All-metal aromaticity. II. Square-planar aromatic clusters

Solá noted in 2017: “The adjective added to aromaticity in each case helps to describe a particular situation. In a sense, they are totally justified, however, the existence of so many types of aromaticity can be perceived as hectic.” [2].

As reported [3], Li et al. discovered the first all-metal aromatic cluster in 2001—the square-planar Al₄²⁻ dianion [4]. Aromaticity is a concept invented to account for the unusual stability of an important class of organic molecules: the aromatic compounds The discovery of Al₄^2- dianion is one of the achievements regarding all-metal aromaticity from Professor Boldyrev's research group. However, Nobel laureate Prof. Hoffmann expressed strong skepticism regarding the aromaticity of Al₄²⁻, arguing that the species lacked sufficient stability [5]. Prof. Boldyrev insisted on claiming that the square-planar Al₄^2– indeed fulfills all the criteria for aromaticity: Hückel’s 4n + 2 (n = 0) π electrons, bond equalization, magnetic shielding, and even high resonance stabilization energy [6].

Electrons within matter must undergo high-speed (10⁶ m/s) orbital motion; otherwise, they would be drawn into the positively charged atomic nucleus. This is an important yet overlooked concept in materials science. In my 2025 paper, "The movement of two parallel unpaired electrons in benzene and aromatic compounds," I provide a detailed discussion of a wide variety of aromatic organic compounds by taking the orbital motion of electrons into account [1]. The ring current and its induced magnetic field are the necessary and sufficient conditions for the existence of aromaticity.

Figure 1 presented dilithium salts of cyclobutadiene dianion pubIished by T. Matsuo and A. Sekiguchi in 2004 [7], along with 2π electrons in a double bond and two lone pairs with 4electrons that I added. The NMR result shows clearly ring current induced magnetic field in the square-planar core by the chemical shift of Li at -5.07 ppm.

In the 2001 article [4], Boldyrev proposed that Al₄²⁻ exhibits characteristics of aromaticity with two delocalized π electrons (thus following the 4n+2 electron-counting rule, with n=0). He offered no explanation about the effect of the two negative charges. In the 2002 article [8], Boldyrev stated: “We believe that the high resonance energies in Na₂Al₄ and in Na₂Ga₄ are due to the presence of three completely delocalized bonds, one π-bond and two σ-bonds, thus confirming the presence of π- and σ-aromaticity.” What do the π-bond and σ-bond refer to here? In 2011, Solà group reported that Al₄^2-, B₄^2- and Ga₄^2- are square-planar aromatic dianion, related to C₄H₄^2- [9]. He pointed out that the clusters not only contain π-electrons but also σ-electrons. C₄H₄²⁻ is already shown in Figure 1, while B₄^2⁻, Al₄^2⁻, and Ga₄^2⁻ are shown in Figure 2.

The valence electron configurations of these three elements are 2s² 2p¹, 3s² 3p¹, and 4s² 4p¹, respectively; they bond covalently to form a square framework, with each atom retaining one unpaired electron. The two newly entering electrons combine with the two unpaired electrons to form two lone pairs of electrons, and the remaining two unpaired electrons on the square ring reorganize into two π-electrons around two nuclei. If lone-pair-electrons are treated as small π-electrons, the active electrons in the Al₄^2- are 6, obeying Hückel’s electron counting rule 4n+2, with n=1, which is completely the same as benzene. Currently, in the field of aromaticity research, it is unclear that π-electrons contain two unpaired electrons with parallel spins, while nuclear magnetic resonance has already confirmed their existence. The σ-electrons often referred to are lone pairs consisting of two unpaired electrons with parallel spins.

Boldyrev’s group often used molecular orbital theory to describe their research findings, as shown in Figure 3. However, this theory fails to account for ring currents and induced magnetic fields—phenomena that are hallmarks of aromaticity. Although the Al₄²⁻ ion is indeed aromatic, and many of the findings regarding aromaticity by Boldyrev’s team are both groundbreaking and outstanding, the associated theoretical explanations do not withstand rigorous scrutiny; this has drawn harsh criticism from eminent scientists such as Hoffmann.

It is evident that the MO model is far removed from real nature of molecule. In several previous papers, I have repeatedly advocated abandoning molecular orbital theory, as it rests on a flawed theoretical foundation by Schrödinger and de Broglie.

In 1977, Cisar and Corbett reported a nearly perfect square-planar four-membered ring structure of dianion Bi₄ ^2-, as shown in Figure 4 [10], which is an inorganic, heavy-element Zintl ion historically viewed as a π-aromatic analogue of cyclobutadiene (Figure 1). It should be said that the first all-metal aromatic cluster was found in 1977, over 20 years earlier than Li’s aromatic Al₄^2- cluster.

The Bi-Bi distance in cluster is 2.936-2.941 Å, shorter than Bi-Bi covalent bond 2.99-3.02 Å and longer than Bi=Bi double bond 2.80-2.85 Å, typical aromatic ring character as benzene. Bi₄^2- is isolable. The electron configuration of Bi atom is [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p³ and the oxidation state is commonly +3. The most active 6p³ electrons in the outer shell of each Bi atom can leave the atomic core to take part in the formation of the cyclobutadiene-like structure. When two additional electrons break one of the double bonds, two lone pairs of electrons are formed. The aromatic current in Bi₄ ^2- is isoelectric with Al₄²⁻ (B₄^2- and Ga₄^2-), involving two parallel (spin) unpaired electrons in π-orbits and four parallel unpaired electrons in two lone pairs respectively.  However, Bi₄^2- utilizes p-electrons of the Bi atoms, with no contribution whatsoever from the s-electrons. According to Boldyrev's classification, σ-aromaticity corresponds to s-orbitals and π-aromaticity to p-orbitals; therefore, an Al₄²⁻-like square-planar aromatic dianion should exhibit both σ- and π-double aromaticity. Clearly, his assertion is incorrect.

