Mathematical Approach to N-Centered DFT and Associated Methods for the Study of Open Systems

A fundamental aspect of the study of N−electronic systems (systems containing N electrons) is to obtain information on the states in which these systems have minimal energy. In practice a numerical search of such states is impossible to carry out, so that alternative approaches have been developped, the one around which this work revolves being to consider electronic systems through their electronic density rather than their state. This approach, known today as Density Functional Theory (DFT), was formalised in Kohn and Sham’s seminal article [1] and its mathematical aspects were studied a few years later by Lieb [2]. Since then, the ideas leading to the construction of DFT have been adapted to the context of electronic systems with a fractionnal number of electrons (open systems), first through PPLB DFT[3] and more recently through the definition of N−centered DFT[4, 5]. In both cases it is unclear wherether the mathematical properties established for classical DFT can be expected to hold true. This question is the main problematic of our work, in which we shall study the analogy between N−centered and classical DFT, from their construction to the methods that are derived from them. This will lead us to construct a Kohn-Sham scheme for N−centered DFT, investigate the links between this theory and optimal transport and present the Hubbard Dimer in this particular situation.

Superconductivity in the two-dimensional nonbenzenoid biphenylene sheet with Dirac cone

During the past decade, two-dimensional materials have attracted much attention in superconductivity due to their feasible physical properties and easy chemical modifications. Herein, we use a recently literature reported novel biphenylene sheet (BP sheet) for investigating superconductivity-related physical properties. The electronic states of BP sheet that appeared near the Fermi level are composed of pz orbital of carbon due to sp2 hybridization. Also, an anisotropic Dirac cone is formed just above the Fermi level by crossing two bands comprised of different carbon atoms. One of the two bands is quasi-flat thus leading to a peak of electronic density of states above the Fermi level. In addition, the rotational-vibration phonon mode of the six-membered carbon ring is strongly coupled with electrons. The electron-phonon coupling induces the superconductivity of 6.2 K in BP sheet. Furthermore, both small uniaxial strains and electronic doping can take the Dirac cone and high electronic density of state close to the Fermi level and further raise the superconducting critical temperature to 27.4 K and 21.5 K, respectively. The obtained result suggests that BP sheet with Dirac fermions and superconductivity can be a potential material for the development of future superconducting devices.

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 density functional theory by discussing Hohenberg-Kohn theorems that form its foundations. We then go on to discuss Kohn-Sham formulation of density-functional theory in its exact form. Next, local density approximation is introduced and solutions of Kohn-Sham equation for some representative systems, obtained using the local density approximation, are presented. We end part-I of the review describing the contents of part-II.

Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Self Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

The estimation of energy and elastic properties of TiAlNb materials based on results of first principles calculations

The results of research of isolated TiAlNb clusters are presented. The models of isolated clusters of 27, 59, 65 atoms in size which is fragments of the bcc structure have been constructed. The models stoichiometry imitate α-, γ-, α+γ- and β-phase TiAlNb alloys. The structural, cohesive and electronic properties of these clusters have been investigated within the framework of electronic density functional theory with PBE0 functional with a set of MINI basis functions with application of Gaussian'03 and GAMESS software packages. It was found that upon transition of the cluster structure from the α- to the β-phase, the cohesion energy increases and the crystal lattice period decreases. This corresponds to an increase in the values of the structure strength and density. For the calculation of the bulk modulus were utilized value of changes in energy and volume of cluster, got in research. The bulk modulus of the isolated β-phase TiAlNb cluster is predicted. This bulk modulus near to 142.4 GPa. The result was extended to volumetric structures. The investigation showed that bulk modulus of Ti2AlNb materials near to 163.6 GPa. Comparison of calculation results with experimental values of elastic moduli of materials with similar structure and composition is carried out. The comparison revealed the agreement between the calculated values and the results of experiments. A method is proposed for evaluating the elastic properties of TiAlNb alloys based on the results of first principles calculations. Keywords: cluster, aluminide titanium, bulk modulus, computer material science.

Potential Use of Cold Plasma Discharges for Frequency Reconfigurability in a Sievenpiper Mushroom Metasurface

This article presents a parametric study using full-wave simulations about the potential use of cold plasma discharges to achieve frequency reconfiguration on a Sievenpiper mushroom metasurface. The study was done by inserting plasma tubes in between the patches of the mushroom structure, in three different positions with respect to the top of the metasurface, and varying the electronic density while keeping the plasma collision frequency. The obtained results show that it is possible to shift the stop-band generated by the metasurface around 25% towards lower frequencies for an electron density value inside the tubes of 1014 cm−3, when they are placed in between the top patches of the metasurface. Additional insertion losses are exhibited when operating near the plasma frequency.

Electronic structure, Mechanical and Thermodynamic properties of CoYSb (Y= Cr, Mo, W) half-Heusler compounds as potential spintronic materials

We used Density Functional Theory (DFT) calculations to investigate the structural, electronic, magnetic, mechanical and thermodynamic properties of CoYSb (Y = Cr, Mo and W) compounds. These are XYZ type half-Heusler alloys, which also exist in the face centred cubic MgAgAs-type structure and conform to F¯43m space group. We computed these properties in three different atomic arrangements known as Type-I, Type-II and Type-III phases. In all these phases, the alloys were found to be in the ferromagnetic state. Furthermore, the calculated electronic band structure and the total electronic density of states indicated a metallic behaviour in CoWSb, nearly half-metallic in CoMoSb and half-metallic in CoCrSb, with a minority-spin band gap of 0.81 eV. Furthermore, the calculated mechanical properties predicted an anisotropic behaviour of these alloys in their stable phase. Finally, due to its high Debye temperature value, CoCrSb shows stronger covalent bonding than CoMoSb and CoWSb, respectively.

QUANTUM-CHEMICAL CALCULATION AND SPECTROSCOPIC STUDY OF π-CONJUGATION PATHWAY IN NH-TAUTOMERS OF THE FREE BASE CORROLES

The π-conjugation pathway was identified and the degree of aromaticity for the NH-tautomers of the free base corroles was determined by quantum chemistry methods and absorption spectroscopy. Different participation of the macrocycle skeletal atoms in formation of the π-conjugation pathway was established, and it was supposed that conjugation pathway consisting of 18 π-electrons were dominating. At the same time, each of two NH-tautomers possesses its own distinct π-conjugation pathway, which provides the differences in the aromaticity degree. It was shown that architecture of the peripheral substitution of a macrocycle influences the degree of aromaticity. Method of the control over the equilibrium between two NH-tautomers was proposed and experimentally proved. It consists in the design of the electronic density distribution in macrocycle which is characteristic for one of the tautomers.