Mulliken Overlap Population Research Articles

Elastic and thermodynamic properties of Al4Si6La3 under pressure from first-principles calculation

The structure stability, mechanical properties and thermodynamic behaviors of Al4Si6La3 compound in a wide pressure range 0–100 ​GPa have been explored by performing first-principles calculations based on density functional theory. The calculated formation enthalpy demonstrates that the Al4Si6La3 compound at 0 ​GPa is thermodynamically stable and exhibits unstable with the increasing of pressure. The single crystal and polycrystalline elastic constants as a function of pressure are also calculated and discussed. Al4Si6La3 compound exhibits ductile nature at pressure up to 100 ​GPa by calculating Cauchy pressure, B/G ratio and Poisson's ratio. It is found that the Debye temperature and minimum thermal conductivity of Al4Si6La3 compound can be improved to some extent when the pressure is increasing. The analysis of electronic structures including charge density difference, Mulliken overlap population and density of state reveal that Al–Si and La–Si can form covalent bonds in Al4Si6La3 compound whereas Al–La form antibonding states at various pressures.

Mechanism of Gold Cyanidation in Bioleaching of Precious Metals from Waste Printed Circuit Boards

Biocyanidation is an environment-friendly technology for recovering precious metals from waste printed circuit boards (WPCBs). Although the leaching mechanism has been studied a lot, Au-release behavior still remains unknown. In this paper, density functional theory (DFT) was employed to investigate the electronic structure of the complex existing in the Au cyanidation process. Extended charge decomposition analysis (ECDA) showed that the adsorption of CN– to Au and the adsorption of O to the formed [AuCN]⁻ caused net electron transfer of 0.356 and 0.574 au, respectively. Dissociation of O from [AuCNO]⁻ had a Gibbs free energy change of −154.229 kcal/mol. Electron localization function (ELF) and localized orbital locator (LOL) confirmed that CN– covalent bonding led to a transformation of the orbit localization region of the adsorbed Au atom. It might cause electrostatic repulsion from the nondirectly contacted Au atom. This speculation was demonstrated by the Mulliken overlap population analysis, which showed that CN– bonding caused antibonding interaction. The repulsive interaction would be an important factor triggering the release of the adsorbed Au atom. This work presented a new interpretation of Au cyanidation, providing important insights into Au-release behavior. It might help construct the leaching kinetics of multimetal resources to facilitate the recovery of precious metals from waste printed circuit boards.

Microscopic theory of hardness and optimized hardness model of MX1B and M2X2B2 (M=W, Mo; X1=Fe, Co, X2=Fe, Co, Ni) transition-metal ternary borides by the first-principles calculations and experimental verification

Hardness is very complex to describe although it was extensively investigated due to its application in industry. A reliable method is necessary to predict the hardness of compounds as the candidates of the hard phase for cermets. The current review presents the four most popular of microhardness models with average energy gap, bond strength, Mulliken overlap populations and electronegativity. The hardness of the MX1B and M2X2B2 ternary borides was predicted using the above models. Specially, the pseudo-binary crystals (chemical bonds), the overlapping of chemical bonds and overlap populations, the total number of different bonds and the deviation caused by metallicity were discussed when using the Gao's model with overlap populations. Meanwhile, the cohesive energy, formation enthalpy and elastic constants of these borides were calculated via the first-principles calculations, and the results indicate that borides are thermodynamically and mechanically stable. Then the selected materials were prepared by reaction boronizing sintering and the hardness of hard phases was measured using a Micro Vickers hardness tester. The calculated hardness was compared with experimental results to evaluate the feasibility of predicting the mechanical properties of borides. A modified micro hardness model was obtained for predicting the hardness of the MX1B and M2X2B2 ternary borides after verified with the experimental data. The modified model can be used as a quantitative guide to accelerate the selection for advanced high hardness ceramic materials.

Sodium rubidium hydrogen citrate, NaRbHC6H5O7, and sodium caesium hydrogen citrate, NaCsHC6H5O7: crystal structures and DFT comparisons.

