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This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, Fn(r), independent of v(r), such that the expression Ev(r)n(r)dr+Fn(r) has as its minimum value the correct ground-state energy associated with v(r). The functional Fn(r) is then discussed for two situations: (1) n(r)=n0+n(r), n/n01, and (2) n(r)= (r/r0) with arbitrary and r0. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

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... In a con form, it is necessary to emphasize that part of the general functional that correspond the exchange correlation interaction. The exchange correlation energy has been expres with density of the particles-n(r) [58,59]: ...

... In a concise form, it is necessary to emphasize that part of the general functional that corresponds to the exchange correlation interaction. The exchange correlation energy has been expressed with density of the particles-n(r) [58,59]: ...

... Equation (3) represents the single-particle Schrödinger equation with a form identical to that of the Schrödinger equation for non-interacting particles in an external potential. The DFT formalism [58,59], proposed by Hohenberg, Kohn and Sham, is suitable for the interaction between electrons and positrons. The positron wave function ϕ + (r) is calculated as follows [57]: The positron annihilation rate λ in an inhomogeneous electron gas is proportional to the overlap of electron n−(r) and positron n + (r) densities in the LDA. ...

... In a con form, it is necessary to emphasize that part of the general functional that correspond the exchange correlation interaction. The exchange correlation energy has been expres with density of the particles-n(r) [58,59]: ...

... In a concise form, it is necessary to emphasize that part of the general functional that corresponds to the exchange correlation interaction. The exchange correlation energy has been expressed with density of the particles-n(r) [58,59]: ...

... Equation (3) represents the single-particle Schrödinger equation with a form identical to that of the Schrödinger equation for non-interacting particles in an external potential. The DFT formalism [58,59], proposed by Hohenberg, Kohn and Sham, is suitable for the interaction between electrons and positrons. The positron wave function ϕ + (r) is calculated as follows [57]: The positron annihilation rate λ in an inhomogeneous electron gas is proportional to the overlap of electron n−(r) and positron n + (r) densities in the LDA. ...

In the presented work, B4C was irradiated with xenon swift heavy ions at the energy of 167 MeV. The irradiation of the substrate was done at room temperature to a fluence of 3.83 × 1014 ion/cm2. The samples were then analyzed with the X-ray diffraction technique to study the structural modification, as it can probe the region of penetration of xenon atoms due to the low atomic number of the two elements involved in the material under study. The nano-cluster formation under ion irradiation was observed. Positron lifetime (PLT) calculations of the secondary point defects forming nanoclusters and introduced into the B4C substrate by hydrogen and helium implantation were also carried out with the Multigrid instead of the K-spAce (MIKA) simulation package. The X-ray diffraction results confirmed that the sample was B4C and it had a rhombohedral crystal structure. The X-ray diffraction indicated an increase in the lattice parameter due to the Swift heavy ion (SHI) irradiation. In B12-CCC, the difference between τ with the saturation of H or He in the defect is nearly 20 ps. Under the same conditions with B11C-CBC, there is approximately twice the value for the same deviation.

... Still, PIMC simulations are feasible over substantial parts of the relevant parameter regime. In addition, we investigate the impact of temperature and density on the real space density, which is the essential quantity governing the celebrated Hohenberg-Kohn theorems [44,45]. The theorems state that the ground-state electronic density of a system n 0 (r) uniquely determines its properties and even constructs a functional E[n] with a global minimum at n 0 (r). ...

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [M.B\"ohme et. al. Phys.Rev.Lett.(in print)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair-potential. We find very favourable convergence behaviour towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyse in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations such as DFT. Our set-up gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange--correlation (XC) kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

... First-principles calculations were performed with the Vienna Ab initio Simulation Package (VASP) 41,42 on the basis of density functional theory (DFT). 43,44 The Perdew−Burke−Ernzerhof (PBE) 45 form of generalized gradient approximation (GGA) exchange−correlation functional was implemented. The projector augmented wave (PAW) pseudopotential method 46,47 was used for the plane-wave expansion with an energy cutoff of 500 eV. ...

Crystal defects play an important role in the degradation and failure of semiconductor materials and devices. Direct determination of band gap of defects is a critical step for clarifying how the defects affect the physical properties of semiconductors. Here, high-quality aluminum nitride (AlN) thin films were grown epitaxially on single-crystal Al2O3 substrates via pulsed laser deposition. The atomic structure and band gap of three types of inversion domain boundaries (IDBs) in AlN were determined using aberration-corrected transmission electron microscopy and atomic-resolution valence electron energy-loss spectroscopy. It was found that the band gap of all of the IDBs reduces evidently compared to that of the bulk AlN. The maximum band gap reduction of the IDBs is 1.0 eV. First-principles calculations revealed that the band gap reduction of the IDBs is mainly due to the rise of pz orbital at the valence band maximum, which originates from the elongated Al-N bonds along the [0001] direction at the IDBs. The successful band gap determination of defects paves an avenue for quantitatively evaluating the effect of defects on the performance of semiconductor materials and devices.

... The calculations in this paper have been carried out at zero temperature. Plane wave-based density functional theory (DFT) calculations were applied using the Vienna Ab initio Simulation Package (VASP) [45][46][47]. The exchange-correlation energy functional were approximated using projected augmented wave (PAW) [48] based on generalized gradient approximation (GGA) [49] with Perdew-Burke-Ernzerhof (PBE) functional [49,50]. ...

