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DOE OSTI2021

First Principles Simulations of Electrified Interfaces in Electrochemistry

This chapter discusses some of the recent advances made in the first principles modeling of electrochemical catalysts. It also discusses the key development, namely the ability to explicitly treat the effects of surface electrification due to electrochemical processes and applied voltages in a computationally efficient manner. The chapter introduces the thermodynamics and statistical mechanics of electrified metal-solution interfaces. It then discusses the structure of the electrode-electrolyte interface and the effects of applied voltages, followed by an overview of the first-principles model and a motivating example. The chapter also provides a brief summary of classical thermodynamics and describes the basics of thermodynamic detour. It considers the thermodynamics of macroscopic systems and introduces several useful fundamental relations. Here, the chapter also considers a system to exist in a certain macrostate, which is a particular thermodynamic state specified by a set of fixed properties such as constant particle number, constant volume, and constant temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Unveiling X-ray absorption signatures of boron nitride via first-principles simulation and machine learning

Boron nitride (BN) allotropes hold great promise in many advanced applications ranging from optical and photonic devices to energy storage and battery systems to tribological components. The diverse functionalities of this material stem from BN’s highly tunable structural and electronic properties, which are governed by the versatile boron–nitrogen bonding configurations. Exploring the structural landscape of BN can unveil novel structures possessing unique properties suited for specific applications, therefore accelerating the design of next-generation advanced functional materials. In this work, we leverage boron K-edge X-ray absorption spectroscopy (XAS) as an effective probe for local structural features and chemical environments. A total of 210 BN crystal structures are generated via analogies to the extensive array of carbon allotropes, and XAS is simulated for each unique local motif within the resulting collection of structures. A mapping between structural features and spectral signatures was established by synergizing first-principle simulations with data-driven based post-analysis approaches. Specifically, we developed a neural network model that can satisfactorily predict spectra line shapes from local structural descriptors. Toward automatic spectroscopic interpretation of any new BN structures, supervised machine learning models, trained on this structure–spectrum dataset, can accurately infer local coordination environments from simulated XAS, highlighting the strength of this unique approach of combining high-fidelity first-principles simulation and machine-learning to accelerate target design of novel BN materials via rational understanding of local structure-spectrum correlations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Best practices for first-principles simulations of epitaxial inorganic interfaces

Abstract At an interface between two materials physical properties and functionalities may be achieved, which would not exist in either material alone. Epitaxial inorganic interfaces are at the heart of semiconductor, spintronic, and quantum devices. First principles simulations based on density functional theory (DFT) can help elucidate the electronic and magnetic properties of interfaces and relate them to the structure and composition at the atomistic scale. Furthermore, DFT simulations can predict the structure and properties of candidate interfaces and guide experimental efforts in promising directions. However, DFT simulations of interfaces can be technically elaborate and computationally expensive. To help researchers embarking on such simulations, this review covers best practices for first principles simulations of epitaxial inorganic interfaces, including DFT methods, interface model construction, interface structure prediction, and analysis and visualization tools.

Physics↗

DOE OSTI2021

On the Structural Transformation of Ni/BaH 2 During a N 2 -H 2 Chemical Looping Process for Ammonia Synthesis: A Joint In Situ Inelastic Neutron Scattering and First-Principles Simulation Study

The demand for decarbonizing the ammonia industry by using renewable energy has invoked increasing research interests into catalyst development for effective N 2 reduction under mild conditions. Hydride-based materials are among some of the emerging catalysts for ammonia synthesis at ambient pressure and low temperatures (< 673 K). A recent chemical looping process based on Ni/BaH 2 showed the most promise as it can realize ammonia production at a temperature as low as 373 K and under ambient pressure. However, the chemical transformation of the hydride catalyst at the molecular level remains unclear in this process. Here, we report detailed in situ neutron spectroscopy and diffraction investigations along with first-principles simulations on the structural transformation of Ni/BaH 2 during the nitridation and hydrogenation steps in the chemical looping process for ammonia synthesis. It was shown that a ball-milling process of the starting Ni/BaH 2 could significantly decrease the size of BaH 2 and increase the density of defects, thus potentially enhancing the reactivity of the hydride. The evolution from BaH 2 to barium imide (BaNH) was evidenced in the inelastic neutron scattering (INS) and neutron diffraction results during the N 2 reaction step. During the hydrogenation study, in addition to the recovery of BaH 2 , a possible intermediate species, N-deficient barium imide, was also detected. In comparing the N 2 and H 2 reaction steps, the neutron results indicate that the hydrogenation step appears more difficult than the nitridation step, confirming the facile N 2 fixation property of Ni/BaH 2 catalyst in ammonia synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Communication—First-Principles Simulations of LiPF 6 Decomposition in Ethylene Carbonate-Based Electrolytes

