Pseudopotential Approximation Research Articles

Electronic phase transformations and energy gap variations in uniaxial and biaxial strained monolayer VS[formula omitted] TMDs: A comprehensive DFT and beyond-DFT study

In the rapidly evolving field of 2D materials, transition metal dichalcogenides (TMDs) have emerged as compelling candidates for electronic applications. This study investigates the electronic structure of the H-phase monolayer VS2 belonging to TMD family and the influence of strain on its band structure through Density Functional Theory (DFT). We employ two different pseudopotential approximations and a suite of computational methods including DFT+U, GAUPBE, G0W0, and self-GW to provide a nuanced understanding of its electronic band structure. A highlight of the study is its focus on how both uniaxial and biaxial strains, ranging from -5% to +5%, affect the electronic properties of the H-phase monolayer VS2. Our comprehensive analysis reveals that these tensile strains significantly widen the energy gap, with uniaxial strains having a more pronounced effect than their biaxial counterparts. Additionally, we identify an intriguing phase transition from a semiconducting to a metallic state under compressive strains, this transition is attributed to both symmetry breaking and bond length variation in the uniaxial case, the bond length in biaxial. These key findings not only enrich our understanding of the intricate electronic behavior of monolayer VS2 under different strains but also pave the way for the design of innovative electronic devices using strain engineering.

Composite ab initio vibrational spectroscopy and thermochemistry of low-valency lanthanide compounds: europium dihalides EuX2 (X = F, Cl, Br, I).

A unique diversity in chemical properties of lanthanide compounds making them very useful in various important applications stems not least from the existence of less common Ln oxidation states, in particular +2. However, the molecular properties of low-valency lanthanide compounds are not yet well studied even for the most stable divalent Ln-containing species, such as europium dihalides. In this paper, highly accurate molecular structures, vibrational spectra, and atomisation energies of the europium dihalides EuX2 (X = F, Cl, Br, I) are obtained at the complete basis set CCSD(T) level. All of the EuX2 species are calculated to be non-linear (C2v) exhibiting a regular increase in X-Eu-X bond angle on passing through the halogen series (F → Cl → Br → I), from 117° in EuF2 to 141° in EuI2, which is accompanied by a rapid decrease in the barriers to linearity, h = E(D∞h) - E(C2v), from 2180 cm-1 to 166 cm-1, respectively. The Eu-X bonds in EuX2 appear to be longer but energetically stronger than those in the respective monohalides EuX, whose properties are studied in this work at the same level of theory as EuX2. The performance of the Ln 4f-in-core pseudopotential (PP) approximation for EuX2 is assessed by comparing the Eu PP-based coupled-cluster (CC) calculations with all-electron CC benchmarks. Incorporating the Eu 4f electrons into the PP is shown to cause large errors: up to 10 deg. in X-Eu-X bond angles, 80% in barriers to linearity, and 0.05 Å in the Eu-X bond lengths, which proves the necessity of an explicit treatment of 4f electrons if high accuracy is the goal. The present results set a benchmark in the field of low-valency lanthanide chemistry, in particular for the calibration of DFT functionals.

Swirling flow of two immiscible fluids in a cylindrical container: Lattice Boltzmann and volume-of-fluid study

An experimental and numerical study of a multicomponent swirl flow of a liquid in a closed cylinder is carried out for various values of the relative cylinder elongation and the Reynolds number. The experimental technique for flow characteristics measurement is based on the PIV (particle image velocimetry) technique. To study the flow characteristics in detail, we simulated the problem numerically using the Palabos and Basilisk software open-source packages. The current implementation of the Palabos package uses the LBM (lattice Boltzmann method) approach, in which the collision integral is determined by the MRT (multiple-relaxation-time) approximation, and the intercomponent interaction is established according to the Shan–Chen pseudopotential approximation. The Basilisk package uses VOF (volume-of-fluid) approach to approximate the fluid interface. In this paper, for the first time, the data considering the emergence conditions for the zone of axial isolated recirculation in a multicomponent vortex flow were obtained at different viscosity ratios of two fluids. It is shown that with a decrease in the viscosities ratio, the recirculation zone existence curve shifts closer to that corresponding to the case of a one-component flow. In the course of numerical analysis, we found that both numerical implementations of this problem describe flow characteristics with high accuracy. Both methods recreate the recirculation zone on the cylinder axis observed experimentally. However, the velocity shift on the interface is observed only in the LBM approach.

Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants.

We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter.

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equationof state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50eV.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism.

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [Lehtola, S. Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [Lehtola, S.; Marques, M. A. L. J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find the BSTEs to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to 0.1 μEh when densities smaller than 10-11a0-3 are screened out.

