Nicht-VSEPR-Strukturen und chemische Bindung in d0-Systemen

New horizons in low oxidation state group 2 metal chemistry

Since the seminal report on Mg in the +I oxidation state in 2007, low-valent complexes featuring a Mg^I-Mg^I bond developed from trophy molecules to state-of-the-art reducing agents. Despite increasing interest in low-valency of the other group 2 metals, this area was restricted for a long time to a rare example of a Ca^I(arene)Ca^I inverse sandwich. This feature article focuses on the most recent developments in the field, highlighting recent breakthroughs for Be, Mg and Ca. The more exotic metal Be was the first to be isolated as a zero-valent complex which could be oxidized to a Be^I species. There also has been interest in breaking the Mg^I-Mg^I bond with superbulky β-diketiminate ligands (BDI) that suppress (BDI)Mg-Mg(BDI) bond formation. This led to Mg-Mg bond elongation or Mg-N bond cleavage. Several reports on attempts to isolate (BDI)Mg˙ radicals by combinations of ligand bulk, addition of neutral ligands or UV(vis) irradiation led to reduction of the aromatic solvents, underscoring the high reactivity of these open shell species. Only recently, zero-valent complexes of Mg were introduced. Double reduction of a (BDI)MgI complex with Na gave [(BDI)Mg^-]Na⁺. This Mg⁰ complex crystallized as a dimer in which the Na⁺ cations bridge the two (BDI)Mg^- anions which react as Mg nucleophiles. Thermal decomposition led to spontaneous formation of Na⁰ and a trinuclear (BDI)MgMgMg(BDI) complex. This mixed-valence Mg₃-complex is a prime example of the fleeting multinuclear Mg_n intermediates discussed on the way from Mg metal to Grignard reagent. Attempts to prepare low-valent Ca^I compounds by reduction of (BDI)CaI led to dearomatization of the arene solvents: (BDI)Ca(arene)Ca(BDI). Reduction in alkanes prevented this decomposition pathway but led to N₂ reduction and isolation of (BDI)Ca(N₂)Ca(BDI), representing the first example of molecular nitrogen fixation with an early main group metal. As the N₂^2- anion reacts in most cases as a very strong two-electron reductant, LCa(N₂)CaL could be seen as a synthon for hitherto elusive Ca^I-Ca^I complexes. Theoretical calculations suggest that participation of Ca d-orbitals is relevant for N₂ activation. These most recent developments in low-valent group 2 metal chemistry will revive this area and undoubtly lead to new reactivities and applications.

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca6 H9 [N(SiMe3 )2 ]3 (pmdta)3 (pmdta=N,N,N',N'',N''-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n-1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.

Metal Alkyls with Alkylidynic Metal-Carbon Bond Character: Key Electronic Structures in Alkane Metathesis Precatalysts

The homologation of alkanes via alkane metathesis is catalyzed at low temperatures (150 °C) by the silica-supported species (≡SiO)WMe₅ and (≡SiO)TaMe₄ , while (≡SiO)TaMe₃ Cp* is inactive. The contrasting reactivity is paralleled by differences in the ¹³ C NMR signature; the former display significantly more deshielded isotropic chemical shifts (δ_iso ) and almost axially symmetric chemical shift tensors, similar to what is observed in their molecular precursors TaMe₅ and WMe₆ . Analysis of the chemical shift tensors reveals the presence of a triple-bond character in their metal-carbon (formally single) bond. This electronic structure is reflected in their propensity to generate alkylidynes and to participate in alkane metathesis, further supporting the role of alkylidynes as key reaction intermediates. This study establishes chemical shift as a descriptor to identify potential alkane metathesis catalysts.

Valence-Shell Electron-Pair Repulsion Theory Revisited: An Explanation for Core Polarization

Valence-shell electron-pair repulsion (VSEPR) theory constitutes one of the pillars of theoretical predictive chemistry. It was proposed even before the advent of the concept of "spin", and it is still a very useful tool in chemistry. In this article we propose an extension of VSEPR theory to understand the core structure and predict core polarization in the main-group elements. We show from first principles (Electron Localization Function analysis) how the inner- and outer-core shells are organized. In particular, electrons in these regions are structured following the shape of the dual polyhedron of the valence shell (3^rd period) or the equivalent polyhedron (4^th and 5^th periods). We interpret these results in terms of "hard" and "soft" core character. All the studied systems follow this trend, providing a framework for predicting electron distribution in the core. We also show that lone pairs behave as "standard ligands" in terms of core polarization. The predictive character of the model was tested by proposing the core polarization in different systems not included in the original set (such as XeF₄ and [Fe(CN)₆ ]^3- ) and checking the hypothesis by means of a posteriori calculations. From the experimental point of view, the extension of VSEPR to the core region has consequences for current crystallography research. In particular, it explains the core polarization revealed by high resolution X-ray experiments.