Effects of surface terminal groups on the structural, mechanical, and electronic properties, as well as the quantum capacitance of Ca2CT2 (T=F-, O-, Cl-, OH-) MXenes are studied by first-principles electronic structure computations. Ca2C(OH)2 is determined to be the most stable structure compared with Ca2C and Ca2CT2 (T=F-, Cl-) MXenes, while Ca2CO2 is mechanically unstable. The surface terminations have a strong influence on the work function of MXene as they can alter the Fermi level and the associated electron transfer. Analyzing the atom projected density of states shows the existence of localized electron states at and around the Fermi level, generating a high charge density close to the Fermi level and resulting in relatively high quantum capacitance. The quantum capacitance of Ca2CCl2 is the highest (152 μF/cm²) among the studied cases, while Ca2C(OH)2 has the lowest quantum capacitance. The observed variations in quantum capacitance are mainly attributed to the creation and annihilation of new electronic states and the shift of Fermi level in the studied MXenes. Also, presence of surface terminations of Ca2C MXenes considerably changes the electrode quantum capacitance and Ca2CCl2 is the most promising one among the studied cases.

... The Vienna ab initio simulation package (VASP) [21] program was used for all the calculation, in the projector augmented wave (PAW) pseudopotential, which is based on density functional theory (DFT) [22]. A spin-polarized generalized gradient approximation (GGA) was used to solve the Kohn-Sham equations with the Perdew-Burke-Ernzerhof functional (PBE) exchange-correlation functional, with plane-wave pseudopotential [23]. ...

The impact of Na atom deintercalation on olivine NaMnPO4 was investigated in a first-principle study for prospective use as cathode materials in Na-ion batteries. Within the generalized gradient approximation functional with Hubbard (U) correction, we used the plane-wave pseudopotential approach. The calculated equilibrium lattice constants are within 5% of the experimental data. The difference in equilibrium cell volumes for all deintercalated phases was only 6%, showing that NaMPO4 is structurally more stable. The predicted voltage window was found to be between 3.997 and 3.848 V. The Na1MnPO4 and MnPO4 structures are likely to be semiconductors, but the Na0.75MnPO4, Na0.5MnPO4, and Na0.25MnPO4 structures are likely to be metallic. Furthermore, all independent elastic constants for NaxMPO4 structures were shown to meet the mechanical stability requirement of the orthorhombic lattice system.

... In contrast with ab initio methods, density functional theory (DFT) methods are based on the Hohenberg-Kohn paradigm [42,43]. From the wide range of functionals, B3LYP is one of the most popular arising from the combination of Becke's exchange functional [44] together with Lee, Yang and Parr correlation functional [45]. ...

... Our first-principles calculations are based on the generalized-gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form [69][70][71][72][73] within the framework of the density-functional theory (DFT) using projector-augmented-wave (PAW) [74] wave functions as implemented in the Vienna Ab-Initio Simulation Package (VASP) [75,76]. The effect of Van-der-Waals (VdW) interactions was taken into account by using the empirical correction scheme of Grimme (DFT-D2) [77]. ...

Chiral edge modes inherent to the topological quantum anomalous Hall (QAH) effect are a pivotal topic of contemporary condensed matter research aiming at future quantum technology and application in spintronics. A large topological gap is vital to protecting against thermal fluctuations and thus enabling a higher operating temperature. From first-principle calculations, we propose Al$_{2}$O$_{3}$ as an ideal substrate for atomic monolayers consisting of Bi and group-III elements, in which a large-gap quantum spin Hall effect can be realized. Additional half-passivation with nitrogen then suggests a topological phase transition to a large-gap QAH insulator. By effective tight-binding modelling, we demonstrate that Bi-III monolayer/Al$_{2}$O$_{3}$ is dominated by $p_{x}, p_{y}$ orbitals, with subdominant $p_z$ orbital contributions. The topological phase transition into the QAH is induced by Zeeman splitting, where the off-diagonal spin exchange does not play a significant role. The effective model analysis promises utility far beyond Bi-III monolayer/Al$_{2}$O$_{3}$, as it should generically apply to systems dominated by $p_{x}, p_{y}$ orbitals with a band inversion at $\Gamma$.

... We performed first-principles quantum mechanical calculations based on the density functional theory (DFT) (Hohenberg and Kohn 1964;Kohn and Sham 1965) using Vienna Ab initio Simulation Package (VASP) (Kresse and Furthmüller 1996a, b;Kresse and Hafner 1993). The local density approximation (LDA) was selected to treat the exchange and correlation (XC) functional (Perdew and Zunger 1981) (Table S1). ...

Here, we investigated high-pressure behaviors of four end-members of K-Na-Ca-Mg alkali-bearing double carbonates (K2Mg(CO3)2, K2Ca(CO3)2, Na2Mg(CO3)2, and Na2Ca(CO3)2) using first-principles calculations up to ~ 25 GPa. For K2Mg, K2Ca, and Na2Mg double carbonates, the transitions from rhombohedral structures (R3-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\stackrel{\mathrm{-}}{3}$$\end{document}m or R3-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\stackrel{\mathrm{-}}{3}$$\end{document}) to monoclinic (C2/m) or triclinic (P1-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\stackrel{\mathrm{-}}{1}$$\end{document}) structures are predicted. While for Na2Ca(CO3)2, the P21ca structure remains stable across the calculated pressure range. But the high-pressure behavior of Na2Ca double carbonate has changed over 8 GPa: the b-axis becomes more compressible than a-axis; [CO3] –I groups tilt out of the a-b plane upon compression and reverse the direction of rotation at 8 GPa. The parameters for the equations of state of these minerals and their high-pressure phases were all theoretically determined. The predicted transformation is driven by the differences in the compressibility of structural units. The K⁺ and Na⁺ coordination polyhedra are more compressible in the structure, compared with the high axial rigidity of C–O bonds in the [CO3] triangle along the a-b plane. Our results provide projections of the high-pressure behaviors of trigonal double carbonates, in part by helping to clarify the relation among the average metallic ionic radius (Ravg), the bulk modulus (K0), and the transition pressure (PT). The transition pressure (PT) is anticorrelated to the average metallic ionic radius (Ravg), and a larger Ravg results in a lower bulk modulus (K0) for the trigonal double carbonates. Furthermore, alkali-bearing double carbonates found as inclusions in the natural diamond may indicate a hydrous parental medium composition and a deeper genesis mechanism.

