Toward a Combined DFT/QTAIM Description of Agostic Bonds: The Critical Case of a Nb(III) Complex

Three-centre electron sharing indices (3c-ESIs) as a tool to differentiate among (an)agostic interactions and hydrogen bonds in transition metal complexes

The agostic bond plays an important role in chemistry, not only in transition metal chemistry but also in main group chemistry. In some complexes with M⋯H-X (X = C, N) interactions, differentiation among agostic, anagostic, and hydrogen bonds is challenging. Here we propose the use of three-centre electron sharing indices to classify M⋯H-X (X = C, N) interactions.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

Hydrogen bond symmetrization and elastic constants under pressure of δ-AlOOH

The elastic constants of δ-AlOOH have been calculated for applied pressures in the range 0-40 GPa using three exchange-correlation functionals, i.e. PBEsol, TCAsol and PBE. PBEsol and TCAsol, which describe the geometry of this system very well, give similar results, while the PBE values are smaller, a consequence of the fact that the PBE lattice parameters are too large. In agreement with the experiments, the calculations show that at low pressure the axial compressibility is greater in the b direction and smaller in the c direction, while the opposite is true at high pressure. This change takes place 5 GPa before the calculated hydrogen bond symmetrization transition. Combining this result with those reported in the experimental papers, one obtains a strong indication that symmetrization takes place at about 15 GPa, in excellent agreement with the PBEsol and TCAsol predictions.

On the relation between carbonyl stretching frequencies and the donor power of chelating diphosphines in nickel dicarbonyl complexes

The relation between spectroscopic observables and the detailed metal-ligand bonding features in chelation complexes is addressed using both experimental and state-of-the-art theoretical and computational methods. We synthesized and characterized a set of six nickel dicarbonyl complexes of general formula [Ni(CO)2(PP)], where PP is an atropoisomeric chelating diphosphine ligand. The analysis of the obtained experimental data and the basicity and oxidative potentials of the free ligands suggests a close relation between the donor ability of the chelating ligand and the carbonyl stretching frequencies observed in the complexes. We then use theory to unravel the detailed mechanisms of chelation-bond formation in terms of partial charge flows between the molecular orbitals of the fragments. By extending the promising, recently published natural orbitals for chemical valence/charge displacement (NOCV/CD) analysis scheme we provide a thorough, quantitative description of the several charge fluxes following the metal-ligand bond formation and demonstrate that the carbonyl stretching frequencies in the considered complexes selectively respond to the σ-donation charge flow from the phosphorus lone pairs of the ligands, with the frequency shift being in quantitative correlation with the extent of the ligand-to-metal charge transfer.

Theoretical investigation on donor–acceptor interaction between a carbonyl compound and an N,N′-dioxide–Sc(iii) complex

The counterion and substituent on amide of the N,N′-dioxide ligand could affect electrostatic energy (ΔV_elstat) as well as orbital energy (ΔE_orb) between CH₂O and Sc(iii)-based catalyst, adjusting the Lewis acidity of the metal centre.

Characterization of B-H agostic compounds involved in the dehydrogenation of amine-boranes by group 4 metallocenes

For over a decade, amine-borane has been considered as a potential chemical hydrogen vector in the context of a search for cleaner energy sources. When catalyzed by organometallic complexes, the reaction mechanisms currently considered involve the formation of β-BH agostic intermediates. A thorough understanding of these intermediates may constitute a crucial step toward the identification of ideal catalysts. Topological approaches such as QTAIM and ELF revealed to be particularly suitable for the description of β-agostic interactions. When studying model catalysts, accurate theoretical calculations may be carried out. However, for a comparison with experimental data, calculations should also be carried out on large organo-metallic species, often including transition metals belonging to the second or the third row. In such a case, DFT methods are particularly attractive. Unfortunately, triple-ζ all electrons basis sets are not easily available for heavy transition metal elements. Thus, a subtle balance should be reached between the affordable level of calculations and the required accuracy of the electronic description of the systems. Herein we propose the use of B3LYP functional in combination with the LanL2DZ pseudopotential for the metal atom and 6-311++G(2d,2p) basis set for the other atoms, followed by a single point using the DKH2 relativistic Hamiltonian in combination with the B3LYP/DZP-DKH level, as a "minimum level of theory" leading to a consistent topological description of the interaction within the ELF and QTAIM framework, in the context of isolated (gas-phase) group 4 metallocene catalysts.