Nonlinear d(10)-ML2 Transition-Metal Complexes

We have investigated the molecular geometries of a series of dicoordinated d(10)-transition-metal complexes ML2 (M=Co(-), Rh(-), Ir(-), Ni, Pd, Pt, Cu(+), Ag(+), Au(+); L=NH3, PH3, CO) using relativistic density functional theory (DFT) at ZORA-BLYP/TZ2P. Not all complexes have the expected linear ligand-metal-ligand (L-M-L) angle: this angle varies from 180° to 128.6° as a function of the metal as well as the ligands. Our main objective is to present a detailed explanation why ML2 complexes can become bent. To this end, we have analyzed the bonding mechanism in ML2 as a function of the L-M-L angle using quantitative Kohn-Sham molecular orbital (MO) theory in combination with an energy decomposition analysis (EDA) scheme. The origin of bent L-M-L structures is π backdonation. In situations of strong π backdonation, smaller angles increase the overlap of the ligand's acceptor orbital with a higher-energy donor orbital on the metal-ligand fragment, and therefore favor π backdonation, resulting in additional stabilization. The angle of the complexes thus depends on the balance between this additional stabilization and increased steric repulsion that occurs as the complexes are bent.

Heavy Grignard Reagents: Challenges and Possibilities of Aryl Alkaline Earth Metal Compounds

Compounds of the type aryl--M--X, with M=Ca, Sr, Ba and X as any kind of ligand (such as halide, phosphanide, amide, aryl), are presented. The low reactivity of the heavy alkaline earth metals calcium, strontium, and barium enforces an activation prior to use for the direct synthesis. The insertion of these metals into C--I bonds of aryl iodides (direct synthesis) yields aryl metal iodides and has to be performed at low temperatures and in THF. Aryl alkaline-earth-metal compounds show some characteristics: 1) the ease of ether cleavage enforces low reaction temperatures, 2) for Sr and Ba the Schlenk equilibrium is shifted towards homoleptic MI2 and MPh2, 3) high solubility of diaryl alkaline-earth-metal derivatives in THF even at low temperatures initiated quantum chemical investigations on the aggregation behavior, and 4) a strong low field shift of the 13C resonances of the ipso carbon atoms in NMR spectra was observed. First results from quantum chemical calculations on diaryl dicalcium(I) suggest a long Ca--Ca bond with a considerable Ca--Ca bond dissociation energy. Initial results on a selection of applications such as metallation, metathesis, and addition reactions of aryl calcium compounds are presented as well.

A Comparative Relativistic DFT and Ab Initio Study on the Structure and Thermodynamics of the Oxofluorides of Uranium(IV), (V) and (VI)

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.

2,2′-Biphosphinines and 2,2′-Bipyridines in Homoleptic Dianionic Group 4 Complexes and Neutral 2,2′-Biphosphinine Group 6 d6 Metal Complexes: Octahedral versus Trigonal-Prismatic Geometries

The geometric and electronic structure of formally d(6) tris-biphosphinine [M(bp)(3)](q) and tris-bipyridine [M(bpy)(3)](q) complexes were studied by means of DFT calculations with the B3LYP functional. In agreement with the available experimental data, Group 4 dianionic [M(bp)(3)](2-) complexes (1P-3P for M=Ti, Zr, and Hf, respectively) adopt a trigonal-prismatic (TP) structure, whereas the geometry of their nitrogen analogues [M(bpy)(3)](2-) (1N-3N) is nearly octahedral (OC), although a secondary minimum was found for the TP structures (1N'-3N'). The electronic factors at work in these systems are discussed by means of an MO analysis of the minima, MO correlation diagrams, and thermodynamic cycles connecting the octahedral and trigonal-prismatic limits. In all these complexes, pronounced electron transfer from the metal center to the lowest lying pi* ligand orbitals makes the d(6) electron count purely formal. However, it is shown that the bp and bpy ligands accommodate the release of electron density from the metal in different ways because of a change in the localization of the HOMO, which is a mainly metal-centered orbital in bp complexes and a pure pi* ligand orbital in bpy complexes. The energetic evolution of the HOMO allows a simple rationalization of the progressive change from the TP to the OC structure on successive oxidation of the [Zr(bp)(3)](2-) complex, a trend in agreement with the experimental structure of the monoanionic complex. The geometry of Group 6 neutral complexes [M(bp)(3)] (4P and 5P for M=Mo and W, respectively) is found to be intermediate between the TP and OC limits, as previously shown experimentally for the tungsten complex. The electron transfer from the metal center to the lowest lying pi* ligand orbitals is found to be significantly smaller than for the Group 4 dianionic analogues. The geometrical change between [Zr(bp)(3)](2-) and [W(bp)(3)] is analyzed by means of a thermodynamic cycle and it is shown that a larger ligand-ligand repulsion plays an important role in favoring the distortion of the tungsten complex away from the TP structure.

