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Density-functional theory of material design: fundamentals and applications-I

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article, we start with an introduction to Schrödinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schrödinger equation is discussed. The resulting Hartree and Hartree–Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas–Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern DFT by discussing Hohenberg–Kohn theorems that form its foundations. We then go on to discuss Kohn–Sham (KS) formulation of DFT in its exact form. Next, local density approximation (LDA) is introduced and solutions of KS equation for some representative systems, obtained using the LDA, are presented. We end part-I of the review describing the contents of part-II.

36 MATERIALS SCIENCE↗

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Properties of the In{sub 2}O{sub 3}-Si interface: An ab initio study of a model geometry

The In{sub 2}O{sub 3}(001)-Si(001) heterojunction is studied by means of the ab initio density functional theory, quasiparticle corrections, and the supercell method. We construct a model interface based on the idea of a coincidence lattice, only Si-O interface bonds and biaxially strained In{sub 2}O{sub 3}. The properties of the interface and their consequences for the junction are mainly described in terms of electronic band levels and charge redistribution. The results indicate a type II heterostructure caused by interface dipole alteration due to electron rearrangements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Epitaxy of polar semiconductor Co{sub 3}O{sub 4} (110): Growth, structure, and characterization

The (110) plane of Co{sub 3}O{sub 4} spinel exhibits significantly higher rates of carbon monoxide conversion due to the presence of active Co{sup 3+} species at the surface. However, experimental studies of Co{sub 3}O{sub 4} (110) surfaces and interfaces have been limited by the difficulties in growing high-quality films. We report thin (10–250 Å) Co{sub 3}O{sub 4} films grown by molecular beam epitaxy in the polar (110) direction on MgAl{sub 2}O{sub 4} substrates. Reflection high-energy electron diffraction, atomic force microscopy, x-ray diffraction, and transmission electron microscopy measurements attest to the high quality of the as-grown films. Furthermore, we investigate the electronic structure of this material by core level and valence band x-ray photoelectron spectroscopy, and first-principles density functional theory calculations. Ellipsometry reveals a direct band gap of 0.75 eV and other interband transitions at higher energies. A valence band offset of 3.2 eV is measured for the Co{sub 3}O{sub 4}/MgAl{sub 2}O{sub 4} heterostructure. Magnetic measurements show the signature of antiferromagnetic ordering at 49 K. FTIR ellipsometry finds three infrared-active phonons between 300 and 700 cm{sup −1}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Surface preparation method for investigating the three-dimensional electronic structure of perovskite nickelates

The investigation of the electronic structures on perovskite oxides using surface-sensitive spectroscopy techniques is often hindered by their “uncleavable” nature, typically requiring expensive and complex in situ experimental setups that integrate the capabilities of sample synthesis and spectroscopy measurement under ultrahigh vacuum condition. Here, we address this challenge by developing an ozone-annealing process that yields atomically flat surfaces on perovskite oxide thin films, making them suitable for high-resolution angle-resolved photoemission spectroscopy measurements. Using this method, we present a three-dimensional electronic structure study of Nd 1−𝑥 ⁢Sr 𝑥 ⁢NiO 3 (𝑥=0 and 0.175) thin films with unprecedented accuracy. The experimentally determined low-energy fermiology exhibits quantitative agreements with two-band tight-binding simulations, which is further validated by first-principles calculations considering the material's actual crystal structure. This work provides an accessible approach for ex situ ARPES measurements on perovskite oxides and other strongly correlated oxides, including the recently discovered high-𝑇 c nickelates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A sparse matrix–vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

Here we present an efficient sparse matrix–vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev–Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix–matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev–Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix–vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

42 ENGINEERING↗

Symmetry and equivalence restrictions in electronic structure calculations

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.

Bauschlicher, Charles W., Jr.↗

Strong O 2p–Fe 3d Hybridization Observed in Solution-Grown Hematite Films by Soft X-ray Spectroscopies

Photoelectrochemical (PEC) water splitting holds the potential as a direct route for solar energy conversation and storage. The performance of a PEC device is strongly influenced by the electronic properties of the photonanode surface. It has been shown that the synthesis methods can have a profound impact on the electronic properties and PEC performance of various photoelectrode materials such as hematite. Soft X-ray spectroscopic techniques, including O K-edge XAS and Fe L-edge XAS/XES, have been employed to investigate how the synthesis methods impact the electronic structure of resulting hematite materials. It is found that the hematite samples via solution regrowth methods show dramatically increased 3d-4sp band ratios in O K-edge XAS spectra and decreased relative elastic peak intensities in Fe L-edge RIXS spectra compared with samples synthesized via ALD or solution grown. The difference observed in O-K and Fe-L spectra indicated that solution regrowth strategy alters the O 2p-Fe 3d hybridization and hence the electronic structure of the hematite films, which proves to be beneficial for PEC performance of the hematite photoanode. Our findings provided new insights and potentially useful strategies for enhancing the PEC performance of photoanode materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessment of DFT methods for the prediction of detachment energies and electronic structures of complex and multiply charged anions