Generalized relativistic small‐core pseudopotentials accounting for quantum electrodynamic effects: Construction and pilot applications

AbstractA simple procedure to incorporate one‐loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape‐consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbersn ≤ 3 for the two former elements andn ≤ 4 for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac–Coulomb–Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two‐valence‐electron atomic systems using the intermediate‐Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high‐accuracy molecular excited state calculations are discussed.

A full-potential and multiscale computational scheme for interactions between ultrafast intense laser pulses and condensed medium

We have presented a multiscale computational scheme for the simulation of interactions between ultrafast intense laser pulses and condensed medium. This approach solves the coupled time-dependent Kohn-Sham (TDKS) and Maxwell equations in real time and provides a unified description of microscopic electron dynamics and macroscopic light propagation from first principles and applicable to wide ultrafast phenomena. Especially, as the TDKS equation was solved within the framework of all-electron full-potential and the augmented plane wave with local orbitals basis sets were adopted, this approach overcomes the drawbacks of real space grids and pseudopotential approximations and works well for some extreme conditions that the information near the nucleus is important. We demonstrated the approach by calculating the microscopic electron dynamics of crystalline silicon (Si) excited with an intense laser pulse and the macroscopic propagation of a laser pulse in a ∼3.5 μm free standing Si film with the feedback of microscopic electron dynamics coupled together. We also verified the availability of this approach under extreme condition with hundreds TPa (1 TPa = 1012 Pa) pressure in a metallic solid neon, and reasonable results were obtained. Our approach provides a new paradigm for multiscale simulations of ultrafast phenomena that induced by intense laser pulses in condensed medium.

Impact of compositional disorder on electron migration in lutetium–yttrium oxyorthosilicate scintillator

A general description of the dynamics of nonequilibrium carriers in multicomponent activated scintillation materials with a compositional disorder of the crystalline matrix is developed and applied for studying the excitation transfer and timing properties of lutetium–yttrium oxyorthosilicate (LYSO). The energy structure, the density of states, and the effective potential of LSO and YSO crystals have been calculated by using the Quantum Espresso package. An analytical form of the potential fluctuations due to compositional disorder is suggested in the pseudopotential approximation. The spatial distribution of lutetium and yttrium cations in the LYSO crystal has been simulated by the Monte Carlo method using the thermodynamic approach for three qualitatively different cases of cation distribution: uniform, heterogeneous neighboring, and clustered. The impact of the compositional disorder on electron migration is found to be qualitatively different in four typical regions of electron energy. The density of localized states in LYSO calculated using the coherent potential approximation (CPA) and the quasiclassical approach is comparable to the density of secondary carriers expected in an ionization track and might have significant influence on the migration of thermalized carriers. The transport mean free path of nonlocalized electrons limited by elastic scattering on pseudopotential fluctuations is shown to be substantially longer than that due to longitudinal optical phonon emission in the low-energy region (calculated using CPA) and the high-energy region (calculated using the Born approximation). The scattering on pseudopotential fluctuations is important for intermediate-energy electrons due to a substantial influence of the core potential fluctuations on high-energy branches.

Першопринципні методи обчислення лінійного коефіцієнта термічного розширення квазібінарних евтектичних систем

To calculate the linear coefficient of thermal expansion (LCTE) and its temperature dependence, a combination of the method of a priori pseudopotential and quasi-harmonic approximation (author's methods) is used. After approximating the results obtained for metal-like materials (carbides, borides, silicides), the LCTE is presented in an analytical form. In the case of quasi-binary eutectic systems based on carbides, borides, silicides, to estimate the interaction energy of the elements of two components, the concept of a virtual crystal (with a virtual cell) along the line of contact of two components is introduced. A virtual cell is assigned a volume average between the volume of a unit cell of two components, taking into account their concentration ratio. The components that make up the eutectic retain their crystal structure, their LCTE can be estimated as for pure components. Without taking into account the influence of interphase interaction, the LCTE of the eutectic system is determined using the rule of mixtures based on the LCTE components, taking into account their volume fraction. Taking into account the influence of the interface on thermal expansion is estimated by the virtual cell assigned to it. To determine the LCTE of the eutectic system, a ratio is proposed that connects the LCTE components and the docking boundaries through the concentration ratio. This method more realistically describes the structure of a quasi-binary eutectic. There is a consistency between the calculated and experimental data. Keywords: electron-ion system energy, interatomic interaction potential, quasiharmonic approximation, linear coefficient of thermal expansion, eutectic temperature.

Spin\u2013spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations

Understanding the quantum dynamics of spin defects and their coherence properties requires an accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from first principles calculations. We present a real-space approach based on density functional theory for the calculation of spin-Hamiltonian parameters, where only selected atoms are treated at the all-electron level, while the rest of the system is described with the pseudopotential approximation. Our approach permits calculations for systems containing more than 1000 atoms, as demonstrated for defects in diamond and silicon carbide. We show that only a small number of atoms surrounding the defect needs to be treated at the all-electron level, in order to obtain an overall all-electron accuracy for hyperfine and zero-field splitting tensors. We also present results for coherence times, computed with the cluster correlation expansion method, highlighting the importance of accurate spin-Hamiltonian parameters for quantitative predictions of spin dynamics.

