Chemical bonding in isostructural Li-containing ternary chalcogenides

First principle calculations were performed for the first time to study the electronic structure of LiGaTe₂, LiInTe₂, and LiInSe₂ chalcogenides with a chalcopyrite structure. Peculiarities of chemical bonding are discussed and electron density and difference density maps are constructed for crystals and sublattices. Major information about chemical bonding in crystals is conveyed by the difference density. The chemical bond in chalcogenides is a donor-acceptor bond.     

Dynamic electron transfers in B2H6 and Cu(PH3)2(BH4)

In order to investigate the coupling of molecular vibrations and electron distribution, dynamic electron transfers in B₂H₆ and Cu(PH₃)₂(BH₄) are lated by using a new variational method. In both molecules, the dynamic electron density near bridging hydrogen atoms decreases to form the density valley by exciting specific vibrational modes. On the other hand, in both sides of the valley density hills grow up. For these molecules, similar contour maps are given by the modes with different symmetry which have large contribution of the bridging ligands. While the dynamic electron transfer of B₂H₆ arises in symmetric form, the vibrational modes of the Cu complex gives the asymmetric redistribution of the dynamic electron density. This is attributed to the difference of the symmetry between the two molecules.     

Chemical Bonding in Thermodynamically Labile Oxyanion Crystals

Crystal valence density and difference density distributions were calculated for NaNO₂, NaNO₃, KClO₃, and NaClO₄ using local density functional theory. Hybridization of the oxygen states is enhanced in compounds with lower symmetry, leading to the formation of oxygen chains in the lattice. Interaction between the oxygen and anion's central atom sublattices gives rise to electron charge maxima in the middle of the A—O bonds and to two terminal oxygen maxima. The complex character of the intraanion electron transfer and the charge transfer between the nonequivalent oxygen sublattices make these compounds susceptible to external energy effects that lead to their solidstate decomposition.     

Measurement of electron densities by a microwave cavity method in 13.56-MHz RF plasmas of Ar,CF4, C2F6, and CHF3

Electron densit ies have been determined /or RF plasmas that were generated within a microwave resonant cavity by measuring the difference of the resonance frequencies with and without plasma. Since that method only yields a value of the electron density weighted ouer the microwave electric field distribution, to obtain real values an assumption on the spatial distribution of the electron density had to he made. Spatial profiles were taken of the emission of a 4s–5p Ar line at 419.8 not (with a small Ar admixture). The electron densities have been determined as a function of pressure and RF power in Ar, CF₄, C₂ F₆ and CHF, plasmas. The results indicate that the electron density for the last three gases decreases as a function of pressure above 50 m Torr. Typical values for the electron density for the investigated parameter range are 1–6 · 10³ cm^–3. Furthermore, the electron density is the lowest in gases with a high attachment cross .section.     

Marginal electron density and density-difference functions

Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y ₀,z ₀) and the two-dimensional cut (x, y, z ₀) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions _x (x) and _xy (x, y) and their difference functions _x (x) and _xy (x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H₂ system.     

Topology of density difference and force analysis

The density difference (r) of a molecule A-B is defined as the difference of the density (r) of the molecule A-B and the density _A(r) + _B(r) put at the position of the atoms A and B. We investigate here the topological features of the density difference and define electron density flow (EDF) as representing the direction and the amount of the electron density flow in the course of the nuclear displacement processes. As such examples, we study H₂ molecule formation reaction and the interaction of two He atoms. By the topological analysis of (r), and by using the Hellmann-Feynman force and its partition into the AD, EC, and EGC forces, the characteristic behaviors of the (r) map are clarified. In particular, the electron cloud preceding and incomplete following are represented by using the concept of the EDF. The natures of the covalent bond are clarified based on the topological properties of the difference density (r) rather than that of the total density (r).On leave from the Department of Chemistry, Hebei Teachers' College, Shijiazhuang, Hebei, 050091, China     

Two-Dimensional Layered Metallic VSe2/SWCNTs/rGO Based Ternary Hybrid Materials for High Performance Energy Storage Applications

In this work, the ternary hybrid structure VSe₂/SWCNTs/rGO is reported for supercapacitor applications. The ternary composite exhibits a high specific capacitance of 450 F g⁻¹ in a symmetric cell configuration, with maximum energy density of 131.4 Wh kg⁻¹ and power density of 27.49 kW kg⁻¹. The ternary hybrid also shows a cyclic stability of 91 % after 5000 cycles. Extensive density functional theory (DFT) simulations on the structure as well as on the electronic properties of the binary hybrid structure VSe₂/SWCNTs and the ternary hybrid structure VSe₂/SWCNTs/rGO have been carried out. Due to a synergic effect, there are enhanced density of states near the Fermi level and higher quantum capacitance for the hybrid ternary structure compared to VSe₂/SWCNTs, leading to higher energy and power density for VSe₂/SWCNTs/rGO, supporting our experimental observation. Computed diffusion energy barrier of electrolyte ions (K⁺) predicts that ions move faster in the ternary structure, providing higher charge storage performance.     

