The Electronic Structure of the Al3(-) Anion: Is it Aromatic?

Unveiling the quantum secrets of triel metal triangles: a tale of stability, aromaticity, and relativistic effects

Low lying electronic states of Al3-, Ga3-, In3-, and Tl3- have been characterized using high level multiconfigurational quasi degenerate perturbation theory on the multiconfigurational self-consistent field. Among these species, the singlet states emerge as the predominant energy minima, displaying remarkable stability. However, within the Tl3- series, our investigation leads to the identification of the high-spin , as the most stable spin state, a result corroborated by previous experimental detection via photoelectron spectroscopy. Similarly, we have also identified the singlet state of In3- as the signal detected previously experimentally. By applying Mandado's rules and an array of aromaticity indicators, it is conclusively demonstrated that both the singlet and quintet states exhibit multiple-fold aromaticity, while the triplets exhibit conflicting aromaticity. Furthermore, this investigation highlights the significant impact of relativistic effects, as they enhance the stability of the state relative to its singlet counterpart. These findings shed new light on the electronic structures and properties of these ions, offering valuable insights into their chemical behavior and potential applications.

Advances for Triangular and Sandwich-Shaped All-Metal Aromatics

Much experimental work has been contributed to all-metal σ, π and δ-aromaticity among transition metals, semimetallics and other metals in the past two decades. Before our focused investigations on the properties of triangular and sandwich-shaped all-metal aromatics, A. I. Boldyrev presented general discussions on the concepts of all-metal σ-aromaticity and σ-antiaromaticity for metallo-clusters. Schleyer illustrated that Nucleus-Independent Chemical Shifts (NICS) were among the most authoritative criteria for aromaticity. Ugalde discussed the earlier developments of all-metal aromatic compounds with all possible shapes. Besides the theoretical predictions, many stable all-metal aromatic trinuclear clusters have been isolated as the metallic analogues of either the σ-aromatic molecule's [H3]+ ion or the π-aromatic molecule's [C3H3]+ ion. Different from Hoffman's opinion on all-metal aromaticity, triangular all-metal aromatics were found to hold great potential in applications in coordination chemistry, catalysis, and material science. Triangular all-metal aromatics, which were theoretically proved to conform to the Hückel (4n + 2) rule and possess the smallest aromatic ring, could also play roles as stable ligands during the formation of all-metal sandwiches. The triangular and sandwich-shaped all-metal aromatics have not yet been specifically summarized despite their diversity of existence, puissant developments and various interesting applications. These findings are different from the public opinion that all-metal aromatics would be limited to further applications due to their overstated difficulties in synthesis and uncertain stabilities. Our review will specifically focus on the summarization of theoretical predictions, feasible syntheses and isolations, and multiple applications of triangular and sandwich shaped all-metal aromatics. The appropriateness and necessities of this review will emphasize and disseminate their importance and applications forcefully and in a timely manner.

Evolution of Triangular All-Metal Aromatic Complexes from Bonding Quandaries to Powerful Catalytic Platforms

This manuscript describes an overview on the literature detailing the observation of trinuclear complexes that present delocalized metal-metal bonds similar to those of regular aromatics, which are formed combining main group elements. A particular emphasis is given to the structural and electronic features of aromatic clusters that are sufficiently stable to allow their isolation. In parallel to the description of their key bonding properties, the work presents reported catalytic applications of these complexes, which already span from elaborated C-C-forming cascades to highly efficient cross-coupling methods. These examples present peculiar aspects of the unique reactivity exerted by all-metal aromatic complexes, which can often be superior to their established, popular mononuclear peers in terms of chemoselectivity and chemical robustness.

Is Aromaticity a Driving Force in Catalytic Cycles? A Case from the Cycloisomerization of Enynes Catalyzed by All-Metal Aromatic Pd3+ Clusters and Carboxylic Acids

The work details a mechanistic study based on density functional theory modeling on the cycloisomerization of polyunsaturated substrates catalyzed by all-metal aromatic tripalladium complexes and carboxylic acids. These clusters are an emerging class of catalysts for a variety of relevant transformations, including C-C forming processes that occur under mild conditions and display synthetic features complementary to those of established mononuclear complexes. This study is the first computational one devoted to the comprehension of the series of elementary steps involved in a synthetic transformation catalyzed by an all-metal aromatic complex. Present results confirm previous experimental hints on the striking mechanistic differences exerted by these clusters with respect to the usual cyclization pathways of related substrates. Moreover, the catalytic cycle involving present all-metal aromatic clusters closely parallels the mechanism of the aromatic substitution of regular arenes.

