All-electron Density Functional Theory Research Articles

Improving the accuracy of ion implantation simulations through the use of DFT-MD methodology

Ion implantation is a crucial process in the fabrication of semiconductor devices, but accurately predicting the impurities distribution in the low energy range is still challenging. The widely used method to simulate this process is molecular dynamics with recoil interaction approximation (RIA-MD), which uses the translational method to replace traditional periodic boundary conditions. However, this approach leads to accuracy loss due to the simplification of atom-atom interactions and bulk crystal properties. Our study presents a method to simulate the impurity distribution after ion implantation at low energy, which combines all-electron density-functional theory (DFT) and full molecular dynamics (MD). Unlike the RIA-MD method, DFT-MD method calculates the movements of all energetic ions and simulates the whole bulk crystal properties. Thus, it provides a more realistic representation of atom-atom interactions. We used not only the experimental values reported by references but also the experimental value measured by actual ion implantation technology samples. This enabled us to make a more accurate comparison between the DFT-MD and RIA-MD methods. Specifically, the dopant profiles and amorphous thickness obtained using the DFT-MD method were found to be in good agreement with experimental data. These findings demonstrate the effectiveness of our method and highlight its potential to advance the field of ion implantation simulation. Moreover, our method has the potential to be useful in developing atomic-scale technology computer-aided design (TCAD) tools, as well as in other fields of research that require accurate ion implantation simulations.

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.

OpenCL-accelerated first-principles calculations of all-electron quantum perturbations on HPC resources.

We have proposed, for the first time, an OpenCL implementation for the all-electron density-functional perturbation theory (DFPT) calculations in FHI-aims, which can effectively compute all its time-consuming simulation stages, i.e., the real-space integration of the response density, the Poisson solver for the calculation of the electrostatic potential, and the response Hamiltonian matrix, by utilizing various heterogeneous accelerators. Furthermore, to fully exploit the massively parallel computing capabilities, we have performed a series of general-purpose graphics processing unit (GPGPU)-targeted optimizations that significantly improved the execution efficiency by reducing register requirements, branch divergence, and memory transactions. Evaluations on the Sugon supercomputer have shown that notable speedups can be achieved across various materials.

Electronic Structure and Core Spectroscopy of Scandium Fluoride Polymorphs.

Microscopic knowledge of the structural, energetic, and electronic properties of scandium fluoride is still incomplete despite the relevance of this material as an intermediate for the manufacturing of Al-Sc alloys. In a work based on first-principles calculations and X-ray spectroscopy, we assess the stability and electronic structure of six computationally predicted ScF3 polymorphs, two of which correspond to experimentally resolved single-crystal phases. In the theoretical analysis based on density functional theory (DFT), we identify similarities among the polymorphs based on their formation energies, charge-density distribution, and electronic properties (band gaps and density of states). We find striking analogies between the results obtained for the low- and high-temperature phases of the material, indirectly confirming that the transition occurring between them mainly consists of a rigid rotation of the lattice. With this knowledge, we examine the X-ray absorption spectra from the Sc and F K-edge contrasting first-principles results obtained from the solution of the Bethe-Salpeter equation on top of all-electron DFT with high-energy-resolution fluorescence detection measurements. Analysis of the computational results sheds light on the electronic origin of the absorption maxima and provides information on the prominent excitonic effects that characterize all spectra. A comparison with measurements confirms that the sample is mainly composed of the high- and low-temperature polymorphs of ScF3. However, some fine details in the experimental results suggest that the probed powder sample may contain defects and/or residual traces of metastable polymorphs.

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

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.

