All-metal aromaticity. I. Smallest triangular aromatic cyclo-clusters

“PubChem, the largest public database of chemical compounds, contains almost 110 million structures. There’s an estimate that two-thirds of them are fully or partially aromatic. The problem with aromaticity is that, despite 200 years of research, there’s no clear definition, rules or experiments that can identify it among all compounds. But with more than 20 different types of aromaticity described so far, how close are chemists to finding a definition that unites all of them?” Krämer, 2021 [1]. In 2025, I published a paper of organic aromaticity [2], which can explain the all-metal aromaticity.

Type 1: Bi₃^3--like triangular aromatic clusters of all lone pairs (σ-electrons)

Recently, Ding et al.  reported in 2026 the cyclo-Bi₃³⁻ − ring which is perfectly (or highly) symmetric, and as an isolated species, as shown in Figure 1. “It is the heaviest three-membered bismuth atoms (purple) between two uranium atoms (green) to date. Its aromaticity is predominantly driven by σ-electrons along the metal-metal bonds rather than π-electrons” [3].

All-metal aromaticity has been classified to  (s)-, π(p)-, δ(d)- and ɸ(f)-electron delocalization. Does the σ-aromaticity mean the σ-covalent bond or the atomic electron s-orbit? Solá et al. pointed out in 2025 that there is no experimental evidence demonstrating the existence of electron delocalization [8]. Electrons within a molecule must undergo high-speed orbital motion; otherwise, they would be drawn into the atomic nucleus. However, delocalization means that electrons are spread out (diffuse) over several atomic nuclei via overlapping orbitals. This concept does not stand up to close scrutiny. What exactly are Ding’s σ-electrons? The key issue is the failure to highlight the role of the lone pairs in the ring current. The electron configuration of the Bi atom indicates that the electrons participating in the cyclo-Bi₃ framework contains exclusively the 6p³ electrons (not s-electrons or σ-electrons). Each bismuth (Bi) atom possesses three unpaired electrons; two of these form covalent bonds with neighboring atoms, while the remaining unpaired electron on each atom will combine with an incoming electron to form a lone pair. Under thermal vibration, the lone pairs of electrons constantly shift their positions, forming a ring current and inducing a whirl-shaped magnetic field around the ring skeleton. This is exactly the same as in the benzene ring (Figure 2) [2].

The induced magnetic field protects the molecular ring and generates special aromatic stability. The active electrons obey Hückel’s 4n+2 electron counting rule (n=1) in Bi₃^3- cluster and in benzene ring. The Bi-Bi distance in Bi₃^3- ring is 2.95Å, shorter than the Bi-Bi single bond length 3.02Å and the C-C distance in benzene is 1.39Å, shorter than C-C single bond length 1.54Å. This is a characteristic feature of aromatic rings, which shorten the bond lengths. As long as the lone pairs are viewed as small π-electrons, the all-metal aromaticity is easily understood. It should also be noted that no chemical bond is formed between the uranium atom and the Bi₃³⁻ cluster; instead, they are held together by coordination. Distinguishing between chemical bonds and coordinate bonds is crucial for understanding all-metal aromaticity.

Among triangular aromatic clusters, there are also many examples of ring currents formed by three lone pairs of electrons—a phenomenon known as "all-σ-aromaticity.", as shown in Figure 3.

In 2007, Averkiev and Boldyrev reported that Hf₃ cluster is triply (σ-, π-, and δ-) aromatic [9]. In fact, its ring current involves only two d-electrons and two s-electrons from each Hf atom. There is nothing to do with p-electrons. As long as electrons leave the atomic core, they then lose their s-, p-, d-, and f-characteristics. All electrons are equivalent. This is a current challenge in understanding all-metal aromaticity. The Bi atom can offer five active electrons, 6s² 6p² 6p¹. When one electron is removed from each Bi site, the Bi₃³⁺ species is valence isoelectronic with Hf₃ and shows the same all-lone-pair aromaticity (σ-aromaticity). The carbon atom has four active electrons 2s² 2p². Three of them formed three covalent bonds with one hydrogen atom and two neighbor carbon atoms. On each C-site remains one unpaired electron. After receiving oncoming electron, each C-site forms a lone pair, which is valence isoelectronic with Hf₃. In all cases, the shifting lone-pair of electrons along the skeleton generates a ring current and an associated whirl-shaped magnetic field that protects the rings, thereby conferring stability. Ring currents shorten the bond lengths. Therefore, there is no need to distinguish between organic aromaticity and metallic aromaticity. In everyday matter, there are only two types of oppositely charged particles. The positively charged nuclei are stable; the various chemical and physical properties are mainly related to the negatively charged electrons, especially the outermost active electrons.