The crystal structure of sodium rubidium hydrogen citrate, NaRbHC6H5O7 or [NaRb(C6H6O7)] n , has been solved and refined using laboratory powder X-ray diffraction data, and optimized using density functional techniques. This compound is isostructural to NaKHC6H5O7. The Na atom is six-coordinate, with a bond-valence sum of 1.16. The Rb atom is eight-coordinate, with a bond-valence sum of 1.17. The distorted [NaO6] octa-hedra share edges to form chains along the a-axis direction. The irregular [RbO8] coordination polyhedra share edges with the [NaO6] octa-hedra on either side of the chain, and share corners with other Rb atoms, resulting in triple chains along the a-axis direction. The most prominent feature of the structure is the chain along [111] of very short, very strong hydrogen bonds; the O⋯O distances are 2.426 and 2.398 Å. The Mulliken overlap populations in these hydrogen bonds are 0.140 and 0.143 electrons, which correspond to hydrogen-bond energies of about 20.3 kcal mol-1. The crystal structure of sodium caesium hydrogen citrate, NaCsHC6H5O7 or [NaCs(C6H6O7)] n , has also been solved and refined using laboratory powder X-ray diffraction data, and optimized using density functional techniques. The Na atom is six-coordinate, with a bond-valence sum of 1.15. The Cs atom is eight-coordinate, with a bond-valence sum of 0.97. The distorted trigonal-prismatic [NaO6] coordination polyhedra share edges to form zigzag chains along the b-axis direction. The irregular [CsO8] coordination polyhedra share edges with the [NaO6] polyhedra to form layers parallel to the (101) plane, unlike the isolated chains in NaKHC6H5O7 and NaRbHC6H5O7. A prominent feature of the structure is the chain along [100] of very short, very strong O-H⋯O hydrogen bonds; the refined O⋯O distances are 2.398 and 2.159 Å, and the optimized distances are 2.398 and 2.347 Å. The Mulliken overlap populations in these hydrogen bonds are 0.143 and 0.133 electrons, which correspond to hydrogen-bond energies about 20.3 kcal mol-1.

Crystal structures of ammonium citrates

The crystal structures of (NH4)H2C6H5O7 and (NH4)3C6H5O7 have been determined using a combination of powder and single crystal techniques. The structure of (NH4)2HC6H5O7 has been determined previously by single crystal diffraction. All three structures were optimized using density functional techniques. The crystal structures are dominated by N-H⋅⋅⋅O hydrogen bonds, though O-H⋅⋅⋅O hydrogen bonds are also important. In (NH4)H2C6H5O7 very strong centrosymmetric charge-assisted O-H-O hydrogen bonds link one end of the citrate into chains along the b-axis. A more-normal O-H⋅⋅⋅O hydrogen bond links the other end of the citrate to the central ionized carboxyl group. In (NH4)2HC6H5O7, the very strong centrosymmetric O-H-O hydrogen bonds link the citrates into zig-zag chains along the b-axis. The citrates occupy layers parallel to the bc plane, and the ammonium ions link the layers through N-H⋅⋅⋅O hydrogen bonds. In (NH4)3C6H5O7, the hydroxyl group forms a hydrogen bond to a terminal carboxylate, and there is an extensive array of N-H⋅⋅⋅O hydrogen bonds. The energies of the density functional theory-optimized structures lead to a correlation between the energy of an N-H⋅⋅⋅O hydrogen bond and the Mulliken overlap population: E(N-H⋅⋅⋅O) (kcal/mole) = 23.1(overlap)½. Powder patterns of (NH4)H2C6H5O7 and (NH4)3C6H5O7 have been submitted to International Centre for Diffraction Data for inclusion in the powder diffraction file.

In-situ studies on the micro-structure evolution of A2W2O7 (A = Li, Na, K) during melting by high temperature Raman spectroscopy and density functional theory