Radial Two-Dimensional Ion Crystals in a Linear Paul Trap.

We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.

Обчислення лінійного коефіцієнта термічного розширення багатоелементних, однофазних металевих сплавів з перших принципів

One of the possible ways to calculate the coefficient of thermal expansion is a method based on determining the dependence of the total energy of the electron-ion system on the parameters of the crystal lattice at different temperatures. There is a relationship between the calculated values of the linear coefficients of thermal expansion and the melting point of the material. For metals and multi-element single-phase alloys, the dependence of the function V = α·Tmax on the parameter T/Tmax (α — the linear coefficients of thermal expansion, Tmax — melting point of the material) is obtained from the first principles, which has the same form for all single-phase multi-element metal alloys and is presented analytically. Using the method of pseudopotential and quasiharmonic approximation, the linear coefficients of thermal expansion of multi-element metal alloys are calculated. The temperature dependence of the coefficient of thermal expansion, after approximating the results of the computational experiment, is presented in analytical form. The results were compared with known tabular data. To confirm the reliability of the model, the calculation was performed for a number of pure metals. The consistency of the calculated and experimental data on the coefficient of thermal expansion of single-phase alloys calculated from the first principles is observed. There is a relationship between the calculated values of the linear coefficients of thermal expansion and the melting point of the material. For metals and multi-element single-phase alloys, the dependence of the function V = α·Tmax on the parameter T/ Tmax (α — the linear coefficients of thermal expansion, Tmax — melting point of the material) is obtained from the first principles, which has the same form for all single-phase multi-element metal alloys and is presented analytically. Keywords: Electron-ion system energy, interatomic interaction potential, force constants, quasiharmonic approximation, coefficient of thermal expansion.

Estimation of the charge state of Th implanted in SiO2 in the different atomic environment

In this work the investigation of the charge states of thorium implanted in SiO2 is in different atomic environments and at different concentrations is presented.. Th was considered as interstitial and substitutional impurity in model cells of 6, 48 and 96 atoms. The estimations of the Bader effective charges of Th was derived from the electronic charge density n(r) calculated in DFT full relativistic PAW pseudopotential approximation. The change in the electron density of thorium due to the environment in the cells was estimated in comparison with the free atomic state.

Cu-Doped KCl Unfolded Band Structure and Optical Properties Studied by DFT Calculations.

The unfolded band structure and optical properties of Cu-doped KCl crystals were computed by first principles within the framework of density functional theory, implemented in the ABINIT software program, utilizing pseudopotential approximation and a plane-wave basis set. From a theoretical point of view, Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method. This procedure shrinks the Brillouin zone, resulting in a folded band structure that is difficult to interpret. To solve this problem and gain insight into the effect of copper ions (Cu+) on electronic properties, the band structure of SC KCl:Cu was unfolded to make a direct comparison with the band structure of the primitive cell (PC) of pristine KCl. To understand the effect of Cu substitution on optical absorption, we calculated the imaginary part of the dielectric function of KCl:Cu through a sum-over-states formalism and broke it down into different band contributions by partially making an iterated cumulative sum (ICS) of selected valence and conduction bands. Consequently, we identified those interband transitions that give rise to the absorption peaks due to the Cu+ ion. These transitions involve valence and conduction bands formed by the Cu-3d and Cu-4s electronic states.

A posteriori error estimation for the non-self-consistent Kohn-Sham equations.

We address the problem of rigorously bounding the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, and (iii) the propagation of rounding errors in floating-point arithmetic. In this contribution, we compute fully-guaranteed bounds on the solution of the non-self-consistent equations in the pseudopotential approximation in a plane-wave basis set. We demonstrate our methodology by providing band structure diagrams of silicon annotated with error bars indicating the combined error.

Upper bound to the gradient-based kinetic energy density of noninteracting electrons in an external potential

We examine a simple upper bound to the gradient-based kinetic energy density (KED) of noninteracting electrons in an external potential: t(r) ≤ [μ−v(r)]n(r)+14∇2n(r), where t(r) is the gradient-based (non-negative) KED, μ is the Fermi energy, v(r) is the external potential, and n(r) is the electron density. The bound emerges naturally from a well-known expression for t(r), leading to an intuitive physical interpretation. For example, t(r) approaches the upper bound in regions where the electron density consists mainly of contributions from states with energies close to the Fermi energy. This upper bound complements the orbital-free lower bound provided by the gradient form of the von Weizsacker (vW) KED, which is also non-negative. Both bounds yield t(r) exactly for single-orbital systems, and accordingly, they merge in single-orbital regions of more general systems. We demonstrate the universality of the two bounds over a wide range of test systems, including model potentials, atoms, diatomic molecules, and pseudopotential approximations of crystals. We also show that the exact t(r) frequently exceeds the sum of the vW and Thomas-Fermi KEDs, rendering that sum unsuitable as a strict upper bound to the gradient-based KED.

