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Chemical bonding in crystals: New directions
Abstract
Analysis of the chemical bonding in the position space, instead of or besides that in the wave function (Hilbert) orbital space, has become increasingly popular for crystalline systems in the past decade. The two most frequently used investigative tools, the Quantum Theory of Atoms in Molecules and Crystals (QTAIMAC) and the Electron Localization Function (ELF) are thoroughly discussed. The treatment is focussed on the topological peculiarities that necessarily arise from the periodicity of the crystal lattice and on those facets of the two tools that have been more debated, especially when these tools are applied to the condensed phase. In particular, in the case of QTAIMAC, the physical and chemical significance of the bond paths for the very weak or the supposedly repulsive interactions, the distinctive features and the appropriateness of the several schemes that have been proposed to classify chemical bonds, and, finally, the relative importance of the local and integrated electron density properties for describing intermolecular interactions. In the case of the ELF, particular attention is devoted to how this function is formulated and to the related physical meaning, and to how can the ELF be chemically interpreted and properly analysed in crystals. Several examples are reported to illustrate all these points and for critically examine the answers obtained and the problems encountered. The discussed examples encompass the case of molecular crystals, Zintl phases, intermetallic compounds, metals, supported and unsupported metal-metal bonds in organometallics, ionic solids, crystal surfaces, crystal defects, etc. Whenever possible joint ELF and QTAIMAC studies are considered, with particular emphasis on the comparison of the bond description afforded by the ELF and the Laplacian of the electron density. Two recently proposed functions, the Localized Orbital Locator (LOL) and the Source Function in its integrated or local form are also presented, in view of their potential interest for studies of chemical bonding in crystals. The use of approximated ELF and LOL, as derived from the density functional form of the positive kinetic energy density, is also discussed.
... [52,53] Notice that the RCPs inside the Zn 2 Sb 2 -rhombus were in close proximity to the Zn─Zn BCP alluding toward a possible bifurcation mechanism [54] between the CPs in which the two RCPs and the single BCP can coalesce into a single RCP, 2RCP + BCP → RCP, consistent with the Morse relation. [55] Stated in reverse, a high-symmetry rhombus such as diborane could distort to give the observed molecular structure of the Zn 2 Sb 2 -rhombus. ...
... Meanwhile, the Zn─Zn and r2 distances are significantly longer than the sum of covalent radii of 2.40 and 2.60 Å, respectively, while r1 is at the midpoint between the sum of radii and r2. All BCPs show similar G/ < 1, H/ < 0, and ∇ 2 ≈ 0 indicating open-shell interactions [55,59] for all bonds in Table 3. The small , positive ∇ 2 , and negative H are typical for heavy element interactions in part because of the missing valence-shell charge concentration of heavy elements. ...
... The small , positive ∇ 2 , and negative H are typical for heavy element interactions in part because of the missing valence-shell charge concentration of heavy elements. [55,59,60] For light elements a |V|/G ratio between one and two is classified as a transient region between closed-and shared-shell interactions interpreted as incipient or incomplete covalent bond formation where the upper limit transitions into open-shell interactions and the lower limit into closed-shell interactions. [55] These limits are not directly applicable to heavy elements, but trends in the parameter can still guide an interpretation: Sb─Sb is the most open-shell-like interaction followed by c1 and c2 and then by r1 and r2, while Zn-Zn is the least open-shell-like interaction. ...
The Zn─Sb binary system contains two high‐performing thermoelectric materials, namely the ordered ZnSb and the disordered Zn13Sb10. Both systems exhibit low thermal conductivity, which is speculated to originate from multicentre bonding within Zn2Sb2‐rhombi. Here, the electron density of ZnSb is reported based on multipole modelling of accurate X‐ray diffraction data measured at 20 K. Topological analysis reveals that the bond paths in the rhombus are endocyclically strained and that electron density is concentrated within the rhombus rather than along its geometric bonds consistent with a multicentre bond description. However, the electron density is not equally shared between the geometric bonds of the rhombus. Electron density analysis and modelling of low‐temperature anharmonicity reveal that one Zn–Sb interaction is weaker than the other. Taken together with the orientation of bonds external to the rhombus structure, an alternative description emerges wherein the multicentre bond is more partially localised along one set of the opposite legs of the rhombus. In this description, the stronger bond can be considered a traditional 2‐centre‐2‐electron bond, while the weaker interaction is coordinative to the covalent bond. The anharmonicity and low thermal conductivity may consequently be understood as Zn rattling along the coordinative interaction.
... To study the peculiarities of ρ(r), we used the program CRITIC2, 22 developed for the topological analysis of scalar fields in periodic structures based on the "Quantum Theory of Atoms in Molecules and Crystals" (QTAIM) method. [23][24][25] According to Bader's QTAIM, the points rc, at which the charge density gradient is equal to zero ∇ρ(rc) = 0, are called critical points. The types of critical points in the charge density distribution are characterized by the rank ω [the number of nonzero eigenvalues λ i -the main values of curvature of the Hesse matrix of the second derivatives of the charge density over coordinates (∂ 2 ρ/∂xi∂xj)] and signature σ-the algebraic sum of λ i signs: (ω, σ). ...
... The types of critical points in the charge density distribution are characterized by the rank ω [the number of nonzero eigenvalues λ i -the main values of curvature of the Hesse matrix of the second derivatives of the charge density over coordinates (∂ 2 ρ/∂xi∂xj)] and signature σ-the algebraic sum of λ i signs: (ω, σ). There are four types of stable critical points: [23][24][25] (3, −3) -nucleus (local maximum), (3, +3) -cage (local minimum), (3, +1) -ring (the first saddle critical point), and (3, −1) -bond (the second saddle critical point). Critical points of the bond type [bond critical points (BCPs)] play an essential role in the classification of the chemical bonding types. ...
... Critical points of the bond type [bond critical points (BCPs)] play an essential role in the classification of the chemical bonding types. Covalent bonding is characterized by the following Bader's parameters for BCPs: [23][24][25] the negative sign of the charge density Laplacian ∇ 2 ρ b < 0, two negative values of curvature λ 1,2 < 0, which are large in absolute values |λ 1,2 | > λ 3 , and large values of the charge density ρ b . While for the ionic bonding, ∇ 2 ρ b > 0, |λ 1,2 | ≪ λ 3 , ρ b is small, and the charge density is concentrated mainly on atoms. ...
The electronic band structure and features of the charge density distribution in lead oxide phosphate Pb10(PO4)6O and the copper-doped compound Pb9Cu(PO4)6O have been studied by the density functional theory. Despite the differences in chemical compositions and crystal structures, the type of chemical bonding in the Pb10(PO4)6O and Pb9Cu(PO4)6O compounds was found to be similar to the type of chemical bonding that we previously revealed in high-temperature superconductors and in parent compounds for their production—monoclinic α-Bi2O3 and orthorhombic La2CuO4. Although the lack of experimental data on the electronic band structure and physical properties of the Pb10(PO4)6O and Pb10−xCux(PO4)6O compounds does not currently allow us to conclude that superconductivity could exist at room temperature and atmospheric pressure in the Pb10−xCux(PO4)6O compound, further studies of the properties of lead oxide phosphate and other minerals of the apatite supergroup might be useful for identifying new types of promising materials for the production of high-temperature superconductors.
... In addition, other BCPs are displayed in tables S2 to S4. According to the established classification (29), vdWi exhibits closed-shell interactions with a small ED ρ, positive Laplacian ∇ 2 ρ, |λ 1 |/λ 3 < 1, positive H, G/ρ ≥ 1, and |V|/G < 1 at the BCPs, where G, V, and H are the kinetic, potential, and total energy density, respectively. The observed O···O interaction satisfies the criteria for vdWi in all Li x CoO 2 states (Table 1). ...
... However, in Li 0.3 CoO 2 , the Co─O bond starts to reverse its length and the H/ρ value (−0.061) at the BCP of Co─O bonds approaches zero (table S2). This implies that the interaction is at the boundary with closed-shell region (29), which indicates a diminished covalency. ...
High-voltage phase transition constitutes the major barrier to accessing high energy density in layered cathodes. However, questions remain regarding the origin of phase transition, because the interlayer weak bonding features cannot get an accurate description by experiments. Here, we determined van der Waals (vdW) interaction (vdWi) in Li x CoO 2 via visualizing its electron density, elucidating the origin of O3─O1 phase transition. The charge around oxygen is distorted by the increasing Co─O covalency. The charge distortion causes the difference of vdW gap between O3 and O1 phases, verified by a gap corrected vdW equation. In a high charging state, excessive covalency breaks the vdW gap balance, driving the O3 phase toward a stable O1 one. This interpretation of vdWi-dominated phase transition can be applied to other layered materials, as shown by a map regarding degree of covalence. Last, we introduce the cationic potential to provide a solution for designing high-voltage layered cathodes.
... Both methods are extensively used to study organometallic compounds with and without transition metal atoms [26]. Additionally, related approaches such as the source function (SF) are also used in the analysis of such compounds [27]. There are only a few research papers available on the electron density topology in the rare category of Cr-Mncarbonyl-chalcogenide clusters. ...
... A (3, + 1) CP is commonly referred to as a ring critical point (RCP), where nuclei are linked by interaction lines to form a ring [43]. Within the QTAIM framework, the molecular graph is composed of the gradient of the topology of bond and ring critical points, along with the bond paths that connect bonded atoms [27]. Based on the QTAIM theory, it has been observed that the molecular graph, shown in Fig . ...
