The QTAIM Approach to Chemical Bonding Between Transition Metals and Carbocyclic Rings: A Combined Experimental and Theoretical Study of (η5-C5H5)Mn(CO)3, (η6-C6H6)Cr(CO)3, and (E)-{(η5-C5H4)CF═CF(η5-C5H4)}(η5-C5H5)2Fe2

Forced bonding and QTAIM deficiencies: a case study of the nature of interactions in He@adamantane and the origin of the high metastability

Calculations within the framework of the interacting quantum atoms (IQA) approach have shown that the interactions of the helium atom with both tertiary, tC, and secondary, sC, carbon atoms in the metastable He@adamantane (He@adam) endohedral complex are bonding in nature, whereas the earlier study performed within the framework of Bader's quantum theory of atoms in molecules (QTAIM) revealed that only He---tC interactions are bonding. The He---tC and He---sC bonding interactions are shown to be forced by the high pressure that the helium and carbon atoms exert upon each other in He@adam. The occurrence of a bonding interaction between the helium and sC atoms, which are not linked by a bond path, clearly shows that the lack of a bond path between two atoms does not necessarily indicate the lack of a bonding interaction, as is asserted by QTAIM. IQA calculations showed that not only the destabilization of the adamantane cage, but also a huge internal destabilization of the helium atom, contribute to the metastability of He@adam, these contributions being roughly equal. This result disproves previous opinions based on QTAIM analysis that only the destabilization of the adamantane cage accounts for the endothermicity of He@adam. Also, it was found that there is no homeomorphism of the ρ(r) and -v(r) fields of He@adam. Comparison of the IQA and QTAIM results on the interactions in He@adam exposes other deficiencies of the QTAIM approach. The reasons for the deficiencies in the QTAIM approach are analyzed.

Advances in understanding of chemical bonding: inputs from experimental and theoretical charge density analysis

The development of charge density analysis has undergone a major renaissance in the last two decades. In recent years, the characterization of bonding features associated with atoms in molecules and in crystals has been explored using high-resolution X-ray diffraction data (laboratory or synchrotron) complemented by high level ab initio theoretical calculations. The extraction of one electron topological properties, namely, electrostatic charges, dipole moment and higher moments, electrostatic potential, electric field gradients, in addition to evaluation of the local kinetic and potential energy densities, have contributed toward an understanding of the electron density distributions in molecular solids. New topological descriptors, namely, the source function (SF) and electron localization function (ELF) provide additional information as regards characterization of the topology of the electron density. In addition, delocalization indices have also been developed to account for bonding features pertinent to M-M bonds. The evaluation of these properties have contributed significantly toward the understanding of intra- and intermolecular bonding features in organic, inorganic, and biomolecules in the crystalline phase, with concomitant applications in the understanding of chemical reactivity and material/biological properties. In recent years, the focus has strongly shifted toward the understanding of structure-property relationships in organometallic complexes containing labile M-C bonds in the crystal structure with subsequent implications in catalysis. This perspective aims to highlight the major developments in electron density measurements in the past few years and provides pointers directed toward the potential use of this technique in future applications for an improved understanding of chemical bonding in systems that have been unexplored.

Bonding between strongly repulsive metal atoms: an oxymoron made real in a confined space of endohedral metallofullerenes

Endohedral metallofullerenes (EMFs) are able to encapsulate up to four metal atoms. In EMFs, metal atoms are positively charged because of the electron transfer from the endohedral metal atoms to the carbon cage. It results in the strong Coulomb repulsion between the positively charged ions trapped in the confined inner space of the fullerene. At the same time, in many EMFs, such as Lu(2)@C(76), Y(2)@C(79)N, M(2)@C(82) (M = Sc, Y, Lu, etc.), Y(3)@C(80), or Sc(4)O(2)@C(80), metals do not adopt their highest oxidation states, thus yielding a possibility of the covalent metal-metal bonding. In some other EMFs (e.g., La(2)@C(80)), metal-metal bonding evolves as the result of the electrochemical or chemical reduction, which leads to the population of the metal-based LUMO with pronounced metal-metal bonding character. This article highlights different aspects of the metal-metal bonding in EMFs. It is concluded that the valence state of the metal atoms in dimetallofullerenes is not dependent on their third ionization potential, but is determined by their ns(2)(n- 1)d(1)→ns(1)(n- 1)d(2) excitation energies. Peculiarities of the metal-metal bonding in EMFs are described in terms of molecular orbital analysis as well as topological approaches such as Quantum Theory of Atoms in Molecules and Electron Localization Function. Interplay of Coulomb repulsion and covalent bonding is analyzed in the framework of the Interacting Quantum Atom approach.