We revisit a theoretical result by Okamoto (2013 Journal of The Electrochemical Society , 160 , A404) who calculated the energy barrier for the decomposition of lithium hexafluorophosphate (LiPF 6 ) into LiF + PF 5 when solvated in Ethylene carbonate (EC)-based electrolyte. Using different numerical techniques to discretize the Density Functional Theory (DFT) equations, and different continuum solvation models with the same dielectric constant, our results largely confirm the original calculation. However, simulations with a higher dielectric permittivity value, closer to that of EC, show a lower energy barrier. More importantly, First-Principles simulations with an explicit solvent show a substantially lower energy barrier.

25 ENERGY STORAGE↗

DOE OSTI2022

Hydration-driven stabilization and volume collapse of grain boundaries in Mg2SiO4 forsterite predicted by first-principles simulations

Grain boundaries in mantle minerals are of critical importance to geophysical and geochemical processes of the Earth’s interior. One of the fundamental issues is to understand how the water (H 2 O) component influences the properties of grain boundaries in silicate materials. Here, we report the results of the structure and stability of several tilt grain boundaries in Mg 2 SiO 4 forsterite over the pressure range 0 to 15 GPa using density functional theory-based first-principles simulations. Here, the results suggest greater energetic stability and hydration-driven volume collapse (negative excess volume) at zero pressure for the majority of hydrous grain boundaries relative to the anhydrous (dry) ones. All the hydrous grain boundaries become increasingly favorable at elevated pressures as the calculated hydration enthalpy systematically decreases with increasing pressure. The hydrous components at the interfacial regions are predominantly in the hydroxyl form and, to a lesser extent, in the molecular H 2 O form. Their calculated ratio ranges from 1.6 to 8.7 among the different grain boundary configurations. Our structural analysis also reveals that the hydroxyls are bound to either both Mg and Si or to Mg only. In comparison, the molecular species are bound only to Mg sites. Besides direct oxygen-hydrogen bonding, intermolecular hydrogen bonding becomes important with compression. On the basis of our results, we suggest that local atomic rearrangements caused by dissociative adsorption of water facilitate efficient compaction of the boundary interfaces, which, in turn, results in greater relative stability of hydrous grain boundaries. This means that water prefers to be incorporated within the grain boundaries over the bulk of silicate materials.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Decoding the Atomic Structure of Ga 2 Te 5 Pulsed Laser Deposition Films for Memory Applications Using Diffraction and First-Principles Simulations

Neuromorphic computing, reconfigurable optical metamaterials that are operational over a wide spectral range, holographic and nonvolatile displays of extremely high resolution, integrated smart photonics, and many other applications need next-generation phase-change materials (PCMs) with better energy efficiency and wider temperature and spectral ranges to increase reliability compared to current flagship PCMs, such as Ge 2 Sb 2 Te 5 or doped Sb 2 Te. Gallium tellurides are favorable compounds to achieve the necessary requirements because of their higher melting and crystallization temperatures, combined with low switching power and fast switching rate. Ga 2 Te 3 and non-stoichiometric alloys appear to be atypical PCMs; they are characterized by regular tetrahedral structures and the absence of metavalent bonding. The sp 3 gallium hybridization in cubic and amorphous Ga 2 Te 3 is also different from conventional p-bonding in flagship PCMs, raising questions about its phase-change mechanism. Furthermore, gallium tellurides exhibit a number of unexpected and highly unusual phenomena, such as nanotectonic compression and viscosity anomalies just above their melting points. Using high-energy X-ray diffraction, supported by first-principles simulations, we will elucidate the atomic structure of amorphous Ga 2 Te 5 PLD films, compare it with the crystal structure of tetragonal gallium pentatelluride, and investigate the electrical, optical, and thermal properties of these two materials to assess their potential for memory applications, among others.