On the inner and outer radial density functions

Starting from the two-electron radial density D ₂(r ₁,r ₂), a generalized partitioning of the one-electron radial density function D(r) into two component densities D _a (r) and D _b (r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D _<(r) and outer D _>(r) radial densities is shown to minimize the average variance of the two component density functions D _a (r) and D _b (r). It is also found that the average radial separation halved, , constitutes a lower bound to the standard deviation σ of D(r).     

Nonlocal energy density functionals: Models plus some exact general results

Holas and March (Phys Rev 1995 A51, 2040) gave a formally exact expression for the force ??V_xc( r )/? r associated with the exchange‐correlation potential V_xc( r ) of density functional theory. This forged a precise link between first‐ and second‐order density matrices and V_xc( r ). Here models are presented in which these low‐order matrices can be related to the ground‐state electron density. This allows nonlocal energy density functionals to be constructed within the framework of such models. Finally, results emerging from these models have led to the derivation of some exact “nuclear cusp” relations for exchange and correlation energy densities in molecules, clusters, and condensed phases. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Sensing and catalytic decomposition of hydrogen peroxide by silicon carbide nanotubes: A DFT study

In this study, by carrying out detailed density functional theory calculations, we investigate the adsorption and stepwise decomposition of hydrogen peroxide (H₂O₂) over (6,0) and (7,0) zigzag silicon carbide nanotubes (SiCNTs). The results indicate that the H₂O₂ can be adsorbed on the exterior surface of the SiCNTs with noticeable adsorption energies and charge transfers. To gain insight into the catalytic activity of the surface, the interaction between the H₂O₂ and SiCNT is analyzed by detailed electronic analysis such as adsorption energy, charge density difference and activation barrier. The decomposition of H₂O₂ into O₂ and H₂ species can be viewed as the kinetically preferred reaction pathway for dehydrogenation of hydrogen peroxide over SiCNTs. There is also a curvature effect on the dehydrogenation kinetics of hydrogen peroxide, that small diameter SiCNTs with large curvature would be beneficial for decomposition of H₂O₂. © 2015 Wiley Periodicals, Inc.     

Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

Core Charge Density Dominated Size-Conversion from Au6P8 to Au8P8Cl2

The stimulus-response of metal nanoclusters is crucial to their applications in catalysis and bio-clinics, etc. However, its mechanistic origin has not been well studied. Herein, the mechanism of the Au^IPPh₃Cl-induced size-conversion from [Au₆(DPPP)₄]²⁺ to [Au₈(DPPP)₄Cl₂]²⁺ (DPPP is short for 1,3-bis(diphenylphosphino)propane) is theoretically investigated with density functional theory (DFT) calculations. The optimal size-growth pathway, and the key structural parameters were elucidated. The Au−P bond dissociation steps are key to the size-growth, the easiness of which was determined by the charge density of the metallic core of the cluster precursors (i.e., “core charge density”). This study sheds light on the inherent structure–reactivity relationships during the size-conversion, and will benefit the deep understanding on the kinetics of more complex systems.     

Decomposition of deformation density into orbital components

In this research, deformation density matrix has been introduced as matrix representation of the density difference between the complex and fragments. The deformation density matrix is then diagonalized to obtain the magnitude of displaced charges as eigenvalues. Correspondingly, the eigenvectors reveal the spaces responsible for reorganization of the electrons because of the complex formation. The formalism has been applied on some CO₂ planar clusters, and the results showed that how the deformation density can be successfully separated into in‐plane and out‐of‐plane contributions. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A zero differential overlap study of chemical binding in ammonia-borane and carbony l-borane

A cndo/2D study of the charge distribution obtained through Mulliken population analysis in the ground state of the title compounds shows that the features of charge distribution found by severalab initio calculations are fairly well reproduced by this method. The one-particle density, the interference density at the mid-point of the bond axis and the kinetic part of the interference energy calculated through the deorthogonalized density matrices over a wide range of intermolecular separation between the donor and the acceptor show that the one-particle density and the interference density steadily grow with decreasing internuclear separation, while the kinetic interference energy starts with negative value at large distance, then decreases and passes through a minima near but above the equilibrium distance and then increases rapidly below it conforming to the characteristic general behaviour of the kinetic component of Morse curve. The orbital pairwise interference density and the corresponding kinetic energy components reveal that the orbitals involved in the covalent binding are σ_2p AO of B and 2S and σ_2p AO of N and C atoms in H₃B-NH₃ and H₃B-CO respectively.     

Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one‐electron density and electronic energy

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a nonlinear, approximate density functional of a three spatial dimension one‐electron density for an N electron system which is tractable in practice, is a long‐desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital‐free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree–Fock (HF) and Kohn–Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫g_i( r ₁)g_k( r ₂)rd r ₁d r ₂, etc.) to estimate electron‐electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc.     

