Path-dependency of energy decomposition analysis & the elusive nature of bonding

Classical versus Collective Interactions in Asymmetric Trigonal Bipyramidal Alkaline Metal-Boron Halide Complexes

Collective interactions are a novel type of chemical bond formed between metals and electron-rich substituents around an electron-poor central atom. So far only a limited number of candidates for having collective interactions are reported. In this work, we extend the newly introduced concept of collective bonding to a series of neutral boron complexes with the general formula M2BX3 (M=Li, Na, and K; X=F, Cl, and Br). Our state-of-the-art ab initio computations suggest that these complexes form trigonal bipyramidal structures with a D3h to C3v distortion along the C3 axis of symmetry. The BX3 unit in the complexes distorts from planar to pyramidal akin to a sp3 hybridized atom. Interestingly, the interaction of the metals with the pyramidal side of BX3, where the lone pair in a hypothetical [BX3]2- should be located, is weaker than the interactions of metals with the inverted side, i. e., the middle of three halogen atoms. The origin of this stronger interaction can be explained by the formation of collective interactions between metals and halogen atoms as we explored via energy decomposition within the context of the theory of interacting quantum atoms, IQA.

Anti-electrostatic cation⋯π-hole and cation⋯lp-hole interactions are stabilized via collective interactions

Collective interactions are a novel type of bond between metals and AX3 fragments with an electropositive central atom, A, and electronegative X substituents. Here, using electrostatic potential maps and state-of-the-art bonding analysis tools we have shown that collective interactions are anti-electrostatic cation⋯π-Hole or cation⋯lp-Hole interactions.

Organometallic Allene [(μ-C)(Fe(CO)4 )2 ]: Bridging Carbon Showing Transformation from Classical Electron-Sharing Bonding to Double σ-Donor and Double π-Acceptor Ligation

Allenes (R2 C=C=CR2 ) have been traditionally perceived to feature localized orthogonal π-bonds between the carbon centres. We have carried out quantum-mechanical studies of the organometallic allenes envisioned by the isolobal replacement of the terminal CH2 groups by the d8 Fe(CO)4 fragment. Our studies have identified two organometallic allenes viz. D2d symmetric [(μ-C)(Fe(CO)4 )2 ] (2) and D3 symmetric [(μ-C)(Fe(CO)4 )2 ] (3) with trigonal bipyramidal coordination at the Fe atoms. Compound 2 features the bridging carbon atom in an equatorial position with respect to the ligands on the TM centre, while 3 features the central carbon atom in an axial position. The bis-pseudoallylic anionic delocalisation proposed in the C2-C1-C3 spine of organic allene is retained in the organometallic allene 2, and is transformed to a typical three-centre bis-allylic anionic delocalisation in the organometallic allene 3. The topological analysis of electron density also indicates a bis-allylic anionic type delocalisation in the organometallic allenes. The quantitative bonding analysis using the EDA-NOCV method suggests a transition from classical electron-sharing bonding between the central carbon atom and the terminal groups in 1 to donor-acceptor bonding in 3. Meanwhile, both electron-sharing and donor-acceptor bonding models are found to be probable heuristic bonding representations in the organometallic allene 2.

Open shell versus closed shell bonding interaction in cyclopropane derivatives: EDA-NOCV analyses

Cyclopropane ring is a very common motif in organic/bio-organic compounds. The chemical bonding of this strained ring is taught to all chemistry students. This three-membered cyclic, C3 ring is quite reactive which has attracted both, synthetic and theoretical chemists to rationalize/correlate its stability and bonding with its reactivity and physical properties over a century. There are a few bonding models (mainly the Bent-Bond model and Walsh model) of this C3 ring that are debated to date. Herein, we have carried out energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) to study the two most reactive bonds of cyclopropane rings of 49 different organic compounds containing different functional groups to obtain a much deeper bonding insight toward a more general bonding model of this class of compounds. The EDA-NOCV analyses of fragment orbitals and susequent bond formation revealed that the nature of the CC bond of the cyclopropane (splitting two bonds at a time out of three CC bonds) ring is preferred to form two dative covalent CC bonds (between a singlet olefin-fragment and an excited singlet carbene-fragment with a vacant sp2 orbital and a filled p-orbital) for the majority (37/49) of compounds over two covalent electron sharing bonds in some (7/49) compounds (between an excited triplet olefin and triplet carbene), while a few (5/49) compounds show flexibility to adopt either the electron sharing or dative covalent bond as both are equally possible. The effects of functional groups on the nature of chemical bond in cyclopropane rings have been studied in detail. Our bonding analyses are in line with the QTAIM analyses which produce small negative values of the Laplacian, significantly positive values of bond ellipticity, and accumulation of electron densities around the ring critical point of C3 -rings. These corresponding QTAIM parameters of C3 -rings are quite different for CC single bonds of normal hydrocarbons as expected. The chemical bonding in the majority of cyclopropane rings can be very similar to those of metal-olefin systems.

