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A general analytic function is proposed to represent the radial distribution of charge density for atoms. The proposed function fits perfectly to the radial charge density generated numerically by local spin density functional method for atoms from He to Kr.

This is an ab initio study based on the density functional theory that uses GGA-PBE as the exchange–correlation potential. The energetic, electronic, magnetic properties, and optical conductivity of the cubic $\beta 2$ of TiCo and TiNi alloys with and without the hydrogen atom are performed. The present alloys are found to be thermodynamically stable and can be created. It can be deduced that the octahedral site has higher energetic stability absorption for the hydrogen atoms compared to the bridge and tetrahedral sites in the TiCo and TiNi alloys. The absorption energy at octahedral site is found to be 2.37eV for TiCo and 2.32eV for TiNi. Hydrogen absorption expands and brittles the host alloy. Hydrogen storage in more than one site in the host alloy is found to be energetically stable and can be formed. The chemical bonding between the constituent atoms of the present alloys is mainly ionic with some covalent bonding. The hydrogen absorption has a clear effect on the magnetic, and electrical conductivity relative to the relaxation time and optical conductivity of the present alloys. Beneficial optical applications can be assumed for the present alloys due to their high optical conductivity.

We present an oscillator model of relativistic spin-0 charges moving in quantum states with minimal electromagnetic field coupling. Rather than using a perturbative approach, we implemented anharmonicity directly under the integer-dependent levels. In this way, the rest mass energy is kept at 280MeV. Within the extended Pekeris approximation, we have also improved the deep approximation to the third and fourth orders near equilibrium at 7.5fm with a width range of $0.43{\mathrm{\text{fm}}}^{-1}$. By taking into account the Morse potential energy, the improved approximation provides a model for the relativistic quantum states of the spatially independent rest mass without an external magnetic field. We considered an extra-energy addition that results in shifted Morse potentials in the depth range of 80–100MeV, yielding positive and negative values for particles and antiparticles, respectively. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels, where we have found about 200MeV for particles and nearly $-$10MeV for antiparticles. In addition to the negative energy states, the wave functions ($n=0$, $\ell =0$) and ($n=1$, $\ell =1$), which correspond to the energy levels, have been followed by the typical probability form, which shows charge distribution.

In this paper, we calculate the proton and neutron unpolarized and transversely polarized densities. We use the light-front wave function (LFWF), which at an initial scale is constrained by the soft-wall anti-de Sitter (AdS) QCD model, for calculating the Dirac and Pauli form factors which transverse densities are in terms of these form factors. Also, we use these form factors for calculating the flavor separated results for the proton and neutron electromagnetic form factors and calculate u and d quark unpolarized and transversely polarized densities. Finally, we compare our results with other previous parametrizations.

A detailed understanding of charge density and its origins during the electrospinning process is desirable for developing new electrospinnable polymer-solvent systems and ensuring mathematical models of the process are accurate. In this work, two different approaches were taken to alter the charge density in order to measure its effect on the Taylor cone, mass deposition rate and initial jet diameter. It was found that an increase in charge density results in a decrease in the mass deposition rate and initial jet diameter. A theory is proposed for this behaviour in that an increase in charge density leads to the tip of the Taylor cone forming a smaller radius of curvature resulting in the concentration of electric stresses at the tip. This leads to the electrostatic forces drawing the initial jet from a smaller effective area or "virtual orifice".

The independent particle model (IPM) coupled with empirical pseudopotential method (EPM) was used to compute the thermalized positron charge densities in specific family of binary tetrahedrally coordinated crystals of formula A^NB^8-N. Initial results show a clear asymmetrical positron charge distribution relative to the bond center. It is observed that the positron density is maximum in the open interstices and is excluded not only from the ion cores but also to a considerable degree from the valence bonds. Electron-positron momentum densities are calculated for the (001, 110) planes. The results are used to analyze the positron effects in GeC and SnC. Our computational technique provides the theoretical means of interpreting the k-space densities obtained experimentally using the two-dimensional angular correlation of annihilation radiation (2D-ACAR).

Electronic structure and electronic charge density in the interatomic bonds are investigated with ab initio calculations based on the density-functional theory. The full potential linearized augmented plane-wave method was used with the generalized gradient approximation. Considering the partial density of states the electron charge density distribution in the Bi, S, Se and Br atomic bonds is caused by Bi-6p, S-3p, Se-4p, Br-4p orbital hybridization. Electronic charge distribution of one BiSBr and BiSeBr molecule range suggest that the Bi–S, Bi–Se and Bi–Br bonds are covalent–ionic type. Bi–S and Bi–Se bonds are strong covalent with a not great ionicity factor (, Bi–S; , Bi–Se). Bi–Br bonds are covalent type with a larger ionicity factor (, Bi–Br).

Atomic and electronic structures of monovacancy (V1), divacancy (V2) and ring hexavacancy (V6) in crystalline silicon are studied using first-principles calculations in periodic supercells. Our results show that the V6 defect is the most stable among V1, V2 and V6 defects, and the V2-RB structure is a little more stable than the V2-LP structure due to lower vacancy formation energy. Furthermore, it is found that both V1 and V2 undergo the Jahn–Teller (JT) distortion while V6 does not. As a result, V1 and V2 have deep levels in the gap which mainly come from the neighboring atoms to vacancy. V6 has tailing bands in the gap, and so has a more stable electronic structure than V1 and V2. In addition, the JT distortion also reflects in the band decomposed charge density and the difference charge density.