Here, in this work, we assess the ability of different density functional theory methods to reproduce the vertical/adiabatic detachment energies (VDEs/ADEs) of a series of 40 anions, including monoanion versus multiply charged anions (MCAs) and covalent versus noncovalent interaction. The statistical analysis of errors is firstly performed by comparing the theoretical values with the experimental benchmark data obtained from the negative ion photoelectron spectroscopy (NIPES). The proposed optimally tuned range-separated (OTRS) functionals are proved to not only well reproduce the experimental VDEs/ADEs, but also simulate experimental NIPES. The result implies a more serious issue of delocalization error for MCAs and a balanced description of electron-rich/- deficient region of anions is necessary. The radius of the spherically symmetric average electron localization function (ELF) region is demonstrated as a useful descriptor for the characterization of electronic structure of anionic systems and a quasilinear fitting model is proposed to efficiently obtain their OTRS parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lifshitz Transitions Induced by Temperature and Surface Doping in Type-II Weyl Semimetal Candidate T d -WTe 2

Using high resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structure of T d -WTe 2 , which has attracted substantial research attention due to its diverse and fascinating properties, especially the predicted type-II topological Weyl semimetal (TWS) phase. The observed significant lattice contraction and the fact that our ARPES measurements are well reproduced by our ab initio calculations under reduced lattice constants support the theoretical prediction of a type-II TWS phase in T d -WTe 2 at temperatures below 10 K. We also investigate the evolution of the electronic structure of T d -WTe 2 and realize two-stage Lifshitz transitions induced by temperature regulation and surface modification, respectively. Furthermore, our results not only shed light on the understanding of the electronic structure of T d -WTe 2 , but also provide a promising method to manipulate the electronic structures and physical properties of the type-II TWS T d -XTe 2 .

36 MATERIALS SCIENCE↗

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin–orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl 6 ] 3– and [Ce(IV)Cl 6 ] 2– complexes show that time-dependent density functional theory with approximate exchange–correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

chemical calculations↗

In Silico Prediction of Structural Properties of a Racemic Porous Organic Cage Crystal

Porous organic cage (POC) solids are porous materials made up of individual porous molecules held together by noncovalent forces. While many examples of POCs have been made in homochiral forms (i.e., crystals in which every molecule has the same chirality), crystallization of POCs that contain mixtures of chiral molecules can also yield useful properties. For example, our previous work has demonstrated that a POC crystal [cage crystal 3 (CC3)-racemic] synthesized using a racemic mixture of diaminocyclohexane has improved sorption properties and stability than a similar POC crystal synthesized with homochiral diaminocyclohexane. The main purpose of this paper is to predict the structure of CC3-racemic with atomic detail because it is challenging to fully resolve the structure of this racemic crystal experimentally since only subtle differences exist between the racemic structure and the known crystal structure of homochiral CC3. Here, we introduce an in silico prediction method that combines electronic structure calculations and atomistic calculations to predict the structure of CC3-racemic. We first enumerate types of cage molecules that can be present in this material and establish their concentrations. A key observation from these calculations is that CC3-racemic is not made up of only CC3-R and CC3-S molecules and that an additional class of heterochiral cages is also present. By studying the packing energy of cage pairs in CC3-racemic, a lattice model representation of the racemic crystal is developed and used in MC simulations to assess the structure of extended crystals. By expanding the lattice model into atomic detail, fully detailed CC3-racemic crystal models are obtained. These models provide the most thorough description available to date of the composition and cage packing of this interesting material.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-principles calculation of principal Hugoniot and K-shell X-ray absorption spectra for warm dense KCl

Principal Hugoniot and K-shell X-ray absorption spectra of warm dense KCl are calculated using the first-principles molecular dynamics (FPMD) method. Evolution of electronic structures as well as the influence of the approximate description of ionization on pressure (caused by the underestimation of the energy gap between conduction bands and valence bands) in the first-principles method are illustrated by the calculation. It is shown that approximate description of ionization in FPMD has small influence on Hugoniot pressure due to mutual compensation of electronic kinetic pressure and virial pressure. The calculation of X-ray absorption spectra shows that the band gap of KCl persists after the pressure ionization of the 3p electrons of Cl and K taking place at lower energy, which provides a detailed understanding to the evolution of electronic structures of warm dense matter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Shubnikov–de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

2D materials↗

Shubnikov-de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe 2 and RbV 3 Sb 5 , by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe 2 and RbV 3 Sb 5 , respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe 2 , the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV 3 Sb 5 , two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