Roles of cations, electronegativity difference, and anionic interlayer interactions in the metallic versus nonmetallic character of Zintl phases related to arsenic

A first-principles Density Functional Theory study of several layered solids structurally related to rhombohedral arsenic has been carried out. The electronic structures of rhombohedral arsenic, CaSi(2), CaAl(2)Si(2), KSnSb, and SrSn(2)As(2) are discussed in detail, emphasizing on the origins of their metallic or nonmetallic behaviours. It is found that all of these systems are metallic except KSnSb. Electronegativity differences between the elements in the anionic sublattice and/or direct interlayer interactions play the main role in controlling the conductivity behavior. CaSi(2) exhibits a peculiar feature since the cation directly influences the conductivity but is not essential for its appearance. Cation-anion interactions are shown to have an important covalent contribution, but despite this fact and the metallic character found for most of these phases, the Zintl approach still provides a valid approximation to their electronic structure.     

Charge‐Scaling Effect in Ionic Liquids from the Charge‐Density Analysis of N,N′‐Dimethylimidazolium Methylsulfate

The charge scaling effect in ionic liquids was explored on the basis of experimental and theoretical charge‐density analyses of [C₁MIM][C₁SO₄] employing the quantum theory of atoms in molecules (QTAIM) approach. Integrated QTAIM charges of the experimental (calculated) charge density of the cation and anion resulted in non‐integer values of ±0.90 (±0.87) e. Efficient charge transfer along the bond paths of the hydrogen bonds between the imidazolium ring and the anion was considered as the origin of these reduced charges. In addition, a detailed QTAIM analysis of the bonding situation in the [C₁SO₄]^? anion revealed the presence of negative π_O→σ*_S‐O hyperconjugation.     

The structures of CaC and Ca<Subscript>2</Subscript>Cin the light of the Extended Zintl–Klemm Concept

The structures of Ca₂C and CaC, recently predicted from evolutionary algorithms to be stable at very high pressures, are rationalized on the basis of the structural transitions undergone by calcium under pressure as well as in the light of the Extended Zintl–Klemm Concept that serve as a guide to explain the structures.     

Evidence of a Mixed Magnetic Phase in EuMgGe: A Semi­metallic Zintl Compound with TiNiSi Structure Type

The ternary Zintl phase EuMgGe was synthesized from the elements, and its structure solved by single‐crystal X‐ray diffraction. Chemical bonding is discussed, by means of electronic structure calculations at the DFT level and its physical properties characterized with respect to electronic conductivity, magnetic susceptibility, specific heat capacity, and magnetoresistivity. The compound may be interpreted according to the Zintl‐Klemm concept as (Eu²⁺)(Mg²⁺)(Ge^4–) with isolated germanium anions. Resistivity measurements reveal a semimetallic character, which is consistent with the vanishing energy gap obtained from our calculations. The magnetic susceptibility and the specific heat indicate that two consecutive transitions take place, at 9 and 16 K, and they show evidence of magnetic frustration. A possible physical scenario for this magnetic behavior is discussed based on known models of partially frustrated magnets.     

The Silicides M4Si4 with M = Na,K, Rb,Cs, and Ba2Si4 – NMR Spectroscopy and Quantum Mechanical Calculations

The Zintl phases M₄Si₄ with M = Na, K, Rb, Cs, and Ba₂Si₄ feature a common structural unit, the Si₄^4– anion. The coordination of the anions by the cations varies significantly. This allows a systematic investigation of the bonding situation of the anions by ²⁹Si NMR spectroscopy. The compounds were characterized by powder X‐ray diffraction, differential thermal analysis, magnetic susceptibility measurements, ²³Na, ²⁹Si, ⁸⁷Rb, ¹³³Cs NMR spectroscopy, and quantum mechanical calculation of the NMR coupling parameter. The chemical bonding was investigated by quantum mechanical calculations of the electron localizability indicator (ELI). Synthesis of the compounds results for all of them in single phase material. A systematic increase of the isotropic ²⁹Si NMR signal shift with increasing atomic number of the cations is observed by NMR experiments and quantum mechanical calculation of the NMR coupling parameter. The agreement of experimental and theoretical results is very good allowing an unambiguous assignment of the NMR signals to the atomic sites. Quantum mechanical modelling of the NMR shift parameter indicates a dominant influence of the cations on the isotropic ²⁹Si NMR signal shift. In contrast to this a negligible influence of the geometry of the anions on the NMR signal shift is obtained by these model calculations. The origin of the systematic variation of the isotropic NMR signal shift is not yet clear although an influence of the charge transfer estimated by calculation using the QTAIM approach is indicated.     