Relativistic density functional theory calculations have been implemented to study the structural configurations, electronic and magnetic properties of exohedral 3d transition metal atoms doping on C60 fullerene (TM-C60) by a full potential local orbital method. The calculated binding energies revealed that the TM-C60 molecules are energetically stable in all adsorption sites. We also found that the TM-doped exohedral C60 complexes are more reactive than pure C60 fullerene. The spin and orbital magnetic moments were also determined. We have indicated that in all of the five adsorption sites, exohedral TM-C60 molecules (except for Ni-C60) are magnetized. Our magnetic calculations show that the total spin magnetic moments of TM-C60 molecules mainly come from the TM atoms. We found that the spin magnetic moments of adsorbed TM atoms in exohedral doping C60 fullerene from Sc to Mn (HH adsorption site) and for Sc to Cr (HP and P adsorption sites) are greater than their free states. Our calculations suggest that exohedral doping 3d TM-C60 complexes can almost maintain spin magnetic moments. We have indicated that the magnetic properties of exohedral TM-C60 molecules change in the presence of spin-orbit coupling. Significant orbital contributions to magnetic moments are recognized in these configurations while the spin moments are unaffected. We found that Co in exohedral doping of C60 fullerene shows a robust orbital moment in all the five adsorption sites.

Structural stability of defect complexes composed of several Ni atoms and C vacancies in diamond are studied by first-principles calculations. Results show that Ni atoms prefer accumulating with C vacancies, forming Ni-Ni complex defects, rather than to be isolated as separated point defects. Focusing on complex defects consisting of one or two Ni, the electronic structures associated with the defects near the band gap are analyzed, and their optical properties including zero-phonon line energies are discussed by comparing with experimental results.

The Hohenberg–Kohn (HK) theorem for interacting electrons is a cornerstone of modern electronic structure calculations. For a general quantum system, a HK‐type Hamiltonian in the form of Ĥhk{gi}=Ĥint+∑igiÔi$\hat {H}_{\rm hk}\lbrace g_i\rbrace =\hat {H}_{\rm int}+\sum_i g_i \hat O_i$ can always be defined, by grouping those terms with fixed or preknown coefficients into an internal part of the Hamiltonian Ĥint$\hat {H}_{\rm int}$, and factorizing the remaining as the superposition of a set of Hermitian operators {Ôi}$\lbrace\hat {O}_i\rbrace$. It is asked whether the HK theorem can be extended to such a general setting, so that the ground‐state expectation values of {Ôi}$\lbrace\hat {O}_i\rbrace$ as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. It is shown that the question can be addressed by the invertibility of generalized density correlation matrix (GDCM) defined with respect to the {Ôi}$\lbrace\hat {O}_i\rbrace$ operators. This criterion is applied to several representative examples, including the quantum Ising dimer, frustration‐free systems, N‐level quantum systems and a fermionic Hubbard chain. It is suggested that for a finite‐size system, finding an invertible GDCM under one single {gi}$\lbrace g_i\rbrace$ configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space. The Hohenberg–Kohn theorem is a cornerstone of modern electronic structure computation. Here, it is aimed to expand its territory from interacting electrons to arbitrary quantum many body systems. By introducing the concept of generalized density correlation matrix, it is shown how the extensibility can be addressed in a mathematically rigorous and practically convenient way.

One‐dimensional systems of titanium dioxide and titanates are interesting for the fundamental study of physical and chemical properties at the nanoscale. In this work we present the electronic structure, mechanical and optical properties of angstrom scale titanate derived nanowires (ASW) by means of density functional theory (DFT) and Density Functional based Tight Binding (DFTB). This one‐dimensional H2TiO3 nanostructure is an interesting real material that could serve for understanding, at a fundamental level, the physical properties of TiO5 concatenated polyhedrons derived from hydrogen titanates. The proposed structural model demonstrates to be locally stable according to phonon analysis, and it can be inferred that the one‐dimension structure is essentially preserved. The mechanical properties put this nanowire as a flexible material, that could be used in flexible substrates maintaining its electronic properties. Also, the capacity of this system to be sensitized with a catechol dye was explored. For this porpoise, the adsorption of the catechol molecule was tested showing that the most stable interaction corresponds to a dissociative chelate configuration. Finally, it was possible to verify the capability of the sensitized system for injecting electrons from the catechol dye to the nanowire under visible light exposure. Thus, we present these extreme one‐dimensional nanostructured materials as candidates for solar cell applications. In this work the electronic structure, mechanical and optical properties of angstrom scale titanate derived nanowires (ASW) H2TiO3 are investigated by means of DFT and DFTB. Additionally, the interaction between this extremely low dimensional semiconductor structure and a catechol molecule acting as a dye is studied, showing the capability of sensation under visible light illumination.

It is not a coincidence that both chirality and noncovalent interactions are ubiquitous in nature and synthetic molecular systems. Noncovalent interactivity between chiral molecules underlies enantioselective recognition as a fundamental phenomenon
regulating life and human activities. Thus, noncovalent interactions represent the narrative
thread of a fascinating story which goes across several disciplines of medical, chemical,
physical, biological, and other natural sciences. This review has been conceived with the
awareness that a modern attitude toward molecular chirality and its consequences needs to be founded on multidisciplinary approaches to disclose the molecular basis of essential enantioselective phenomena in the domain of chemical, physical, and life sciences. With the primary aim of discussing this topic in an integrated way, a comprehensive pool of rational and systematic multidisciplinary information is provided, which concerns the fundamentals of chirality, a description of noncovalent interactions, and their implications in enantioselective processes occurring in different contexts. A specific focus is devoted to enantioselection in chromatography and electromigration techniques because of their unique feature as “multistep” processes. A second motivation for writing this review is to make a clear statement about the state of the art, the tools we have at our disposal, and what is still missing to fully understand the mechanisms underlying enantioselective recognition.