Theoretical characterization and design of small molecule donor material containing naphthodithiophene central unit for efficient organic solar cells

To seek for high‐performance small molecule donor materials used in heterojunction solar cell, six acceptor–donor–acceptor small molecules based on naphtho[2,3‐b:6,7‐b′]dithiophene ( NDT ) units with different acceptor units were designed and characterized using density functional theory and time‐dependent density functional theory. Their geometries, electronic structures, photophysical, and charge transport properties have been scrutinized comparing with the reported donor material NDT(TDPP)₂ ( TDPP = thiophene‐capped diketopyrrolopyrrole). The open circuit voltage (V_oc), energetic driving force(ΔE_L‐L), and exciton binding energy (E_b) were also provided to give an elementary understanding on their cell performance. The results reveal that the frontier molecular orbitals of 3–7 match well with the acceptor material PC₆₁BM , and compounds 3–5 were found to exhibit the comparable performances to 1 and show promising potential in organic solar cells. In particular, comparing with 1 , system 7 with naphthobisthiadiazole acceptor unit displays broader absorption spectrum, higher V_oc, lower E_b, and similar carrier mobility. An in‐depth insight into the nature of the involved excited states based on transition density matrix and charge density difference indicates that all S₁ states are mainly intramolecular charge transfer states with the charge transfer from central NDT unit to bilateral acceptor units, and also imply that the exciton of 7 can be dissociated easily due to its large extent of the charge transfer. In a word, 7 maybe superior to 1 and may act as a promising donor candidate for organic solar cell. © 2013 Wiley Periodicals, Inc.     

Theoretically Calculated Deformation Density of Small Molecules

Analysis of the theoretical electron deformation density based on EHMO and ab initio calculations has been applied to the simple molecules F₂, H₂O and SO₂ The effects from varied basis sets for such deformation density were sought. The accumulation of electron density between the bonded atoms calculated from EHMO and ab initio methods with STO-3G is generally under-estimated. Such phenomena are significantly improved by using split-valence basis sets e.g. 3–21G and 4–31G. The addition of d polarization functions is apparently important for the sulfur atom in sulfur-related bonding. 3–21G or 3–21G^* basis sets were found to provide not only valuable deformation density distributions of molecules but also comparable orbital energy states with respect to the experimental values.     

Electronic structure and coordination chemistry of phenanthridine ligand in first‐row transition metal complexes: A DFT study

The geometric parameters, electronic structures, and haptotropic migration of a series of hypothetical compounds of general formula CpM(C₁₃H₉N) and (CO)₃M(C₁₃H₉N) (M = fist row transition metal, Cp = C₅H₅, and C₁₃H₉N = phenanthridine ligand) are investigated by means of the density functional theory. The phenanthridine ligand can bind to the metal through η¹ to η⁶ coordination mode, in agreement with the electron count and the nature of the metal, showing its capability to adapt itself to the electronic demand of the metal as well as to the polycyclic aromatic hydrocarbons. In the investigated species, the most favored closed‐shell count is 18‐electron except for the Ti and V models which are deficient open‐shell 16‐electron configuration. This study has shown the difference in coordination ability of this heteropolycyclic ligand: the coordination of the central C₅N ring is less favored than the terminal C₆ rings, in agreement with the π‐electron density localization. Most of the investigated complexes are expected to exhibit a rich fluxional behavior. This flexibility favors the possibility for the existence of several isomers as well as their interconversion through haptotropic shifts. © 2012 Wiley Periodicals, Inc.     

The molecular and electronic structure features of silatranes, germatranes, and their carbon analogs

Molecular geometries of fifty-six metallatranes N(CH₂CH₂Y)₃M-X and fifty-six carbon analogs HC(CH₂CH₂Y)₃M-X (M = Si, Ge; X = H, Me, OH, F; Y = CH₂, O, NH, NMe, NSiMe₃, PH, S) were optimized by the DFT method. Correlations between changes in the bond orbital populations, electron density ρ(r), electron density laplacian ∇²ρ(r), |λ₁|/λ₃ ratio, electronic energy density E(r), bond lengths, and displacement of the central atom from the plane of three equatorial substituents and the nature of substituents X and Y were studied. As the number of electronegative substituents at the central atom increases, the M←N, M-X, and M-Y bond lengths decrease, while the M←N bond strength and the electron density at critical points of the M←N, M-X, and M-Y bonds increase. An increase in electronegativity of a substituent (X or Y) is accompanied by a decrease in the ionicities of the other bonds (M-X, M-Y, and M←N) formed by the central atom (Si, Ge). A new molecular orbital diagram for bond formation is proposed, which takes into account the interaction of all five substituents at the central atom (M = Si, Ge) in atrane molecules. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 448–460, March, 2006.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001