Probing the Zintl–Klemm Concept: A Combined Experimental and Theoretical Charge Density Study of the Zintl Phase CaSi

The nature of the chemical bonds in CaSi, a textbook example of a Zintl phase, was investigated for the first time by means of a combined experimental and theoretical charge density analysis to test the validity of the Zintl–Klemm concept. The presence of covalent Si? Si interactions, which were shown by QTAIM analysis, supports this fundamental bonding concept. However, the use of an experimental charge density study and theoretical band structure analyses give clear evidence that the cation–anion interaction cannot be described as purely ionic, but also has partially covalent character. Integrated QTAIM atomic charges of the atoms contradict the original Zintl–Klemm concept and deliver a possible explanation for the unexpected metallic behavior of CaSi.     

Joint QTAIM and Hirshfeld study of the sigma and pi charge distribution and electron delocalization in carbonyl compounds: a comparative study with the resonance model

Atomic charges and delocalization indexes (DIs) for a series of carbonyl compounds comprising dimethyl ketone, acetaldehyde, acetic acid, methyl acetate, acetamide, methyl vinyl ketone, divinyl ketone, and benzoic acid were studied using two different atomic partitionings: the QTAIM and the Hirshfeld (stockholder) scheme. The resonance model, traditionally employed to explain the reactivity of these compounds, is not in line with the total atomic charges and DIs calculated by both methodologies. However, the resonance model is supported to some extent by the pi charges and pi DIs calculated by both schemes, but the calculated values indicate that the pi population delocalizes only to a small degree. Although the absolute values of QTAIM and stockholder atomic charges are significantly different, the pi charges and the values of the DIs show similar trends for all the atoms and molecules of this study; this is especially the case for the pi DIs. A study of the electron density on the level of a single MO performed for CO, H2CO, F2CO, and H2CS reveals that the differences in the atomic sigma charges computed with both partitionings can be traced back to their different treatment of interatomic regions.     

On the Volume Chemistry of Solid Compounds: the Legacy of Wilhelm Biltz

For the calculation of the atomic or ionic volumes the Quantum Theory of Atoms In Molecules method was applied. The regions (basins) around the nuclei confined by the zero‐flux surfaces in the electron density gradient are called QTAIM atoms. They are non‐overlapping and completely fill the space. The volume of the basins gives volumes of atoms or ions. The integration of the electron density within the volumina yields effective charges, defining neutral or ionic character of the given QTAIM species. Present investigations refer to metal hydrides, metal nitrides and to intermetallic compounds of the system Al‐Pt. A linear relation between the ionic volumina of hydrogen or nitrogen established according to QTAIM and after Biltz has been found with (homodesmic) binary metal hydrides and binary metal nitrides, but has been observed merely as a trend with stronger deviations for heterodesmic compounds, such as ternary hydrido‐ and nitridometallates A_a[M_mX_x] (A – alkali or alkaline earth metal, M – transition metal and X – H or N). The deviation from linearity for heterodesmic compounds is caused by the different kinds of chemical bonds being present within the [M_mX_x] anions on the one hand and between the anions and the cations on the other hand reflected by the calculated volumes and the QTAIM charges of M and X components. Concerning the intermetallic compounds of the system Al‐Pt, the quantum chemical calculations reveal negative charges for the platinum atoms and positive ones for the aluminium atoms in accordance with their electronegativities. Introducing the variation of the atomic volume with the composition extends the Vegard's approach and gives a non‐linear slope for the concentration dependence of mean atomic volume which explains qualitatively the experimental results.     

Electron density distributions calculated for the nickel sulfides millerite, vaesite, and heazlewoodite and nickel metal: a case for the importance of ni-ni bond paths for electron transport