The new halogen-containing oxide double perovskites A2BXO6 (X = Cl, Br, and I) have attracted much attention because of their superb electronic properties in halide double perovskites and their high stability in oxide double perovskites. Herein, 408 A2BXO6 double perovskites have been systematically screened by high-throughput computation. Refer to the empirical structural factors phase diagram (t-u), which uses large-scale first-principles calculations. Fourteen stable perovskites are finally confirmed; moreover, 11 of them have never been reported before. Our results show that Ba2AgIO6 and Sr2AgIO6 are the most preferable candidates for photovoltaic applications, of which Sr2AgIO6 has balanceable electron and hole effective masses, a quasi-direct band gap, and strong optical absorption. Importantly, Sr2AgIO6 was successfully synthesized by the solution method. Our work enriches the family of double perovskites, and the tentative experimental evidence undoubtedly hints at their great potential applications in the near future.

Many-body perturbation theory is a powerful method to simulate electronic excitations in molecules and materials starting from the output of density functional theory calculations. By implementing the theory efficiently so as to run at scale on the latest leadership high-performance computing systems it is possible to extend the scope of GW calculations. We present a GPU acceleration study of the full-frequency GW method as implemented in the WEST code. Excellent performance is achieved through the use of (i) optimized GPU libraries, e.g., cuFFT and cuBLAS, (ii) a hierarchical parallelization strategy that minimizes CPU-CPU, CPU-GPU, and GPU-GPU data transfer operations, (iii) nonblocking MPI communications that overlap with GPU computations, and (iv) mixed precision in selected portions of the code. A series of performance benchmarks has been carried out on leadership high-performance computing systems, showing a substantial speedup of the GPU-accelerated version of WEST with respect to its CPU version. Good strong and weak scaling is demonstrated using up to 25 920 GPUs. Finally, we showcase the capability of the GPU version of WEST for large-scale, full-frequency GW calculations of realistic systems, e.g., a nanostructure, an interface, and a defect, comprising up to 10 368 valence electrons.

Crystalline structures of trimethylamine N-oxide (TMAO) and its isomorphic, perdeuterated analogue (TMAO-d9) were investigated using Raman spectroscopy, X-ray crystallography, and electronic structure theory. Shifts to higher vibrational energy were observed in both Raman Under liquid Nitrogen Spectroscopy (RUNS) and high pressure Raman spectroscopy studies. Agreement between experimental Raman spectra and electronic structure computations performed on individual TMAO molecules was poor; however, better agreement was obtained when model unit cells were considered. These results also show that TMAO-d9’s spectra are significantly less perturbed than those for TMAO, suggesting weaker interactions between neighboring TMAO molecules when deuterated.

A new allotrope of sp³ hybrid superhard carbon, tP176 carbon, is proposed and investigated in this work. The tP176 carbon is dynamically, thermodynamically and mechanically stable, respectively. The bulk modulus (B) and shear modulus (G) of tP176 carbon are 242 GPa, and 192 GPa, respectively. In addition, tP176 carbon is a wide band gap semiconductor material with quasi-direct band gap, and the band gap is 2.892 eV. The hardness of tP176 carbon is 55 GPa, which implies that it is a potentially superhard material.

Manipulating the exchange bias (EB) effect using an electronic gate is a significant goal in spintronics. The emergence of van der Waals (vdW) magnetic heterostructures has provided improved means to study interlayer magnetic coupling, but to date, these heterostructures have not exhibited electrical gate-controlled EB effects. Here, we report electrically controllable EB effects in a vdW heterostructure, FePS3-Fe5GeTe2. By applying a solid protonic gate, the EB effects were repeatably electrically tuned. The EB field reaches up to 23% of the coercivity and the blocking temperature ranges from 30 to 60 K under various gate-voltages. The proton intercalations not only tune the average magnetic exchange coupling but also change the antiferromagnetic configurations in the FePS3 layer. These result in a dramatic modulation of the total interface exchange coupling and the resultant EB effects. The study is a significant step toward vdW heterostructure-based magnetic logic for future low-energy electronics.

After the Fukushima nuclear accident in 2011, U3Si2 was predicted to be an important accident tolerant fuel that can replace UO2. The results of recent studies have shown that the simulation at the micro-scale of U3Si2 as a candidate for accident tolerant fuel is not deep enough. It is not sufficient to build fuel databases and models at the macro-scale to effectively predict some properties of U3Si2. Therefore, employing the first principles to calculate some physicochemical data of U3Si2 nuclear fuel has received extensive attention. In previous work, we predicted the ideal strength of U3Si2 in several low-index crystal planes/directions by the first-principles computational tensile/shear test (FPCTT/FPCST) approach. However, there was no excess explanation for the fracture behavior of U3Si2. Therefore, in this paper, the effect of ideal tensile/shear strain on the chemical bond length and charge density distribution of U3Si2 was discussed to analyze the fracture behavior of U3Si2 in these low-index crystal planes/directions. The effect of strain was achieved by applying incremental simulation elements on the specified crystal planes/directions. The crystal structure of U3Si2 under different strains was optimized using the first principles based on density functional theory. The variation range of chemical bond length and the charge density distribution of U3Si2 under different ultimate strains were summarized and calculated respectively. The results show that the elongation of the U-U bond is the main contributor to the tensile deformation of U3Si2 in the[100] crystal direction under tensile load. The toughness of U3Si2 in the[001] crystal direction is mainly due to the elongation of the U-Si bond and U-U bond. However, the tensile deformation produced in the[110] crystal direction of U3Si2 is mainly related to the elongation of the Si-Si bond. In the (100)[010] slip system, U3Si2 has a large amount of deformation and the crystal breaks when the Si-Si bond length reaches the limit of 3.038 Å. For the (001)[100], (110)[10] and (001)[110] slip systems of U3Si2, the crystal is broken under small shear deformation, and the change of its bond length is not obvious, reflecting that the sudden decrease of the strain energy or stress in these several slip systems may be related to the strain-induced structural phase transition of U3Si2.