The nature of the chemical bonding interactions in the trigonal–bipyramidal chromium–manganese chalcogenide clusters, [E2CrMn2(CO)9]⁻² (E = S, Se, and Te), has been studied using two methods of the quantum chemical topology analysis: electron density q(r) and electron localization function (ELF). The evaluation of these properties reveals important details about chemical bond interactions within the clusters. According to the results, it has been confirmed that the bonding between Mn–Mn and Mn–Cr is absent in all three trinuclear clusters 1–3. The presence of bridging chalcogenide atoms (S, Se, and Te) concerning M–M is a key factor in determining the distribution of electron densities. This factor has a significant impact on the formation of bonds between these transition metal atoms. Calculations of the non-negligible delocalization index for clusters 1–3 confirm a 5c–12e bonding interaction that is delocalized over the five-membered CrMn2(μ−E)2 ring. In clusters 1–3, the M–E bonds between Mn and Cr metal atoms and E ligands (S, Se, and Te) exhibit similar topological parameters that are comparable to that of pure covalent single bonds between nonmetal atoms. Furthermore, the source function calculations reveal that the bonded E atoms contribute the most at each Mn–E and Cr–E bcps, with a small contribution from the bonded metal atom and OCO atoms. Interestingly, non-bonded transition metal atoms act as sinks rather than sources of electron density. The M…OCO delocalization indexes and SF calculations indicate significant CO to M π-back-donation. This work aims to provide insights into the interactions between Mn–Mn and Mn–Cr, and the changes in bonding interactions across the di-bridging chalcogen elements series. It also aims to examine the role of carbonyl groups in M–M interaction within the clusters.
... The intramolecular NÀ H···O=C interaction in the BCP exhibits an electron density (ρ b ) of 0.0133 au, a Laplacian value (r 2 ρ b ) of 0.0534 au, and an ellipticity (ɛ) value of 0.0584, whose magnitudes and signs are consistent with the values proposed by Gatti for its classification as a closed-shell hydrogen bond. [25] The value of r 2 ρ b = 0.05 au for this BCP lies in the middle of the reported Laplacian values for highly polar NÀ H···O=C interactions (r 2 ρ b = 0.07 au), such as in the case of urea crystal, [26] and typical values (r 2 ρ b = 0.03 au) reported for this type of interaction. [27] The value of ɛ = 0.0584 in the BCP is similar to the reported ellipticity values for intramolecular O···H-type interactions (0.07 � ɛ � 0.04), indicating significant delocalization of the π-conjugated system in the crystal of compound 1 through this hydrogen bond. ...
... The most significant changes in the topological properties of the BCPs in the central amide fragment of compound 1, occurring upon crystallization, are observed in the absolute values of ellipticity (j Δ% j > 20 %) and Laplacian (j Δ% j > 7 %), especially in the carbonyl C11 = O1 and amide C11À N1 bonds. According to the classification of bonds as shared-shell interactions (r 2 ρ b < 0) or closed-shell interactions (r 2 ρ b > 0) reported by Gatti, [25] these changes indicate an increase in the covalent character of the C11À N1 bond at the expense of a reduction in the covalent character of the C=O bond. Moreover, the changes in ellipticity values indicate that upon crystallization, the carbonyl C11À O1 bond loses a significant part of its π character, whereas the C11À N1 bond experiences an increase in π character. ...
The synthesis of four novel amide compounds (R¹C(O)NHR²) is reported, which contain both bulky (R¹=phenyl and adamantyl) and hydrophilic (R²=hydroxyl, methoxyl) groups. The incorporation of such substituents provides compounds with unique properties that combine steric hindrance and hydrophilicity. The synthesized amides were fully characterized by ¹H and ¹³C nuclear magnetic resonance (NMR) and analysed using infrared (IR) and Raman spectroscopy to investigate their vibrational properties in the solid phase, specifically focusing on the amide‐type normal modes of vibrations. Furthermore, the crystal structures of three derivatives were determined by single‐crystal X‐ray diffraction, which provided insights into their molecular arrangements. The occurrence of N−H⋅⋅⋅O=C hydrogen bonding intermolecular interaction is clearly observed and characterized by Hirschfeld surface analysis. Topology analysis using the Quantum Theory of Atom in Molecules and Crystals (QTAIM−C) were employed to investigate the electronic properties of the isolated amide molecules and to analyse the intermolecular interactions within the crystalline structure. The periodic calculations for the crystal revealed a higher electronic density in the C−N bond, indicating an increased covalent character in this bond compared with the C=O bond. This observation indicates the presence of resonance‐assisted hydrogen bonds within the amide core, leading to π electronic delocalization.
... Both approaches revealed a significant contribution of the nitrogen atom to the B-N bonding, which is in agreement with a formal dative mechanism of its formation. Consequently, unlike the C-C or N-N covalent bonds, the N→B bonds should be considered as dative QTAIM analysis of N-phenyl iminoborane 18 provides electron density ρ(r) values higher than 0.22 e·Å −3 for both CP1 and CP2, suggesting covalent interactions [20]. However, both CPs present a high positive Laplacian ∇ 2 ρ(r) value and a negative local energy density H(r), suggesting an intermediate interaction such as highly polar covalent bonds or dative bonds (see Table 1) [20][21][22][23][24]. ...
... Consequently, unlike the C-C or N-N covalent bonds, the N→B bonds should be considered as dative QTAIM analysis of N-phenyl iminoborane 18 provides electron density ρ(r) values higher than 0.22 e·Å −3 for both CP1 and CP2, suggesting covalent interactions [20]. However, both CPs present a high positive Laplacian ∇ 2 ρ(r) value and a negative local energy density H(r), suggesting an intermediate interaction such as highly polar covalent bonds or dative bonds (see Table 1) [20][21][22][23][24]. The H(r)/ρ(r) << 0 and G(r)/ρ(r) > 1 found at CP1 and CP2 are also characteristic of intermediate interactions. ...
The reaction of N-phenyl iminoborane with benzaldehyde yielding a fused aromatic compound, recently reported by Liu et al., has been studied within the Molecular Electron Density Theory (MEDT). Formation of the fused aromatic compound is a domino process that comprises three consecutive reactions: (i) formation of a weak molecular complex between the reagents; (ii) an intramolecular electrophilic attack of the activated carbonyl carbon of benzaldehyde on the ortho position of the N-phenyl substituent of iminoborane; and (iii) a formal 1,3-hydrogen shift yielding the final fused aromatic compound. The two last steps correspond to a Friedel–Crafts acylation reaction, the product of the second reaction being the tetrahedral intermediate of an electrophilic aromatic substitution reaction. However, the presence of the imino group adjacent to the aromatic ring strongly stabilizes the corresponding intermediate, being the reaction product when the ortho positions are occupied by t-butyl substituents. This domino reaction shows a great similitude with the Brønsted acid catalyzed Povarov reaction. Although N-phenyl iminoborane can experience a formal [2+2] cycloaddition reaction with benzaldehyde, its higher activation Gibbs free energy compared to the intramolecular electrophilic attack of the activated carbonyl carbon of benzaldehyde on the ortho position of the N-phenyl substituent, 6.6 kcal·mol−1, prevents the formation of the formal [2+2] cycloadduct. The present MEDT study provides a different vision of the molecular mechanism of these reactions based on the electron density.
... The most stable doping configuration was discussed in previous work [30]. The Quantum Theory of Atoms in Molecules and Crystals (QTAIMC) [31,32] implemented in the TOPOND code, was used to understand the chemical nature of interactions. Several descriptors, such as the electronic density (ρ) and the Laplacian of the electron density ( ∇ 2 ρ b ) at the bond critical points (BCPs) [33] were employed. ...
... The vibrational modes at the Γ point were evaluated using the numerical second derivatives of the total energies estimated with the coupled perturbed HF/Kohn−Sham (CPKS) algorithm. 55 The quantum theory of atoms in molecules and crystals (QTAIMC) 56,57 was employed to characterize the nature of chemical bonds. This approach uses the electronic density (ρ(r)) at the bond critical points (BCPs) to obtain topological parameters, such as the laplacian (∇ 2 ρ(r)), the potential energy density (V(r)), the kinetic energy density (G(r)), and the total electronic energy density (H(r) = V(r) + G(r)). ...
The two-dimensional (2D) materials class earned a boost in 2021 with biphenylene synthesis, which is structurally formed by the fusion of four-, six-, and eight-membered carbon rings, usually named 4-6-8-biphenylene network (BPN). This research proposes a detailed study of electronic, structural, dynamic, and mechanical properties to demonstrate the potential of the novel biphenylene-like indium nitride (BPN-InN) via density functional theory and molecular dynamics simulations. The BPN-InN has a direct band gap energy transition of 2.02 eV, making it promising for optoelectronic applications. This structure exhibits maximum and minimum Young modulus of 22.716 and 22.063 N/m, Poisson ratio of 0.018 and −0.008, and Shear modulus of 11.448 and 10.860 N/m, respectively. To understand the BPN-InN behavior when subjected to mechanical deformations, biaxial and uniaxial strains in armchair and zigzag directions from −8 to 8% were applied, achieving a band gap energy modulation of 1.36 eV over tensile deformations. Our findings are expected to motivate both theorists and experimentalists to study and obtain these new 2D inorganic materials that exhibit promising semiconductor properties.
... All of the bonds have relatively small ρ values, accompanied by positive ∇ 2 ρ values, predominantly indicating an ionic character. 51,52 However, there are significant differences between the Cs−Br and Sn−Br bonds. Initially, a more concentrated electron density is observed along the Sn−Br pair bond than in the Cs−Br pair. ...