In this paper, we discuss the charge and magnetization densities for proton and neutron in the transverse plane, whereas there are links between the generalized parton distributions (GPDs) and elastic form factors by means of sum rules. We use the extended Regge parameterization for large momentum transfer region for calculating Dirac and Pauli form factors which have been described in the electromagnetic form factors data, so we want to calculate the charge and magnetization densities for proton and neutron in the transverse plane and we also calculate $u$ and $d$ quark charge and magnetization densities. The extracted results are compared with other previous parameterizations.

In this paper, we present first principles calculations of the energetic, electronic and magnetic properties of the variant termination of TiAl (001) and Ni/TiAl (001) surfaces with and without hydrogen atoms. The calculations have been performed within the density functional theory using full-potential linearized augmented plane wave method. The generalized gradient approximation (GGA) is utilized as the exchange-correlation energy. The octahedral site is the stable absorption site of H atom in the β-TiAl system. This absorption reduces the cohesive energy of β-TiAl system due to increase in the lattice constant. The surface energy for both TiAl (001) terminations is calculated. The stable adsorption site of H atoms on the variant termination of TiAl (001) surface is performed. The adsorption energy of hydrogen on Ti is more energetic than that on Al. The adsorption of H atom on both terminations of H/Ni/TiAl (001) is more preferable at the bridge site. The adsorption energies are enhanced on Ni atom due to the contraction between d-Ni bands and TiAl substrate band.

The geometrical and electronic structures of [M₆O${}_{19}$]${}^{n-}$ (M $=$ Mo, W, $n=2$; M $=$ V, Nb, Ta, $n=8$) and their derivatives were investigated by using density functional theory methods. The results indicate that the geometrical structure of [V₆O${}_{19}$]${}^{8-}$ is not different from other Lindqvist-type anions. The energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) (HOMO$-$LUMO energy gap) of [V₆O${}_{19}$]${}^{8-}$ is smaller than those of same charge anions, [Nb₆O${}_{19}$]${}^{8-}$ and [Ta₆O${}_{19}$]${}^{8-}$. In addition, the charge density ${\rho }_{\mathrm{\text{CD}}}$ of [V₆O${}_{19}$]${}^{8-}$ is larger when compared with those of other studied clusters. The investigation on the derivatives shows that the valence of V atom (V${}^{4+}$ or V${}^{5+}$) and the methoxy ligand influence the HOMO$-$LUMO energy gap and the charge density ${\rho }_{\mathrm{\text{CD}}}$ of the studied clusters.

Nanoparticles of bimetallic alloys have been shown to possess composition dependent characteristics which distinguish themselves from the corresponding bulk alloys. Taking the 34-atom nanoalloy of Ag and Cu (Ag₂₇Cu₇), we show using first principles electronic structure calculations that this core-shell alloy indeed has perfect D_5h symmetry and consists of only 6 non-equivalent (2 Cu and 4 Ag) atoms. Analysis of the interatomic bond lengths and detailed electronic structure further reveal that the Cu atoms play a major role in controlling the characteristics of the nanoalloy. The higher cohesive energy, together with shorter bond length for Cu, compared to Ag, conspire to produce a hierarchy in the relative strengths of the Ag – Cu, Ag – Ag, and Cu – Cu bonds and corresponding interatomic bond lengths, point to the uniqueness in the characteristics of this nanoalloy. Charge density plots of Ag₂₇Cu₇ provide further insights into the relative strengths of the various interatomic bonds.

The structure, packing, and charge distribution in molecules of nonlinear optical materials have been analysed with reference to their counterparts in centrosymmetric structures based on low temperature X-ray measurements. The systems studied are the centric and noncentric polymorphs of 5-nitrouracil as well as the diamino, dithio, and thioamino derivatives of 1,1-ethylenedicarbonitrile; the latter possesses a noncentric structure. The molecular structure of 5-nitrouracil is invariant between the two forms, while the crystal packing is considerably different, leading to dimeric N–H⋯O rings in the centric polymorph and linear chains in noncentric one. There is an additional C–H⋯O contact in the centric form with a significant overlap of the electrostatic potentials between the alkenyl hydrogen atom and an oxygen atom of the nitro group. The dipole moment of 5-nitrouracil in the noncentric form is much higher (μ=9 D) than in the centric form (≈6 D). Among the 1,1-ethylenedicarbonitriles, there is an increased charge separation in the noncentric thioamino derivative, leading to an enhanced dipole of 15 D compared to the centric diamino (5 D) and dithio (6 D) derivatives. The effect of the crystal field is borne out by semiempirical AM1 calculations on the two systems. Dipole moments calculated for the molecules in the frozen geometries match closely with those abtained fro centric crystals from the experimental charge densities. The calculated values of the dipole moment in the frozen or optimized geometries in the noncentric structures are, however, considerably lower than the observed value. Furthermore, the conformation of the S–CH₃, group in the noncentric crystal is anti with respect to the central C=C bond while the syn conformation is anti with respect to the central C=C bond while the syn conformation is predicted for the free molecule in the optimized geometry.

The charge density, electronic energy band and density of states of Au-doped armchair graphene nanoribbons (AGNRs) with one-edge are investigated using the local density approximation based on density function theory. Our results indicate the charge density is transferred and mainly located on the Au atoms. The one-edge Au -doped AGNRs have low formation energy. So we predict that one-edge Au-doped AGNRs is an energetically favorable practice. The energy band structure of Au-doped AGNRs shows extra bands at near Fermi level in the valence band, which is cause to promote conductivity. The project density of states is calculated and reveals that the localization and hybridization between C-2p and Au-6s, 6p, 5d electronic states are much stronger in the valence band and the conduction band group. A localization state is induced due to the absence of the bonding charge between Au and H atoms, which contributes to H-1s electronic states at -0.13 eV near the Fermi level. It causes Fermi level is crossed by the conduction band to make becoming metallic.