A theoretical investigation of the nonrigid six-coordinate compounds [Mo(R)F5], [W(R)F5], and related compounds

Density functional calculations for [M(CH3)F5], [M(CF3)F5], [M(CH3S)F5], and [M(CF3S)F5] (M=Mo, W) show that they are expected to be nonrigid molecules, with energy barriers for the octahedral-trigonal-prismatic interchange as low as 7.2 kJ mol(-1). The ground state for the CH3- and CF3- compounds is trigonal prismatic, for the CH3S- and CF3S- compounds, (distorted) octahedral. All calculated compounds [M(C6F5)nF(6-n)] (M=Mo, W) have a trigonal-prismatic ground state, whereas the situation for [M(C6H5)nF(6-n)] (M=Mo, W) is more complex.

Recent developments in the field of organic heterobimetallic compounds of the alkaline-earth metals

Heterobimetallic compounds of the alkaline-earth metals show a wide structural variety with strongly differing reactivity patterns. The combination of magnesium and alkali metal amides yields cyclic molecules with an extreme high reactivity which often are considered as "inverse crowns" with the metal atoms as coordination sites for Lewis bases. In other metallates of the alkaline-earth metals an activation of alkyl groups succeeds. In alkaline-earth metal zincates an inverse coordination of the type M(2)[(mu-R)(2)ZnR](2) is observed and the alkyl groups are in bridging positions between zinc and the s-block metals thus forming a very reactive M-C-Zn three-center-two-electron bond. Furthermore, the metals of the carbon group form alkaline-earth metal-silicon, -germanium and -tin bonds or, in the presence of very strong Lewis bases, even solvent-separated ion pairs. For electronegative substituents at tin an inverse coordination mode such as M[(mu-R)(2)SnR](2) is observed.

The role of radial nodes of atomic orbitals for chemical bonding and the periodic table

The role of radial nodes, or of their absence, in valence orbitals for chemical bonding and periodic trends is discussed from a unified viewpoint. In particular, we emphasize the special role of the absence of a radial node whenever a shell with angular quantum number l is occupied for the first time (lack of "primogenic repulsion"), as with the 1s, 2p, 3d, and 4f shells. Although the consequences of the very compact 2p shell (e.g. good isovalent hybridization, multiple bonding, high electronegativity, lone-pair repulsion, octet rule) are relatively well known, it seems that some of the aspects of the very compact 3d shell in transition-metal chemistry are less well appreciated, e.g., the often weakened and stretched bonds at equilibrium structure, the frequently colored complexes, and the importance of nondynamical electron-correlation effects in bonding.

Valence Shell Charge Concentrations at Pentacoordinate d0 Transition-Metal Centers: Non-VSEPR Structures of Me2NbCl3 and Me3NbCl2

The molecular structures of the monomeric, pentacoordinated methylchloroniobium(IV) compounds Me3NbCl2 and Me2NbCl3 have been determined by gas electron diffraction (GED) and density functional theory (DFT) calculations, and, for Me3NbCl2, by single crystal X-ray diffraction. Each of the molecules is found to have a heavy-atom skeleton in the form of a trigonal bipyramid (TBP) with Cl atoms in the axial positions, in accord with their vibrational spectra. The TBP is somewhat distorted in the case of Me2NbCl3 with the two axial Nb--Cl bonds bent away from the equatorial, slightly shorter Nb--Cl bond. In the case of Me3NbCl2, moreover, the X-ray model suggests structural distortions away from the idealized C3h geometry, in line with the results of quantum chemical calculations. Structure optimizations by DFT calculations and least-squares refinement to the GED data yield the following structural parameters (calcd/exptl; eq=equatorial; ax=axial; distances in A, angles in degrees; average values in brackets): Me3NbCl2, in C(3v) symmetry, Nb--Cl 2.370/2.319(3), Nb--C 2.173/2.152(4), C--H 1.096/1.124(5), angle-spherical NbCH 109.3/105.2(8), angle-spherical ClNbC 92.2/93.3(2), angle-spherical CNbC 119.9/119.7(1); Me2NbCl3, in C(2v) symmetry, Nb--Cl(ax) 2.361/2.304(5), Nb--Cl(eq) 2.321/2.288(9), Nb--C 2.180/2.135(9), C--H 1.094/1.12(1), angle-spherical Cl(ax)NbCl(eq) 98.5/96.5(6), angle-spherical CNbC 121.0/114(2), angle-spherical NbCH 108.9/109(2). The electronic structures of Me2NbCl3 and Me3NbC(2 have been explored by rigorous analysis of both the wavefunction and the topology of the electron density, employing DFT calculations. Hence the structures of these compounds are shown to reflect repulsion between the Nb--C and Nb--Cl bonding electron density and charge concentrations induced by the methyl ligands in the valence shell of the Nb atom and arising mainly from use of Nb(4d) functions in the Nb--C bonds.