Direct Space Decomposition of ELI-D: Interplay of Charge Density and Pair-Volume Function for Different Bonding Situations

Role of Partial Vacancy and Structural Distortion in the Stability of Nonstoichiometric Phases Ni7-δInSe2-xSx (1.26 ≥ δ ≥ 0.94; 0 ≤ x ≤ 1.33)

This study explores the structure and stability of partly disordered sulfur-substituted Ni5.74InSe2 (I4/mmm, a = 3.6766(1) Å, c = 18.8178(10) Å, Z = 2). The structure of Ni7-δInSe2-xSx (x = 0.2, 0.36, 0.66, 0.80, 0.94) compounds is isotypic to their parent Ni5.74InSe2 and can be viewed as alternating heterometallic Cu3Au-type ∞2[Ni3In] slabs and defective Cu2Sb-type ∞2[Ni4-δ(Se/S)2] slabs along the [001]-axis. Similar to the parent Se-compound, the Ni-Ch (Ch = chalcogen) fragment is non-stoichiometric and possesses a partially occupied Ni-site. It was observed that with sulfur insertion at the selenium site of Ni5.74InSe2, the interatomic distance between the partially occupied nickel and mixed (S/Se) sites decreases from ∼2.24 to ∼1.95 Å, and the occupancy of the disordered nickel site simultaneously increases. The limiting composition Ni6.06InSe0.67S1.33 (x = 1.33, δ = 0.94) is formed in the sulfur-rich region. Its average structure resembles the Ni6SnS2-type and has a similar motif to Ni5.74InSe2; the only difference is that Cu3Au-type ∞2[Ni3In] alternates with two types of Ni-Ch fragments (Cu2Sb or Li2O type units). By using first-principles electronic structure calculations, we explained the presence of partially disordered nickel sites in the Ni-Ch fragment and rationalized why the nickel site occupancy increases with sulfur insertion.

Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl3 (RE = Sc, Y, Lanthanides) Series

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of REAl₃ (RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu₃ type) and hexagonal close packed (HCP, Ni₃Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni₃Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu₃ type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu₃ type offers more electronic stability with an 18-n closed-shell configuration that is not available in the Ni₃Sn type (due to electron transfer from the RE d_z² atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the REAl₃ series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.

Flux Growth, Crystal Structure, and Chemical Bonding of Yb2PdGe3, an AlB2 Superstructure within the Rare-Earth Series

The complete structure revision of the RE₂PdGe₃ (RE = rare-earth metal) series revealed that Yb₂PdGe₃ is the only AlB₂ ordered superstructure. Good-quality single crystals of this compound were successfully grown from molten indium flux, enabling accurate single-crystal investigations. Yb₂PdGe₃ crystallizes with the Ce₂CoSi₃-type structure in the hexagonal space group P6/mmm (no. 191) with lattice parameters a = 8.468(1) Å and c = 4.0747(7) Å. This structure is a four-order derivative of AlB₂, composed of planar _∞²[PdGe₃] honeycomb layers spaced by Yb species, located at the center of Ge₆ and Ge₄Pd₂ hexagons. A superconducting transition is observed below the critical temperature of 4 K. A divalent state of Yb is deduced from magnetic susceptibility measurements below room temperature, which indicate an almost nonmagnetic behavior. A charge transfer from Yb to Pd and Ge was evidenced by the Quantum Theory of Atoms in Molecules (QTAIM) effective charges; polar four-atomic Ge-Pd/Yb and two-atomic Pd-Yb bonds were observed from the ELI-D (electron localizability indicator), partial ELI-D, and ELI-D/QTAIM intersections. The bonding interactions between Ge atoms within regular Ge₆ hexagons are found to be intermediate between single bonds, as in elemental Ge, and higher-order bonds in the hypothetic Ge₆H₆ and Ge₆^6- aromatic molecules.

