxial characteristics of the w-BeO. Calculated components of static dielectric constant, refractive index and reflectivity decreases, while critical point energy in the spectra of each component of ε2(ω), k(ω), σ(ω) and α(ω) increases with increasing pressure and vice versa. Calculated optical energy-gap (Eopt) of w-BeO increases like Eg with increasing pressure and vice versa. The transmission cutoff energy (ECutoff) is shifted towards the higher energy region with increasing pressure.

Learning Electron Densities in the Condensed Phase.

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centered auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that, using this formulation, the electron densities of metals, semiconductors, and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the nonorthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties, which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous data sets SALTED can predict electron densities with errors below 4%.