Developing highly efficient and stable electrocatalysts for oxygen reduction reaction (ORR) is a challenging task in energy conversion technologies. In this work, diverse axial ligands have been used to modify...

To study the structural, electronic, and optical properties of lead-free Barium titanate BaTiO3 (BT) ferroelectric material in its tetragonal structure, a combination of experimental and theoretical studies has been used and the obtained results were discussed. The studied BT compound was prepared via the sol–gel technique. The calculated bandgap energy (Eg) and structural parameters of BT are determined using four types of exchange–correlation functionals (PBE, PBEsol, LDA, and PW91) in the perspective of the density functional theory (DFT). XRD and Raman analysis have shown that BT ceramic exhibits a tetragonal phase structure without any trace of impurity phases. The UV–vis investigation showed that BT has a bandgap energy of 3.19 eV, which is larger than the theoretically calculated values. The computed lattice parameter c is overestimated (as large as ~1% deviation) when using the LDA approximation. In contrast, PBEsol proved that those lattice constants were close to the experimental values (a deviation of less than 1%).

Lithium-sulfur batteries (LSBs) have stimulated burgeoning interest in both the academic and industrial communities due to their ultrahigh energy density and high cost-effectiveness. However, the real-world application of LSBs has long been plagued by the shuttling effect and sluggish conversion kinetics of soluble lithium polysulfides (LiPSn). Herein, we have designed and synthesized creative metallic and polar Co9S8 nanoparticles with in situ growth of CNTs anchored on pyrrole-modified graphene (Co9S8/CNTs-Gr) via a facile pyrolysis method, which further demonstrates superior electrochemical performance for the fixation of sulfur and effective activation of LiPSn redox conversion. The in situ growth of CNTs and introduction of pyrrole-modified graphene are beneficial for electron migration, thus significantly boost the rate performance of LSBs. Concurrently, the Co9S8 electrocatalyst shows high catalytic activity to reinforce the polysulfide conversion. Benefiting from this exquisite nanoarchitecture design, LSBs with a [email protected]9S8/CNTs-Gr cathode exhibit outstanding performance, delivering a high reversible specific capacity of 950 mA h g⁻¹ at 1 C with a decay rate of only 0.01% per cycle. Moreover, the [email protected]9S8/CNTs-Gr electrode still achieves good cycling stability with a high sulfur loading of 7.2 mg cm⁻², and the specific area capacity reaches as high as ∼6 mA h cm⁻². This work provides a delicate design to construct Co9S8-based media for high-performance LSBs and can also promote one’s understanding of the advantages of the process of adsorption and redox conversion of LiPSn.

FeCrAl-based materials have attracted ever-increasing attentions due to their excellent resistances against high-temperature oxidation and stress-corrosion cracking, while enhancement of their mechanical properties can expand their potential applications. In this work, the micro-alloying method by adding Nb was applied to enhance the mechanical property of FeCrAl. The FeCrAl thin films with different Nb contents (Fe-16Cr-5Al, Fe-14Cr-5Al-1Nb, Fe-12Cr-5Al-2Nb, Fe-13Cr-3Al-7Nb, in wt%) were synthesized using magnetron co-sputter deposition. Benefiting from the refined grain size, the as-deposited Fe-13Cr-3Al-7Nb thin film exhibited the highest hardness (3.3 GPa), followed by Fe-14Cr-5Al-1Nb (1.5 GPa) and Fe-12Cr-5Al-2Nb (1.2 GPa), whereas the hardness of Nb-free film was the lowest (0.8 GPa). The fracture resistance (which is related to the ratio of hardness and elastic modulus) also enhances with the addition of Nb. After annealing (873 K for 6 h), the hardness of the Fe-13Cr-3Al-7Nb thin film further increased to ~6.7 GPa, in contrast to the as-annealed Nb-free thin film with no obvious hardness change. The CALPHAD (CALculation of PHAse Diagram) results indicate that with adding Nb the original single BCC (body centered cubic) phase tended to decompose into the Fe-rich and Cr-rich BCC domains, which is consistent with the transmission electron microscopic (TEM) observations. The observed strengthening of the annealed Nb-containing samples is therefore attributed to the phase separation. The first-principles calculations also support this notion. Thus, the current work has delineated the effect of Nb addition on both deposited and annealed FeCrAl-based thin films, which shows the usefulness of combined experimental and computational methods in interpreting microstructure and mechanical property evolutions of engineering materials.

Mononuclear transition metal complexes based on ionic liquid have been prepared and characterized in detail. The biological properties of the three complexes were evaluated using radical scavenging activity, reducing power, antibacterial effect, DNA binding and cleavage activity. Among the complexes, [3-[(2R)-2-({[dichloro(η⁶-benzene)ruthenium]diphenylphosphanyl}oxy)-2-phenylethyl]-1-methyl-1H-imidazol-3-ium chlo- ride] (4), demonstrated the highest radical scavenging (64.7 %) and reducing power activity (0.467) at 200 μg/ml concentration. The highest zone of inhibition was obtained from [3-[(2R)-2-({[dichloro(η⁶-p-cymene)ruthenium]diphenyl phosphanyl}oxy)-2-phenylethyl]-1-methyl-1H-imidazol-3-ium chloride] (3), against Bacillus cereus as 14 mm. Furthermore, all complexes were determined to have DNA binding and cleavage activities. Furthermore, theoretical DFT computations have also been carried out for the cationic complexes, to obtain minimum energy configuration of molecules. The effects of the chemical structures of three cationic complexes were also examined in relation to the variable property of electron-donating ligands for ruthenium-based complexes and iridium complex and their potential energy levels in ground and excited states HOMO and LUMO were determined.

We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for insulators at zero Fermi-temperature. We discuss potential consequences of this observation for modelling the potential energy landscape, as well as for solving the electronic structure problem.