Chemical Bonding in the Catalytic Platform Material Ga1-x Snx Pd2

The underlying reasons for the catalytic activity of Ga_1-x Sn_x Pd₂ (0 ≤ x ≤ 1) in the semi-hydrogenation of acetylene are analyzed considering electronic structure and chemical bonding. Analysis of the chemical bonding shows pronounced charge transfer from the p elements to palladium and an unusual appearance of the Pd core basins at the surface of the QTAIM (quantum theory of atoms in molecules) atoms. The charge transfer supports the formation of the negatively charged palladium catalytic centers. Gallium-only-coordinated palladium atoms reveal a smaller effective charge in comparison with palladium species having tin in their coordination sphere. Within the empirical tight-binding approach, different influence of the E-Pd distances on the calculation matrix for the energy eigenvalues and the electronic density of states (DOS) leads to an S-like shape of the plot of the energy position of the 4d band center of gravity versus substitution level x. The latter correlates strongly with the catalytic activity and with the varying charge transfer to palladium. The optimal value of negative palladium charge and the closest position of Pd d-states gravity center towards the Fermi level correlates well with the catalytically most active composition x. Combination of all features of the chemical bonding and electronic structure allows more insight into the intrinsic reasons for the catalytic activity variation in the platform material Ga_1-x Sn_x Pd₂ (0 ≤ x ≤ 1).

La2Pd3Ge5 and Nd2Pd3Ge5 Compounds: Chemical Bonding and Physical Properties

The two La₂Pd₃Ge₅ and Nd₂Pd₃Ge₅ compounds, crystallizing in the oI40-U₂Co₃Ge₅ crystal structure, were targeted for analysis of their chemical bonding and physical properties. The compounds of interest were obtained by arc melting and characterized by differential thermal analysis, scanning electron microscopy, and X-ray diffraction both on powder and on a single crystal (for the La analogue), to ensure the high quality of the samples and accurate crystallographic data. Chemical bonding was studied by analyzing the electronic structure and effective QTAIM charges of La₂Pd₃Ge₅. A significant charge transfer mainly occurs from La to Pd so that Ge species assume tiny negative charges. This result, together with the -(I)COHP analysis, suggests that, in addition to the expected homopolar Ge bonds within zigzag chains, heteropolar interactions between Ge and the surrounding La and Pd occur with multicenter character. Covalent La–Pd interactions increase the complexity of chemical bonding, which could not be adequately described by the simplified, formally obeyed, Zintl–Klemm scheme. Electric resistivity, specific heat, magnetization, and magnetic susceptibility as a function of temperature indicate for both compounds a metallic-like behavior. For Nd₂Pd₃Ge₅, two low-temperature phase transitions are detected, leading to an antiferromagnetic ground state.

The chemical bonding and physical properties of the two isotypic R₂Pd₃Ge₅ (R = La and Nd) intermetallics are presented. La₂Pd₃Ge₅ shows polar Ge−Pd/La multicenter interactions in addition to covalent Ge−Ge bonds. The bonding scenario is further complicated by the fact that Pd and La are also covalently interacting. For Nd₂Pd₃Ge₅, an antiferromagnetic ground state is established after a long-range magnetic ordering (at ∼7.5 K) followed by a spin-reorientation transition (at ∼6.2 K).

Properties of gaseous closo-[B6X6]2- dianions (X = Cl, Br, I)