QTAIM-based comparison of agostic bonds and intramolecular charge-inverted hydrogen bonds

Using DFT-based calculations with seven exchange-correlation functionals (BP86, B3LYP, B3PW91, PBE0, TPSSh, M06-L, M06) we have performed comparative studies on α-, β-, γ-, and δ-agostic bonds (ABs) and intramolecular charge-inverted hydrogen bonds (IMCIHBs). Our detailed analysis of values of QTAIM parameters computed at bond (BCP) and ring critical points (RCP) as well as of the curvatures of bond paths tracing agostic bonds and intramolecular charge-inverted hydrogen bonds gives the opportunity to distinguish between both these types of interactions. In the case of molecules with agostic bonds, the BCP is significantly closer to the agostic hydrogen, whereas in systems with IMCIHB the BCP is, instead, somewhat closer to the metal atom. Agostic bonds are characterized by H···M bond paths being straight in the BCP···M section and then highly curved near the agostic hydrogen, whereas in the case of IMCIHB any substantial curvature of BP in the vicinity of hydrogen is not present. Quite the contrary, the significant curvature of BP near the metal atom can be obtained, instead. One can also distinguish IMCIHBs and ABs on the basis of values of bond ellipticity at BCP and the electron density at RCP which are either somewhat (PBE0) or considerably (M06) greater for the latter type of interaction. It has also been shown that, in general, the exchange-correlation functional has small influences on most of QTAIM parameters computed at BCP and RCP. More significant influences have only been obtained for Laplacian of the electron density, some its components, and the bond ellipticity.

Reactivity of coordinatively unsaturated bis(N-heterocyclic carbene) Pt(II) complexes toward H(2). Crystal structure of a 14-electron Pt(II) hydride complex

The reactivity toward H2 of coordinatively unsaturated Pt(II) complexes, stabilized by N-heterocyclic carbene (NHC) ligands, is herein analyzed. The cationic platinum complexes [Pt(NHC')(NHC)](+) (where NHC' stands for a cyclometalated NHC ligand) react very fast with H2 at room temperature, leading to hydrogenolysis of the Pt-CH2 bond and concomitant formation of hydride derivatives [PtH(NHC)2](+) or hydrido-dihydrogen complexes [PtH(H2)(NHC)2](+). The latter species release H2 when these compounds are subjected to vacuum. The X-ray structure of complex [PtH(IPr)2][SbF6] revealed its unsaturated nature, exhibiting a true T-shaped structure without stabilization by agostic interactions. Density functional theory calculations indicate that the binding and reaction of H2 in complexes [PtH(H2)(NHC)2](+) is more favored for derivatives bearing aryl-substituted NHCs (IPr, 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene and IMes = 1,3-dimesityl-1,3-dihydro-2H-imidazol-2-ylidene) than for those containing tert-butyl groups (I(t)Bu). This outcome is related to the higher close-range steric effects of the I(t)Bu ligands. Accordingly, H/D exchange reactions between hydrides [PtH(NHC)2](+) and D2 take place considerably faster for IPr and IMes* derivatives than for I(t)Bu ones. The reaction mechanisms for both H2 addition and H/D exchange processes depend on the nature of the NHC ligand, operating through oxidative addition transition states in the case of IPr and IMes* or by a σ-complex assisted-metathesis mechanism in the case of I(t)Bu.

Analysis of M···H-Si interactions in [{M(CpSiMe2H)Cl3}2], (M = Zr, Hf, Ti and Mo) complexes

For the d(0) complex [{Zr(CpSiMe(2)H)Cl(3)}(2)] which contains a linear Si-H···Zr interaction across the dimer, DFT calculations are in good agreement with X-ray structures. The BP86 functional shows a slightly stronger interaction than B3LYP but for qualitative purposes either functional is sufficient. QTAIM analysis shows a bond critical point (bcp) for the interaction, a small negative value for the total energy density [H((r))] and the H atomic basin decreases in energy, E(H), and atomic volume compared to the free ligand. NBO analysis showed E(2) for Si-H σ to Zr(dz(2)) donation at 42.8 kcal mol(-1) and a 34% spatial overlap for the interaction consistent with an inverse hydrogen bond. The Wiberg bond index for the interaction is 0.1735 (0.7205 for the Si-H bond), ν((Si-H)) and (1)J((Si-H)) at 2060 cm(-1) and 145.4 Hz compared to 2183 cm(-1) and 172.1 Hz in the free ligand. Using a "synthesis by computation" approach to forming like complexes, similar features were found for [{Hf(CpSiMe(2)H)Cl(3)}(2)]. The titanium complex [{Ti(CpSiMe(2)H)Cl(3)}(2)] does not contain any Si-H···Ti interaction as rotation about the C-Si bond of the ligand occurs to place the Si-H bond hydrogen closer to a terminal chloro ligand across the dimer. An increase in electron density on the metal in the d(2) complex [{Mo(CpSiMe(2)H)Cl(3)}(2)] results in a stronger interaction with a distinct QTAIM analysis bcp [ρ((r)) 0.0448 a.u.], a small negative value for H((r)) and a much reduced H atomic volume. NBO analysis shows E(2) for Si-H σ to Mo(dz(2)) donation at 143.1 kcal mol(-1) and a 29% spatial overlap. Mo(dz(2)) to Si-H σ* donation (back donation) is minimal [E(2) 1.3 kcal mol(-1), ~1% spatial overlap]. The Wiberg bond index is 0.3114 (0.5667 for the Si-H bond), ν((Si-H)) 2015 cm(-1) and (1)J((Si-H)) 120.6 Hz.