Metal halide perovskites with a two-dimensional structure are utilized in photovoltaics and optoelectronics. High-crystallinity CsSn2Br5 specimens have been synthesized via ball milling. Differential scanning calorimetry curves show melting at 553 K (endothermic) and recrystallization at 516 K (exothermic). Structural analysis using synchrotron X-ray diffraction data, collected from 100 to 373 K, allows for the determination of Debye model parameters. This analysis provides insights into the relative Cs−Br and Sn−Br chemical bonds within the tetragonal structure (space group: I4/mcm), which remains stable throughout the temperature range studied. Combined with neutron data, X−N techniques permit the identification of the Sn2+ lone electron pair (5s2) in the two-dimensional framework, occupying empty space opposite to the four Sn−Br bonds of the pyramidal [SnBr4] coordination polyhedra. Additionally, diffuse reflectance UV−vis spectroscopy unveils an indirect optical gap of approximately ∼3.3 eV, aligning with the calculated value from the B3LYP-DFT method (∼3.2 eV). The material exhibits a positive Seebeck coefficient as high as 6.5 × 10**4 μV K−1 at 350 K, which evolves down to negative values of −3.0 × 10**3 μV K−1 at 550 K, surpassing values reported for other halide perovskites. Notably, the thermal conductivity remains exceptionally low, between 0.32 and 0.25 W m−1 K−1 .
... The QTAIMAC method, 84 as implemented in the Critic2 code, 85 was utilized to systematically investigate the chemical bonding present in Au, Zn/Fe(111) materials. This methodology offers a precise manner of identifying the strength, nature, and locations of the chemical bonds. ...
Noble metals such as gold (Au), zinc (Zn), and iron (Fe) are highly significant in both fundamental and technological contexts owing to their applications in optoelectronics, light-emitting devices, photovoltaics, nanotechnology, batteries, and thermal barrier coatings.
... The topological analysis of the electron density ρ(r) is performed using the TOPOND code [36,37] according to the Quantum Theory of Atoms In Molecules And Crystals (QTAIMAC). This analysis provides the critical points (CPs) r CP where the gradient of the density vanishes: ∇ρ(r CP ) = 0. CPs can be classified in terms of their type (r, s), where r is the rank and s is the signature. ...
In the wide group of thermoelectric compounds, the half-Heusler ZrNiSn alloy is one of the most promising materials thanks to its thermal stability and narrow band gap, which open it to the possibility of mid-temperature applications. A large variety of defects and doping can be introduced in the ZrNiSn crystalline structure, thus allowing researchers to tune the electronic band structure and enhance the thermoelectric performance. Within this picture, theoretical studies of the electronic properties of perfect and defective ZrNiSn structures can help with the comprehension of the relation between the topology of defects and the thermoelectric features. In this work, a half-Heusler ZrNiSn alloy is studied using different defective models by means of an accurate Density Functional Theory supercell approach. In particular, we decided to model the most common defects related to Ni, which are certainly present in the experimental samples, i.e., interstitial and antisite Ni and a substitutional defect consisting of the replacement of Sn with Sb atoms using concentrations of 3% and 6%. First of all, a comprehensive characterization of the one-electron properties is performed in order to gain deeper insight into the relationship between structural, topological and electronic properties. Then, the effects of the modeled defects on the band structure are analyzed, with particular attention paid to the region between the valence and the conduction bands, where the defective models introduce in-gap states with respect to the perfect ZrNiSn crystal. Finally, the electronic transport properties of perfect and defective structures are computed using semi-classical approximation in the framework of the Boltzmann transport theory as implemented in the Crystal code. The dependence obtained of the Seebeck coefficient and the power factor on the temperature and the carrier concentration shows reasonable agreement with respect to the experimental counterpart, allowing possible rationalization of the effect of the modeled defects on the thermoelectric performance of the synthesized samples. As a general conclusion, defect-free ZrNiSn crystal appears to be the best candidate for thermoelectric applications when compared to interstitial and antisite Ni defective models, and substitutional defects of Sn with Sb atoms (using concentrations of 3% and 6%) do not appreciably improve electronic transport properties.
... To determine the nature of Y-Pd and Pd-As bonds, a deeper analysis must be carried out. The Laplacian of electron density Δρ b (r) = ∇ 2 b at the BCPs makes it possible to differentiate between a covalent or ionic bond based on its sign [65], but this principle alone is therefore insufficient for other types of bonds (metallic, dative, intermediate, Fig. 6. Curves of projected band structure (fat-band) and partial densities of states obtained by TB-mBJ + SOC for YPd HC As. ...
... The quantum theory of atoms in molecules (QTAIM), proposed by Bader [59] and extended for crystals by Gatti [59,60], is implemented in the CRYSTAL17, and adopted here to understand the nature of chemical bonds based on the electronic density (ρ(r)) at the bond critical points (BCPs). Some topological parameters, such as the electronic density laplacian (∇ 2 ρ(r)), the potential energy density (V(r)), the kinetic energy density (G(r)), and the total electronic energy density (H(r) = V(r) + G(r)), when evaluated on the BCPs, can provide valuable information regarding the type of bond interaction. ...
... The unique bonding characteristics of the SeÀ N bond discovered here with XWR are apparent in various other properties that can be derived from electron density topological studies, such as potential energy density (V), kinetic energy density (G), and their ratios G/ρ and j V j /G. For any shared-shell interaction, as a general trend, the j V j /G ratio tends to be greater than 2, whereas the G/ρ ratio lies in a range of values less than 1. [47] It is clear from Table 1 that the SeÀ N bond shows a low j V j /G value and a high G/ρ ratio which shows an ambiguous trend -in contrast to those values obtained for SeÀ C and CÀ H covalent bonds in this molecule. In Figure 3. Electron density deformation maps plotted for the unfitted wavefunctions at the HAR geometry (λ = 0) and the X-ray fitted wavefunctions (λ = λ max ) obtained for (a,b) ebselen,1 and (c,d) pyridin-3-yl ebselen, 1 p (ρ values in eB À 3 ). ...
Dynamic bonds are essential structural ingredients of dynamic covalent chemistry that involve reversible cleavage and formation of bonds. Herein, we explore the electronic characteristics of Se−N bonds in the organo‐selenium antioxidant ebselen and its derivatives for their propensity to function as dynamic covalent bonds by employing high‐resolution X‐ray quantum crystallography and complementary computational studies. An analysis of the experimentally reconstructed X‐ray wavefunctions reveals the salient electronic features of the Se−N bonds with very low electron density localized at the bonding region and a positive Laplacian value at the bond critical point. Bond orders and percentage covalency and ionicity estimated from the X‐ray wavefunctions, along with localized orbital locator (LOL) and electron localization function (ELF) analyses show that the Se−N bond is unique in its closed shell‐like features, despite being a covalent bond. Time‐dependent DFT calculations simulate the cleavage of Se−N bonds in ebselen in the excited state, further substantiating their nature as dynamic bonds.
... The molecular graphs of dimers show the bond critical points (BCPs) for the intermolecular interactions illustrated in Fig. S6 and S7 (ESI †), and the topological parameters for the intermolecular interactions are summarized in Table S1 (ESI †). All the observed interactions are closed-shell interactions according to the value of j-V(r)/G(r)j < 1, V 2 r(r) > 0 and H(r) > 1. 58 In 1, the dissociation energies (D e ) for two of the C-H/F interactions are relatively higher compared to other interactions observed. It is of interest to note that the dissociation energy of C16-F1/F2-C16 interaction is comparable to the strength of two of the C-H/F interactions. ...
Two 1,3,4-oxadiazole-2-thione-N-Mannich derivatives, specifically 5-(4-chlorophenyl)-3-[(2-trifluoromethylphenylamino)methyl]-1,3,4-oxadiazole-2(3H)-thione (1) and 5-(4-chlorophenyl)-3-[(2,5-difluorophenylamino)methyl]-1,3,4-oxadiazole-2(3H)-thione (2), were synthesized and then characterized by elemental analysis and NMR (¹H and ¹³C) spectroscopy and the single crystal X-ray diffraction method. The formed weak intermolecular interactions in the solid-state structures of these derivatives were thoroughly investigated utilizing a variety of theoretical tools such as Hirshfeld surface analysis and quantum theory of atoms in molecules (QTAIM). Furthermore, the CLP-PIXEL and density functional theory calculations were used to study the energetics of molecular dimers. Numerous weak intermolecular interactions such as C–H⋯S/Cl/F/π interactions, a directional C–Cl⋯Cl halogen bond, π-stacking, type C–F⋯F–C contact and a short F⋯O interaction, help to stabilize the crystal structure of 1. Crystal structure 2 also stabilizes with several weak intermolecular contacts, including N–H⋯S, C–H⋯N//Cl/F interactions, a highly directional C1–Cl1⋯C(π) halogen bond and C(π)⋯C(π) interaction. In vitro antimicrobial potency of compounds 1 and 2 was assessed against various Gram-positive and Gram-negative bacterial strains and the pathogenic yeast-like Candida albicans. Both compounds showed marked activity against all tested Gram-positive bacteria and weak activity against Escherichia coli and lacked inhibitory activity against Pseudomonas aeruginosa. In addition, compounds 1 and 2 displayed good in vitro anti-proliferative activity against hepatocellular carcinoma (HepG-2) and mammary gland breast cancer (MCF-7) cancer cell lines. Molecular docking studies revealed the binding modes of title compounds at the active sites of prospective therapeutic targets.
... The Bader analysis was conducted [57] to understand the interaction between hydrogen molecules with pristine IGP-SiC and Li(Na)@IGP-SiC systems. On the other hand, it is analyzed the electron density topology via the Quantum Theory of Atoms in Molecules (QTAIM) proposed by Bader and Essen [58] and posteriorly extended for crystals by Gatti [59]. The 3D visualization and post-processing of data from the topological analyses were performed in the TopIso3D viewer [60], a graphical user interface program for Topond [61] calculations. ...
Efficient H2 storage is one of the keys to the energy transition toward global sustainability. Hydrogen energy sources on functionalized 2D materials by metals have been shown as promising alternatives for clean energy systems. In a particular way, we have demonstrated here that the inorganic graphenylene-like silicon carbide (IGP-SiC) weakly adsorbs H2. At the same time, the Li/Na decoration significantly enhances the H2 interaction, accommodating up to 48H2 molecules by a stronger physisorption. Also, scanning bond critical points (BCPs) confirms a great interaction between the Li(Na)@IGP-SiC systems and the hydrogen, a distinct scenario for the pristine IGP-SiC. Gravimetrically, hydrogen densities reach 8.27 wt% (Li) and 6.78 wt% (Na), exceeding the U.S. Department of Energy (5.6 wt%) benchmark. Regarding thermodynamic stability, the desorption temperatures at ambient conditions are suitable for hydrogen storage devices. Therefore, Li(Na)@IGP-SiC systems emerge as high-capacity hydrogen storage materials.