Electronic structure, collision-induced dissociation (CID) and bond properties of closo-[B₆X₆]^2- (X = Cl-I) are investigated in direct comparison with their closo-[B₁₂X₁₂]^2- analogues. Photoelectron spectroscopy (PES) and theoretical investigations reveal that [B₆X₆]^2- dianions are electronically significantly less stable than the corresponding [B₁₂X₁₂]^2- species. Although [B₆Cl₆]^2- is slightly electronically unstable, [B₆Br₆]^2- and [B₆I₆]^2- are intrinsically stable dianions. Consistent with the trend in the electron detachment energy, loss of an electron (e^- loss) is observed in CID of [B₆X₆]^2- (X = Cl, Br) but not for [B₆I₆]^2-. Halogenide loss (X^- loss) is common for [B₆X₆]^2- (X = Br, I) and [B₁₂X₁₂]^2- (X = Cl, Br, I). Meanwhile, X˙ loss is only observed for [B₁₂X₁₂]^2- (X = Br, I) species. The calculated reaction enthalpies of the three competing dissociation pathways (e^-, X^- and X˙ loss) indicated a strong influence of kinetic factors on the observed fragmentation patterns. The repulsive Coulomb barrier (RCB) determines the transition state for the e^- and X^- losses. A significantly lower RCB for X^- loss than for e^- loss was found in both experimental and theoretical investigations and can be rationalized by the recently introduced concept of electrophilic anions. The positive reaction enthalpies for X^- losses are significantly lower for [B₆X₆]^2- than for [B₁₂X₁₂]^2-, while enthalpies for X˙ losses are higher. These observations are consistent with a difference in bond character of the B-X bonds in [B₆X₆]^2- and [B₁₂X₁₂]^2-. A complementary bonding analysis using QTAIM, NPA and ELI-D based methods suggests that B-X bonds in [B₁₂X₁₂]^2- have a stronger covalent character than in [B₆X₆]^2-, in which X has a stronger halide character.

Metallic alloys at the edge of complexity: structural aspects, chemical bonding and physical properties

Complex metallic alloys belong to the vast family of intermetallic compounds and are hallmarked by extremely large unit cells and, in many cases, extensive crystallographic disorder. Early studies of complex intermetallics were focusing on the elucidation of their crystal structures and classification of the underlying building principles. More recently, ab initio computational analysis and detailed examination of the physical properties have become feasible and opened new perspectives for these materials. The present review paper provides a summary of the literature data on the reported compositions with exceptional structural complexity and their properties, and highlights the factors leading to the emergence of their crystal structures and the methods of characterization and systematization of these compounds.

Revealing electronic features governing hydrolysis of cephalosporins in the active site of the L1 metallo-β-lactamase

The QM/MM simulations followed by electron density feature analysis are carried out to deepen the understanding of the reaction mechanism of cephalosporin hydrolysis in the active site of the L1 metallo-β-lactamase. The differences in reactivity of ten similar cephalosporin compounds are explained by using an extended set of bonding descriptors. The limiting step of the reaction is characterized by the proton transfer to the nitrogen atom of the cephalosporin thiazine ring accompanied with formation of the C₄ Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> C₃ double bond in its N–C₄–C₃ fragment. The temporary N⋯H–O_w hydrogen bond, which is formed in the transition state of the limiting step of the reaction was recognized as a key atomic interaction governing the reactivity of various cephalosporins. Non-local real-space bonding descriptors show that different extent of localization of electron lone pair at N atom in the transition state affect the reactivity of compounds: smaller electron localization is typical for the less reactive species. In particular, the Fermi hole analysis shows how exchange electron correlation in the N⋯H–O_w fragment control electron lone pair localization. Delocalization tensor, linear response kernel and source function indicate that features of electron delocalization in the N–C₄–C₃ fragment of cephalosporins in the transition state complexes determine the differences in C₄–C₃ bond for substrates with high and low rate constants. The C₄–C₃ bond of the N–C₄–C₃ fragment at the transition state is similar to that of the preceding intermediate for the less reactive species and resembles the features of the enzyme–product complex for more reactive compounds. The power and limitations of the descriptors applied for solving the problem are discussed and the generality of approach is stressed.

Combination of QM/MM and modern bonding descriptors explains different reactivity of cephalosporins in the active site of the L1 metallo-β-lactamase.