In-situ high temperature Raman spectroscopic (HTRS) technique in combination with density functional theory (DFT) analysis has been adopted to investigate the micro-structure of solid and molten A2W2O7 (A=Li, Na, K). The [WO6] octahedra were found to be connected to each other by corner and edge sharing in the crystalline Li2W2O7 and K2W2O7 compounds. In the crystal lattice of Na2W2O7, on the other hand, the [WO4] tetrahedra and [WO6] octahedra were found to coexist and paired by corner sharing. Although the structural diversity has clearly led to distinct Raman spectra of the crystalline A2W2O7 compounds, the spectra of their melts tended to be analogous, showing the typical vibration modes of (W2O7)2− dimer. A mechanism was then proposed to explain the structure evolution occurring during the melting process of A2W2O7. The effect of A+ cation on the Raman bands of (W2O7)2− dimer in molten A2W2O7 has also been investigated. Both the wavenumber and full width at half-height (FWHH) of the characteristic band assigned to the symmetrical stretching vibration mode of WOnb (non-bridging oxygen) in (W2O7)2− were found to decrease in the sequence of Li+, Na+ and K+, indicating the cation effect on the mean bond length and its distribution range of WOnb. In addition, the relative intensity of this band was also influenced by the cation and it was increased in the order of Li2W2O7, Na2W2O7 and K2W2O7, which has been explained by the charge transfer process and confirmed by Mulliken overlap population analysis.

First-principles investigation of mechanical and electronic properties of MFeAs (M = Cu, Li, and Na)

Mechanical and electronic properties of Cu2Sb-type compounds MFeAs (M = Cu, Li, and Na) have been studied by the first-principles calculations. The main trends in structure parameters, mechanical parameters, electronic bands, and densities of states (DOS) for MFeAs are analyzed according to the variable cation M sites. Our results show that the lattice constants increase, while the bulk modulus, shear modulus, and Young's modulus decrease with the increasing radii of M sites in the sequence CuFeAs → LiFeAs → NaFeAs. Mulliken overlap population indicates that different M atoms in MFeAs (M = Cu, Li, and Na) would influence the bond nature of Fe-As, which may induce the superconductivity. The disappearance of the hole-pockets affects the superconductivity in CuFeAs. Although the value of the DOSs N(EF) at the Fermi level grows with decreasing radii of M sites, it is not the only factor influencing the superconductivity. Due to the repulsive interaction between Cu-3d and Fe-3d states in CuFeAs phase, it would change the position of Fe-3d orbits and Fermi energy level after introducing Cu in this structure. Therefore, after introducing Cu in the structure would induce the different position of Fe-3d states and Fermi energy level. Therefore, we believe that the component M has an important influence on the superconductivity.

Sodium potassium hydrogen citrate, NaKHC6H5O7.

The crystal structure of sodium potassium hydrogen citrate has been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional theory techniques. The Na(+) cation is six-coordinate, with a bond-valence sum of 1.17. The K(+) cation is also six-coordinate, with a bond-valence sum of 1.08. The distorted [NaO6] octahedra share edges, forming chains along the a axis. The likewise distorted [KO6] octahedra share edges with the [NaO6] octahedra on either side of the chain, and share corners with other [KO6] octahedra, resulting in triple chains along the a axis. The most prominent feature of the structure is the chain along [111] of very short, very strong hydrogen bonds; the O⋯O distances are 2.414 and 2.400 Å. The Mulliken overlap populations in these hydrogen bonds are 0.138 and 0.142 e, which correspond to hydrogen-bond energies of 20.3 and 20.6 kcal mol(-1).

Prediction of Stable Ruthenium Silicides from First-Principles Calculations: Stoichiometries, Crystal Structures, and Physical Properties.

We present results of an unbiased structure search for stable ruthenium silicide compounds with various stoichiometries, using a recently developed technique that combines particle swarm optimization algorithms with first-principles calculations. Two experimentally observed structures of ruthenium silicides, RuSi (space group P2(1)3) and Ru2Si3 (space group Pbcn), are successfully reproduced under ambient pressure conditions. In addition, a stable RuSi2 compound with β-FeSi2 structure type (space group Cmca) was found. The calculations of the formation enthalpy, elastic constants, and phonon dispersions demonstrate the Cmca-RuSi2 compound is energetically, mechanically, and dynamically stable. The analysis of electronic band structures and densities of state reveals that the Cmca-RuSi2 phase is a semiconductor with a direct band gap of 0.480 eV and is stabilized by strong covalent bonding between Ru and neighboring Si atoms. On the basis of the Mulliken overlap population analysis, the Vickers hardness of the Cmca structure RuSi2 is estimated to be 28.0 GPa, indicating its ultra-incompressible nature.