Revisiting fundamental properties of TiO2 nanoclusters as condensation seeds in astrophysical environments

Context. The formation of inorganic cloud particles takes place in several atmospheric environments, including those of warm, hot, rocky, and gaseous exoplanets, brown dwarfs, and asymptotic giant branch stars. The cloud particle formation needs to be triggered by the in situ formation of condensation seeds since it cannot be reasonably assumed that such condensation seeds preexist in these chemically complex gas-phase environments. Aims. We aim to develop a method for calculating the thermochemical properties of clusters as key inputs for modelling the formation of condensation nuclei in gases of changing chemical composition. TiO2 is used as benchmark species for cluster sizes N = 1–15. Methods. We created a total of 90000 candidate (TiO2)N geometries for cluster sizes N = 3−15. We employed a hierarchical optimisation approach, consisting of a force-field description, density-functional based tight-binding, and all-electron density-functional theory (DFT) to obtain accurate zero-point energies and thermochemical properties for the clusters. Results. In 129 combinations of functionals and basis sets, we find that B3LYP/cc-pVTZ, including Grimme’s empirical dispersion, performs most accurately with respect to experimentally derived thermochemical properties of the TiO2 molecule. We present a hitherto unreported global minimum candidate for size N = 13. The DFT-derived thermochemical cluster data are used to evaluate the nucleation rates for a given temperature-pressure profile of a model hot-Jupiter atmosphere. We find that with the updated and refined cluster data, nucleation becomes unfeasible at slightly lower temperatures, raising the lower boundary for seed formation in the atmosphere. Conclusions. The approach presented in this paper allows finding stable isomers for small (TiO2)N clusters. The choice of the functional and basis set for the all-electron DFT calculations has a measurable impact on the resulting surface tension and nucleation rate, and the updated thermochemical data are recommended for future considerations.

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.

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.

WloopPHI: A tool for ab initio characterization of Weyl semimetals

WloopPHI is a Python code that expands the features of WIEN2k, a full-potential all-electron density functional theory package, by the characterization of Weyl semimetals. It enables the calculation of the chirality (or “monopole charge”) associated with Weyl nodes and nodal lines. The theoretical methodology for the calculation of the chirality is based on an extended Wilson loop method and a Berry phase approach. We validate the code using TaAs, which is a well-characterized Weyl semimetal, both theoretically and experimentally. Afterwards, we applied the method to the characterization of YRh6Ge4 and found two sets of Weyl points (ca. 0.2 eV below the Fermi energy) together with a topological nodal line (protected by mirror symmetry) crossing the Fermi energy and mapped their chiralities.

Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

We present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham DFT calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block-diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit-cells and supercells. The benchmark studies show a staggering $130\times$ speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the LAPW+lo basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of $\sim$10,000 electrons.

Machine-learning interatomic potential for W–Mo alloys

In this work, we develop a machine-learning interatomic potential for W x Mo1−x random alloys. The potential is trained using the Gaussian approximation potential framework and density functional theory data produced by the Vienna ab initio simulation package. The potential focuses on properties such as elastic properties, melting, and point defects for the whole range of W x Mo1−x compositions. Moreover, we use all-electron density functional theory data to fit an adjusted Ziegler–Biersack–Littmarck potential for the short-range repulsive interaction. We use the potential to investigate the effect of alloying on the threshold displacement energies and find a significant dependence on the local chemical environment and element of the primary recoiling atom.

Accurate frozen core approximation for all-electron density-functional theory.

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr3 with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

Treecode-accelerated Green iteration for Kohn-Sham density functional theory

We present a real-space computational method called treecode-accelerated Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory. TAGI is based on a reformulation of the Kohn-Sham equations in which the eigenvalue problem in differential form is converted into a fixed-point problem in integral form by convolution with the modified Helmholtz Green's function. In each self-consistent field (SCF) iteration, the fixed-points are computed by Green Iteration, where the discrete convolution sums are efficiently evaluated by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in TAGI include a-priori adaptive mesh refinement, Fejér quadrature, singularity subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate convergence of the SCF and Green Iterations. Ground state energy computations of several atoms (Li, Be, O) and small molecules (H2, CO, C6H6) demonstrate TAGI's ability to efficiently achieve chemical accuracy.

Orthogonalized Enriched Finite Elements - A Robust, Accurate and Efficient Basis for All-Electron Density Functional Theory Calculations

Orthogonalized Enriched Finite Elements - A Robust, Accurate and Efficient Basis for All-Electron Density Functional Theory Calculations