... The study of the reactivity of transition metal clusters has been the subject of extensive research in the fields of inorganic and organometallic chemistry because of their potential usefulness in enhancing stoichiometric or catalytic reactivity [1]. Of particular interest are heterometallic cluster complexes, which consist of cluster cores containing different kinds of metals. ...
The electron density of the [(μ³-S) Fe3(CO)9(μ³-CO)] cluster was analyzed using the quantum theory of atoms in molecules (QTAIM) to explore its topological properties. This analysis provides valuable insight into the interactions between Fe–Fe, Fe–C, and Fe–S as well as other important topological properties of the compounds. Analysis of the core part, especially the S–Fe3–CO region, does not show the presence of bcp (bonding critical points) and bp (bonding pathways) for any pair of M–M (metal–metal) bonds, indicating significant delocalization. There may be multicentric (5c–4e) interactions in the central region of the junction. Examining topological data for Fe–Fe, Fe–S, and Fe–CO bonds, we find that all of these bonds exhibit typical properties of closed-shell metal–metal interactions. However, there is evidence that there is an actual chemical bond between the Fe metal and the carbon atoms of the CO ligand, rather than just an “interaction.” The presence of sulfide-bridging ligands plays an important role in effectively reducing the delocalization of electron density between sulfide-bridged iron pairs as opposed to iron pairs that are not bridging and are coordinated by carbonyl ligands.
... The dimensionless |V (r)|/G(r) ratio is commonly used to determine the characteristic bonding regime [42]. When |V (r)|/G(r) > 1, this gives evidence of relatively stable bonding dominated by the potential energy [43]. ...
Density functional theory (DFT) was used to study the electronic and vibrational properties of the chemical bond between the [6,6]-phenyl-C61-Butyric acid methyl ester (PCBM) and (CuO)n clusters. After chemical adsorption, the HOMO orbitals of PCBM primarily shifted towards (CuO)n, leading to a noticeable reduction in the band gap. Similarly, the bond established is responsible for the spatial redistribution of boundary orbitals, mainly towards the clusters. In addition, the orbital analysis revealed that the primary contributions to the chemical bond originated from the Cu atoms. The PCBM Raman intensity shows a meaningful enhancement consequence of the chemical bond established with the clusters. In addition, new normal modes of PCBM are observed in the Raman activity spectrum after the chemical adsorption.
... However, it is well known that the integrated topological properties are more useful than the local topological properties for describing M-M interactions [53]. In this sense, the delocalization index, δ(A, B), which estimates the number of electron pairs delocalized between two atoms, is one of the most powerful tools in theoretical studies of QTAIM [25,54]. On the other hand, no bond critical point or bond path was found between the Cr, Cr atoms in compounds 2 and 3, which are bridged by a H, P, and S groups, respectively. ...
Chromium–chromium and chromium–ligand bonding interactions existing in the [Cp*2Cr2(CO)2(μ-PMe2)2], [Cp*2Cr2(CO)4(μ-H) (μ-PMe2)], and [Cp*3Cr3(CO)3(μ-S) (μ-PMe2)] complexes are studied at DFT level of theory. Several local and integral topological parameters of the electron density such as electron density ρ(b), Laplacian ∇²ρ(b), local energy density H(b), local kinetic energy density G(b), potential energy density V(b), ε(b), and bond localization index (A, B) were evaluated according to QTAIM (quantum theory of atoms in a molecule). The calculated topological parameters are consistent with the relevant transition metal complexes in the literature. The computed data allow comparisons between the topological properties of related but different atom–atom interactions, such as other ligand-bridged Cr–Cr interactions and H-bridged ligand interactions versus S and P ligands. The QTAIM results confirm that the metal atoms bridged by two phosphorus atoms in binuclear complex1 are connected through a localized Cr–Cr bond that implicates little electron density (0.040). In contrast, such bonding was not found in binuclear complexes 2 (bridged by H and P) and trinuclear complex 3 (bridged by S and P). A multicenter 4c–5e, 4c–3e, and 4c–4e interactions are proposed to exist in the bridged parts, Cr(1)–P(1)–Cr(2)–P(2) in complex 1, Cr(1)–H–Cr(2)–P in complex 2, and Cr3–S in complex 3, respectively. Finally, the delocalization indices δ(Cr····O) calculated for the Cr–CO bonds in the three compounds confirm the presence of significant CO to Cr π-back-donation except for Cr(2)–O(2) and Cr(3)–O(1) bonds in complex 3, indicating that there is no π-back-donation.
... Values of kinetic (G b ), potential (V b ), and total energy (H b ) densities at bcps of the metal−ligand bond are derived from ρ and its derivative, Laplacian (∇ 2 ρ). 25 These local energy densities disclose the ionic and covalent contribution to the respective metal−ligand bonds. 26 Positive Laplacian values along with kinetic energy per electron greater than one (G b /ρ ∼ 1.22−1.45) reflect the closed shell polar nature of these metal−ligand bonds. ...
Mechanically induced glass (MIG) formation of coordination polymers (CPs) is a rare phenomenon, and the origin of the mechanical stability in CPs remains largely unknown. Here, we report accurate X-ray electron densities of three two-dimensional CPs, an orthorhombic Mn(1,2,4-triazole)2(H2PO4)2 (Mn-Tz) CP, which undergoes MIG formation, and the isostructural Co-Tz and Zn-Tz materials, which remain crystalline under mechanical milling. Chemical bonding analysis shows that the framework composed of Mn–N bonds is predominantly ionic in nature, while the Co–N and Zn–N bonds have distinct covalent features. High-pressure single-crystal X-ray diffraction measurements carried out to mimic mechanical milling reveal that Mn-Tz undergoes a pressure-induced phase transition above 3.1 GPa to a new monoclinic γ-phase. The γ-Mn-Tz phase exhibits severe structural instability up to 4.5 GPa due to local distortions caused by folding of the ionic Mn-triazole-Mn framework. In contrast, the covalent frameworks stabilize Co-Tz and Zn-Tz up to 4.6 GPa beyond which they transform to a less distorted different monoclinic β-phase. Our results demonstrate the exclusive role of the nature of metal–ligand bonds on the mechanical stability of CPs, and they further aid the rational design of MIG-forming CPs.
... ELF provides insights into the nature of chemical bonding, electron pair localization, and regions of high electron density in molecular systems, and the ELF value at a specific point in a molecule indicates the probability of finding an electron pair at that point. It is particularly useful for analyzing molecular structures with complex bonding patterns or investigating weak interactions like hydrogen bonding [35]. ELF is derived from the electron density and its gradient, utilizing quantum mechanical calculations, often based on density functional theory (DFT) [36,37] The topological analyses of the ELF, η(r) were carried out with the Multiwfn_3.7 program [38], and the graphical representations were visualized by the Chimera 1.16 program [39]. ...
The reaction mechanism for the synthesis of quinoline-fused benzo/dia/oxa/thia/zepins is investigated using the DFT/B3LYP/6-31G(d) method. DFT conceptual reactivity indices analysis allows classification of o-aminophenol (2, X = O), o-aminothiophenol (2, X = S) and o-phenylenediamine (2, X = N) and R-substituted 2-chloroquinoline-3-carbaldehydes (1 ac) as strong electrophiles, suggesting a polar process. Besides, Parr functions and Fukui indices predict the most reactive sites for observed experimentally product formation, in agreement with the dual descriptor analysis. In the energy aspect, there is no effect of the R (R = CH3, OCH3) substituent on the thermodynamic quantities, whereas the substitution of the X has a remarkable effect. The products (4a–c, X = N) are the most stable, and their cyclizations are the easiest. An extended analysis was performed using the activation strain model/energy decomposition analysis ASM/EDA model. The obtained results indicate that the orbital interaction and electrostatic stabilizations are the principal factors favoring the reaction with X = N. Topological analysis of the electron localization function (ELF) of the bending point structures along the reaction path indicates that the reaction occurs via a non-concerted two-step mechanism.
... Moreover, the positive V 2 r(r) and small r(r) represent ionic bond between atoms. 84,85 As shown in Table S3, † V 2 r(r) at BCPs in the Ca-H and Ca-ISQ bond paths are 0.26176 and 0.00051 e Å −5 , respectively, while corresponding r(r) values are 0.0406 and 0.0325 e Å −3 , indicating that ionic bonding between Ca and H as well as the one between Ca and ISQs accord with Bader charge analysis (Table S2 †) and the ELF (Fig. 2c). In addition, the Ca-H bond strength is stronger than that of the Ca-ISQ pseudo-bond because of the slightly large r(r) at BCPs of the Ca-H bond compared to the Ca-ISQ pseudo-bond. ...
Hydrogen-abundant compounds, as the highly potential candidates of near- or room-temperature superconductors, have recently attracted substantial attention. It is noted that metal-rich hydrides may exhibit unique electride feature, together with potential superconductivity, which indicates they could be regarded as electride superconductors (ESCs) hydrides. Herein, we performed the first-principles structure searches of calcium-rich hydrides for designing ESCs hydrides. Strikingly, unprecedented calcium-based hydride Ca2H with robust stability and excellent metallicity is determined under compression, where it possesses the zero-dimensional distribution feature of interstitial electrons serving as interstitial quasiatoms (ISQ), mainly originating from the donation of calcium atoms. Interestingly, cubic Fm-3m Ca2H, with antifluorite-type configuration, consists of host Ca sublattice and guests H and ISQ confined in the center of Ca8 cubes. Furthermore, Ca2H is predicted to have a superconducting critical temperature Tc of 6 K at 100 GPa and exhibit significantly enhanced superconductivity up to 11 K when dynamically stabilized to 30 GPa, which is predominantly attributed to the remarkable softening of low-frequency acoustic phonon modes involving Ca-dominated vibrations, accompanied by the strong coupling with Ca 3d states near the Fermi energy. Additionally, the yielded electride Na2H via substituting Ca with Na in Ca2H is found to have a notably high Tc of 46 K at 30 GPa. Our current work improved the understanding of structures and properties of electrides, as well as paving the way for hunting emergent ESCs in hydride systems.