Superelectrophilic Behavior of an Anion Demonstrated by the Spontaneous Binding of Noble Gases to [B12 Cl11 ]<sup/>

It is common and chemically intuitive to assign cations electrophilic and anions nucleophilic reactivity, respectively. Herein, we demonstrate a striking violation of this concept: The anion [B₁₂ Cl₁₁ ]^- spontaneously binds to the noble gases (Ngs) xenon and krypton at room temperature in a reaction that is typical of "superelectrophilic" dications. [B₁₂ Cl₁₁ Ng]^- adducts, with Ng binding energies of 80 to 100 kJ mol^-1 , contain B-Ng bonds with a substantial degree of covalent interaction. The electrophilic nature of the [B₁₂ Cl₁₁ ]^- anion is confirmed spectroscopically by the observation of a blue shift of the CO stretching mode in the IR spectrum of [B₁₂ Cl₁₁ CO]^- and theoretically by investigation of its electronic structure. The orientation of the electric field at the reactive site of [B₁₂ Cl₁₁ ]^- results in an energy barrier for the approach of polar molecules and facilitates the formation of Ng adducts that are not detected with reactive cations such as [C₆ H₅ ]⁺ . This introduces the new chemical concept of "dipole-discriminating electrophilic anions."

Torquoselectivity in Cyclobutene Ring Openings and the Interatomic Interactions That Control Them

Torquoselectivity has explained diasteromeric preferences of a number electrocyclic ring openings. The quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the interacting quantum atoms (IQA) energy partition method are used to evaluate qualitatively and quantitatively the atomic interactions behind the torquoselectivity of a series of 3-substituted cyclobutenes. ELI-D topology and IQA energies show that the interaction between the distal terminus carbon atom of cyclobutene (C4) with the substituent at C3 (R5) in the transition state governs torquoselectivities. In the case of 3-borylcyclobutene, this interaction is so strong that a protocovalent bond is actually formed between B5 and C4. The evaluation of the interatomic energies allowed us to identify an additional interaction that contribute to a minor extent to the stabilization of the TS. Despite the fact that C4,R5 interaction is the main cause of the torquoselectivity, a bonding path (BP) between these two atoms was not observed. However, the lack of a BP between C4 and R5 does not mean that the topology of the electron density was not affected by the interaction of these two atoms. Surprisingly, we found a strong correlation between the density at the bond critical point (BCP) and the BP shape of C3-C4 breaking bond with the observed activation energies and torquoselectivities.

Heteropolar bonding and a position-space representation of the 8 − N rule

The 8 − N rule in solid-state chemistry is represented by two complementary views. This contribution highlights the new quantum-chemical position-space representation of the 8 − N rule which unites the two classical views and shows promising predictive capabilities, in particular for heteropolar bonding situations.

S⋯O chalcogen bonding in sulfa drugs: insights from multipole charge density and X-ray wavefunction of acetazolamide

Experimental charge density analysis combined with the quantum crystallographic technique of X-ray wavefunction refinement (XWR) provides quantitative insights into the intra- and intermolecular interactions formed by acetazolamide, a diuretic drug.

On the chemical shifts of agostic protons

Agostic hydrogen atoms in planar d(8) transition metal complexes display a remarkable wide range of chemical shifts from +5 to -10 ppm in the proton NMR spectra. It is therefore surprising that a simple recipe can be elaborated to predict the influence of the local electronic structure of the metal atom on the shielding of the coordinating protons: In cases where the agostic hydrogen atom is pointing to a local Lewis acidic center at the metal the (1)H NMR signal is shifted upfield relative to the scenario where the proton is opposing a local charge concentration at the metal. To trace the physical origin of this empirical relationship, a systematic study has been performed to understand how the (i) topology of the electron density and (ii) orientation of the magnetic field vector, B0, control the paratropic or diatropic characteristics of the induced current density at the metal atom and thus the shielding or deshielding of the agostic protons.