Strong carbon - noble gas covalent bond and fluxionality in hypercoordinate compounds

Thermodynamic, kinetic, and chemical bonding analysis at the coupled cluster level has been carried out for a series of hypercoordinated carbon compounds with formula CH4Ng2+ (Ng = He-Rn). Results show that these compounds could be stable at room temperature and Born-Oppenheimer molecular dynamics simulations (BOMD) in conjunction with activation energies indicate high kinetic stability. In addition, all chemical bonding descriptors agree with a strong C-Ng covalent bond and a bonding pattern similar to that of CH5+. Finally, BOMD simulations showed that these compounds are fluxional, with a continuous formation/breaking of H-H and C-H bonds. To the best of the authors' knowledge, these results represent the first series of fluxional compounds possessing a covalent bond between a main group element and a noble gas atom.

Valence Bond Theory Allows a Generalized Description of Hydrogen Bonding

This paper describes the nature of the hydrogen bond (HB), B:---H-A, using valence bond theory (VBT). Our analysis shows that the most important HB interactions are polarization and charge transfer, and their corresponding sum displays a pattern that is identical for a variety of energy decomposition analysis (EDA) methods. Furthermore, the sum terms obtained with the different EDA methods correlate linearly with the corresponding VB quantities. The VBT analysis demonstrates that the total covalent-ionic resonance energy (RECS) of the HB portion (B---H in B:---H-A) correlates linearly with the dissociation energy of the HB, ΔEdiss. In principle, therefore, RECS(HB) can be determined by experiment. The VBT wavefunction reveals that the contributions of ionic structures to the HB increase the positive charge on the hydrogen of the corresponding external/free O-H bonds in, for example, the water dimer compared with a free water molecule. This increases the electric field of the external O-H bonds of water clusters and contributes to bringing about catalysis of reactions by water droplets and in water-hydrophobic interfaces.

Revisiting the origin of the bending in group 2 metallocenes AeCp2 (Ae = Be-Ba)

Metallocenes are well-established compounds in organometallic chemistry, and can exhibit either a coplanar structure or a bent structure according to the nature of the metal center (E) and the cyclopentadienyl ligands (Cp). Herein, we re-examine the chemical bonding to underline the origins of the geometry and stability observed experimentally. To this end, we have analysed a series of group 2 metallocenes [Ae(C₅R₅)₂] (Ae = Be-Ba and R = H, Me, F, Cl, Br, and I) with a combination of computational methods, namely energy decomposition analysis (EDA), polarizability model (PM), and dispersion interaction densities (DIDs). Although the metal-ligand bonding nature is mainly an electrostatic interaction (65-78%), the covalent character is not negligible (33-22%). Notably, the heavier the metal center, the stronger the d-orbital interaction with a 50% contribution to the total covalent interaction. The dispersion interaction between the Cp ligands counts only for 1% of the interaction. Despite that orbital contributions become stronger for heavier metals, they never represent the energy main term. Instead, given the electrostatic nature of the metallocene bonds, we propose a model based on polarizability, which faithfully predicts the bending angle. Although dispersion interactions have a fair contribution to strengthen the bending angle, the polarizability plays a major role.

Comment on "The oxidation state in low-valent beryllium and magnesium compounds" by M. Gimferrer, S. Danés, E. Vos, C. B. Yildiz, I. Corral, A. Jana, P. Salvador and D. M. Andrada, Chem. Sci. 2022, , 6583

We challenge the assignment of the oxidation state +2 for beryllium and magnesium in the complexes Be(cAAC^Dip)₂ and Mg(cAAC^Dip)₂ as suggested by Gimferrer et al., Chem. Sci. 2022, 13, 6583 in a recent study. A careful review of the data in the ESI contradicts their own statement and shows that the results support the earlier suggestion that the metals are in the zero oxidation state. The authors reported wrong data for the excitation energies of Be and Mg to the ¹D (np²) state. We also correct some misleading statements about the EDA method.