... Generally, all topological values agree with the expected values for covalent and intermolecular interactions, according to Gatti (2005), and only small differences are observed even for the Supernova dataset. One exception is that this dataset does not give a bcp for the weak intermolecular interaction between C1 and C2 iii , in contrast to the rest of the datasets. ...
Five different electron density datasets obtained from conventional and synchrotron single crystal X-ray diffraction experiments are compared. The general aim of the study is to investigate the quality of data for electron density analysis from current state-of-the-art conventional sources, and to see how the data perform in comparison with high-quality synchrotron data. A molecular crystal of melamine was selected as the test compound due to its ability to form excellent single crystals, the light atom content, and an advantageous suitability factor of 3.6 for electron density modeling. These features make melamine an optimal system for conventional X-ray diffractometers since the inherent advantages of synchrotron sources such as short wavelength and high intensity are less critical in this case. Data were obtained at 100 K from new in-house diffractometers Rigaku Synergy-S (Mo and Ag source, HyPix100 detector) and Stoe Stadivari (Mo source, EIGER2 1M CdTe detector), and an older Oxford Diffraction Supernova (Mo source, Atlas CCD detector). The synchrotron data were obtained at 25 K from BL02B1 beamline at SPring-8 in Japan (λ = 0.2480 Å, Pilatus3 X 1M CdTe detector). The five datasets were compared on general quality parameters such as resolution, 〈I/σ〉, redundancy and R factors, as well as the more model specific fractal dimension plot and residual density maps. Comparison of the extracted electron densities reveals that all datasets can provide reliable multipole models, which overall convey similar chemical information. However, the new laboratory X-ray diffractometers with advanced pixel detector technology clearly measure data with significantly less noise and much higher reliability giving densities of higher quality, compared to the older instrument. The synchrotron data have higher resolution and lower measurement temperature, and they allow for finer details to be modeled (e.g. hydrogen κ parameters).
... In a real atomic-molecular system the exchange correlation mostly impacts spatial distribution of the electron pairs in the position space [41,42]. This makes the use of the exchange hole-based descriptors a natural procedure for the evaluation of electron (de)localization in molecules and crystals [43,44]. The exchange (or Fermi) hole density is expressed as [43]: finding an electron at the point while the reference electron ′ is in the position. ...
Using the advanced analyses of electron density and fermionic potential, we show how electron delocalization influences the ability of defect-containing graphene to form tetrel bonds. The Cg atoms of a vacancy defect can produce one nonpolar interaction, alongside a peculiar polar Cg⋯Cg bond. The latter stems from the presence of a localized electron pair on a vacancy defect Cg atom and the local depletion of electron localization on another Cg atom. This interaction is an example of intralayer tetrel bond. In the presence of an absorbed molecule of bisphenol A diglycidyl ether (DGEBA), graphene is able to form incipient tetrel Cg⋯O bonds with an ether group oxygen. In contrast to an epoxy group oxygen, the disposition of the ether oxygen often causes the orientation of electron-rich π-domains of graphene carbon on the weakly expressed electrophilic region of the oxygen. In the case of graphene with a point Si defect, the Si atom can form quite strong Si⋯C interactions with the DGEBA aryl carbons. In contrast to other noncovalent bonds, this interaction significantly alters the electron (de)localization on the Si atom and in the aryl ring. The reliability of the obtained results is enhanced by the use of multiple 2D periodic models with defects located at different positions along the DGEBA skeleton.
Understanding of bonding is key to modeling materials and predicting properties thereof. A widely adopted indicator of bonds and atomic shells is the electron localization function (ELF). The building blocks of the ELF are also used in the construction of modern density functional approximations. Here, we demonstrate that the ELF breaks down when applied beyond regular nonrelativistic quantum states. We show that for tackling general noncollinear open-shell solutions, it is essential to address both the U(1) gauge invariance, i.e., invariance under a multiplication by a position dependent phase factor, and SU(2) gauge invariance, i.e., invariance under local spin rotations, conjointly. Remarkably, we find that the extended ELF also improves the description of paradigmatic collinear states.
Efficient, miniaturized, and highly sensitive sensors to detect volatile organic compounds (VOCs) have become vital tools to minimize pulmonary diseases and other sicknesses. Therefore, the adsorption capabilities of methanol and ethanol were investigated on the recently synthesized biphenylene (BPN) monolayer using the Ag decoration. Although the pristine BPN has suitable VOCs adsorption, the lower adsorption strength and the small charge transfer affect the sensor performance. On the other hand, the Ag decoration increases the gas sensitivity, with moderate chemisorption values of –0.67eV and –0.83eV for methanol and ethanol, respectively, and transitory chemical bond character (neither ionic nor covalent) between Ag atoms and the –OH radical. In addition, significative work function changes (Δϕ > 0.23 eV), huge charge transfer, and rapid recovery times at room temperature, τ = 0.18s and τ = 87.9s for methanol and ethanol, respectively, indicate a great VOCs sensitivity. The feasibility of the Ag-BPN and Ag-BPN + VOCs systems by ab initio molecular dynamics (AIMDs) was analyzed, which confirms that both systems are stable at 500K. Therefore, the DFT calculations employed here can guide experimentalists in exploring new miniaturized sensor devices based on BPN.
Silver vanadate (Ag3VO4) is considered one of the most important semiconductors. It finds practical applications in electrochemical cells, as bactericidal and virucidal agents, in photocatalysis, and environmental remediation. Despite the impressive experimental progress, the dependence of the properties of a material is strongly linked to its chemical composition and structure. In this sense, the peculiar physical-chemical properties of the vanadate's class have become important. However, the fundamentals of structure in this material remain poorly understood, and the theoretical insight into the morphology linked to its properties is completely missing. In the present study, different synthesis times were tested in the obtention of Ag3VO4 crystals by the microwave-assisted hydrothermal method, and their properties were discussed based on experimental results and quantum mechanics simulations. Structural characterizations (XRD, Raman and UV–vis spectroscopy, FE-SEM, and TEM analyses) confirmed the material order at short, medium, and long-range. Theoretical calculations contributed to identifying the atom distribution in the structure, nature of the type of electronic transition, and density of states present in the valence and conduction bands. The topological analysis of the electron density indicated transit chemical interactions and unexpected argentophilic interactions, and Mulliken, Hirshfeld and Bader population analysis provided the charges present on the chemical elements of the crystal. Predicted theoretical surface shapes and their stabilities were evaluated along with FE-SEM images.
В рамках метода функционала плотности с помощью комплекса программ WIEN2k выполнены расчеты электронной зонной структуры орторомбической фазы соединения La2CuO4, являющегося исходным для нескольких семейств высокотемпературных сверхпроводников. Вычисления проводились с использованием двух обменно-корреляционных функционалов: первый представлял собой сумму модифицированного Траном и Блахой обменного потенциала Беке и Джонсона и корреляций в локальном приближении, в качестве второго был выбран функционал Пердью - Бурке - Эрнзерхофа. Расчеты с учетом спиновой поляризации выявили наличие антиферромагнитного основного состояния орторомбического La2CuO4. В случае использования первого функционала найдены магнитный момент атомов меди MCu = 0.725µB и полупроводниковая щель Eg = 2 эВ, а во втором случае MCu = 0.278µB и Eg = 0. Результаты расчетов оптических свойств орторомбического La2CuO4 - функции энергетических потерь электронов, действительной части оптической проводимости и коэффициента отражения, оказались в хорошем согласии с экспериментальными данными. Рассчитанное пространственное распределение зарядовой плотности в орторомбическом La2CuO4 было проанализировано с целью выявления седловых критических точек, параметры которых дают возможность классифицировать тип химической связи в кристалле. Совокупность параметров критических точек в орторомбическом La2CuO4 была аналогична найденной нами ранее в тетрагональном La2CuO4 и родственных высокотемпературных сверхпроводниках. В частности, положительный знак лапласиана зарядовой плотности в критических точках типа bond, в соответствии с классификацией типов химической связи, принятой в «Квантовой теории атомов в молекулах и кристаллах» Бадера, свидетельствует об отсутствии ковалентной связи в La2CuO4.
Computational simulations based on density functional theory (DFT) were carried out to show that biaxial strain (ε; −10% to +10%) engineering is a smart choice to modify the main properties of the two-dimensional inorganic graphenylene-like silicon carbide (IGP-SiC). It was demonstrated that the compressive deformation leads to a buckling effect on the IGP-SiC; however, the planar configuration remains along the tensile strain. The IGP-SiC under both compressive (ε = 0 to −10%) and tensile (ε = 0 to +10%) regimes is thermally stable at 700 K, as unveiled by ab initio molecular dynamics simulations. By assessing the Raman spectrum, the E2g modes are red-shifted with tensile strain, which is similar to the graphene’s tendency. Also, tensile deformation reduces the band gap energy from 3.22 eV (ε = 0%) to 2.48 eV (ε = +10%), leading the IGP-SiC to a visible-light spectrum. On the other hand, the compressive regime induces an opening of the band gap energy to 4.05 eV (ε = −10%). Other remarkable results for strained IGP-SiC are the photocatalytic properties maintained at biaxial strain because the band edges meet the oxidation and reduction standard potentials, especially for strain regimes from +4% to +10%. Besides this, the IGP-SiC under strain application is a suitable alternative in photocatalytic degradation and water desalination due to its good performance in all pH environments.