36 MATERIALS SCIENCE↗

DOE OSTI2024

First-Principles Simulation of Beam-Induced Processes Underlying Atomic Manipulation in Electron Microscopes

The development of experimental methods and apparatuses capable of promoting atomically precise material manipulations holds great promise for realizing the ultimate limit of feature miniaturization in materials and devices. The ability to modify materials atom by atom is anticipated to usher in new technologies in areas as diverse as separation science, medicine, and quantum information science. Historically, scanning probe-based techniques have been the most prominent approaches in this space. However, these methods are best suited for the manipulation of surface-exposed regions of materials, as the strong perturbations required for bond scission are delivered most effectively to atoms in the near-proximity to the scanning probe. In contrast, convergent electron beams with energies tuned slightly below the threshold for inducing irreversible knock-on damage have recently been employed (within scanning transmission electron microscopy) to promote atomic-scale bond rearrangements in various beam-stable solids. Currently, however, the efficiency and selectivity of beam-induced atomic manipulation processes with focused electron beams are such that long irradiation times are required to induce a desired atomic rearrangement. With a better understanding of the underlying physics dictating the outcome of a given irradiation event, methods can be devised to improve the efficiency of these techniques so that their promise can be fully realized through widespread adoption.To this end, this Account details our recent efforts to develop and apply tractable first-principles simulation approaches for studying the response of materials to electric beam-like external electric potentials applied in real space. We briefly review the concepts and capabilities in the area of atomically precise materials manipulation and review the early demonstrations of accomplishments in this area, focusing on studies using scanned convergent electron beam probes in particular. We expound upon the depth of the challenge and identify critical shortcomings of theoretical methods that have previously been employed in the simulation of beam-induced processes. We then describe the computational methods that we have generalized from the concepts and tools most commonly applied to the study of molecular photochemistry and how our adaptations of these methods can be employed to capture the relevant dynamical phenomena for beam-induced processes ranging from the initial electron scattering to the ensuing multistate reactions. Here, we contextualize these methods within the current state of the art in this area, which has historically focused primarily on the simulation of inelastic image formation in the electron microscope for the purpose of interpreting the results of quantitative electron microscopy experiments. We demonstrate that the spatial distribution of state-specific excitation rates due to the presence of an external (probe) electric charge is inhomogeneous, such that irradiation at particular locations in materials can favor specific electronic transitions (and disallow others). In addition to the potential for excited-state reaction pathways to be accessed through the initial inelastic scattering of the tightly focused electron beam from the targeted atoms, we also identify favorable conditions for the electronically nonadiabatic evolution of the highly vibrationally excited system to open complex multistate reaction pathways. Implications of the early results for understanding the mechanisms and potential routes to improved efficiency and selectivity in beam-induced reactions are discussed. We conclude with a summary of the current state of theory and modeling capabilities in this area and provide our perspective on future directions for theoretical and experimental developments that we view as crucial to advancing the use of convergent electron beams in mode-specific, atomically precise platforms for direct-write materials modifications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

First-Principles Simulations Correlating X-ray Absorption Spectroscopy Features to Point Defects in h -BN

Hexagonal boron nitride (h-BN) is a promising material for a range of emerging applications in electronics, quantum information technology, and energy storage. Soft X-ray absorption spectroscopy (XAS) is powerful to reveal atomic details of BN, especially in the presence of defects. However, correlating XAS spectral features with specific defect types remains elusive. In this Letter, we report B K-edge XAS measurements of sputter-deposited turbostratic h-BN films and use a combination of first-principles spectroscopic simulations and analysis of detailed electronic structure and local charge transfer characteristics to elucidate their unique spectroscopic features. Our results show that the two main defect-related peaks, between the main π* resonances of h-BN and B2O3, as typically observed in BN films deposited by energetic condensation or bombarded with energetic ions, are associated with electronic states of H-passivated B atoms bonded to one and two oxygen impurity atoms, respectively. These conclusions hold significant implications for applications relying on defect-mediated properties of h-BN.