Reactivity differences between α,β-unsaturated carbonyls and hydrazones investigated by experimental and theoretical electron density and electron localizability analyses

It is still a challenge to predict a compound's reactivity from its ground-state electronic nature although Bader-type topological analyses of the electron density (ED) and electron localizability indicator (ELI) give detailed and useful information on electron concentration and electron-pair localization, respectively. Both ED and ELI can be obtained from theoretical calculations as well as high-resolution X-ray diffraction experiments. Besides ED and ELI descriptors, the delocalization index is used here; it is likewise derived from theoretical calculations as well as from experimental X-ray results, but in the latter case, demonstrated here for the first time. We investigate α,β-unsaturated carbonyl and hydrazone compounds because resonance exhibited by these compounds in the electronic ground-state determines their reactive behavior. The degree of resonance as well as the reactivity contrast are quantified with the electronic descriptors. Moreover, competitive mesomeric substituent effects are studied using the two biologically important compounds acrolein and acrylamide. The reactivity differences predicted from the analyses are in line with the known reactivity of these compounds in organic synthesis. Hence, the capability of the ED and ELI for rationalizing and predicting different and competing substituent effects with respect to reactivity is demonstrated.

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

We are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives, i.e. minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science.

Metal-metal and metal-ligand bonding at a QTAIM catastrophe: a combined experimental and theoretical charge density study on the alkylidyne cluster Fe3(μ-H)(μ-COMe)(CO)10

The charge density in the tri-iron methoxymethylidyne cluster Fe(3)(μ-H)(μ-COMe)(CO)(10) (1) has been studied experimentally at 100 K and by DFT calculations on the isolated molecule using the Quantum Theory of Atoms in Molecules (QTAIM). The COMe ligand acts as a nearly symmetric bridge toward two of the Fe atoms (Fe-C = 1.8554(4), 1.8608(4) Å) but with a much longer interaction to the third Fe atom, Fe-C = 2.6762(4) Å. Complex 1 provides a classic example where topological QTAIM catastrophes render an exact structure description ambiguous. While all experimental and theoretical studies agree in finding no direct metal-metal interaction for the doubly bridged Fe-Fe vector, the chemical bonding between the Fe(CO)(4) unit and the Fe(2)(μ-H)(μ-COMe)(CO)(6) moiety in terms of conventional QTAIM descriptors is much less clear. Bond paths implying direct Fe-Fe interactions and a weak interaction between the COMe ligand and the Fe(CO)(4) center are observed, depending on the experimental or theoretical density model examined. Theoretical studies using the Electron Localizability Indicator (ELI-D) suggest the metal-metal bonding is more significant, while the delocalization indices imply that both Fe-Fe bonding and Fe···C(alkylidyne) bonding are equally important. The source functions at various interfragment reference points are similar and highly delocalized. The potential-energy surface (PES) for the migration of the alkylidyne group from a μ(2) to a semi-μ(3) coordination mode has been explored by DFT calculations on 1 and the model complexes M(3)(μ-H)(μ-CH)(CO)(10) (M = Fe, 2; Ru, 3; and Os, 4). These calculations confirm a semi-μ(3) bridging mode for the alkylidyne ligand as the minimum-energy geometry for compounds 2-4 and demonstrate that, for 1, both Fe-Fe and Fe···C(alkylidyne) interactions are important in the cluster bonding. The PES between μ(2) and semi-μ(3) alkylidyne coordination for 1 is extremely soft, and the interconversion between several topological isomers is predicted to occur with almost no energy cost. Analysis of the density ρ(r) and the Laplacian of the density ▽(2)ρ(r(b)) in the methoxymethylidyne ligand is consistent with a partial π-bond character of the C-O bond, associated with an sp(2) hybridization for these atoms.

Electron localizability indicators ELI-D and ELIA for highly correlated wavefunctions of homonuclear dimers. II. N2, O2, F2, and Ne2

Electron localizability indicators based on the electron pair density ELI-D and ELIA Electron localizability indicators ELI-D and ELIA based on the electron pair density are studied for the correlated ground-state wavefunctions of N(2), O(2), F(2), and Ne(2) diatomics. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two indicators. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for O(2) and F(2), the reliable topology of ELI-D is obtained only at the correlated level of theory.