This chapter traces, to the current day, one‐electron quantum mechanical concepts as applied to intermetallic compounds and alloys. Three main threads are followed: the evolution over time of the tight‐binding model, the role of nearly free‐electron theory, and the adaption of one‐electron ideas to experimentally derived phenomenological theories as applied to these systems.
Analysis of tight‐binding theory begins with the two‐electron bond: The case of hydrogen is contrasted to the alkali metals. The connection between tight‐binding theory and density functional theory is explored: Tight‐binding theory is found to reproduce well the more computationally precise DFT band structures. Models that emanate from tight‐binding theory include the COOP and COHP analysis of the metallic bond, site preferences (the coloring problem), and Mulliken populations. Tight‐binding moment theory is also shown to account for crystalline structural preferences. The Dronskowski–Landrum model for magnetically ordered systems is presented. Recent developments focused on localized orbitals (Wannier functions), and transition metal electron‐counting (for half‐Heusler, Nowotny chimney ladder phases, and other phases) is explored. Reversed approximation molecular orbital analysis to these latter systems is presented.
The role of nearly free electron theory and its role in the understanding of Hume‐Rothery electron phases is presented. The importance of the Jones zone is made clear, not just for these phases but also for more complex phases, including the Samson phase, Cd 3 Cu 4 , with 1124 atoms in its unit cell. Recent work combining the Jones model of orbital mixing with the Zintl concept of electropositive to electronegative atom electron transfer is found to lead to corrected Jones zones for the quasi‐crystalline approximant phase Li 52.0 Al 88.7 Cu 19.3 . An explanation of the unusual electron count of the 1 e ⁻ / a γ‐brass structure Li 33 Ag 19 is derived. The role of pseudopotentials in accounting for structural distortions is reviewed.
Finally, a look at how well‐known phenomenological analyses have evolved into modern quantum theory‐based models is explored. Among these is the role of structure maps, where the Pettifor tight‐binding model for structure maps is presented. The phenomenological Pearson analysis of steric strain is shown to lead to chemical pressure analysis via ‐based Hückel theory. The classic Brewer analysis of electron transfer from electropositive to electronegative atoms evolves into the ‐Lewis acidity model.
It is a general observation that local maxima in charge distributions of many-electron systems occur only at the positions of nuclei. Gatti, Fantucci and Pacchioni have recently shown that non-nuclear maxima are found in the charge distributions of Li clusters. This paper reports on the same behaviour for Na clusters. The discovery of non-nuclear maxima in clusters of both Li and Na atoms, together with the observation that the properties of the resulting pseudo atoms as determined by the theory of atoms in molecules are similar for both sets of clusters, suggests that non-nuclear attractors may be typical of the alkali metals and are responsible for their characteristic properties.
The heavier halide molecules form layered crystals indicative of the presence of a specific directed intermolecular interaction. It is shown that this interaction within the crystal can be defined and characterized using the topology of the electron density within the theory of atoms in crystals. It is also shown that its presence in the crystal and the resulting geometry of the layered structure can be predicted in terms of the topology of the Laplacian distribution of an isolated Cl-2 molecule, as it relates to the definition of Lewis acid and base sites within the valence shell of an atom. The generality of the definition of both primary and secondary interactions in terms of the topology of the electron density is demonstrated for all types of crystal. The electron density of solid molecular chlorine was determined by fitting the experimental X-ray structure factors and by theoretical calculation and its topology determined. Each Cl atom is found to be linked by bond paths, lines of maximum electron density, to twelve other atoms in the crystal: to four atoms in the same layer parallel to the be plane, one of which defines the intramolecular bond of the Cl-2 group, to six atoms in the four neighbouring molecules lying in the same stack parallel to the b axis and to two atoms in molecules situated in a neighbouring stack.
The degree of precision and accuracy in molecular geometry attainable with modern X-ray diffraction and cryogenic techniques is documented by presenting the results of a low-temperature study of syn-1,6:8,13 biscarbonyl[14]annulene, tricyclo[8.4.1.1(3,8)]hexadeca-2,4,6,8,10,12,14-heptaene-15,16-dione. Intensity data up to sin theta/lambda = 1.14 Angstrom(-1) have been measured from a spherical crystal at T = 19 K. Their multipolar analysis, up to the octopole level for C and O atoms, and to quadrupoles for anisotropically described H atoms, has led to precisions in the coordinates of the heavy atoms which are better than 0.0004 Angstrom. Root mean square (r.m.s.) amplitudes of vibration for C and O atoms have been determined to a precision of ca 0.0006 Angstrom. Based on the least-squares sigma's, uncertainties for the C-C and C-O bond lengths are 0.0005 Angstrom, and those of the C-H bond distances 0.006-0.007 Angstrom. The topological properties of the experimentally derived charge density of the annulene molecule in the crystal have been determined by evaluating the location and nature of its critical points (points where del rho = 0). Contour maps of rho(exp) and its negative Laplacian (-del(2) rho(exp)) are presented. The occurrence of a bond critical point midway between the two C atoms of the carbonyl bridges seems to indicate the existence of a chemically unexpected weak bond between the two C atoms.
Topological analysis of the experimental and theoretical electron densities in [EtTiCl3(dmpe)] (dmpe = Me2PCH2CH2PMe2) suggests the presence of a (3, –1) bond critical point (CP) between titanium and the β-agostic hydrogen atom; the characteristic curvature in the Ti–Cα bond is proposed as a more general criterion for identifying a β-agostic interaction.
That guest atoms donate electrons to framework atoms is a generally accepted concept. Nevertheless, evidence for the presence of neutral guest atoms in thermoelectric clathrate structures is presented in the form of experimental X-ray charge density analysis and X-ray absorption near-edge structure (XANES) data. The picture shows the deformation density (DD) determined by the maximum entropy method for Ba8Ga16Ge30; the DD shows that both the Ba guest atoms are disordered.
The pulsed structure of synchrotron radiation and thermal neutrons enters into chemical crystallography by two ways. Nuclear resonant scattering may profit from the time structure of synchrotron radiation yielding more detailed information about molecular structure? whereas time resolved experiments reveal their dynamics. As the time of flight techniques of neutron scattering and time resolved scattering experiments are covered elsewhere, the impact of Mößbauer methods will be discussed here in more detail. Nuclear resonant scattering may gain considerable importance in macromolecular structure research? as some nuclei have large resonant scattering lengths. The potential of nuclear resonant scattering is compared with some recent developements of anomalous X-ray scattering and nuclear spin dependent neutron scattering.
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In this study, the physical meaning and mutual relations of multicenter bond indices arising from various population analysis schemes is analyzed and discussed. The reported relations were numerically tested at ab initio SCF level on a series of molecules involving the representatives of systems with classical two-center two-electron (2c-2e) bonds as well as three-center two-electron (3c-2e) and three-center four-electron (3c-4e) bonds. The results show that the generalized population analyses are very suitable tools for detecting the presence and localization of multicenter bonding in moleclues.
The crystal structure and the bond critical point, bcp, properties of the electron density distribution for the high-pressure silica polymorph coesite were generated for pressures up to similar to 17 GPa, using first-principles calculations. The nonequivalent SiO bond lengths and the SiOSi and OSiO angles of the generated structures agree with those observed to within similar to1%. With compression, the SiO bond lengths and the variable SiOSi angles of the structures both decrease while the value of the electron density, p(r(c)), the curvatures, and the Laplacian of the electron density distribution at the bond critical points each increases slightly. As found in a recent modeling of the structure of low quartz, the calculated electron density distributions are nearly static and change relatively little with compression. The bcp properties of the model structure agree with those observed at ambient conditions to within similar to 10%, on average, with several of the properties observed to correlate with the observed SiO bond lengths, R(SIO). This agreement is comparable with that observed for several other silicates. As predicted, the bonded radius of the oxide anion, the curvatures of p(r(c)) paralleling the bond paths and the Laplacian of p(r(c)) each correlates with the observed bond lengths. However, the observed p(r(c)) values and the curvatures of p(r(c)) perpendicular to the paths fail to show a correlation with the observed bond lengths. The ellipticity of the SiO bonds in both the model and the observed structures tends to decrease in value as the SiOSi angle approaches 180 degrees, indicating that the bonds become more circular in cross sections as the angle widens. Ridges of electron density and bond critical points were found between the intertetrahedral oxide anions at each pressure. The existence of these features appears to be closely related to purely geometrical factors of the coesite structure rather than to bonded interactions. None of these features was found between the intratetrahedral oxide anions.
For Abstract see ChemInform Abstract in Full Text.
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Professor Ziman's classic textbook on the theory of solids was first pulished in 1964. This paperback edition is a reprint of the second edition, which was substantially revised and enlarged in 1972. The value and popularity of this textbook is well attested by reviewers' opinions and by the existence of several foreign language editions, including German, Italian, Spanish, Japanese, Polish and Russian. The book gives a clear exposition of the elements of the physics of perfect crystalline solids. In discussing the principles, the author aims to give students an appreciation of the conditions which are necessary for the appearance of the various phenomena. A self-contained mathematical account is given of the simplest model that will demonstrate each principle. A grounding in quantum mechanics and knowledge of elementary facts about solids is assumed. This is therefore a textbook for advanced undergraduates and is also appropriate for graduate courses.
Experimental studies on compounds of alkali and alkaline earth metals with semi- and metametals have considerably broadened the basis for a discussion of the transition from metallic to ionic bonding. Current interest is focused mainly upon the elucidation of the principles governing the structure of such compounds which are subject to a wide range of variation within this class of materials. A new definition of the term Zintl phase is proposed after consideration of available findings.