Effects of B and Al on tensile strengths and electronic structure of CuZr: A first-principles study

We investigate effects of B or Al impurities on structure and tensile strengths of CuZr by using first-principles density functional calculations. The calculations indicate that B or Al atoms doped on Zr atoms are energies favorable structure. We present stress–strain relationships for Cu–Zr–X (X = B, Al) systems along chosen directions. Both B and lower concentrations of Al decrease the tensile strengths, although there exists stronger covalent bonds between X and nearest neighbor Cu/Zr of Cu–Zr–X than that of CuZr, and plasticity in these systems can be triggered by electronic instabilities under tension. CuZr0.5Al0.5 possesses larger tensile strengths than CuZr, and we analyze mechanism of different tensile strengths for different concentrations of impurities by Mulliken overlap populations. All calculations show that the effects of B or Al impurities on tensile strengths of CuZr are quite composition-dependent.

First-Principles Study of Electronic and Elastic Properties of Hexagonal Layered Crystal MoS2 Under Pressure

Abstract The structural, electronic, and elastic properties of hexagonal layered crystal MoS2 under pressure are investigated using first-principles calculations within the local density approximation (LDA). The calculated lattice parameters a 0, c 0, and cell volume V 0 of MoS2 are in good agreement with the available experimental data. Our calculations show that MoS2 is an indirect band gap semiconductor and there is a vanishing anisotropy in the rate of structural change at around 25 GPa, which is consistent with the experimental result. We also analyse the partial density of states (PDOS) of MoS2 at 0 and 14 GPa, which indicate that the whole valence bands of MoS2 are mainly composed by the Mo-4d and S-3s states at 0 GPa, while they are mainly composed by the Mo-4p, Mo-4d, and S-3p states at 14 GPa. The electronic charge density difference maps show the covalent characteristic of Mo–S, and the bonding properties of MoS2 are investigated by using the Mulliken overlap population. In addition, the elastic constants C ij , bulk modulus B, shear modulus G, Young’s modulus Y, the Debye temperature Θ D , and hardness H of MoS2 are also obtained successfully. It is found that they all increase monotonically with the increasing pressure.

Mechanical Properties and Electronic Structure of N and Ta Doped TiC: A First-Principles Study

The first principles calculations based on density functional theory (DFT) are employed to investigate the mechanical properties and electronic structure of N and Ta doped TiC. The result shows that the co-doping of nitrogen and tantalum dilates the lattice constant and improves the stability of TiC. Nitrogen and tantalum can signiβcantly enhance the elastic constants and elastic moduli of TiC. The results of B/G and C12–C44 indicate tantalum can markedly increase the ductility of TiC. The electronic structure is calculated to describe the bonding characteristic, which revealed the strong hybridization between C-p and Ta-d and between N-p and Ti-d. The hardnessis is estimated by a semi-empirical model that is based on the Mulliken overlap population and bond length. While the weakest bond takes determinative role of the hardness of materials, the addition of Ta sharply reduces the hardness of TiC.

Bonding in Group 1 Citrate Salts

Computational studies of > 15 new crystal structures and the 10 previously-reported structures of alkali metal citrates provide insight into why the atoms are where they are. The metal-citrate bonding is predominantly ionic, with very little covalent character, which decreases as the cation size increases. Bond valence calculations indicate that most cations are crowded, and that the crowding decreases as the cation size increases. Although most oxygen atoms coordinate to the metals, a few do not, and they tend to be the least-negative oxygens. Both the citrate hydroxyl groups and water molecules tend to bridge two cations, and the carboxylate coordination is more varied. The solid state energy differences are dominated by differences in van der Waals and electrostatic energy contributions. In the Li and Na salts, the citrate anion occurs predominantly in a higher-energy "kinked" conformation, rather than the extended lowest-energy conformation observed in salts of the larger cations. Detailed conformational analysis of the citrate anions enables quantification of the conformational energy costs in these solids. Hydrogen bonding is important to the stability of these salts. The Mulliken overlap population in the hydrogen bonds provides a quantitative measure of their strength, and permits identification of long (weak) interactions which are significant in some of these compounds. Patterns in both the local environments of the hydrogen bonds and the more-extended features (graph sets) are noted. Polymorphs and sets of isostructural compounds permit more-detailed analysis of the structures and energetics in these compounds. The order of ionization of the three carboxylic acid groups is in general central/terminal/terminal, but there are two exceptions. While we have concentrated on salts containing a single alkali metal cation (and hydrogen), the structures of NaK2C6H5O7 and NaKHC6H5O7 provide an exciting window on a larger universe of mixed salts.