Bond paths and the bond critical point properties (the electron density (rho) and the Hessian of rho at the bond critical points (bcp's)) have been calculated for the bonded interactions comprising the nickel sulfide minerals millerite, NiS, vaesite, NiS(2), and heazlewoodite, Ni(3)S(2), and Ni metal. The experimental Ni-S bond lengths decrease linearly as the magnitudes of the properties each increases in value. Bond paths exist between the Ni atoms in heazlewoodite and millerite for the Ni-Ni separations that match the shortest separation in Ni metal, an indicator that the Ni atoms are bonded. The bcp properties of the bonded interactions in Ni metal are virtually the same as those in heazlewoodite and millerite. Ni-Ni bond paths are absent in vaesite where the Ni-Ni separations are 60% greater than those in Ni metal. The bcp properties for the Ni-Ni bonded interactions scatter along protractions of the Ni-S bond length-bcp property trends, suggesting that the two bonded interactions have similar characteristics. Ni-Ni bond paths radiate throughout Ni metal and the metallic heazlewoodite structures as continuous networks whereas the Ni-Ni paths in millerite, a p,d-metal displaying ionic and covalent features, are restricted to isolated Ni(3) rings. Electron transport in Ni metal and heazlewoodite is pictured as occurring along the bond paths, which behave as networks of atomic size wires that radiate in a contiguous circuit throughout the two structures. Unlike heazlewoodite, the electron transport in millerite is pictured as involving a cooperative hopping of the d-orbital electrons from the Ni(3) rings comprising Ni(3)S(9) clusters to Ni(3) rings in adjacent clusters via the p-orbitals on the interconnecting S atoms. Vaesite, an insulator at low temperatures and a doped semiconductor at higher temperatures, lacks Ni-Ni bond paths. The net charges conferred on the Ni and S atoms are about a quarter of their nominal charges for the atoms in millerite and vaesite with the net charge on Ni increasing with increasing Ni-S bond length. Reduced net charges are observed on the Ni atoms in heazlewoodite and are related to its Ni-Ni metal bonded interactions and to the greater covalent character of its bonds. Local energy density and bond critical point properties of the electron density distributions indicate that the Ni-S and Ni-Ni bonded interactions are intermediate in character between ionic and covalent.     

Covalence and Ionicity in MgAgAs‐Type Compounds

MgAgAs‐type “half‐Heusler” compounds are known to realize two out of three possible atomic arrangements of this structure type. The number of transition metal components typically determines which of the alternatives is favored. On the basis of DFT calculations for all three variants of 20 eight‐ and eighteen‐valence‐electron compounds, the experimentally observed structural variant was found to be determined by basically two different bonding patterns. They are quantified by employing two complementary position‐space bonding measures. The Madelung energy ${E_{\rm{M}}^{{\rm{QTAIM}}} }$ calculated with the QTAIM effective charges reflects contributions of the ionic interactions to the total energy. The sum of nearest‐neighbor delocalization indices ?_nn characterizes the covalent interactions through electron sharing. With the aid of these quantities, the energetic sequence of the three atomic arrangements for each compound is rationalized. The resulting systematic is used to predict a scenario in which an untypical atomic arrangement becomes most favorable.     

pi-H...O hydrogen bonds: multicenter covalent pi-H interaction acts as the proton-donating system

The MP2 method and the Pople-style basis sets 6-311++G(d,p), 6-311++G(2df,2pd), and 6-311++G(3df,3pd) were used to perform calculations on H3O+...C2H2 and C2H3+...C2H2 complexes and related species. Hydrogen bonds existing for the analyzed complexes were investigated as well as related pi-H...O --> pi...H-O and pi-H...pi --> pi...H-pi proton-transfer processes. For some of the complexes analyzed the multicenter pi-H interaction possessing the properties of a covalent bond acts as a proton donor; more generally it is classified as the Lewis acid. The quantum theory of "atoms in molecules" (QTAIM) was also applied to deepen the nature of these interactions in terms of characteristics of bond critical points. The pi-H...O, O-H...pi, and pi-H...pi interactions analyzed here may be classified as hydrogen bonds since their characteristics are the same as or at least similar to those of typical hydrogen bonds. H...pi interactions are common in crystal structures of organic and organometallic compounds. The analyses performed here show a continuum of such interactions since there are H...pi contacts possessing the characteristics of weak intermolecular interactions on the one hand and pi-H multicenter covalent bonds on the other. Ab initio and QTAIM results support the latter statements.     

Metal-thiolate bonds in bioinorganic chemistry

Metal-thiolate active sites play major roles in bioinorganic chemistry. The M--S(thiolate) bonds can be very covalent, and involve different orbital interactions. Spectroscopic features of these active sites (intense, low-energy charge transfer transitions) reflect the high covalency of the M--S(thiolate) bonds. The energy of the metal-thiolate bond is fairly insensitive to its ionic/covalent and pi/sigma nature as increasing M--S covalency reduces the charge distribution, hence the ionic term, and these contributions can compensate. Thus, trends observed in stability constants (i.e., the Irving-Williams series) mostly reflect the dominantly ionic contribution to bonding of the innocent ligand being replaced by the thiolate. Due to high effective nuclear charges of the Cu(II) and Fe(III) ions, the cupric- and ferric-thiolate bonds are very covalent, with the former having strong pi and the latter having more sigma character. For the blue copper site, the high pi covalency couples the metal ion into the protein for rapid directional long range electron transfer. For rubredoxins, because the redox active molecular orbital is pi in nature, electron transfer tends to be more localized in the vicinity of the active site. Although the energy of hydrogen bonding of the protein environment to the thiolate ligands tends to be fairly small, H-bonding can significantly affect the covalency of the metal-thiolate bond and contribute to redox tuning by the protein environment.     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Electron density distribution of an oxamato bridged Mn(II)-Cu(II) bimetallic chain and correlation to magnetic properties