chemical structure↗

DOE OSTI2022

Machine learning prediction of the mechanical properties of refractory multicomponent alloys based on a dataset of phase and first principles simulation

In this work, a dataset including structural and mechanical properties of refractory multicomponent alloys was developed by fusing computations of phase diagram (CALPHAD) and density functional theory (DFT). The refractory multicomponent alloys, also named refractory complex concentrated alloys (CCAs) which contain 2–5 types of refractory elements were constructed based on Special Quasi-random Structure (SQS). The phase of alloys was predicted using CALPHAD and the mechanical property of alloys with stable and single body-centered cubic (BCC) at high temperature (over 1,500°C) was investigated using DFT-based simulation. As a result, a dataset with 393 refractory alloys and 12 features, including volume, melting temperature, density, energy, elastic constants, mechanical moduli, and hardness, were produced. To test the capability of the dataset on supporting machine learning (ML) study to investigate the property of CCAs, CALPHAD, and DFT calculations were compared with principal components analysis (PCA) technique and rule of mixture (ROM), respectively. It is demonstrated that the CALPHAD and DFT results are more in line with experimental observations for the alloy phase, structural and mechanical properties. Furthermore, the data were utilized to train a verity of ML models to predict the performance of certain CCAs with advanced mechanical properties, highlighting the usefulness of the dataset for ML technique on CCA property prediction.

36 MATERIALS SCIENCE↗

DOE OSTI2021

First-Principles Simulations of CuCl in High-Temperature Water Vapor

Experimental data suggest that the solubility of copper in high-temperature water vapor is controlled by the formation of hydrated clusters of the form CuCl(H 2 O) n , where the average number of water molecules in the cluster generally increases with increasing density [Migdisov, A. A.; et al. Geochim. Cosmochim. Acta2014, 129, 33–53]. However, the precise nature of these clusters is difficult to probe experimentally. Moreover, there are some discrepancies between experimental estimates of average cluster size and prior simulation work [Mei, Y. Geofluids2018, 2018, 4279124]. Here, we have performed first-principles Monte Carlo (MC) and molecular dynamics (MD) simulations to explore these clusters in finer detail. We find that molecular dynamics is not the most appropriate technique for studying aggregation in vapor phases, even at relatively high temperatures. Specifically, our MD simulations exhibit substantial problems in adequately sampling the equilibrium cluster size distribution. In contrast, MC simulations with specialized cluster moves are able to accurately sample the phase space of hydrogen-bonding vapors. At all densities, we find a stable, slightly distorted linear H 2 O–Cu–Cl structure, which is in agreement with the earlier simulations, surrounded by a variable number of water molecules. The surrounding water molecules do not form a well-defined second solvation shell but rather a loose network of hydrogen-bonded water with molecular CuCl on the outside edge of the water cluster. We also find a broad distribution of hydration numbers, especially at higher densities. In contrast to previous simulation work but in agreement with experimental data, we find that the average hydration number substantially increases with increasing density. Moreover, the value of the hydration number depends on the choice of cluster definition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

First-principles simulation of light-ion microscopy of graphene

The extreme sensitivity of 2D materials to defects and nanostructure requires precise imaging techniques to verify presence of desirable and absence of undesirable features in the atomic geometry. Helium-ion beams have emerged as a promising materials imaging tool, achieving up to 20 times higher resolution and 10 times larger depth-of-field than conventional or environmental scanning electron microscopes. Here, we offer first-principles theoretical insights to advance ion-beam imaging of atomically thin materials by performing real-time time-dependent density functional theory simulations of single impacts of 10–200 keV light ions in free-standing graphene. Here we predict that detecting electrons emitted from the back of the material (the side from which the ion exits) would result in up to three times higher signal and up to five times higher contrast images, making 2D materials especially compelling targets for ion-beam microscopy. This predicted superiority of exit-side emission likely arises from anisotropic kinetic emission. The charge induced in the graphene equilibrates on a sub-fs time scale, leading to only slight disturbances in the carbon lattice that are unlikely to damage the atomic structure for any of the beam parameters investigated here.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Intercalation of Lithium into Graphite: Insights from First-Principles Simulations