Hitting the Bull's Eye: Stable HeBeOH+ Complex

It is now known that the heavier noble gases (Ng=Ar-Rn) show some varying degrees of reactivity with a gradual increase in reactivity along Ar-Rn. However, because of their very small size and very high ionization potential, helium and neon are the hardest targets to crack. Although few neon complexes are isolated at very low temperatures, helium needs very extreme situations like very high pressure. Here, we find that protonated BeO, BeOH⁺ can bind helium and neon spontaneously at room temperature. Therefore, extreme conditions like very low temperature and/or high pressure will not be required for their experimental isolation. The Ng-Be bond strength is very high for their heavier homologs and the bond strength shows a gradual increase from He to Rn. Moreover, the Ng-Be attractive energy is almost exclusively originated from the orbital interaction which is composed of one Ng(s/p_σ )→BeOH⁺ σ-donation and two weaker Ng(p_π )→BeOH⁺ π-donations, except for helium. Helium uses its low-lying vacant 2p orbitals to accept π-electron density from BeOH⁺ . Previously, such electron-accepting ability of helium was used to explain a somewhat stronger helium bond than neon for neutral complexes. However, the present results indicate that such π-back donations are too weak in nature to decide any energetic trend between helium and neon.

Formation of exceptional monomeric YPhos-PdCl2 complexes with high activities in coupling reactions

The use of well-defined palladium(ii) complexes as precatalysts for C-X cross-coupling reactions has improved the use of palladium catalysts in organic synthesis including large-scale processes. Whereas sophisticated Pd(ii) precursors have been developed in the past years to facilitate catalyst activation as well as the handling of systems with more advanced monophosphine ligands, we herein report that simple PdCl₂ complexes function as efficient precatalysts for ylide-substituted phosphines (YPhos). These complexes are readily synthesized from PdCl₂ sources and form unprecedented monomeric PdCl₂ complexes without the need for any additional coligand. Instead, these structures are stabilized through a unique bonding motif, in which the YPhos ligands bind to the metal through the adjacent phosphine and ylidic carbon site. DFT calculations showed that these bonds are both dative interactions with the stronger interaction originating from the electron-rich phosphine donor. This bonding mode leads to a remarkable stability even towards air and moisture. Nonetheless, the complexes readily form monoligated LPd(0) complexes and thus the active palladium(0) species in coupling reactions. Accordingly, the YPhos-PdCl₂ complexes serve as highly efficient precatalysts for a series of C-C and C-X coupling reactions. Despite their simplicity they can compete with the efficiency of more complex and less stable precatalysts.

Clarifying notes on the bonding analysis adopted by the energy decomposition analysis

We discuss the fundamental aspects of the EDA-NOCV method and address some critical comments that have been made recently. The EDA-NOCV method unlike most other methods focuses on the process of bond formation between the interacting species and not just only on the analysis of the finally formed bond. This is demonstrated using LiF as an example. There is a difference between the interactions between the initial species which form the bond and are also the final product of bond cleavage, and the interactions between the fragments in the eventually formed molecule. The flexibility of the method allows the choice of the interacting fragments which helps to identify the charge and electron configuration of the fragments which describe the bond. This is very helpful in cases where the bond may be described with several Lewis structures. We reject the idea that it would be a disadvantage to have "bond path functions" as the energy components in the EDA, which actually indicate the variability of the method. The bonding analysis in a different sequence of the bond formation gives important results for the various questions that can be asked. This is demonstrated by using CH₂, CO₂ and the formation of a guanine quartet as examples. The fact that a bond is always defined by the bound molecule, the fragments, and their states is universal and deeply physical, as we show here again for various examples. The results of the EDA-NOCV method are in full accordance with the physical mechanism of the chemical bond as revealed by Ruedenberg.

The oxidation state in low-valent beryllium and magnesium compounds

Low-valent group 2 (E = Be and Mg) stabilized compounds have been long synthetically pursued. Here we discuss the electronic structure of a series of Lewis base-stabilized Be and Mg compounds. Despite the accepted zero(0) oxidation state nature of the group 2 elements of some recent experimentally accomplished species, the analysis of multireference wavefunctions provides compelling evidence for a strong diradical character with an oxidation state of +2. Thus, we elaborate on the distinction between a description as a donor-acceptor interaction L(0) ⇆ E(0) ⇄ L(0) and the internally oxidized situation, better interpreted as a diradical L(-1) → E(+2) ← L(-1) species. The experimentally accomplished examples rely on the strengthened bonds by increasing the π-acidity of the ligand; avoiding this interaction could lead to an unprecedented low-oxidation state.