Type 2, C₃H₃⁺-like species of π-electrons and cation.

In 2025, I published a paper “The movement of two parallel unpaired electrons in benzene and aromatic compounds” [2]. It mentions the formation of the aromatic current in C₃H₃⁺ cluster.  The thermal vibration and the attraction of positive charge for π-electrons causes continuous shifting of the two parallel unpaired electrons. along the skeleton, generating a ring current and a magnetic field, which ultimately results in aromatic stability. The ¹H-NMR 11.2 ppm indicates a strong aromatic current comparing to benzene (δ=7.26 ppm). The ¹H NMR chemical shift induced by the π-electrons of the double bond is approximately 5.7 ppm. This indicates that for both C₃H₃⁺ and benzene, two components contribute to the ring magnetic field: π-electrons and ring currents. The shifting of unpaired electron orbits can be caused by the electron-electron repulsion resulting from thermal vibrations, or by the attraction of the electron orbits and the positive charge. The ring current induced by the positive charge is stronger. Cyclo-Bi₃⁺ has completely the same electronic structure as cyclo-C₃H₃⁺, and the ring current shortened the bond length, shown in Figure 4.

There are many other such triangular aromatic species. Figure 5 illustrates Au₃⁺, Ag₃⁺, Cu₃⁺, and B₃⁺ [3]. One electron completely leaves the atomic core, forming a positive charge, while the other two unpaired electrons combine to form π-electrons around two atomic cores; such an electronic structure is identical to that of cyclo-C₃H₃⁺. Ring currents shorten the bond lengths.

When determining these electronic structures of the clusters, one should first examine the electron configurations of the atoms to identify which electrons might participate in aromatic clusters, and then consider the oxidation states, the bond lengths. These are real entities, not virtual things.

Figure 6 shows further triangular aromatic Ge₃⁺ and Si₃⁺ clusters [4].

Ge atom and Si atom have four active electrons respectively. The precursors display the existence of the double bonds. The electronic structure of the final products is identical to that of C₃H₃⁺. Ring currents shorten the bond lengths.

Regarding how cyclo-Au₃⁺ clusters actually bind to their ligands: since all three active electrons in the gold atom participate in the aromaticity of the cyclo-Au₃⁺ cluster, they are unable to form covalent bonds to ligands any more. Figure 7 shows two examples. The Au₃⁺ has no chemical bonds with surrounding compounds. The lone pairs of electrons on the ligands act as electron-donors (dative bond) to hold the whole species together [4]. In the same way, Pd has oxidation state of +5. Each atom can provide 5 active electrons. Pd-S and Pd-Pd use four valent electrons to form covalent bonds to construct the framework. Still one unpaired electron on each Pd atom. After losing one electron to aryl sulfonate, the electronic structure of Pd₃⁺ is the same as C₃H₃⁺. Three P atoms in the ligands possess lone pairs to build dative bonds to the main core. Although Pd-Pd distance (2.89 Å) in cluster is longer than Pd-Pd single bond (2.75 Å), This is likely related to the constraints of the supporting ligands [10].

Type 3, H₃⁺-like species due to two parallel unpaired electrons enveloping the three atomic cores.

H₃⁺ is the simplest aromatic polyatomic molecule. Its three protons are well bound by two electrons in an equilateral triangle structure. Havenith et al. [11] have dissected the ring-current maps and verified that H₃⁺ is σ-aromatic. No covalent bonds will form among these three protons, because forming a triangular structure requires six valence electrons. To understand this type of special aromatic cluster, one must begin with the single-electron covalent bond. Figure 8 are the two-electrons covalent σ-bond and one-electron covalent σ-bond [2].

The hypothesis regarding this structure is based on the premise that matter consists solely of positive and negative charges. The range of electron motion corresponds to the region where the electric fields generated by two positive charges undergo maximum superposition. When two electrons with opposite spins enter this region, they cancel out the orbital magnetism and form a stable, low-energy covalent bond. If only a single electron enters, a less stable one-electron covalent bond is formed—a structure that has been experimentally confirmed. Replacing the carbon atoms with hydrogen atoms and introducing an electron, the H₂⁺ one-electron covalent bond is formed, as shown in Figure 9.

This issue has puzzled scientists for years. Analogous to H₂⁺, the two electrons in H₃⁺ should circle around the region where the superposition of electric fields generated by the three positive charges is strongest. The circling two parallel unpaired electrons create whirl-shaped magnetic field to protect the cluster. Additionally, the magnetic field lines inside the ring make the proton spins to align in the same direction (ortho-configuration), which further strengthened the electron orbital magnetic field. The H₃⁺ species is the most abundantly produced interstellar molecule. There must be reasons for its relative stability.