Dispersion correction in theoretical determination of cyclopeptide conformations is emphasized. Whether in gas approximation or in solvation simulation, the density functional theory with London dispersion correction (DFT-D3) demonstrates that only 2∼3 conformers can stably coexist for cycloaspeptides (A, D, G) at B3LYP-D3 and CAM-B3LYP-D3. Conformational rationality is confirmed by electronic circular dichroism (ECD). Whether for Cotton effect or for excitation energy, TD-B3LYP-D3 has better performances than TD-CAM-B3LYP-D3 because the former can better reproduce the experiment. A molecular orbital analysis is used to interpret ECD, where two energy bands observed in experiment originates from the ππ* transitions other than the σπ* transitions. Long-range correction and solvent effect make H-bonds shorten, and dispersion correction makes them further shorten.

MXenes are two-dimensional layered materials that have attracted increased attention for technological applications, e.g., electrodes, support for single atom catalysts, etc. Several experimental and computational studies have been reported, however, our atomistic understanding is still far from good, in particular, for MXene-ionic liquid interfaces, which is crucial to predict and control the charge-discharge rate of those systems. Here, we have assessed the adsorption of ionic liquids forming species, on surfaces of Ti3C2Tx (where T = F, O or OH) MXenes by means of abinitio calculations at density functional theory level. The F and O terminated MXenes showed to be stables upon the adsorption, whereas the OH terminated one suffered important structural deformations when interacting with cationic species. The adsorption of molecular species are stronger, with values ranging in between -1.10 and -7.36eV, indicating the contribution of Coulombic and induction interactions as a result of the charge transference among MXenes and adsorbates. The adsorption of ionic pairs on the Ti3C2F2 and Ti3C2O2 monolayers were driven by dispersion interactions, that represent at least 84% of the total adsorption energy. Additionally, the work function of the stable MXenes structures were barely affected by the adsorption of the ionic pairs, and hence, the adsorption process did not affect the electronic properties of the single Ti3C2Tx monolayers.

Density functional theory (DFT) is a widely adopted methodology that gives quantum-level understanding of matter and guides materials discovery. In parallel, artificial intelligence (AI) for materials is an emerging interdisciplinary research direction whose major purpose is to accelerate the process of materials discovery. However, the shortage of informative data—which are crucial for model training—makes accurate prediction, design, synthesis, and characterization a challenge for materials. Experimental data are regarded as expensive, while the relatively less expensive data obtained from DFT calculations suffer from systematic errors rooted in approximated density functionals. Recently, Kirkpatrick et al. constructed the density functional DeepMind 21 (DM21) via deep learning, which solved fractional electron problems and outperformed hand-designed functionals. The foundation of DM21 reveals that data calculated from accurate AI-designed functionals can be supplementary to experimental data in prediction models training and improve models’ performance, thus accelerating material discovery processes.

Electrochromic materials can tune the illumination and heat exchange of a building with the environment and thereby save energy in lighting, heating, and air conditioning in a cost‐effective way, which is vital in realizing carbon neutrality. 2D frameworks such as coordination nanosheets (CONASHs) that are widely explored for a wide range of applications in energy storage and conversion can be a cluster of novel electrochromic materials. In this work, a series of transition metal benzenehexathiol (TM‐BHT) CONASHs are theoretically investigated via first‐principles simulations. During ion intercalation and deintercalation in TM‐BHTs, changes in lattice structures, lithium diffusion barriers, atomic charges, bond strength, and electronic properties are explored in‐depth. The incurred changes are then correlated with critical electrochromic properties, including the transmittance adjustment ranges in the visible light, near‐infrared, solar spectrum, and mid‐infrared. Among the various TM‐BHT systems, Cu‐BHT and Ag‐BHT are the most promising broadband electrochromic materials for optical and thermal management in the wavelength range from visible to mid‐infrared. The theoretical guidance from this work paves a new path toward electrochromic applications of CONASHs that exploit the versatility of these 2D materials.

Here, the optical, dielectric and electronic properties of two-dimensional (2D) isomers of NbS2 monolayer, namely planar isomer (P–NbS2 isomer) and hexagonal isomer (H–NbS2 isomer), are being explored. It is found that the P–NbS2 isomer is an indirect band gap semiconducting, and it has a band gap of approximately 0.36 eV between the valence and conduction bands. On the other hand, the H–NbS2 isomer exhibit metallic characteristics, which is evident from the band structure and also from the density of states. The optical properties such as absorption coefficient, dielectric function, and optical conductivity, along with the refractive index, reflection, and extinction coefficients in both the isomers, have also been calculated. These isomers of NbS2 exhibit excellent optical response and high dielectric behavior in the low-energy region. The dielectric study suggests that both the isomers are highly anisotropic in nature. These monolayers of NbS2 isomer may be a potential candidate for futuristic metal-based electronic applications such as nanoelectronics, optoelectronics, and photonics.

The knowledge about the mechanisms of the morphological control of nanoparticles (NPs) is directly correlated with the atomic configurations of their exposed surfaces, which can facilitate materials functionalization according to the surface-dependent properties. In this context, this study focused on modeling via the density functional theory (DFT) the (001), (100), (101), (103), (110), (111), and (112) surfaces of the CaXO4 (X = Mo or W) (scheelite phase) to offer a comprehensive study of their structural and electronic properties. Additionally, a systematic mapping of the NPs morphology was elaborated as a function of the modulation of the surface energies. For the surfaces of both systems, a stability order of (001) > (112) > (111) > (101) > (110) > (103) > (100) was observed. Differences were observed in both systems concerning the outermost polyhedral distortion and their atomic charges. The analysis of the energy band alignment of the surfaces revealed the potential use of both materials in photocatalytic environmental remediation. The methodology and results presented herein can be useful for targeting the synthesis and functionalization of CaXO4 and related materials.