ChelpG and QTAIM atomic charge and dipole models for the infrared fundamental intensities of the fluorochloromethanes

ChelpG atomic charges and dipoles and the charge–charge flux–dipole flux (CCFDF) model have been used to quantitatively estimate the fundamental infrared intensities of the fluorochloromethanes. Since the ChelpG calculational procedure includes the constraint that the atomic charges and dipoles reproduce the equilibrium dipole moments the model results in accurate intensity values that have a root mean square error of 0.7 km mol^?1 compared to those determined directly from the MP2/6-311G++(3d,3p) electronic density and 23.1 km mol^?1 relative to the experimental intensities. Although these ChelpG results for total dipole moment derivatives are almost the same as those obtained previously using QTAIM (Quantum Theory of Atoms in Molecules) atomic charges and dipoles in the CCFDF model, their charge, charge flux and dipole flux contributions are completely different. Whereas the contributions calculated using the QTAIM parameters have values following expectations based on electronegativity concepts this is not true for those obtained from the ChelpG parameters. Mean dipole moment derivatives determined from experimental fundamental infrared intensities are compared with the ChelpG and QTAIM atomic charges. Furthermore, Generalized Atomic Polar Tensor Charges (GAPT) are found to need correction for their dynamic contributions if they are to be used as static atomic charges.     

Crystal structure and electron density of alpha-silicon nitride: experimental and theoretical evidence for the covalent bonding and charge transfer

Crystal structure and electron-density distribution of alpha-silicon nitride (alpha-Si3N4, space group: P31c) have been investigated by a combined technique of the Rietveld method, the maximum-entropy method (MEM), and MEM-based pattern-fitting of high-resolution synchrotron powder diffraction data. In combination with density functional theory calculations, the present experimental electron-density distribution of the alpha-Si3N4 indicates covalent bonds between Si and N atoms and charge transfer from the Si to N atom. The triangular distribution around the N atoms, which is attributable to the nitrogen sp2 hybridization for the nearest silicon and nitrogen pairs, was found in both experimental and theoretical electron density distributions. The minimum electron density in an intralayer Si-N bond was a little lower than that in an interlayer bond, which would be responsible for the inequality between elastic constants, C33 > C11. The present work suggests that the high bulk modulus of the alpha-Si3N4 is attributable to the high minimum electron density of the Si-N bond.     

Chemical bonds without "chemical bonding"? A combined experimental and theoretical charge density study on an iron trimethylenemethane complex

High-resolution X-ray diffraction data, in conjunction with DFT(B3LYP) quantum calculations, have been used in a QTAIM analysis of the charge density in the trimethylenemethane (TMM) complex Fe(eta(4)-C[CH(2)](3))(CO)(3). The agreement between the theoretical and experimental topological properties is excellent. Only one bond path is observed between the TMM ligand and the Fe atom, from the central C(alpha) atom. However, much evidence, including from the delocalization indices and the source function, suggests that there is a strong chemical interaction between the Fe and C(beta) atoms, despite the formal lack of chemical bonding according to QTAIM.     

The Zintl Phase Cs7NaSi8 – From NMR Signal Line Shape Analysis and Quantum Mechanical Calculations to Chemical Bonding

Powder samples as well as red and transparent single crystals of the Zintl phase Cs₇NaSi₈ were synthesized and characterized by means of X‐ray diffraction and differential thermal analysis. Cs₇NaSi₈ was found to be isotypic to the recently reported phase Rb₇NaSi₈. It crystallizes in the Rb₇NaGe₈ structure type forming trigonal pyramidal Si₄^4– anions. Two unique environments of the cations are observed, a linear arrangement [Na(Si₄)₂]^7– with short Na–Si distances of 3.0 Å and a Cs2 atom coordinated by six Si₄^4– anions with long Cs–Si distances of 4.2 Å. The bonding situation was investigated by a combined application of ²⁹Si, ²³Na, and ¹³³Cs solid‐state NMR spectroscopy and quantum mechanical calculations of the NMR coupling parameters. In addition the electronic density of states (DOS), the electron localizability indicator (ELI) and the atomic charges using the QTAIM approach were studied. Good agreement of the calculated and experimental values of the NMR coupling parameters was obtained. An anisotropic bonding situation of the silicon atoms is indicated by the chemical shift anisotropy being similar to Rb₇NaSi₈. Confirmation is given by the observation of one lone‐pair‐like feature for each silicon atom and two types of two‐center Si–Si bonds using the ELI. Calculation and NMR spectroscopic determination of the ²³Na and ¹³³Cs electric field gradients prove anisotropies of the charge distribution around the cations. Due to the similar values for the Na atoms in M₇NaSi₈ (M = Rb, Cs) equal bonding situations can be concluded. The much larger anisotropy of the charge distribution of the Cs atoms can be addressed as the main difference to Rb₇NaSi₈.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Bonding study in all-metal clusters containing Al4 units

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.     

