Large Supercells Research Articles

Vibrational and vibronic structure of isolated point defects: The nitrogen-vacancy center in diamond

We present a theoretical study of vibrational and vibronic properties of a point defect in the dilute limit by means of first-principles density functional theory calculations. As an exemplar we choose the negatively charged nitrogen-vacancy center, a solid-state system that has served as a testbed for many protocols of quantum technology. We achieve low effective concentrations of defects by constructing dynamical matrices of large supercells containing tens of thousands of atoms. The main goal of the paper is to calculate luminescence and absorption lineshapes due to coupling to vibrational degrees of freedom. The coupling to symmetric $a_1$ modes is computed via the Huang-Rhys theory. Importantly, to include a nontrivial contribution of $e$ modes we develop an effective methodology to solve the multi-mode $E \otimes e$ Jahn-Teller problem. Our results show that for NV centers in diamond a proper treatment of $e$ modes is particularly important for absorption. We obtain good agreement with experiment for both luminescence and absorption. Finally, the remaining shortcomings of the theoretical approach are critically reviewed. The presented theoretical approach will benefit identification and future studies of point defects in solids.

Electronic Structure of Molecules, Surfaces, and Molecules on Surfaces with the Local Modified Becke-Johnson Exchange-Correlation Potential.

The knowledge of electronic properties of matter is the key to the understanding of its properties and to propose useful applications. To model hybrid organic/inorganic systems with the plane-wave approach, large supercells with many atoms are usually necessary to minimize artificial interactions between periodic images. For such systems, accurate approximations to the exchange-correlation functional of density functional theory, such as hybrid functionals, become computationally expensive, and cheaper approaches need to be considered. Here, we apply the local modified Becke-Johnson exchange-correlation potential to free molecules and surfaces and study its accuracy for calculated ionization potentials. This quantity being important to understand the band alignment of composite heterogeneous systems, we demonstrate the application of the potential to the electronic structure calculation of an exemplary composite semiconductor/molecule system, namely, a F6-TCNNQ molecule adsorbed on a hydrogenated Si(111) surface.

Theoretical Mapping of Interaction between Alkali Metal Atoms Adsorbed on Graphene‐Like BC3 Monolayer

First‐principles calculations using density functional theory and two methods in comparison, Quantum ESPRESSO and Siesta, are done on large supercells which describe different placements of two identical adsorbed alkali metal atoms (of either Na or K species) on the monolayer of boron carbide BC3. The energy of single‐atom adsorption over the center of C6 ring, the center of C4B2 hexagon, and over a boron atom are preliminarily estimated, the effect of applying the Grimme D2 correction on the adsorption characteristics is evaluated, and the comparison of these results with available data is discussed. The interaction of two identical Na or K atoms adsorbed at close enough distances (less than ≃10 Å) is negligible if the adsorption occurs at the opposite sides of the BC3 layer, but creates a steep repulsive potential at distances less than ≃8 Å if both atoms are adsorbed on the same side of the monolayer. Relaxation patterns resulting from the two K atoms being trapped at adjacent adsorption sites in the lattice are explained. The results suggest that the density of adsorbed K atoms on BC3 can be interestingly high.

Entropic broadening of the spin-crossover pressure in ferropericlase

The pressure-induced spin crossover of iron in ferropericlase, the Fe-bearing MgO, is a key to understanding the seismological observations in the lower mantle. However, the experimentally measured spin-crossover pressure zone (SCPZ) shows large variations, which disagree with the theoretically predicted values that are generally less than half of experimental ones. Here, we resolve this outstanding controversy by revealing the critical role of Fe distribution in MgO in broadening the Fe SCPZ, using comprehensive first-principles calculations combined with cluster expansion approach and Monte Carlo simulations. By employing a large supercell containing up to $\ensuremath{\sim}{10}^{6}$ atoms, we derive the spin-crossover pressures as functions of Fe concentration for different Fe distributions. We determine a critical temperature of ${T}_{c}\ensuremath{\sim}900\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, below which Fe segregation (clustering) occurs, in accordance with the thermodynamic phase diagram. Above ${T}_{c}$, an entropy-driven randomized Fe distribution creates large variations in Fe local environments, which in turn broadens the SCPZ, such as 17.5 GPa for 25 mol % Fe-bearing MgO in good agreement with experiments. Therefore, the broad SCPZ, rendering a smooth change of ferropericlase mechanical properties during the spin crossover, should be mainly caused by entropy, consistent with the high-temperature state of the lower mantle.