Unraveling the stability of cyclobutadiene complexes using aromaticity markers

Cyclobutadiene (CBD) is the paradigmatic antiaromatic molecule but is known to form highly stable aromatic complexes, e.g. CBD-Fe(CO)3. This intriguing reversal of aromaticity from antiaromatic to aromatic terrain during the complexation process cannot be appropriately handled with single-reference-based theoretical techniques. We explore this aromaticity reversal, for the first time, by a detailed aromaticity analysis using magnetically induced current densities (MICD) and nucleus independent chemical shifts (NICS) using genuine ab initio multi-reference wavefunction-based theory. We trace the dramatic change of aromaticity for a prototypical cyclobutadiene complex, CBD-CH+ (CH+Fe(CO)3), considering a 3D potential energy surface for two independent parameters, namely the approach of CH+ and the automerization cross-section of cyclobutadiene. The 3D potential energy surfaces indicate the presence of a conical intersection/avoided crossing between the ground and the first excited state. The plot of aromaticity indices and the corresponding numerical values show that the change of aromaticity indices is drastic around the conical intersection/avoided crossing and automerization of cyclobutadiene plays a crucial role in the formation of cyclobutadiene complexes. Computations on analogous CBD-Be and CBD-CO systems (Be/COFe(CO)3) emphasize the generality of the conclusions drawn from the CBD-CH+ system.

Electronic Structure and Electron Delocalization in Bare and Dressed Boron Pentamer Clusters

The electronic structures of the lowest energy spin-states of the cationic, neutral and anionic bare boron pentamer clusters have been investigated by means of high level multiconfigurational type calculations, in view of the large static and dynamical electron correlation effects for these species. We found that B 5 + resembles a singlet spin-state perfect pentagon, which bears no intra-annular chemical bonding interactions, as shown by our analysis of the electron delocalization carried out in terms of the normalized Giambiagi ring-current index, and the total and adjacent atom-pair delocalization indices. However, its lowest-energy triplet and quintet spin-state isomers have C2v symmetry, with large intra-annular chemical bonding interactions. This geometrical feature extends to both the neutral and the anionic species. Namely, the lowest-energy isomers of boron pentamer neutral and anionic clusters have peripheral and intra-annular sizable bonding interactions reflected in the delocalization of both π- and σ-type valence natural orbitals over the whole molecular plane, which impart large structural stability. In accordance to our calculations, the lowest energy triplet spin-state isomer of the anionic boron pentamer cluster has C2 symmetry, and consequently, it should show optical activity. Finally, we have studied the change of the geometrical structure of the boron pentamer clusters from planar to compact three-dimensional structures caused by the bonding of ligands to the boron atoms. Our explicit all-electron calculations have been rationalized in terms of the shell-closure of the delocalized valence orbitals of the clusters as predicted by the jellium model extended to nonspherical confinement potentials, circumscribing the role of the ligand to modulate the total number of valence electrons assigned to the core cluster.

How do the Hückel and Baird Rules Fade away in Annulenes?

Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.

Electron Delocalization in Planar Metallacycles: Hückel or Möbius Aromatic?

In this work the relationship between the formal number of π-electrons, d-orbital conjugation topology, π-electron delocalization and aromaticity in d-block metallacycles is investigated in the context of recent findings concerning the correlation of π-HOMO topology and the magnetic aromaticity indices in these species. It is demonstrated that for π-electron rich d-metallacycles the direct link between aromaticity, the number of π-electrons and the frontier π-orbital topology does not strictly hold and for such systems it is very difficult to unambiguously associate their aromaticity with the "4n+2" (Hückel) and "4n" (Möbius) rules. It is also shown that the recently proposed electron density of delocalized bonds (EDDB) method can successfully be used not only to quantify and visualize aromaticity in such difficult cases, but also - in contrast to magnetic aromaticity descriptors - to provide a great deal of information on the real role of d-orbitals in metallacycles without the ambiguity of bookkeeping of electrons in the π-subsystem of the molecular ring. Interestingly, some of the metallacycles studied cannot be classified exclusively as Hückel or Möbius because they have a hybrid Hückel-Möbius or even quasi-aromatic nature.