Effects of pressure on electronic structure and magnetic properties of cerium boride CeB6 cathode crystalline material

The thermal stabilities, electronic structures, magnetic properties and the charge transfers of the rare earth Cerium hexaborides CeB6 under isostatic pressure of 0 GPa and 1 GPa are systematically investigated in detail within the framework of density functional theory method with pseudopotential approximation. The analyzing results show that the Cerium Boride CeB6 under 1 GPa has relatively lower total energy of −1526.1675 eV than that of Cerium Boride CeB6 under 0 GPa. The Cerium Boride CeB6 under 1 GPa has band gap of 1.305 eV, which is 0.152 eV lower than that of the Cerium Boride CeB6 under 0 GPa of 1.457 eV. The work function of electrons is also decreased by 0.465 eV. There are three energy valleys in the bottom conduction band and four energy peaks in the top valance band, the emission efficiency should be high. The quantity of electrons that are readily to be motivated for emission is larger for Cerium hexaborides CeB6 under 1 GPa. The total partial density of states for Cerium Boride CeB6 under different isostatic pressure is mainly formed by B p electrons. The B should play more important role in electron emission for CeB6 under 1 GPa. The CeB6 under different isostatic pressure is ferromagnetic material. The combination bond effect between B is enhanced for Cerium Boride CeB6 under 1 GPa.

Carbon-Based Aromatic-Like Nanostructures on the Vicinal SiC Surfaces Induced by Ba Adsorption

The electronic structure of the SiC/Si(111)-8° and SiC/Si(111)-4° epitaxial layers with adsorbed Ba submonolayers is thoroughly studied in situ in ultrahigh vacuum by synchrotron-based photoemission spectroscopy. The SiC epitaxial layers were grown on the vicinal Si(111)-8°, Si(111)-4° surfaces by the original method of substitution of atoms. The C 1s and Si 2p сore level spectra are investigated in relation to the different Ba coverages. A substantial change in the C 1s spectra induced by Ba adsorption is revealed. It is found that the effect results from the formation of a new, previously unknown carbon-based structure consist of nanoclusters on the surface. Experimental data show that the nanoclusters can be created exclusively on the vicinal SiC surfaces in the presence of stabilizing adsorbed metal atoms, specifically, Ba atoms. Density functional theory using the basis of plane waves with the pseudopotential approximation is applied to calculate the spatial configuration of this clusters structure. It is shown that the surface nanoclusters are formed due to local interaction between silicon vacancies, carbon atoms and Ba adatoms. It is established that the carbon clusters is composed of carbon rings, in which the chemical bonds are close in nature to the bonds inherent in aromatic-like compounds.

First-principles study of structural, elastic, thermodynamic, electronic and optical properties of cubic boron nitride and hexagonal boron nitride at high temperature and high pressure

On the basis of the density functional theory of the first-principles, we employ the plane wave pseudopotential method and local density approximation to optimize the geometrical structure of cubic boron nitride and hexagonal boron nitride; then we study their mechanical properties, electronic structures and optical properties at zero temperature and zero pressure, and the thermodynamic properties at different temperatures and different pressures. By means of geometry optimization, we systematically investigate the elastic constant, bulk modulus, shear modulus, hardness and phonon spectrum for each of cubic boron nitride and hexagonal boron nitride. The results show that both cubic boron nitride and hexagonal boron nitride are structurally stable and brittle materials. Besides, cubic boron nitride is more stable than hexagonal boron nitride and it can be used as a superhard material. However, the thermal stability of hexagonal boron nitride is poor. The research results of electrical properties show that both cubic boron nitride and hexagonal boron nitride are indirect bandgap semiconductors, and the localization of cubic boron nitride is stronger than hexagonal boron nitride. The optical studies show that both cubic boron nitride and hexagonal boron nitride have good passivity to incident light. The c-BN is more sensitive to the incident light in high energy region. Last but not least, the thermodynamic properties of cubic boron nitride at high temperature and high pressure are also investigated. The relationships of thermodynamic expansivity, heat capacity, Debye temperature and Grüneisen parameter of c-BN with temperature and pressure are obtained. And the heat capacity of cubic boron nitride is found to be close to the Dulong-Petit limit at high temperatures. In this paper the relevant properties of cubic boron nitride and hexagonal boron nitride under high pressure are described theoretically, and a relatively reliable theoretical basis is provided for relevant experimental research.