To study the structural properties of Co2FeZ (Z = Al, Si, Ga) (CFZ) alloys, we will use the approximation method GGA-PBE based on the method of plane waves increased by linear waves at full potential using the theory of functional density in both the Hg2CuTi and Cu2MnAl-type structures. From the most stable state we determine the other properties such as the magnetic, elastic and thermoelectric properties. The band structure calculation reveals indirect band gap in spin down channel and zero band gap in spin up channel of valence and conduction bands confirming the spin gapless semiconducting nature of these compounds. Calculated Seebeck coefficient in spin up and spin down channel reveals that the CFZ behaves as both n and p type thermoelectric materials with better output efficiency. The transport properties of these materials are discussed on the basis of Seebeck coefficient, electrical conductivity coefficient, thermal conductivity and figure-of-merit coefficient. By analyzing the nature of the bonding between the different atoms that form CFZ that each of them has a strong covalent character.

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically motivated orbital-density-dependent corrections. These corrections act on a set of localized orbitals that, in periodic systems, resemble maximally localized Wannier functions. At variance with the original, direct supercell implementation (Phys. Rev. X 2018, 8, 021051), we discuss here (i) the complex but efficient formalism required for a periodic boundary code using explicit Brillouin zone sampling and (ii) the calculation of the screened Koopmans corrections with density functional perturbation theory. In addition to delivering improved scaling with system size, the present development makes the calculation of band structures with Koopmans functionals straightforward. The implementation in the open-source Quantum ESPRESSO distribution and the application to prototypical insulating and semiconducting systems are presented and discussed.

Peptides and foldamers have recently gained increasing attention as chiral catalysts to achieve challenging (asymmetric) transformations. We previously reported that short helically folded aliphatic oligoureas in combination with achiral Brønsted bases are effective H-bonding catalysts for C-C bond-forming reactions─i.e., the conjugate addition of 1,3-dicarbonyl pronucleophiles to nitroalkenes─with high reactivity and selectivity and at remarkably low chiral catalyst/substrate molar ratios. This theoretical investigation at the density functional theory level of theory, aims to both analyze how the substrates of the reaction interact with the foldamer catalyst and rationalize a chain-length dependence effect on the catalytic properties. We confirm that the first two ureas are the only H-bond donors available to interact with external molecules. Moreover, each urea site interacts with one of the two reactants allowing a short distance between the two reacting carbons, thus facilitating the conjugated addition. Additionally, it was observed that the molecular recognition and catalyst-substrate interactions are mainly governed by electrostatic interactions but not orbital interactions (see from NBO if this is finally true). On these grounds, an electrostatic potential (ESP) analysis showed an important internal charge separation in the catalyst, the positive ESP region being concentrated around the first two ureas, with its area extending as the number of residues increases.

The energetics of the regioselective mononitration of 9,10-BN-naphthalene with acetyl nitrate (H3C2NO4) were modeled with ab initio simulations in the gas phase and an acetonitrile solvent. The single-electron-transfer (SET) nitration mechanism leading to a σ-complex and a single-step nitration mechanism were modeled. The energy barrier for the single-step mechanism was lower than that for the SET mechanism in the gas phase. However, the two are much more energetically competitive in the solvent. The σ-complex was found to be unstable in the gas phase owing to the interaction with the counterion. Using the single-step mechanism, the carbon site 1 nearest boron had the lowest activation energy for nitration of 22.6 kcal/mol, while site 3 had the second lowest barrier of 24.6 kcal/mol. Details on the molecular structures at intermediate and transition states as well as charges in different configurations are discussed.

The quasi-classical limit of the many-particle perturbation theory is considered for electrons moving in the Coulomb potential of the nucleus. The problem is analyzed using the Green's function formulation of many-particle physics. When corrections involving the gradient of the self-consistent potential are neglected, the results agree to all orders in the interaction strength with the procedure of Lewis for including correlation corrections in the Thomas-Fermi model. The disagreement between the work of Lewis and the recent work of Baraff is shown to be due to the latter's neglect of anomalous contributions to the perturbation theory which arise, because the local Fermi momentum is a function of the interaction strength. The calculation of inhomogeneity corrections is also considered.

A systematic method is presented for deriving the Thomas-Fermi equation for an atom and the quantum corrections from the many-body description. The novel feature of the method is that it does not require any a priori assumptions about the assignment of electrons to fully occupied single-particle states or about the distribution of electrons in phase space, but shows instead that the distribution which is usually assumed, or derived from the assumption of fully occupied single particle states, is a direct consequence of specifying that the many particle system is in its ground state. The procedure used in the derivation is the expansion of the mixed position-momentum representation of the Green's function in a series of powers of ℏ. The lowest order term is found to correspond with the Thomas-Fermi density. The form of the higher order terms, which are to be considered as corrections to zeroth order term, depends on the approximations made in the many-body equations for obtaining the Green's function. This paper deals only with the Hartree-Fock approximation, but the methods presented here allow generalization to other approximations which can include correlation effects.

The Fermi-Thomas-Dirac equation is modified tc include correlations ; between electrons. An application is made to the equation of state. No ; numerical work with the modified equation is reported. (anth);

The limits of validity of the correlation-energy calculations in the regions of high density, low density, and actual metallic electron densities are discussed. Simple physical arguments are given which show that the high-density calculation of Gell-Mann and Brueckner is valid for rs1 while the low-density calculation of Wigner is valid for rs20. For actual metallic densities it is shown that the contribution to the correlation energy from long-wavelength momentum transfers (k<βk0<0.47rs12k0) may be accurately calculated in the random phase approximation. This contribution is calculated using the Bohm-Pines extended Hamiltonian, and is shown to be E(β)=-0.458β2rs+0.866β3rs32-0.98β4rs2+0.019β4rs+0. 706β5rs52+ry. An identical result is obtained by a suitable expansion of the result of Gell-Mann and Brueckner; the validity of the Bohm-Pines neglect of subsidiary conditions in the calculation of the ground-state energy is thereby explicitly established. The contribution to the correlation energy from sufficiently high momentum transfers (kk0) will arise only from the interaction between electrons of antiparallel spin, and may be estimated using second-order perturbation theory. The contribution arising from intermediate momentum transfers (0.47rs12k0kk0) cannot be calculated analytically; the interpolation procedures for this domain proposed by Pines and Hubbard are shown to be nearly identical, and their accuracy is estimated as ∼15%. The result for the over-all correlation energy using the interpolation procedure of Pines is Ec(-0.115+0.031 lnrs)ry.