The behavior of the aluminum trimer when combining with different superatom clusters

The interaction between the aluminum trimer and representative (super)halogens X (X = F, LiF₂, BeF₃, BF₄) and (super)alkalis M (M = Li, FLi₂, OLi₃, NLi₄) has been theoretically investigated at the MP2/6-311+(3df) level. Various geometrical structures were obtained for the resulting Al₃-X and Al₃-M superatom compounds, respectively. Natural bond orbital analysis reveals that the Al₃ moiety exists in a cationic state in Al₃-X while in an anionic state in Al₃-M compounds. And the charge transfer between Al₃ and (super)atoms is found to be enhanced in either polar or nonpolar solvent. The studied superatom compounds feature large bond energies, binding energies, and HOMO-LUMO gaps, which not only reflect their stability but indicate strong interactions between Al₃ and (super)atoms. Although the solvent effect is not significant for the stability of Al₃-X, the Al₃-superalkali compounds can be better stabilized in the presence of solvent molecules. In addition, these superatom compounds exhibit aromaticity both in the gas phase and in solution.

The electron density of delocalized bonds (EDDB) applied for quantifying aromaticity

In this study the recently developed electron density of delocalized bonds (EDDB) is used to define a new measure of aromaticity in molecular rings. The relationships between bond-length alternation, electron delocalization and diatropicity of the induced ring current are investigated for a test set of representative molecular rings by means of correlation and principal component analyses involving the most popular aromaticity descriptors based on structural, electronic, and magnetic criteria. Additionally, a qualitative comparison is made between EDDB and the magnetically induced ring-current density maps from the ipsocentric approach for a series of linear acenes. Special emphasis is given to the comparative study of the description of cyclic delocalization of electrons in a wide range of organic aromatics in terms of the kekulean multicenter index KMCI and the newly proposed EDDB^k index.

Electron correlation effects in third-order densities

The electronic energy of a system of fermions can be obtained from the second-order reduced density matrix through the contracted Schrödinger equation or its anti-Hermitian counterpart. Both energy expressions depend on the third-order reduced density matrix (3-RDM) which is usually approximated from lower-order densities. The accuracy of these methods depends critically on the set of N-representability conditions enforced in the calculation and the quality of the approximate 3-RDM. There are no benchmark studies including most 3-RDM approximations and, thus far, no assessment of the deterioration of the approximations with correlation effects has been performed. In this paper we introduce a series of tests to assess the performance of 3-RDM approximations in a model system with varying electron correlation effects, the three-electron harmonium atom. The results of this work put forward several limitations of the currently most used 3-RDM approximations for systems with important electron correlation effects.

The aromatic character of [10]annulenes and dicupra[10]annulenes from current density calculations

We have investigated the aromatic properties of seven low-lying isomers of [10]annulene and of the recently synthesized dicupra[10]annulene compounds that were crystallised with two or four lithium counterions (Wei et al., J. Am. Chem. Soc., 2016, 138, 60–63).

The role of the long-range exchange corrections in the description of electron delocalization in aromatic species

In this article, we address the role of the long-range exchange corrections in description of the cyclic delocalization of electrons in aromatic systems at the density functional theory level. A test set of diversified monocyclic and polycyclic aromatics is used in benchmark calculations involving various exchange-correlation functionals. A special emphasis is given to the problem of local aromaticity in acenes, which has been a subject of long-standing debate in the literature. The presented results indicate that the noncorrected exchange-correlation functionals significantly overestimate cyclic delocalization of electrons in heteroaromatics and aromatic systems with fused rings, which in the case of acenes leads to conflicting local aromaticity predictions from different criteria. © 2017 Wiley Periodicals, Inc.

The aromaticity of dicupra[10]annulenes

The aromaticity of dicupra[10]annulenes closely resembles that of naphthalene.

An electronic aromaticity index for large rings

We introduce a new electronic aromaticity index, AV1245, consisting of an average of the 4-center indices along the ring that keep a positional relationship of 1, 2, 4, 5.

The stability of biradicaloid versus closed-shell [E(μ-XR)]2 (E = P, As; X = N, P, As) rings. Does aromaticity play a role?

High-level CASSCF calculations, supplemented with MCQDPT ab initio calculations, demonstrate that the [E(μ-XH)]₂ (E = P, As; X = N, P, As) compounds possess one planar and one butterfly-like isomers.

Planar vs. three-dimensional X62−, X2Y42−, and X3Y32− (X, Y = B, Al, Ga) metal clusters: an analysis of their relative energies through the turn-upside-down approach

Despite the fact that B and Al belong to the same group 13 elements, the B₆²⁻ cluster prefers the planar D_2h geometry, whereas Al₆²⁻ favours the O_h structure, which is caused by orbital interactions.