Electronic State Unfolding for Plane Waves: Energy Bands, Fermi Surfaces, and Spectral Functions.

Present day computing facilities allow for first-principles density functional theory studies of complex physical and chemical phenomena. Often such calculations are linked to large supercells to adequately model the desired property. However, supercells are associated with small Brillouin zones in the reciprocal space, leading to folded electronic eigenstates that make the analysis and interpretation extremely challenging. Various techniques have been proposed and developed to reconstruct the electronic band structures of super cells unfolded into the reciprocal space of an ideal primitive cell. Here we propose an unfolding scheme embedded directly in the Vienna Ab initio Simulation Package (VASP) that requires modest computational resources and allows for an automatized mapping from the reciprocal space of the supercell to the primitive cell Brillouin zone. This algorithm can compute band structures, Fermi surfaces, and spectral functions by using an integrated postprocessing tool (bands4vasp). Here the method is applied to a selected variety of complex physical situations: the effect of doping on the band dispersion in the BaFe2(1–x)Ru2xAs2 superconductor, the interaction between adsorbates and polaronic states on the TiO2(110) surface, and the band splitting induced by noncollinear spin fluctuations in EuCd2As2.

Are the St John's wort Hyp-1 superstructures different?

Two commensurately modulated structures (PDB entries 4n3e and 6sjj) were solved using translational noncrystallographic symmetry (tNCS). The data required the use of large supercells, sevenfold and ninefold, respectively, to properly index the reflections. Commensurately modulated structures can be challenging to solve. Molecular-replacement software such as Phaser can detect tNCS and either handle it automatically or, for more challenging situations, allow the user to enter a tNCS vector, which the software then uses to place the components. Although this approach has been successful in solving these types of challenging structures, it does not make it easy to understand the underlying modulation in the structure or how these two structures are related. An alternate view of this problem is that the atoms and associated parameters are following periodic atomic modulation functions (AMFs) in higher dimensional space, and what is being observed in these supercells are the points where these higher dimensional AMFs intersect physical 3D space. In this case, the two 3D structures, with a sevenfold and a ninefold superstructure, seem to be quite different. However, describing those structures within the higher dimensional superspace approach makes a strong case that they are closely related, as they show very similar AMFs and can be described with one unique (3+1)D structure, i.e. they are two different 3D intersections of the same (3+1)D structure.

Interfacial Enhancement of Photovoltaic Performance in MAPbI3/CsPbI3 Superlattice.

Perovskite solar cells have continued to fascinate over the past decade due to fast increasing power conversion efficiency and very low fabrication cost but still suffered from poor stability. Interface engineering is evolved to be one of the most promising solutions to the instability problem. In this work, we perform a first-principles study on the MAPbI3/CsPbI3 interface system, aiming at clarifying the underlying mechanism of interfacial enhancement of solar cell performance. We devise the atomistic modeling of superlattices as increasing the number of included unit cells and carry out structural optimizations, revealing that the binding strength between the perovskite layers becomes stronger while the band gap decreases as the supercell size increases. Using enough large supercells of the interface system, we further estimate the formation energies of the interfacial vacancy defects and activation barriers for vacancy-mediated I atom migrations. Our calculations show the shallow transition states for most of the defects and the higher activation barriers for I atom migrations across the interface, providing an evidence of performance enhancement by the interface formation. By giving an insightful understanding of the MAPbI3/CsPbI3 heterojunction, this work definitely contributes to the design of interface systems for high-performance solar cells.