Interatomic interactions such as hydrogen bonds (HB) can be adequately described and classified by the topological properties of the electron density ρ(r) at the (3,−1) critical points rCP where the gradients of ρ(r) vanish. We have analysed the topological properties of ρ(r) at the intermolecular critical points of 83 experimentally observed HBs [X–H⋯O (X=C,N,O)], using accurate X-ray diffraction experiments. In spite of different models, methods and experimental conditions employed to obtain the topological properties of ρ(r), we show that, for closed-shell interactions, the kinetic energy density G(rCP) and the potential energy density V(rCP) at the critical point depend exponentially on the H⋯O distance. Moreover, theoretical calculations for several HB dissociation energies follow the same law as does V(rCP), with a simple change of scale.
A new method for dividing a crystalline electron distribution into molecular fragments is proposed, based on Hirshfeld's partitioning scheme. Unlike other approaches, the method partitions the crystal into smooth molecular volumes as well as intermolecular voids of low electron density. To compare the new method with several other schemes which subdivide a crystal into molecules, numerical integration is performed on two model electron densities (one representing a superposition of isolated molecules, the other interacting molecules) for ice VIII, formamide and urea. The new scheme is simply to apply, aesthetically appealing, and offers some promise in routine partitioning of crystalline electron densities or in computer graphics to provide additional insight into molecular packing in crystals.
The pair population analysis developed some time ago as a straightforward link between quantum chemical and classical picture of bonding was generalized by incorporating its formalism into the framework of AIM theory. A detailed numerical comparison between the results derived from the original pair population analysis and those from AIM generalization is reported. On the basis of this comparison, the reliability of both approaches is evaluated. In addition to this a numerical test of the accuracy of the Lewis electron pair model is also reported.
The bonding in a number of σ‐bonded diatomic and linear triatomic molecules is interpreted in terms of the one‐particle density matrix (ODM) along the bond axis. Special attention is drawn to the off‐diagonal contributions of the ODM in a two‐dimensional position space representation, which are shown to be indicative of a bonding or antibonding covalent interaction between the atomic centers.
We have applied Bader’s topological analysis to the study of the B1-B2 phase transition in the alkali halides. Our results shed light upon the phase stability rules of the traditional ionic model: by using topological ionic radii, a connection between the topologies of the electron density and the energy surface is found. The topological description of the transition that emerges puts an emphasis on the creation of two new bond points in passing from coordination 6 to 8, and makes a unique definition of structural change. As we have found in previous papers, topological isomerization, as a case of structural change, is mainly dominated by geometric relations involving topological ionic radii. Further relations between the structural diagram and the energy surface features are also investigated.
A structure analysis of the Si(111)2©1 surface is performed using extensive new low-energy electron-diffraction data (12 beams). Although the π-bonded chain model in its original form shows gross disagreement with low-energy electron diffraction, a modification of that structure gives moderate agreement. The major modifications are a buckling in the outer chain and an overall compression.
The nature of C−Li bonding in CH3Li and CLi6 was reconsidered using two recently proposed new methodologies, namely the AIM generalized population analysis and Fermi hole analysis. The calculations were performed at HF level of the theory using 6-311G** basis sets. The main issue was the realistic estimation of the polarity of C−Li bonds. The analysis confirms that C−Li bonds in CH3Li are predominantly ionic but some slight modifications of the contemporary picture of bonding in CLi6 is proposed.
The electron densities determined by the maximum entropy method and by the multipole refinement approach are compared with each other, in terms of some topological properties according to the Bader formalism (Laplacian and eigenvalues of the Hessian matrix of the electron density at the critical points). The cases of MgO, (Mg,Fe)O and Cu2O are examined. The best agreement is observed for the critical points along the Mg–O, (Mg,Fe)–O and Cu–O directions, whereas larger discrepancies occur at the other critical points. Plots of the electron densities generated by the maximum entropy method and the multipole formalism along the most representative crystallographic directions contribute to elucidating the comparison between approaches.
We report about the LMTO-ASA band structure, ELF and COHP calculations for a number of alkali metal rare earth tellurides of the formulas ALnTe4 (A=K, Rb, Cs and Ln=Pr, Nd, Gd) and KLn3Te8 (Ln=Pr, Nd) to point out structure-properties relations. The ALnTe4 compounds crystallize in the KCeSe4 structure type with Te ions arranged in the form of 4.32.4.3 nets, in which interatomic homonuclear distances indicate an arrangement of isolated dumbbells. This could be verified by the COHP and ELF calculations, both of which revealed isolated [Te2] units. But in contrast to the ionic formulation as A+Ln3+ ([Te2]2−)2, which can be deduced from this observation, the band structure calculations for KPrTe4, KNdTe4, RbNdTe4 and CsNdTe4 reveal metallic conductivity. This behavior was verified for KNdTe4 by resistivity measurements performed by a standard four-probe technique. We explain these results by an incomplete carryover of electrons from the rare earth cation onto tellurium due to covalent bonding leaving parts of the Te–Te ppπ* antibonding states unoccupied. On the other hand the calculations suggest insulating behavior for KGdTe4 resulting from a complete filling of the Te–Te ppπ* antibonding states due to the increased stability of the half filled 4f shell. The ALn3Te8 compounds crystallize in the KNd3Te8 structure type, a distorted addition-defect variant of the NdTe3 type with 44 Te nets. As polyanionic fragments L-shaped [Te3]2− and infinite zig-zag chains ∞1[Te4]4− are observed (with interatomic homonuclear distances in the range 2.82–3.00 Å), which are separated from each other by distances in the range 3.27–3.49 Å. Again COHP calculations made evident that these latter interactions are secondary. Within the infinite zig-zag chains ∞1[Te4]4− the Te ions at the corners of the chain have a higher negative charge than the linear coordinated ones in the middle. KPr3Te8 and KNd3Te8 are semiconductors, verified for the latter by resistivity measurements.
Metal–metal bonds belong, from the topological point of view, to the wide class of the closed shell interactions proposed by Bader. Such a simple classification is, however, not satisfying in the description of these bonds and the nature of the metal–metal bond, in particular in polynuclear complexes, is debated. Using some topological and energy parameters, a comparison is made between polynuclear complexes and bulk metals and indicates the similar nature of these bonds.
A simple model of the charge distribution in a π-system is used to explain the strong geometrical requirements for interactions between aromatic molecules. The key feature of the model is that it considers the σ-framework and the π-electrons separately and demonstrates that net favorable π-π interactions are actually the result of π-σ attractions that overcome π-π repulsions. The calculations correlate with observations made on porphyrin π-π interactions both in solution and in the crystalline state. By using an idealized π-atom, some general rules for predicting the geometry of favorable π-π interactions are derived. In particular a favorable offset or slipped geometry is predicted. These rules successfully predict the geometry of intermolecular interactions in the crystal structures of aromatic molecules and rationalize a range of host-guest phenomena. The theory demonstrates that the electron donor-acceptor (EDA) concept can be misleading: it is the properties of the atoms at the points of intermolecular contact rather than the overall molecular properties which are important.
The structure of sodium electrosodalite (SES), Na{sub 8}(AlSiO{sub 4}){sub 6}, has been determined at 20 K using synchrotron powder diffraction. Subsequently the electron density was calculated through a periodic unrestricted Hartree-Fock approach and analyzed by topological methods. The F center is found to manifest itself as a maximum in the electron density at a non-nuclear position. Thus it possesses a separate identity and behaves quantum mechanically as an open system, bounded by a surface of local zero flux in the gradient vector field of the electron density. Different basis sets have been considered, and the introduction of a basis set capable of describing the F center leads to a large drop in the total energy. The F center contains almost solely unpaired electron density which is loosely bound and exhibits a very low kinetic energy density. Calculations on both a ferromagnetic and an antiferromagnetic phase have been performed and the total electron densities in the two phases are found to be very similar, with the alternating ordering of the spin density being the only difference between the two phases. The electron localization function has been introduced for an open-shell system and has been used to illustrate the magnetic phase transition. {copyright} {ital 1999} {ital The American Physical Society}
Crystal structures of fused-ring aromatic hydrocarbons may be predicted from molecular structures using a model where carbon and hydrogen atoms in a molecule are designated ‘stack’ and ‘glide’ promoting solely on the basis of their topological connectivity.
The experimental charge density distribution of 5,6,7-trihydroxyflavone (1), has been determined from high-resolution X-ray diffraction data collected at 100 K. Additionally, high level single-point gas-phase calculations as well as periodic calculations have been carried out for (1). To our surprise, the topological analysis of the experimental electron density revealed a cage critical point in the geometric center of the tri-hydroxy substituted aromatic ring. This feature was independently confirmed by analysis of another study of 1. However, both high-level gas-phase and periodic ab initio calculations failed to reproduce this feature. The degree of bias on the electron density by using the Hansen–Coppens multipole model was tested by a multipole refinement of generated theoretical structure factors. This clearly showed that the cage critical point is not an artefact resulting from the use of the multipole model. Compound 1 contains a large number of weak, intermolecular hydrogen bonds and these are analysed using the Atoms in Molecules (AIM) approach, which leads to quantitative measures for hydrogen bond strength. The experimentally derived lattice energy of −467 kJ mol−1 shows a rather strongly held crystal lattice.
We have recently described a remarkable new way of exploring packing modes and intermolecular interactions in molecular crystals using a novel partitioning of crystal space. These molecular Hirshfeld surfaces reflect intermolecular interactions in a novel visual manner, offering a hitherto unseen picture of molecular shape in a crystalline environment. The surfaces encode information about all intermolecular interactions simultaneously, but sophisticated interactive graphics are required in order to extract the information most efficiently. To overcome this we have devised a two-dimensional mapping which summarizes quantitatively the nature and type of intermolecular interaction experienced by a molecule in the bulk, and presents it in a convenient graphical format. The mapping takes advantage of the triangulation of the Hirshfeld surfaces, and plots the fraction of points on the surface as a function of the closest distances from the point to nuclei inside and outside the surface.