Synthesis,structural characterization,and electronic structure of the novel Zintl phase Ba2ZnP2

The novel Zintl phase dibarium zinc diphosphide (Ba₂ZnP₂) was synthesized for the first time. This was accomplished using the Pb flux technique, which allowed for the growth of crystals of adequate size for structural determination via single‐crystal X‐ray diffraction methods. The Ba₂ZnP₂ compound was determined to crystallize in a body‐centered orthorhombic space group, Ibam (No. 72). Formally, this crystallographic arrangement belongs to the K₂SiP₂ structure type. Therefore, the structure can be best described as infinite [ZnP₂]^4? polyanionic chains with divalent Ba²⁺ cations located between the chains. All valence electrons are partitioned, which conforms to the Zintl–Klemm concept and suggests that Ba₂ZnP₂ is a valence‐precise composition. The electronic band structure of this new compound, computed with the aid of the TB–LMTO–ASA code, shows that Ba₂ZnP₂ is an intrinsic semiconductor with a band gap of ca 0.6 eV.     

Quantum chemistry aspects of the solvent effects on the ene reaction of 1‐Phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene

A density functional theory study was used to investigate the quantum aspects of the solvent effects on the kinetic and mechanism of the ene reaction of 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene. Using the B3LYP/6–311++ G(d,p) level of the theory, reaction rates have been calculated in the various solvents and good agreement with the experimental data has been obtained. Natural bond orbital analysis has been applied to calculate the stabilization energy of N18? H19 bond during the reaction. Topological analysis of quantum theory of atom in molecule (QTAIM) studies for the electron charge density in the bond critical point (BCP) of N18? H19 bond of the transition states (TSs) in different solvents shows a linear correlation with the interaction energy. It is also seen form the QTAIM analysis that increase in the electron density in the BCP of N18? H19, raises the corresponding vibrational frequency. Average calculated ratio of 0.37 for kinetic energy density to local potential energy density at the BCPs as functions of N18? H19 bond length in different media confirmed covalent nature of this bond. Using the concepts of the global electrophilicity index, chemical hardness and electronic chemical potentials, some correlations with the rate constants and interaction energy have been established. Mechanism and kinetic studies on 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene ene reaction suggests that the reaction rate will boost with interaction energy enhancement. Interaction energy of the TS depends on the solvent nature and is directly related to electron density of the bonds involved in the reaction proceeding, global electrophilicity index and electronic chemical potential. However, the chemical hardness relationship is reversed. Finally, an interesting and direct correlation between the imaginary vibrational frequency of the N18? H19 critical bond and its electron density at the TS has been obtained. © 2014 Wiley Periodicals, Inc.     

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.     

Periodic projector augmented wave density functional calculations on the hexachlorobenzene crystal and comparison with the experimental multipolar charge density model

The projector augmented wave (PAW) methodology has been used to calculate a high precision electron density distribution ρ(r) for the hexachlorobenzene crystal phase. Implementing the calculation of the crystallographic structure factors in the VASP code has permitted one to obtain the theoretical multipolar ρ(r). This electron density is compared with both the DFT electron density and the experimental multipolar model obtained from high-resolution X-ray diffraction data. This comparison has been carried out in intra- and intermolecular regions within the framework of the quantum theory of atoms-in-molecules (QTAIM) developed by Bader and co-workers. The characterization of the electron density in both C-Cl and Cl···Cl regions, as well as within the atomic basins, shows similar features for the three models. As a consequence, the observation of charge depletion and charge concentration regions around the halogen nuclei (along the C-Cl bonding axis and in the perpendicular plane, respectively) underlines the nature of halogen bonding in terms of electrophilic and nucleophilic interactions.     

Si-E (E = N, O, F) bonding in a hexacoordinated silicon complex: new facts from experimental and theoretical charge density studies

The concept of hypervalency in molecules, which hold more than eight valence electrons at the central atom, still is a topic of constant debate. There is general interest in silicon compounds with more than four substituents at the central silicon atom. The dispute, whether this silicon is hypervalent or highly coordinated, is enlightened by the first experimental charge density determination and subsequent topological analysis of three different highly polar Si-E (E = N, O, F) bonds in a hexacoordinated compound. The experiment reveals predominantly ionic bonding and much less covalent contribution than commonly anticipated. For comparison gas-phase ab initio calculations were performed on this compound. The results of the theoretical calculations underline the findings of the experiment.     

Electron Density of Two Bioactive Oligocyclic Indole and Oxindole Derivatives Obtained from Low‐Order X‐Ray Data and Invariom Application

For two indole and oxindole bioactive molecules, low‐order room‐temperature X‐ray data were used to generate aspherical electron density (ED) distributions by application of the invariom formalism. An analysis of the ED using the quantum theory of atoms in molecules (QTAIM) was carried out, which allowed for quantitatively examining bond orders and charge separations in various parts of the molecules. The inspection of electrostatic potentials (ESPs) and Hirshfeld surfaces provided additional information on the intermolecular interactions. Thus, reactive regions of the molecules could be identified, covalent and electrostatic contributions to interactions could be visualized, and the forces causing the crystal packing scheme could be rationalized. As the used invariom formalism needs no extra experimental effort compared to routine X‐ray analysis, its wide application is recommended because it delivers information far beyond the normally obtained steric properties. In this way, complementary contributions to drug design can be given as is demonstrated for indoles in this study, which are involved in the metabolism of plants and animals as well as in cancer therapy.