Li₃⁺ cluster was the smallest all-metal σ-aromatic cluster with 2 delocalized σ electrons [12]. The Li₃⁺ cluster itself typically exists as a gas-phase. It should be the unique analog to H₃⁺[13]. The distance between Li-Li in clusters is 2.95 Å, indicating that no chemical bonds have formed (Li-Li single bond length is 2.65 Å). Naturally occurring lithium is composed of two stable isotopes, ⁶Li and ⁷Li, the latter being the more abundant (95.15% natural abundance), therefore the ⁷Li nucleus has spin, just like the hydrogen nucleus. These spins must align with the magnetic field within the orbit, further reinforcing the protective effect of the magnetic field on the cluster to result in relative stability, as shown in Figure 10.

The aromatic H₃⁺ and Li₃⁺ can trap noble gases (He-Kr), as shown in Figure 11 [14].

This peculiar behavior of theirs must be understood in terms of their electronic structure. The positive electric fields on the sides of H₃⁺ and Li₃⁺ are exposed, enabling them to attract the outermost electron shells of neon atoms, as shown in Figure 12. This explains why H₃⁺ and Li₃⁺ can trap neutral noble gases.

In fact, the ring magnetic fields in H₃⁺ and Li₃⁺ arise from two electron orbits with identical spins; they do not originate from the ring currents characteristic of a benzene ring. There is no movement of π-orbits associated with double bonds within the structure. At best, the aromatic ring currents of H₃⁺ an Li₃⁺ can be regarded as an enlarged version of a lone pair of electrons. Few such clusters form in nature. It is reported that relatively stable Na₃⁺ species can also be formed. They have two active valence electrons to participate in the triangular clusters.

Although they are all cyclic trimetallic aromatic cationic clusters, H₃⁺ and Li₃⁺ belong to the same class, distinct from Au₃⁺, Ag₃⁺, Cu₃⁺, Pd₃⁺, and B₃⁺, which contribute three active electrons of each atom to participate in the triangular aromatic clusters.

Type 4, Na₂Ga₃H₃-like neutral triangular aromatic core.

In 1996, Robinson’s group published a paper “Are Cyclogallenes [M₂(GaH)₃] (M = Li, Na, K) Aromatic?” [6]. Upfield changes in the chemical shifts for the alkali metal atoms over and under the ring plane are taken as strong evidence for ring currents in the cyclogallene moiety. To understand the electronic structure of this aromatic compound, it is necessary to correctly understand the structures of conventional double bond and H₆B₂ banana bond. Figure 13 shows H₄C₂ double bond and H₆B₂ double bond. ¹H-NMR confirmed the two parallel unpaired electrons in the π-orbits separated by σ-bond for H₄C₂.

However, the structure of H₆B₂ has never been associated with double bonds. In 1976, Lipscomb introduced the concept of "banana bonds" (i.e., three-center, two-electron bonds) [15]. This concept continues to exert a profound influence on molecular orbital theory to this day. Based on NMR data, orbital magnetism arising from π-electrons exists in the H₆B₂ molecule. The two bridging hydrogens (H_b) are located at the interior diamagnetic field region of the orbits and the four terminal hydrogens (H_t) are located at exterior paramagnetic field region. The ¹H-NMR of H_b at -2.5 ppm and H_t at +4.5 ppm prove precisely that point. It is currently experimental evidence demonstrating that H₆B₂ possesses a double-bond structure. Each boron atom has three valence electrons, all of which are utilized in covalent bonds. The two π-electrons are donated from over and under hydrogen atoms, therefore, the π-electrons do not affect the B–B single bond length (1.75 Å). The real B=B double bond length is about 1.56 Å [16], while the B=B dianion double bond length is 1.77 Å. This experimental fact further confirms that the H₆B₂ has double bond structure, rather than a banana bond. This also touches upon the definition of basic chemical bonds. According to molecular orbital theory, the π-bond in a double bond is formed by the overlap of p-orbitals. This is a consequential error stemming from Schrödinger's flawed atomic orbital theory. Once an electron leaves the atomic core, it no longer retains the characteristics of p-, d-, and f-sub-orbits. Both external electrons and the electrons of the atom itself can form π-orbits. It can be said that the structure of H₆B₂—a subject of long-standing dispute—has now been correctly explained.

Figure 14 shows Na₂H₄Ga₂ and Na₂H₃Ga₃ compounds.