Composition-dependent bonding and hardness of γ-aluminum oxynitride: A first-principles investigation

Spinel phase aluminum oxynitride solid solution (γ-alon, with formula of Al(8+x)/3O4−xNx) exists in the narrow Al2O3-rich region of Al2O3-AlN systems. The first-principles calculations were developed to investigate the composition-dependent bonding and hardness of γ-alon. Six supercell model for Al(8+x)/3O4−xNx (x = 0, 0.25, 0.44, 0.63, 0.81, and 1) was constructed to perform our calculations with high accuracy. It was found that the lattice constant increases with increasing composition of nitrogen in γ-alon. The bond lengths of AlIV–O, AlVI–O, AlIV–N, and AlVI–N all increase with the expansion of crystal structure. The well-known Mulliken overlap populations were calculated to estimate the bonding and hardness. As the content of nitrogen substitute increases, the Al–N bonds present more covalent characteristic, while the Al–O bonds present more ionic characteristic. The AlIV–N is the hardest bond in γ-alon. The theoretical hardness of γ-alon could be slightly enhanced from 17.16 GPa to 17.97 GPa by increasing content of nitrogen in full solubility range. The contribution ratio, CHμ, was proposed to quantify the contribution of bonds to hardness of γ-alon. The Al–O bonds are found to contribute more to the hardness. The Al–N bonds are the main influencing factor to enhance the hardness of γ-alon. These calculated results provide the basis for understanding the composition-dependent bonding and hardness of γ-alon.

Structural stability and elastic properties of IrSi in B31 and B20-phase from first-principles calculations

Abstract A systematic study of the structural stability, elastic properties and electronic structures for iridium silicide (IrSi) in B31 and B20-phase has been carried out with the generalized gradient approximation (GGA) and local density approximation (LDA) in framework of density functional theory (DFT). The obtained formation enthalpies, energy–volume (E–V) curves and enthalpy–pressure (H–P) curves indicate that orthorhombic B31-IrSi is more stable than cubic B20-IrSi at both ambient and pressure conditions. The elastic stiffness constants, bulk moduli, shear moduli, Young’s moduli, Poisson’s coefficients and elastic anisotropy factors of the two phases IrSi are studied for the first time. The small elastic stiffness constant C22 of B31-IrSi induces easily compressibility along the b axis. Moreover, based on the Mulliken overlap population analysis, the hardness Hv of B31-IrSi (Hv = 11.9 GPa) and B20-IrSi (Hv = 13.4 GPa) are evaluated.

Phase stability, physical properties of rhenium diboride under high pressure and the effect of metallic bonding on its hardness

Using first-principles calculations, the elastic constants, thermodynamic property and structural phase transition of rhenium diboride under pressure are investigated by means of the pseudopotential plane-waves method, as well as the effect of metallic bond on its hardness. Eight candidate structures of known transition-metal compounds are chosen to probe for rhenium diboride ReB2. The calculated lattice parameters are consistent with the experimental and theoretical values. Based on the third order Birch–Murnaghan equation of states, the transition pressure Pt between the ReB2–ReB2 and MoB2–ReB2 phases is firstly determinate. Elastic constants, shear modulus, Young’s modulus, Poisson’s ratio and Debye temperature are derived. The single-bonded B–B feather remains in ReB2 compounds. Furthermore, according to Mulliken overlap population analysis, a semiempirical method to evaluate the hardness of multicomponent crystals with partial metallic bond is presented. Both strong covalency and a zigzag topology of interconnected bonds underlie the ultraincompressibilities. In addition, the superior performance and large hardness (39.1GPa) of ReB2–ReB2 indicate that it is a superhard material.