Collective interactions among organometallics are exotic bonds hidden on lab shelves

Recent discovery of an unusual bond between Na and B in NaBH₃^- motivated us to look for potentially similar bonds, which remained unnoticed among systems isoelectronic with NaBH₃^-. Here, we report a novel family of collective interactions and a measure called exchange-correlation interaction collectivity index (ICI_XC; [Formula: see text]) to characterize the extent of collective versus pairwise bonding. Unlike conventional bonds in which ICI_XC remains close to one, in collective interactions ICI_XC may approach zero. We show that collective interactions are commonplace among widely used organometallics, as well as among boron and aluminum complexes with the general formula [M^a+AR₃]^b- (A: C, B or Al). In these species, the metal atom interacts more efficiently with the substituents (R) on the central atoms than the central atoms (A) upon forming efficient collective interactions. Furthermore, collective interactions were also found among fluorine atoms of XF_n systems (X: B or C). Some of organolithium and organomagnesium species have the lowest ICI_XC among the more than 100 studied systems revealing the fact that collective interactions are rather a rule than an exception among organometallic species.

Diarylpnictogenyldialkylalanes─Synthesis, Structures, Bonding Analysis, and CO2 Capture

Several new diphenylamino- and diphenylphosphanyldialkylalanes are reported, which were characterized in solution and in the solid state, assisted by in-depth bonding analysis within the DFT framework. In the case of bulky alkyl substituents on the aluminum atom, the species are stable in their monomeric form and were structurally characterized by single crystal X-ray diffraction, expanding the relatively small field of monomeric pnictogenylalanes. In the case of oligomeric diphenylpnictogenyldimethylalanes, their reactivity toward different σ-donor ligands was studied, and several examples of monomeric adducts could be structurally characterized, including the first cyclic(alkyl)(amino)carbene complexes. The reactivity of these CAAC complexes, their oligomeric precursors, and an unstabilized monomeric aminoalane toward CO₂ was probed, leading to different insertion products that could be characterized. Additionally, the mechanism was elucidated by DFT calculations.

12-Membered Ring Carbides with Stabilization of Actinide Atoms

Actinide (Th and U) carbides as the potential nuclear fuels in nuclear reactors require basic research in order to understand the thermodynamic stability and performance of these substances. Here we report the structural characterization and bonding analyses of [C₁₂], ThC₁₂, and UC₁₂ clusters via a global-minimum search combined with relativistic quantum chemistry calculations to elucidate the stability and bonding nature of An-C bonds. We predict that these [C₁₂], ThC₁₂, and UC₁₂ compounds have a planar structure with C_6h, D_12h, and D_12h symmetry, respectively. [C₁₂] has a hyperconjugation structure containing alternating single and double bonds. The significant stabilization when forming AnC₁₂ predominantly comes from the electrostatic interaction between An⁴⁺ and [C₁₂]^4- and also from a certain degree of orbital interaction between the An 5f6d7s valence shell and [C₁₂] π orbitals. The covalent character of the An-C bonds exhibits a direct in-plane σ-type overlap of the C 2p-derived MOs of [C₁₂] and the An 5f_ϕ AO, thus leading to an unprecedented electronic configuration of d¹f¹ for U in UC₁₂. Our results present an example of the novel properties that can be expected for actinide compounds and would provide the knowledge required to obtain novel structures of AnC₁₂ in future experiments.

Classical Electrostatics Remains the Driving Force for Interanion Hydrogen and Halogen Bonding

Interanion hydrogen bonding (IAHB) and halogen bonding (IAXB) have emerged as a counterintuitive linker in a range of fascinating applications. Despite the overall repulsive (positive) binding energy, anions are trapped in a local minimum with its corresponding transition state (TS) preventing dissociation. In other words, the adduct of anions is metastable. Seemingly, the electrostatic paradigm and force field description of hydrogen/halogen bonding (HB/XB) are challenged, because of the preconceived Coulombic repulsion. Aiming at an insightful understanding of these interanion phenomena, we employed the energy decomposition approach based on the block-localized wavefunction method (BLW-ED) to investigate a series of exemplary interanion complexes. As expected, the key distinction from the conventional HB/XB lies in the electrostatic interaction, which is not increasingly repulsive as anions gradually approach to each other. Rather, there is a Coulombic barrier at a certain point. After this point, the electrostatic repulsion diminishes with the decreasing distance between anions. Differently, other energy components vary monotonically just like in conventional cases. The nonmonotonic characteristic of the electrostatic interaction in interanion complexes was reproduced using the multipole expansion in AMOEBA polarizable force field in which the state-specified atomic multipoles were adopted. This suggests that the nonmonotonicity can be well interpreted by classical electrostatic theory and there is no conceptual difference between conventional HB/XB and IAHB/IAXB. The stability of IAHB/IAXB depends on the competition between the local attractive HB/XB and the global Coulombic repulsion of net charges, though there is cooperativity between these two contrasting forces. This concise model was supported by the attractive IAHB/IAXB in modified molecular capsules, which exhibit strong quadruple HB/XBs and a considerable distance between charged substituents.