Flows in horizontal thermohaline convection with differential diffusion

Oceanographers use the term “differential diffusion” to express a greater value of bulk turbulent diffusivity of temperature within the ocean than the value of bulk diffusivity of salinity, the ratio quantified by Lewis number. Investigation of horizontal thermohaline convection at Prandtl number 1 and infinity over the range reveals a variety of new flow patterns. The chamber has a linearly changing temperature T and salinity S along the top extending from the cold, fresh “polar” end to the hot, salty “tropics” end. It has an aspect ratio of 8 and sides and bottom are insulated and impermeable. Five transition flow patterns occur with little hysteresis for a fixed salinity Rayleigh number Ras of order 105 as Rayleigh number Ra changes from 3.2 × 106 down to 1. They are: 1. A steady T-cell with sinking at the cold end flowing into a bottom flow that feeds up into a top thermal boundary layer. 2. Salty blobs in the boundary layer that amplify and move from the hot to cold end. Each cold end arrival triggers a sudden increase in overturning velocity. 3. A “stripes” pattern where top to bottom cells (alternating T and S cells) move toward the cold end. 4. An S-cell that is a mirror image of the T-cell near the top along with small T-cells lying at the bottom that move toward the cold end 5. A steady S-cell. Each pattern has a distinct volumetric signature in a T-S diagram. Ranges of Ra with various patterns are sizeable at Ras=7.5 × 105 if Le >4/3 but insensitive to Pr. Balanced convection at Ra = Ras >106 adopts a large unsteady supercell containing smaller T and S cells. Exact ranges of the supercell are unknown. Since differential diffusion produces a large collection of flows compared to thermal convection alone, it might produce unexpected new results if added into numerical models of the ocean.

TB2J: A python package for computing magnetic interaction parameters

We present TB2J, a Python package for the automatic computation of magnetic interactions, including exchange and Dzyaloshinskii–Moriya, between atoms of magnetic crystals from the results of density functional calculations. The program is based on the Green’s function method with the local rigid spin rotation treated as a perturbation. As input, the package uses the output of either Wannier90, which is interfaced with many density functional theory packages, or of codes based on localized orbitals. One of the main interests of the code is that it requires only one first-principles electronic structure calculation in the non-relativistic case (or three in the relativistic case) and from the primitive cell only to obtain the magnetic interactions up to long distances, instead of first-principles calculations of many different magnetic configurations and large supercells. The output of TB2J can be used directly for the adiabatic magnon band structure and spin dynamics calculations. A minimal user input is needed, which allows for easy integration into high-throughput workflows. Program summaryProgram Title: TB2JCPC Library link to program files:https://doi.org/10.17632/dm45fcn69d.1Developer’s repository link:https://github.com/mailhexu/TB2JCode Ocean capsule:https://codeocean.com/capsule/6486145Licensing provisions: BSD 2-clauseProgramming language: PythonNature of problem: TB2J is a package for the computing of parameters in the extended Heisenberg model of the magnetic interaction, including the isotropic exchange, anisotropic exchange and Dzyaloshinskii–Moriya interactions from first principles result. It can make use of the Wannier function Hamiltonian, which can be constructed from many first principles codes, or localized orbital based codes.Solution method: It uses the magnetic force theorem and takes the rigid spin rotation as a perturbation to the electronic structure. The energy variation is calculated from the Green’s functions from tight-binding like Hamiltonian based on Wannier functions or localized orbitals.Additional comments including restrictions and unusual features: Isotropic exchange, anisotropic exchange, and Dzyaloshinskii–Moriya interactions can all be computed with the input of many DFT codes through the interface of Wannier90, or directly from localized orbital codes. The magnetic interaction parameters up to any distance can be computed from one DFT calculation. A minimum user-input is required which provides a black-box like experience. It generates output for several spin dynamics codes and thus bridges the first principles electronic structure simulation with the large scale spin dynamics simulation.

Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride

We study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Structural relaxation has been performed for commensurate supercells of the heterostructures with different twist angles () and stackings between TBG and BN. We find that the slightly misaligned configuration with and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moiré interlayer potentials and thus the greatly enhanced relaxation in its 1 × 1 commensurate supercell. Gaps are opened at the Fermi level (E F ) for small supercells with the stackings that enable strong breaking of the C 2 symmetry in the atomic structure of TBG. For large supercells with close to those of the 1 × 1 supercells, the broadened flat bands can still be resolved from the spectral functions. The is also identified as a critical angle for the evolution of the electronic structure with , at which the energy range of the mini-bands around E F begins to become narrower with increasing and their gaps from the dispersive bands become wider. The discovered stablest TBG/BN with a finite of about 0.54∘ and its gapped flat bands agree with recent experimental observations.

Structural phase transitions in the geometric ferroelectric LaTaO4

The recent report of an intermediate incommensurately modulated orthorhombic phase in $\mathrm{LaTa}{\mathrm{O}}_{4}$ has prompted a re-examination of the phase transition sequence in $\mathrm{LaTa}{\mathrm{O}}_{4}$ as a function of temperature. With falling temperature, the sequence of phases examined is (orthorhombic) $Cmc{2}_{1}(\mathrm{C})\ensuremath{\leftrightarrow}Cmc{2}_{1}(\mathrm{IC})\ensuremath{\leftrightarrow}(\mathrm{monoclinic})P{2}_{1}/c$, with C and IC denoting commensurate and incommensurate phases, respectively. The orthorhombic to monoclinic transition, ${T}_{\mathrm{m}\ensuremath{-}\mathrm{o}}$, is a first order reconstructive transition occurring at 440 K and ${T}_{\mathrm{IC}\ensuremath{-}\mathrm{C}}$ is a first-order displacive transition occurring at 500--530 K. Strain and elasticity data confirm a first-order transition between the basic and modulated $Cmc{2}_{1}$ phases, with similarities to the isostructural fluoride $\mathrm{BaMn}{\mathrm{F}}_{4}$. A Raman spectroscopic study of the $\mathrm{LaTa}{\mathrm{O}}_{4}$ phase transition indicates that the IC-C phase transition is driven by a soft zone-boundary phonon (unstable) of the commensurate orthorhombic ($Cmc{2}_{1}$) phase. The soft phonon is found to appear (underdamped) above 443 K and vanishes (overdamped) around 528 K. A large supercell of the monoclinic phase below ${T}_{\mathrm{m}\ensuremath{-}\mathrm{o}}$ is proposed based on the Raman spectroscopic results.

Regional Embedding Enables High-Level Quantum Chemistry for Surface Science.

Compared to common density functionals, ab initio wave function methods can provide greater reliability and accuracy, which could prove useful when modeling adsorbates or defects of otherwise periodic systems. However, the breaking of translational symmetry necessitates large supercells that are often prohibitive for correlated wave function methods. As an alternative, this paper introduces the regional embedding approach, which enables correlated wave function treatments of only a target fragment of interest through small, fragment-localized orbital spaces constructed using a simple overlap criterion. Applications to the adsorption of water on lithium hydride, hexagonal boron nitride, and graphene substrates show that regional embedding combined with focal-point corrections can provide converged CCSD(T) (coupled-cluster) adsorption energies with very small fragment sizes.

Waveguide Superlattice-Based Optical Phased Array

High-density low-crosstalk waveguide superlattices can potentially help shrink the pitch of an optical phased array to half-wavelength, which may lead to superior beam characteristics. While a superlattice's longitudinal coherence is exploited to create phase mismatch and reduce crosstalk, its transverse coherence is also modified and will inevitably disturb the beam forming of the optical phased array. Our theory shows that the transverse and longitudinal coherence can be balanced in a nontrivial superlattice such that superlattice-induced disturbance of the beam can be suppressed without compromising crosstalk. Large supercells less restrained by symmetry offer more degrees of freedom for finding a desirable superlattice structure. The supercell configuration order and structural modulation strength are crucial to balancing coherence and approaching the ideal characteristics of a half-wavelength pitch optical phased array. Experimental results show a high main-beam energy ratio, low sidelobe levels, and a wide angular scanning range. Such optical phased arrays may potentially open up further opportunities for light detection and ranging (LIDAR), wireless optical communications, and biomedical scanning imaging.