Phase Stability, Physical Properties, and Hardness of Transition-Metal Diborides MB2 (M = Tc, W, Re, and Os): First-Principles Investigations

Using first-principles calculations, the structural stability, elastic strength, and formation enthalpies of four diborides MB2 (M = Tc, W, Re, and Os) are investigated by means of the pseudopotential plane-waves method, as well as the roles of covalency and bond topology in the phase incompressibility. Three candidate structures of known transition-metal diborides are chosen to probe. The calculated lattice parameters, elastic properties, Poisson’s ratio, and B/G ratio are derived. It is observed that the ReB2-type structure containing well-defined zigzag covalent chains exhibits an unusual incompressibility along the c axis comparable to that of diamond. Formation enthalpy calculations demonstrate that the ground-state phase is synthesizable at low pressure, whereas the other phase can be achieved through the phase transformation. Moreover, according to Mulliken overlap population analysis, a semiempirical method to evaluate the hardness of multicomponent crystals with a partial metallic bond is presented. The predicted hardness of WB2–WB2, ReB2–ReB2, and OsB2–OsB2 is in reasonable agreement with experiment data. Both strong covalency and a zigzag topology of interconnected bonds underlie the ultraincompressibilities. In addition, the superior performance and largest hardness of ReB2–ReB2 indicate that it is a superhard material. This work provides a useful guide for designing novel borides materials having excellent mechanical performances.

Effect of pressure on structural phase transition and elastic properties in NiSi

A systematic study of the structural phase transition, elastic, and electronic properties for nickel silicide (NiSi) under high pressure has been carried out by using the pseudopotential plane-wave density functional theory. Among them, the mechanism of the high pressure structural phase transition has been studied in a detailed manner. Our results show that the structural phase transition pressure from MnP- to CuTi-structure in NiSi is 14.6 GPa, which is in good agreement with other theoretical report. We have also calculated the elastic constants, bulk modulus, shear modulus, Young's modulus, Poisson's coefficients, and elastic anisotropy factors of MnP-type NiSi under high pressure. We find that the pressure has an important influence on the elastic modulus. Moreover, on the basis of the Mulliken overlap population analysis, the hardness H ν (H ν=11.3 GPa) of the MnP-type NiSi has been obtained, which is compatible with the experimental value.

Mechanical properties and electronic structure of TiC, Ti0.75W0.25C, Ti0.75W0.25C0.75N0.25, TiC0.75N0.25 and TiN

The first-principles calculations are performed to investigate the mechanical properties and electronic structure of TiC, Ti0.75W0.25C, Ti0.75W0.25C0.75N0.25, TiC0.75N0.25 and TiN. Density functional theory and ultrasoft pseudopotentials are used in this study. From the formation energy, it is found that nitrogen can increase the stability of TiC. The calculated elastic constants and elastic moduli of TiC compare favorably with other theoretical and experimental values. Tungsten and nitrogen are observed to significantly increase the bulk, shear and Young's modulus of TiC. Through the analysis of B/G and Cauchy pressure, tungsten can significantly improve the ductility of TiC. The electronic structure of TiC, TiN, Ti0.75W0.25C, Ti0.75W0.25C0.75N0.25, and TiC0.75N0.25 are used to describe nonmetal–metal and metal–metal bonds. Based on the Mulliken overlap population analysis, the hardness values of TiC, Ti0.75W0.25C, Ti0.75W0.25C0.75N0.25, TiC0.75N0.25 and TiN are estimated.

The Effect of Impurity Atoms on the Structural and Electronic Properties of Au<sub>3</sub> Clusters

With density functional theory, the structural and electronic properties of Au3 and Au2M (M=Ag, Cu, Pd and Pt) clusters have been studied. The structural results indicate that by substituting one Au atom with M atom, the corresponding geometries are changed slightly. To investigate the electronic properties, bonding properties and highest occupied molecular orbital (HOMO) were observed. It is found that most trends in Au2Pd and Au2Pt are similar and it also happens in the other two doped clusters. In addition, the calculated mulliken overlap populations suggest that doping modify the localized electron between Au and Au atom. It is also found that the contributions from various atoms on HOMO and energies of HOMO are changed. These may make difference in the adsorption of clusters.