Understanding ion intercalation at electrode–electrolyte interfaces is key to the development of energy storage and water desalination. Here, we investigate Li + kinetics at a prototypical interface between graphite anodes and an organic electrolyte, and we elucidate key factors that determine ion transport, using first-principles methodology coupling ab initio molecular dynamics simulations with a solvation model. We show that surface chemical composition significantly influences the kinetics of ion intercalation from the liquid into graphite. We find that this is partly related to the ion desolvation process, which varies notably for different graphite surface chemical terminations. In addition, interfacial polarization is found to play an important role in determining energy barriers for ion transfer. We also discuss the impact of electrode potentials, which is often neglected in conventional first-principles calculations despite being a key factor in device configurations. Our study provides insights into the coupling of electronic and ionic effects of interfacial chemistry on ion transport at complex electrode–electrolyte interfaces.

25 ENERGY STORAGE↗

DOE OSTI2023

Voltage-Dependent First-Principles Simulation of Insertion of Chloride Ions into Al/Al 2 O 3 Interfaces Using the Quantum Continuum Approximation

Experiments have shown that pitting corrosion can develop in aluminum surfaces at potentials > − 0.5 V relative to the standard hydrogen electrode (SHE). Until recently, the onset of pitting corrosion in aluminum has not been rigorously explored at an atomistic scale because of the difficulty of incorporating a voltage into density functional theory (DFT) calculations. We introduce the Quantum Continuum Approximation (QCA) which self-consistently couples explicit DFT calculations of the metal-insulator and insulator-solution interfaces to continuum Poisson-Boltzmann electrostatic distributions describing the bulk of the insulating region. By decreasing the number of atoms necessary to explicitly simulate with DFT by an order of magnitude, QCA makes the first-principles prediction of the voltage of realistic electrochemical interfaces feasible. After developing this technique, we apply QCA to predict the formation energy of chloride atoms inserting into oxygen vacancies in Al(111)/α-Al 2 O 3 (0001) interfaces as a function of applied voltage. We predict that chloride insertion is only favorable in systems with a grain boundary in the Al 2 O 3 for voltages > − 0.2 V (SHE). Here our results roughly agree with the experimentally demonstrated onset of corrosion, demonstrating QCA's utility in modeling realistic electrochemical systems at reasonable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Quantifying Temperature Dependence of Electronic Band Gaps and Optical Properties in SnO 2 and SnO via First-Principles Simulations

Tin metal oxides SnO x ( x = 1, 2) have gained interest as gas-sensing materials. For their applications as high-temperature sensors, however, a better understanding of their temperature dependence sensing responses is needed. Here, we comparatively quantify the temperature-dependent electronic band gaps and optical properties of SnO 2 and SnO using first-principles calculations. Without considering the temperature effect, SnO 2 and SnO are predicted to have direct and indirect band gaps of 2.18 and 1.66 eV, respectively, at the PBE + U -GGA level that we employed. The temperature effect on the electronic and optical properties is captured by taking account of the electron–phonon interaction. Band gap renormalization with temperature is calculated via the Allen–Heine–Cardona theory. For both oxides, we find a monotonic decrease in the electronic band gap such that renormalization at zero point (0 K) is ~–0.17 and ~–0.52 eV at 1000 K. These results are also analyzed by employing an analytical equation that helps characterize the band gap shift with temperature. In addition, the optical properties at finite temperatures are simulated using the frozen-phonon method that combines electron–phonon coupling with the momentum matrix. As temperature increases, the optical property spectra are smoothed because of the smearing effect, which diminishes optical constants at shorter wavelengths. Our results are of interest for high-temperature functional materials in applications of optical detection.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Electronic Properties of Ultra‐Wide Bandgap B x Al 1− x N Computed from First‐Principles Simulations