The structure of Na₂H₄Ga₂ [17] can be fully explained by drawing an analogy to the double-bond structure of H₆B₂. Two Na atoms just like two H_b atoms donate π-electrons. The ¹H-NMR chemical shift of the four protons (δ=6.8-7.2 ppm) confirmed the presence of π-orbital magnetism. Same as H₆B₂, Ga-Ga distance in Na₂H₄Ga₂ is nearly the Ga-Ga single bond length. When three Ga atoms are covalently bonded to form a triangular ring, each Ga atom can still be able to bond a hydrogen atom [18]. Cyclo-Ga₃H₃ is electrically neutral and exhibits no ring current. Two Na atoms positioned above and below the plane of the ring donate two electrons to form larger π-electrons; ¹H-NMR analysis reveals orbital magnetism (δ=4.0-7.0 ppm), consistent with the observations made by Robinson et al. in 1996 [6]. The Na₂Ga₃H₃ has a trigonal bipyramidal shape. The Ga-Ga distance in triangular ring is almost the same as Ga-Ga single bond. This also indicates that the ring current and ring magnetic field are not provided by Ga atoms, but originate from electrons donated by Na atoms.

Figure 15 [19] is a top view of a real complex of Ga₃^2- core. In fact, the two Na atoms play important roles for the ring current and aromatic stability.

Conclusively, the two parallel unpaired electrons circling above and below the Ga-triangular plane can be regarded as enlarged π-electrons or lone pair among three atomic cores.

Robinson et al. conducted theoretical calculation in the metallic ring of group 13, e.g. Ga₃^2-. They believed that cyclogallenes were metallic analogues of the smallest main group triangular aromatic structure: cyclopropenium cation (C₃H₃⁺), as shown in Figure 16 [20].

It must be clearly stated here that these two species are different. There is an intrinsic double bond in C₃H₃⁺.  The ¹H-NMR chemical shift of a intrinsic double bond is approximately δ = 5.7 ppm. This double bond continuously shifts, generating a ring current. During ¹H-NMR measurement, the magnetic field environment experienced by hydrogen proton is B₀ (external magnetic field) + B_π (π-orbital magnetic field) + B_ring (ring current magnetic field). Finally, the chemical shift is δ=11.1 ppm. The protons in Na₂Ga₃H₃ experience B₀ + B_ring (δ=4.0-7.0 ppm). The molecular orbital theory obscures electron spin, electron orbital motion, and the orbital magnetic fields induced by two parallel unpaired electrons—all of which are fundamental to the origin of aromaticity.

In 2022, Kysliak et al. published a paper “A Planar Five-Membered Aromatic Ring Stabilized by Only Two π-Electrons”. Cyclopentagallene was isolated as green crystals and its molecular solid-state structure was established by X-ray diffraction analysis, as shown in Figure 17 [7].

The pentagonal bipyramidal structure of K₂Ga₅H₅ bears a striking resemblance to the trigonal bipyramidal structure of Na₂Ga₃H₃. This strongly corroborates the earlier hypothesis regarding the presence of expanded π-orbitals in the trigonal bipyramidal Na₂Ga₃H₃ cluster. Both Ga₃H₃ and Ga₅H₅ are neutral species unrelated to orbital magnetism; the two Na (K) atoms contribute two electrons.

Facit:

The analysis of triangular aromatic clusters relies first on X-ray structural data to understand the surrounding environment. If the interatomic distance within a core are shorter than those of a single bond, one can generally conclude that a ring current is present. Ideally, NMR data should be obtained, as NMR provides definitive evidence of the magnetic field generated by an aromatic ring current. Finally, by examining electron configurations and oxidation states, one can determine which electrons participate in the covalent bonding of the triangular framework and which contribute to the ring current.

Type 1. All-lone pairs: Bi₃^3-, P₃^3-, Sb₃^3-, (CH)₃^3-, Hf₃⁰, Te₃⁰, Po₃⁰, Bi₃³⁺.

Type 2. π-electrons and cation: (CH)₃⁺, Bi₃⁺, Sb₃⁺, Au₃⁺, Ag₃⁺, Cu₃⁺, B₃⁺, Ge₃⁺, Si₃⁺, Pt₃⁺, Pd₃⁺.

Type 3. Two parallel unpaired electrons envelop three cations: (H⁺)₃^2-, (Li⁺)₃^2-.

Type 4. Neutral triangular core: B₃H₃, Al₃H₃, Ga₃H₃ (Ga₅H₅), In₃H₃. Donators: Li₂, Na₂, K₂ bipyramid construction.

The key factor of the triangular aromatic clusters is the two parallel unpaired electrons creating ring current and whirl-shaped magnetic field to stabilize the skeletons of the species.

This work provides a comprehensive overview of how traditional aromaticity concepts—typically reserved for carbon rings like benzene—extend to inorganic and all-metal aromatic compounds.

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