In this manner all interaction types (for example, hydrogen bonding, close and distant van der Waals contacts, C–Hπ interactions, π–π stacking) are readily identifiable, and it becomes a straightforward matter to classify molecular crystals by the nature of interactions, and to rapidly identify similarities and differences which can become obscured when examining crystal packing diagrams. These plots are a novel visual representation of all the intermolecular interactions simultaneously, and are unique for a given crystal structure and polymorph. Applications to a wide variety of molecular crystals and intermolecular interactions are presented, including polymorphic systems, as well as crystals where Z′ > 1.
Potential Docking Sites and Positions of Hydrogen in High-Pressure Silicates
The structure and bonding in cis-HMn(CO)âPPhâ have been studied by low-temperature neutron and high-resolution X-ray diffraction, the latter study using a charge-coupled device (CCD) area detector. A charge density analysis, including the deformation density, a full topological analysis of -â²Ï, has been conducted. The electrostatic component of the H{sup δ+}{hor_ellipsis}H{sup δ-} interaction energy is calculated to be 5.7 kcal/mol from the experimental data. This electrostatic evidence coupled with the geometry C-H{hor_ellipsis}H 129.0(2)° and H{hor_ellipsis}H-Mn 126.5(1)° and the identification of an H{hor_ellipsis}H bond path in the charge density distribution strongly supports the characterization of this interaction as an intramolecular C-H{hor_ellipsis}H-Mn hydrogen bond. Both the deformation density and the topological study clearly illustrate the Ï-donor nature of both the H-Mn and PhâP-Mn interactions and the Ï-donor/Ï-acceptor nature of the manganese-carbonyl bonds. The topological study further confirms the decrease in C-O bond order upon coordination to the metal and demonstrates for the first time by this method that the metal-ligand bonds, although showing characteristics of a closed-shell interaction, do have a significant dative covalent component to the bond. The latter is reinforced by a study of the derived Mn d-orbital populations, in which populations of the d{sub z²} and d{sub x²-y²} orbitals are significantly higher than would be predicted by a simple crystal field theory model of metal-ligand bonding.
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Several qualitatively different structural models have been examined in a critical evaluation of spectroscopic and other data for the Si(111)-(2×1) surface. Within the one-electron theory, only a novel pi-bonded chain model with a covalent surface, and not the generally accepted buckled model with an ionic surface, is consistent with the data.
The nonlinear population analysis recently formulated at the level of semiempirical MO methods was generalized so as to be applicable to the ab initio SCF closed shell level of theory. The method provides a new, efficient means of visualization of molecular structure especially for molecules with complex bonding patterns such as multicenter bonding. The approach was applied to the visualization of bonding in several simple boranes like B2H6, B4H10, B5H9, and B5H11. In all cases the approach was able to detect and to correctly localize the three-center bonds in these molecules.
This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, Fn(r), independent of v(r), such that the expression Ev(r)n(r)dr+Fn(r) has as its minimum value the correct ground-state energy associated with v(r). The functional Fn(r) is then discussed for two situations: (1) n(r)=n0+n(r), n/n01, and (2) n(r)= (r/r0) with arbitrary and r0. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.
The high-pressure structural chemistry of main group elements in the metallic state is reviewed under consideration of more recent determinations of atomic arrangements with to some extend unexpected complexity. Following the concept of the pressure-coordination rule, the number of nearest neighbours is employed as a guiding quantity to reveal systematic trends. Violations of the rule will be mainly discussed in the light of electronic ground state changes upon compression.
In this work, we present a theoretical study (based on DFT-calculations) in a wide pressure range of the structural and electronic properties and the stability of compounds crystallising in a TlI- or CrB-type structure. Both structure types have the characteristic structural feature of zigzag chains with unusual short homonuclear distances. The main focus of this study is to elucidate the nature of bonding within these zigzag chains at ambient and elevated pressure. For this purpose we discuss the evolution of the distances within the zigzag chains with pressure, the transition pressure of the phase transition to a CsCl-type arrangement (high-pressure phase) and compressibilities of the low- and high-pressure phases. For a better understanding of the structure and bonding, the band structures of these compounds are evaluated. The calculations are complemented by an orbital analysis using the crystal orbital Hamilton population (COHP) and an analysis of the electronic density topology with the electron localisation function (ELF). Our study indicates that there is a bonding electron pair in compounds crystallising in the CrB-type structure and that the nature of the electron pair does not change significantly at elevated pressure up to the phase transition. However, the "character" of the additional electron pair in the In-monohalides (TlI-type structure) changes with increasing pressure from nonbonding to bonding. The phase transition to a CsCl-type structure implies a fundamental change to nonbonding stereochemically inert electron pairs for all compounds.
The element Sn has the outstanding property that it appears in a metallic and a semi-metallic modification, which possess almost the same stability. The associated interplay between delocalized and localized bonding governs the structures of alkali and alkaline earth metal stannides and leads to a large variety of different structure types. Even though the element Pb crystallizes in the
During the last decade several new structures in the phase systems of alkali or alkaline-earth metals with tin or lead were characterized. Many examples show the gradual transition from valence compounds to intermetallic phases and present new possibilities for structural and bonding motives for Sn and Pb. These structures reinforce interesting links between the various structure types. Structural relationships of Zintl phases containing discrete and linked polyhedra, as well as the gradual transition to typical intermetallic compounds are highlighted.
An atom is defined as a region of space bound by a surface of local zero flux in the gradient vector field of the electron density. The same boundary condition defines a proper open system, one whose observables and their equations of motion are defined by quantum mechanics. Applied to a crystal, this boundary condition coincides with the original definition of the atomic cell in metallic sodium given by Wigner & Seitz. It is proposed that it be used to generalize the concept of a Wigner-Seitz cell, defining it as the smallest connected region of space bounded by a 'zero-flux surface' and exhibiting the translational invariance of the crystal. This definition, as well as removing the arbitrary nature of the original method of construction of the cell in the general case, maximizes the relation of the cell and the derived atomic form factors to the physical form exhibited by the charge distribution of its constituent atoms. The topology of the electron density, as summarized in terms of its critical points, also defines the atomic connectivity and structure within a cell. Attention is drawn to the correspondence of the symmetries of the structural elements determined by the critical points with the site symmetries tabulated in International Tables for Crystallography. The atomic scattering factor is defined for an atom in a crystal and determined in ab initio calculations for diamond and silicon. The transferable nature of atomic charge distributions is demonstrated. It enables one to estimate a structure factor and its phase in a crystal using the density of an atom or functional group obtained in a molecular calculation. Atoms in a crystal, along with defects and vacancies, are identifiable with bounded regions of real space. Their properties are additive and are defined by quantum mechanics.
The molecular dipole moment of the 3 4-bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) molecule and its enhancement in the crystal was evaluated by periodic RHF ab initio computations. A discrete boundary partitioning of the electronic density that allows an unambiguous partitioning of the molecular space in the condensed phase was adopted. The resulting molecular dipole in the crystal compares favorably with the experimental value obtained by a multipolar analysis of single-crystal X-ray diffraction data recorded at 20 K, using a fuzzy boundary partitioning of the derived pseudoatom densities. We show that a large and highly significant molecular dipole enhancement may occur upon crystallization, despite the lack of a strongly hydrogen bonded environment in the crystal. The 23 unique C-H . . .O interactions which are formed upon packing of the DMACB molecule induce an increase in the molecular dipole (over 75%) that is comparable to or greater than that found in systems which are characterized by the stronger O-H . . .O and N-H . . .O hydrogen bonds. The DMACB molecule constitutes an excellent system for the study of C-H . . .O interactions in the condensed phase, since no other kind of competing hydrogen bonds is present in its crystal. A simple and qualitative model for the matrix contribution to the DMACB molecular dipole enhancement in the crystal is proposed. The formation of several weak C-H . . .O bonds is found to yield a small (about 0.2 e) net flux of electronic charge flowing from the hydrogens of the methyl groups to the carbonyl oxygen atoms. Despite the limited increase of the intramolecular charge transfer upon crystallization, a large molecular dipole enhancement occurs because the centroids of the positive and negative induced charges are quite far apart. This work highlights a new and important role of the C-H . . .O bond, besides those already known in the literature.
The nature of bonding in isocoordinated molecules of SF6 and CLi6 was analyzed using the recently proposed approach based on the scrutiny of the so-called domain-averaged Fermi holes. It has been shown that although the molecule of SF6 does not satisfy the charge criterion of hypervalence, the actual picture of bonding is consistent with the traditional hypervalent model assuming the existence of six localized albeit very polar SF bonds around the central atom. On the other hand, while the molecule of CLi6 represents the ideal candidate for hypervalence according to charge criterion, the picture of bonding is, in this case, considerably different from what the concept of hypervalence is traditionally associated with and can be better characterized by the term hypercoordination.
Single crystals of aluminum diboride (space group P6/mmm, No. 191) a=3.0050(1)Å, c=3.2537 (8) Å; Z=1) were prepared by the aluminum flux method. Crystal structure refinement shows defects at the aluminum site and resulted in composition Al0.894(9)B2≈Al0.9B2. The defect structure model is confirmed by the measured mass density ρexp=2.9(1)g/cm3 in comparison with a calculated value ρx=3.17g/cm3 for full occupancy of the aluminum position. The results of 11B NMR measurements support the defect model and are in agreement with the structure obtained by X-ray diffraction methods. Electrical resistivity measured on a single crystal parallel to its hexagonal basal plane with ρ(300K)−ρ(2K)=2.35μΩcm shows temperature dependence like a typical metal. Charge is dominantly carried by holes (Hall-coefficient R=+2×10−11m/C). Respective, p-type conductivity is confirmed by theoretical calculations. Chemical bonding in aluminum diboride is discussed using the electron localization function.