The electron density distribution of the ferrimagnetic MnCu(pba)(H2O)3.2H2O chain compound, where pba stands for 1,3-propylenebis(oxamato), has been derived from high resolution X-ray diffraction measurements at 114 K using a multipolar model. The analysis of the chemical bonding has been carried out through the "Atoms in Molecules" formalism and thoroughly interpreted with regards to the strong intrachain and weak interchain magnetic couplings. The topological properties of the electron density on the oxamato bridge indicate large electron delocalization and conjugation effects, in addition to high charge transfer from both metals to the bridge. The resulting positive charges on Mn (+1.45 e) and Cu (+1.56 e) induce charge polarization of the bridge, leading to a shift of electron density from the central C atoms to the metal coordinating O and N atoms. The Mn-bridge interactions are mainly closed-shell interactions with low electron density at the corresponding bond critical points, whereas the Cu-bridge interactions exhibit significant covalent character. The Cu-N bonds are moreover stronger than the Cu-O bonds. The 3d Cu and Mn orbital populations are consistent with pyramidal and regular octahedral environments, respectively, in agreement with the loss of degeneracy due to ligand field effects. Interchain interaction pathways are evidenced by the existence of four bond critical points in hydrogen bond regions. Finally, these intrachain and interchain bonding features are correlated to the results of experimental and theoretical spin density distributions, as well as magnetic measurements.     

Electron localization and delocalization indices for solids

The electron localization and delocalization indices obtained by the integration of exchange‐correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis

We present the Voronoi Deformation Density (VDD) method for computing atomic charges. The VDD method does not explicitly use the basis functions but calculates the amount of electronic density that flows to or from a certain atom due to bond formation by spatial integration of the deformation density over the atomic Voronoi cell. We compare our method to the well-known Mulliken, Hirshfeld, Bader, and Weinhold [Natural Population Analysis (NPA)] charges for a variety of biological, organic, and inorganic molecules. The Mulliken charges are (again) shown to be useless due to heavy basis set dependency, and the Bader charges (and often also the NPA charges) are not realistic, yielding too extreme values that suggest much ionic character even in the case of covalent bonds. The Hirshfeld and VDD charges, which prove to be numerically very similar, are to be recommended because they yield chemically meaningful charges. We stress the need to use spatial integration over an atomic domain to get rid of basis set dependency, and the need to integrate the deformation density in order to obtain a realistic picture of the charge rearrangement upon bonding. An asset of the VDD charges is the transparency of the approach owing to the simple geometric partitioning of space. The deformation density based charges prove to conform to chemical experience.     

Interplay between hydrogen-bond formation and multicenter pi-electron delocalization: intramolecular hydrogen bonds

The specific case of intramolecular hydrogen bonds assisted by pi-electron delocalization is thoroughly investigated using multicenter delocalization analysis. The effect of the pi-electron delocalization on the intramolecular hydrogen-bond strength is determined by means of the relative molecular energies of "open" and "closed" structures, calculated at the B3LYP/6-311++G(d,p) level of theory. These relative energies are compared to variations in the multicenter electron delocalization indices and covalent hydrogen-bond indices, which are shown to correlate very well with the relative strength of the intramolecular hydrogen bonds studied. The multicenter electron delocalization indices and covalent bond indices have been computed using the quantum theory of atoms in molecules approach. The hydrogen bonds are formed with oxygen, nitrogen, or sulfur as acceptor atom, which are also the atoms considered to be bonded to the donor hydrogen. Malonaldehyde is taken as reference; the substitution of oxygen by other atoms at the acceptor and donor positions and the effect of the aromaticity have been studied. The results shown here match perfectly with the qualitative expectations derived from the resonance models. In addition, they provide a quantitative picture of the role played by the pi-electron delocalization on the relative strength of intramolecular hydrogen bonds.     

An atomic charge study of highly ionic diatomic molecular systems

Four atomic charge formalisms are compared using highly ionic diatomic molecules, such as LiF, NaF, KF, LiCl, NaCl, KCl, BF, AlF, GaF, BeO, and MgO. All calculations were done at the QCISD/6‐311G(2df) level. The only formalism consistent with the characteristics of all these systems is Quantum theory of atoms in molecules (QTAIM). Absolute Mulliken charge values are small. ChelpG charges are not reliable for systems in which the atoms are largely anisotropic. Generalized atomic polar tensor values are contaminated with charge fluxes and atomic dipole fluxes and fail when these contributions are important and do not cancel each other. Finally, the charge–charge flux–dipole flux model was applied to dipole moment derivatives with QTAIM. This analysis shows that charge flux and atomic dipole flux contributions during bond stretching are almost null, except for oxides. There are also evidences that the lone electron pair at Group 13 elements in fluorides becomes less localized as the bond is stretched. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.     