A new method is described for computing the effect of correlation, inhomogeneity, and exchange on the Thomas-Fermi model of the atom. The method makes use of the many-body point of view, rather than an independent-particle point of view, by considering the hierarchy equation linking the n-particle Green's functions. The hierarchy is truncated by a prescription equivalent to the Gell-Mann and Brueckner theory of the high-density electron gas, resulting in a description of the atom in which the exchange interaction is replaced by the effective interaction. The physical significance of this replacement is noted. The Green's function for this model is then expanded as a series in powers of ℏ. The lowest order term is found to describe the Thomas-Fermi model of the atom. The equation for the next higher term contributing to this expansion is manipulated so as to yield an ordinary differential equation for the corresponding correction to the potential. This equation contains a term which expresses the effect of inhomogeneity and another which arises from the correlation of the electrons and from exchange. The inhomogeneity term is one which has been found previously. Study of the correlation term shows that it depends on the separation energy of an electron from an infinite electron gas, which suggests a generalization by which the method might be made applicable to those outer regions of the atom for which the electron density is below that to which the Gell-Mann and Brueckner theory would apply.

A theoretical investigation is made of the distribution of electrons round a positively charged impurity dissolved in a monovalent metal. Applications are made to dissolved hydrogen, where the impurity is a proton, and to atoms such as zinc, gallium, etc., which are usually considered to contribute their electrons to the conduction electrons. In all cases the positive charge must be screened; and in many cases this is shown to occur through the formation of bound states below the level of the Fermi distribution. The relation of these results to the Hume-Rothery rule is discussed. The ideas introduced are used to calculate the heats of solution of hydrogen and of polyvalent metals in the noble metals, and to discuss the magnetic properties of these alloys. A detailed discussion is given of x-ray emission and absorption, the vacancy left in the x-ray shell being here treated as the positive impurity. In certain cases quantitative predictions are made about the energies of x-ray absorption edges.Discussions along the same lines are given of the optical absorption of the noble metals, and of the x-ray emission spectra of certain alloys.

The shielding of a small fixed charge in a high-density electron gas is calculated by means of a technique similar to that used by Gell-Mann and Brueckner for calculating the correlation energy. A closed expression for the density of displaced electrons is derived and evaluated numerically for several densities of the electron gas. An asymptotic form is also given.

The energy of interaction between free electrons in an electron gas is considered. The interaction energy of electrons with parallel spin is known to be that of the space charges plus the exchange integrals, and these terms modify the shape of the wave functions but slightly. The interaction of the electrons with antiparallel spin, contains, in addition to the interaction of uniformly distributed space charges, another term. This term is due to the fact that the electrons repell each other and try to keep as far apart as possible. The total energy of the system will be decreased through the corresponding modification of the wave function. In the present paper it is attempted to calculate this "correlation energy" by an approximation method which is, essentially, a development of the energy by means of the Rayleigh-Schr\"odinger perturbation theory in a power series of ${e}^{2}$.

The quantity εc is defined as the correlation energy per particle of an electron gas expressed in rydbergs. It is a function of the conventional dimensionless parameter rs, where rs-3 is proportional to the electron density. Here εc is computed for small values of rs (high density) and found to be given by εc=Alnrs+C+O(rs). The value of A is found to be 0.0622, a result that could be deduced from previous work of Wigner, Macke, and Pines. An exact formula for the constant C is given here for the first time; earlier workers had made only approximate calculations of C. Further, it is shown how the next correction in rs can be computed. The method is based on summing the most highly divergent terms of the perturbation series under the integral sign to give a convergent result. The summation is performed by a technique similar to Feynman's methods in field theory.

- Phys Pershan
- Rev

Pershan, Phys. Rev. 127, 1918 (1962); Z. Fried s.nd W. M. Frank,
Nuovo Cimento 27, 218 (1963).

Dominicis for valuable discussions

- J Friedel
- . R Dr
- Dr C Balian
- De

J. Friedel, Dr. R. Balian, and Dr. C. De Dominicis
for valuable discussions.
PHYSICAL REVIEW
VOLUME 136, NUM BER 3 B
9 iVOVEM B ER 1964

Enrico Fermi International School of Physics, Varenna, 1963 (unpublished). second area of concentration is the question of proper description of the electromagnetic radiation emanating from a laser; i.e. , questions of coherence and correlation

- Jr Lamb

Lamb, Jr., Lecture Notes, Enrico Fermi International School of
Physics, Varenna, 1963 (unpublished).
second area of concentration is the question of proper
description of the electromagnetic radiation emanating
from a laser; i.e., questions of coherence and correlation. ' And finally, the problem of interaction of laser
light with matter has attracted considerable interest. '
It is this latter question to which we are devoting ourselves in this paper.
a
' R. Glauber, Phys. Rev. 130, 2529 (1963);

- E C G Sudarshan

E. C. G. Sudarshan,
Phys. Rev. Letters 10, 277 (1963);

- E Wolf

E. Wolf, Proc. Phys. Soc.
(London) 80, 1269 (1962).

- Pershan

Pershan, Phys. Rev. 127, 1918 (1962);

- Z Fried S.Nd
- W M Frank

Z. Fried s.nd W. M. Frank,
Nuovo Cimento 27, 218 (1963).