Modelling of high-temperature order-disorder phase transitions of non-stoichiometric Mo2C and Ti2C from first principles.

High-temperature order-disorder phase transitions play an important role in determining the structure and physical and chemical properties of non-stoichiometric transition metal carbides. Due to the large number of possible carbon vacancy arrangements, it is difficult to study these systems with first-principles calculations. Here, we construct a simple atomistic potential capable of accurately reproducing the energetics of the carbon vacancy arrangements in cubic Mo2C and Ti2C obtained from density functional theory calculations. We show that this potential can be applied to correctly predict the transition temperatures between the ordered and disordered states in Monte Carlo simulations on large supercells and reveal the extend of local order in the disordered phases of Mo2C and Ti2C that show interesting physical and chemical properties. We find that even the high-temperature disordered phase exhibit a relatively high degree of local order as indicated by the relatively small change in the root mean square number of C atom neighbours of Mo/Ti compared to the ordered phase (from 3.0 to 3.1-3.2). This atomistic potential enables the study of how the structure of these carbides can be tuned through the synthesis temperature to control the properties of carbide materials that are related to the degree of disorder in the system such as catalytic activity and electrical conductivity and play an important role in applications of these carbides. Fundamentally, the successful modelling of these carbides suggests that despite the presence of metallic, covalent and ionic interactions, bonding in carbides can be modelled by simple and physically intuitive interatomic potentials.

Density Functional Theory and Experimental Determination of Band Gaps and Lattice Parameters in Kesterite Cu2ZnSn(SxSe1–x)4

The structures and band gaps of copper-zinc-tin selenosulfides (CZTSSe) are investigated for a range of anion compositions through experimental analysis and complementary first-principles simulations. The band gap was found to be extremely sensitive to the Sn-anion bond length, with an almost linear correlation with the average Sn-anion bond length in the mixed anion phase Cu2ZnSn(SxSe1-x)4. Therefore, an accurate prediction of band gaps using first-principles methods requires the accurate reproduction of the experimental bond lengths. This is challenging for many widely used approaches that are suitable for large supercells. The HSE06 functional was found to predict the structure and band gap in good agreement with the experiment but is computationally expensive for large supercells. It was shown that a geometry optimization with the MS2 meta-GGA functional followed by a single point calculation of electronic properties using HSE06 is a reasonable compromise for modeling larger supercells that are often unavoidable in the study of point and extended defects.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals.

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

The effect of isovalent doping on the electronic band structure of group IV semiconductors

The band gap engineering of group IV semiconductors has not been well explored theoretically and experimentally, except for SiGe. Recently, GeSn has attracted much attention due to the possibility of obtaining a direct band gap in this alloy, thereby making it suitable for light emitters. Other group IV alloys may also potentially exhibit material properties useful for device applications, expanding the space for band gap engineering in group IV. In this work the electronic band structure of all group IV semiconductor alloys is investigated. Twelve possible A:B alloys, where A is a semiconducting host (A = C, Si, and Ge) and B is an isovalent dopant (B = C, Si, Ge, Sn, and Pb), were studied in the dilute regime (0.8%) of the isovalent dopant in the entire Brillouin zone (BZ), and the chemical trends in the evolution of their electronic band structure were carefully analyzed. Density functional theory with state-of-the-art methods such as meta-GGA functionals and a spectral weight approach to band unfolding from large supercells was used to obtain dopant-related changes in the band structure, in particular the direct band gap at the Γ point and indirect band gaps at the L(X) points of the BZ. Analysis of contributions from geometry distortion and electronic interaction was also performed. Moreover, the obtained results are discussed in the context of obtaining a direct fundamental gap in Ge:B (B = C, Sn, and Pb) alloys, and intermediate band formation in C:B (B = Sn and Pb) and Ge:C. An increase in localization effects is also observed: a strong hole localization for alloys diluted with a dopant of a larger covalent radius and a strong electron localization for alloys with a dopant of smaller radius. Finally, it is shown that alloying Si and Ge with other elements from group IV is a promising way to enhance the functionality of group IV semiconductors.