Stockholder projector analysis: a Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.     

Interplay between hydrogen bond formation and multicenter pi-electron delocalization: intermolecular hydrogen bonds

The interplay between aromatic electron delocalization and intermolecular hydrogen bonding is thoroughly investigated using multicenter delocalization analysis. The effect on the hydrogen bond strength of aromatic electron delocalization within the acceptor and donor molecules is determined by means of the interaction energies between monomers, calculated at the B3LYP/6-311++G(d,p) level of theory. This magnitude is compared to variations of multicenter electron delocalization indices and covalent hydrogen bond indices, which are shown to correlate perfectly with the relative values of the interaction energies for the different complexes studied. The multicenter electron delocalization indices and covalent bond indices have been computed using the quantum theory of atoms in molecules approach. All the hydrogen bonds are formed with oxygen as the acceptor atom; however, the atom bonded to the donor hydrogen has been either oxygen or nitrogen. The water-water complex is taken as reference, where the donor and acceptor molecular environments are modified by substituting the hydrogens and the hydroxyl group by phenol, furan, and pyrrole aromatic rings. The results here shown match perfectly with the qualitative expectations derived from the resonance model.     

Propagation of polar substituent effects in 1-(substituted phenyl)-6,7-dimethoxy-3,4-dihydro- and -1,2,3,4-tetrahydroisoquinolines as explained by resonance polarization concept

[structures: see text] Propagation of inductive and resonance effects of phenyl substituents within 1-(substituted phenyl)-6,7-dimethoxy-3,4-dihydro- and -1,2,3,4-tetrahydroisoquinolines were studied with the aid of 13C and 15N NMR chemical shifts and ab initio calculations. The substituent-induced changes in the chemical shift (SCS) were correlated with a dual substituent parameter equation. The contributions of conjugative (rhoR) and nonconjugative effects (rhoF) were analyzed, and mapping of the substituent-induced changes is given over the entire isoquinoline moiety for both series. The experimental results can be rationalized with the aid of the resonance polarization concept. This means the consideration of the substituent-sensitive balance of different resonance structures, i.e., electron delocalization, and the effect of the aromatic ring substituents on their relative contributions. With tetrahydroisoquinolines, the delocalization of the nitrogen lone pair (stereoelectronic effect) particularly contributes. Correlation analysis of the Mulliken atomic charges for the dihydroisoquinoline derivatives was also performed. The results support the concept of the substituent-sensitive polarization of the isoquinoline moiety even if the polarization pattern achieved via the NMR approach is not quite the same as that predicted by the computational charges. Previously the concepts of localized pi-polarization and extended polarization have been used to explain polar substituent effects within aromatic side-chain derivatives. We consider that the resonance polarization model effectively contributes to the understanding of the polar substituent effects.     

簇电荷对金属—金属键影响的量子化学研究

在探讨过渡金属原子簇化合物的金属——金属键的本质时,簇电荷的影响已引起人们的注意。簇电荷对金属——金属键的作用比较复杂,其中有价电子的成键效应和金属原子氧化数变化所产生的电荷效应。键长与簇电荷之间很难找到简单的关系。Cotton等曾对此问题做过初步讨论,但尚缺定量或半定量的理论计算依据,本文采用改进的电荷自洽EHMO程序(MAD—SCCO-EHMO)计算一系列Mo,Tc,Ru,Rh,和Re等二核簇的电子结构,根据M(?)lliken重迭集居分析,讨论簇电荷对金属——金属键的影响。     

Strong support effects on the insulator to metal transition in supported Pt clusters as observed by X-ray absorption spectroscopy

The development of a new in situ probe of metallic character in supported metal clusters utilizing X-ray absorption spectroscopy is described. The technique is based on the extent of screening of the core-hole left in the neutral final state after the X-ray absorption. The technique allows for the clear differentiation between local interatomic charge transfer and more delocalized metallic screening. The particle size at the metal-insulator transition is found to depend strongly on the electron richness of the support oxygen atoms (i.e., ionic vs covalent oxides). Pt particles on supports with electron poor oxygen atoms (covalent) show metallic screening for sizes as small as 12 A in diameter. In contrast, on supports with electron rich oxygen atoms (ionic) the Pt particles do not show metallic behavior until around 20 A. The wide variation of previously reported estimates of the particle size at which the insulator to metal transition occurs is explained, giving a consistent picture for the onset of metallic character, and the reasons for the strong support effect.     

Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al(n)P(n) clusters (n=2-9) and the prolate clusters (Al(2)P(2))(N) and (Al(3)P(3))(N) (N≤6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al(5)P(5) and Al(7)P(7) due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al(n)P(n) cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al(2)P(2) and Al(3)P(3) in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.