Does covalency increase or decrease across the actinide series? Implications for minor actinide partitioning

A covalent chemical bond carries the connotation of overlap of atomic orbitals between bonded atoms, leading to a buildup of the electron density in the internuclear region. Stabilization of the valence 5f orbitals as the actinide series is crossed leads, in compounds of the minor actinides americium and curium, to their becoming approximately degenerate with the highest occupied ligand levels and hence to the unusual situation in which the resultant valence molecular orbitals have significant contributions from both actinide and the ligand yet in which there is little atomic orbital overlap. In such cases, the traditional quantum-chemical tools for assessing the covalency, e.g., population analysis and spin densities, predict significant metal-ligand covalency, although whether this orbital mixing is really covalency in the generally accepted chemical view is an interesting question. This review discusses our recent analyses of the bonding in AnCp3 and AnCp4 (An = Th-Cm; Cp = η(5)-C5H5) using both the traditional tools and also topological analysis of the electron density via the quantum theory of atoms-in-molecules. I will show that the two approaches yield rather different conclusions and suggest that care must be taken when using quantum chemistry to assess metal-ligand covalency in this part of the periodic table. The implications of this work for minor actinide partitioning from nuclear wastes are discussed; minor actinide extractant ligands based on nitrogen donors have received much attention in recent years, as have comparisons of the extent of covalency in actinide-nitrogen bonding with that in analogous lanthanide systems via quantum-chemical studies employing the traditional tools for assessing the covalency.

A bond path and an attractive Ehrenfest force do not necessarily indicate bonding interactions: case study on M2X2 (M = Li, Na, K; X = H, OH, F, Cl)

Interactions in dimers of model alkali metal derivatives M(2)X(2) (M = Li or Na or K; X = H or F, Cl, OH) are studied in the frame of the quantum theory of atoms in molecules (QTAIM) using the interacting quantum atoms approach (IQA). Contrary to opinion prevalent in QTAIM studies, the interaction between two anions linked by a bond path is demonstrated to be strongly repulsive. One may therefore say that a bond path does not necessarily indicate bonding interactions. The interactions between two anions or two cations that are not linked by a bond path are also strongly repulsive. The repulsive anion-anion and cation-cation interactions are outweighed by much stronger attractive anion-cation interactions, and the model molecules are therefore in a stable state. The attractive Ehrenfest forces (calculated in the frame of the QTAIM) acting across interatomic surfaces shared by anions in the dimers do not reflect the repulsive interactions between anions. Probable reasons of this disagreement are discussed. The force exerted on the nucleus and the electrons of a particular atom by the nucleus and the electrons of any another atom in question is proposed. It is assumed that this force unambiguously exposes whether basins of two atoms are attracted or repelled by each other in a polyatomic molecule.

Bond characterization on a Cr-Cr quintuple bond: a combined experimental and theoretical study

A combined experimental and theoretical charge density study on a quintuply bonded dichromium complex, Cr(2)(dipp)(2) (dipp = (Ar)NC(H)N(Ar) and Ar = 2,6-i-Pr(2)-C(6)H(3)), is performed. Two dipp ligands are bridged between two Cr ions; each Cr atom is coordinated to two N atoms of the ligands in a linear fashion. The Cr atom is in a low oxidation state, Cr(I), and in low coordination number condition, which stabilizes a metal-metal multiple bond, in this case, a quintuple bond. Indeed, it gives an ultrashort Cr-Cr bond distance of 1.7492(1) Å in the complex. The bond characterization of such a quintuple bond is undertaken both experimentally by high-resolution single-crystal X-ray diffraction and theoretically by density functional calculation (DFT). Electron densities are depicted via deformation density and Laplacian distributions. Bond characterizations of the complex are presented in terms of topological properties, Fermi hole function, source function (SF), and natural bonding orbital (NBO) analysis. The electron density at the Cr-Cr bond critical point (BCP) is 1.70 e/Å(3), quite a high value for metal-metal bonding and mainly contributed from the metal ion itself. The quintuple bond is confirmed with one σ, two π, and two δ interactions by NBO analysis and Fermi hole function. The molecular orbitals (MOs) illustrate that five bonding orbitals are predominantly contributed from the 3d orbitals of the Cr(I) ion. The effective bond order from NBO analysis is 4.60. The detail comparison between experiment and theory will be given. Additionally, three closely related complexes are calculated for systematic comparison.

On the nature of Ni···Ni interaction in a model dimeric Ni complex

A new dinuclear complex (NiC(5)H(4)SiMe(2)CHCH(2))(2) (2) was prepared by reacting nickelocene derivative [(C(5)H(4)SiMe(2)CH=CH(2))(2)Ni] (1) with methyllithium (MeLi). Good quality crystals were subjected to a high-resolution X-ray measurement. Subsequent multipole refinement yielded accurate description of electron density distribution. Detailed inspection of experimental electron density in Ni···Ni contact revealed that the nickel atoms are bonded and significant deformation of the metal valence shell is related to different populations of the d-orbitals. The existence of the Ni···Ni bond path explains the lack of unpaired electrons in the complex due to a possible exchange channel.

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

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