Abstract Ultra‐wide bandgap (UWBG) materials such as AlN and BN hold great promise for future power electronics due to their exceptional properties. They exhibit large bandgaps, high breakdown fields, high thermal conductivity, and high mechanical strengths. AlN and BN have been extensively researched, however, their alloys, B x Al 1− x N, are much less studied despite their ability to offer tunable properties by adjusting x . In this article, the electronic properties of 17 recently predicted ground states of B x Al 1− x N in the x = 0 − 1 range are predicted using first‐principles density functional theory and many‐body perturbation theory within GW approximation. All the B x Al 1− x N structures are found to be UWBG materials and have bandgaps that vary linearly from that of wurtzite‐phase ( w ) AlN (6.19 eV) to that of w ‐BN (7.47 eV). The bandstructures of B x Al 1− x N show that a direct‐to‐indirect bandgap crossover occurs near x = 0.25. Furthermore, it is found that B x Al 1− x N alloys have much larger dielectric constants than the constituent bulk materials (AlN = 9.3 ɛ 0 or BN = 7.3 ɛ 0 ), with values reaching as high as 12.1 ɛ 0 . These alloys are found to exhibit large dielectric breakdown fields in the range 9–35 MV cm −1 with a linear dependence on x . This work provides the much needed advancement in the understanding of the properties of B x Al 1− x N to aid their application in next‐generation devices.

Milne, Cody L.↗

DOE OSTI2023

First principles simulation of reacting hypersonic flow over a blunt wedge

This article presents molecular-level analysis of a reactive, near-continuum, Mach 21 nitrogen flow over a blunt wedge using the direct molecular simulation (DMS) method. The flow conditions lead to internal energy excitation and dissociation in the flow field, resulting in thermal and chemical nonequilibrium in the flow. Thermal nonequilibrium in the vibrational mode is observed to extend to the molecular level, where the vibrational energy distributions at various points in the flow field are observed to be non-Boltzmann. Furthermore, this is the first reactive DMS calculation where the wall is assumed to be isothermal and full momentum accommodation of the particles is enforced, hence incorporating viscous wall effects. Since the DMS method uses a quantum mechanically generated interaction potential as its only modeling input, all thermochemical and transport properties of the flow field can directly be attributed to the ab initio potential energy surface. Using the DMS solution as a benchmark, this article assesses the performance of Navier–Stokes computational fluid dynamics solutions using lower fidelity two-temperature models. Two models are chosen as points of comparison: the well-known Park two-temperature model and the recently developed modified Marrone and Treanor model.

Mechanics↗

DOE OSTI2021

Algorithm advances and applications of time‐dependent first‐principles simulations for ultrafast dynamics

Abstract Far from equilibrium phenomenon is a central theme of contemporary material research. Such phenomenon can exhibit itself in atomic structure and dynamics, but very often it also happens as non‐equilibrium phenomenon in the electronic structure. In ab initio material simulation, density functional theory (DFT) has played an essential role in studying electronic ground state problems. For excited states, besides many‐body perturbation theory, another powerful tool is the time dependent DFT (TDDFT) method. In particular, the real‐time TDDFT (rt‐TDDFT) method can be used to simulate many non‐equilibrium phenomena directly. Here we introduce our works on some algorithm advances based on our recently rt‐TDDFT method. This method uses the plane‐wave basis set, and significantly accelerates its efficiency by increasing the time step from 0.1–1 as in traditional methods to 0.2–0.5 fs. The noncollinear magnetic moments and spin–orbit coupling have also been included in our rt‐TDDFT method. Furthermore, a Boltzmann‐TDDFT algorithm has been developed to solve the hot carrier overheating problem in Ehrenfest dynamics, and a natural orbital branching algorithm has been developed to overcome the mean‐field approximation in Ehrenfest dynamics nuclear trajectory, thus allows stochastic multiple paths in chemical reactions. Utilizing these methods, we have studied the photoinduced ultrafast demagnetization, ultrafast phase transition, energy transfer between plasmon and hot carriers, as well as the high‐energy ion implantation and low‐energy atomic diffusion in semiconductors. We believe the tools as the ones introduced here can enable us to study a wide range of phenomena which are of great interest in modern day material research. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Liu, Wen‐Hao↗