First-principles study of intrinsic point defects and Xe impurities in uranium monocarbide

Based on density functional theory (DFT) calculations, we perform an extensive investigation of intrinsic point defects and Xe impurities in uranium monocarbide (UC). The DFT calculations involve both the conventional generalized gradient approximation (GGA) and the GGA+U approach with the Hubbard parametric term (U), using up to 5×5×5 supercells. GGA calculations for the formation energy of intrinsic defects demonstrate the significant effect of using larger supercells than in previous studies. Results confirm that the ⟨111⟩ and ⟨100⟩ dumbbell interstitials are the most stable interstitial configurations for U and C, respectively. The interstitial mechanisms are favored for self-diffusion of both uranium and carbon and diffusion of Xe under equilibrium conditions. Calculations also reveal that the Xe substitutional defect at the C lattice site tends to adopt an off-site configuration, which can be interpreted as a Xe interstitial–C vacancy complex. We also utilize GGA+U to assess the impact of effective U parameter (Ueff) on the results. Moreover, we introduce a method to estimate the carbon chemical potential by fitting the phase diagram composition data and propose a selection Ueff=1.25 eV based on the experimental Xe diffusion activation energy. With this approach, GGA+U calculations reproduce the available experimental data for the formation energy of the carbon Frenkel pair and can explain the stepwise recovery of intrinsic properties and burst Xe release behavior in UC observed in annealing experiments.

Moiré potential impedes interlayer exciton diffusion in van der Waals heterostructures.

The properties of van der Waals heterostructures are drastically altered by a tunable moiré superlattice arising from periodically varying atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers suggested that carriers and excitons exhibit long diffusion, a rich variety of scenarios can exist. In a moiré crystal with a large supercell and deep potential, interlayer excitons may be completely localized. As the moiré period reduces at a larger twist angle, excitons can tunnel between supercells and diffuse over a longer lifetime. The diffusion should be the longest in commensurate heterostructures where the moiré superlattice is completely absent. Here, we experimentally demonstrate the rich phenomena of interlayer exciton diffusion in WSe2/MoSe2 heterostructures by comparing several samples prepared with chemical vapor deposition and mechanical stacking with accurately controlled twist angles.

Hydrogen Adsorption on Ordered and Disordered Pt-Ni Alloys

The bulk properties and chemical reactivity of disordered Pt-Ni alloys in the A1 (fcc) structure are investigated using different methods: Virtual Crystal Approximation (VCA), Korringa–Kohn–Rostoker Coherent Potential Approximation (KKR-CPA), and large explicit supercells generated using Super-Cell Random Approximates (SCRAPs). While VCA predicts lattice constants that closely follow Vegard’s law, the large supercells and KKR-CPA predict lattice constants that are consistently larger than Vegard’s law. KKR-CPA results closely agree with those from the large supercells for the disordered alloys, producing similar projected density of states and magnetic moment across the composition range. For instance, while VCA predicts the disordered alloys to be non-magnetic at a Pt concentration (xPt) ≥ 0.5, KKR-CPA and SCRAPs predict the disordered alloys to remain ferromagnetic to higher Pt concentrations. As xPt decreases, the adsorption of H becomes more exothermic on bulk-terminated (111) surfaces but less exothermic on Pt monolayer-terminated (111) surfaces due largely to strain effects. (111) surfaces cut from the large supercells predict average H adsorption energies on the disordered alloys similar to those on the ordered phases of the same compositions, while VCA predicts H adsorption to be more exothermic.