In 2005, Chaitanya et al. Published “Evidence for d Orbital Aromaticity in Square Planar Coinage Metal Clusters”. It was alleged that this study provides the first quantitative evidence of aromaticity involving transition metal d-orbitals, rather than traditional p-orbitals [11]. Figure 5 is cited from Chaitanya’s work for Au₄^2- cluster. The doubly bridged square-planar coinage metal clusters (M₄Li₂, M = Cu, Ag, and Au) are symmetric inorganic aromatic rings. Lithium atoms give up their outer electrons to the gold ring. Therefore, no chemical bond is formed between the Li and the gold ring; instead, electrostatic attraction holds them together. Comparing Au₄^2- to Bi₄^2-(Figure 4), the two have the same common oxidation states +3. The most active 5d² 6s¹ electrons in the outer shell of each Au atom can leave the atomic core to take part in the formation of the cyclobutadiene-like structure. When two additional electrons from two Li atoms break one of the double bonds, two lone pairs of electrons are formed. All square-planar aromatic dianion clusters (C₄H₄^2-, B₄^2-, Al₄^2-, Ga₄^2-, Bi₄^2-, Au₄^2-, Ag₄^2- and Cu₄^2-) have the same electronic structure for the aromaticity, no matter s-, p-, or d-orbits are involved.

Based on my recently published paper "New understanding of atomic structure" [12], all electrons in an atom are equivalent. The repulsive force between the electrons limits the number of electrons in each shell and is also the supporting force for constructing several shells in an atom. If two electrons in the same shell, but in different orbits, run into the same place, one of them must be repelled a little away from the main shell. The more the electrons in the same shell, the more repelling events occur. Statistically, we can find out the regularities of the repelling events and classify them into s-, p-, d-, and f-, sub-orbits according to their different shapes and different energies. When an electron leaves its parent atomic core to participate in the activity of surroundings, it immediately loses its s-, p-, d-, and f- characteristics, becoming a generic electron. Therefore, the σ-, π-, δ- and ɸ-aromaticity contributing from s-, p-, d, and f-orbitals is meaningless.

It is reported that the ring-current susceptibility of the Cu₄^2- ring is 2-3 times weaker than for the Al₄^2- species [13]. First, the atoms within transition-metal aromatic clusters possess unpaired electrons in atomic core and exhibit orbital magnetism; these exert a braking effect on the π-electrons and lone-pair electrons in the ring currents. Second, the number of positive charges on the atoms and the number of surrounding negative charges of electrons also influence the properties of the aromatic clusters.

In 2001, Boldyrev's team published a paper titled "Aromatic Mercury Clusters in Ancient Amalgams." Mercury forms a wide range of alloys (amalgams), some of which are known from ancient times. Research indicates that the planar square Hg₄⁶⁻ unit is a particularly favorable structural motif in many amalgams. The paper points out that this unique square Hg₄⁶⁻ structure exhibits aromaticity, analogous to the recently discovered all-metal Al₄²⁻ ion [14]. Figure 6(a) displays the X-ray crystal structure of Na₆Hg₄, determined by Andriy V. Tkachuk and Arthur Mar in 2006 [15]. The sodium amalgam Na₃Hg₂ adopts a unique structural type containing isolated square Hg₄ clusters. The electron configuration of mercury (Hg) is [Xe] 4f¹⁴ 5d¹⁰ 6s². The outermost 6s² electrons form covalent bonds, creating a planar square ring. Six Na atoms transfer six electrons to the four Hg atoms; all electrons participating in the ring current originate entirely from the sodium atoms. By mapping the electronic structure of Al₄²⁻ onto the Hg₄ ring, the electronic structure diagram shown in Figure 6(b) is obtained. A ring current arises from the continuous displacement of lone pairs and π electrons—a process independent of the Hg atoms themselves. This system contains 4n+2 (n=1) active electrons, similar to benzene. It serves as an excellent example demonstrating that electrons are equivalent and that there is no such thing as σ, π, δ, or φ aromaticity.

There is another class of dianion aromatic clusters that differs from the systems discussed before. These cluster frameworks are neutral. Figure 7 shows the square bipyramidal structure of Na₂B₄H₄ and Na₂Al₄H₄.

“Na₂Al₄H₄ is a fundamental model cluster used to study all-metal π-aromaticity. In this compound, the two sodium (Na) atoms function as countercations that transfer their valence electrons to a square-planar Al₄H₄ framework. This turns the core into an Al₄H₄²⁻ dianion, which mimics the electronic structure of organic aromatic systems. The chemical bonding between the countercations (Na⁺) and the cluster is highly ionic, leaving the aromatic ring structurally intact. [18]”. In the previous article, I discussed trigonal bipyramidal Na₂Ga₃H₃ and pentagonal bipyramidal Na₂Ga₅H₅, noting that their currents and magnetic fields arise from expanded lone pairs or expanded pi- electrons. Planar molecules expose the positive electrostatic fields above and below their central atoms; consequently, the superimposed electric field generated by these multiple atomic cores is capable of accommodating orbital electrons. The orbiting electrons with parallel spins generate whirl shaped magnetic field enveloping the two orbits, making them relatively stable.

Al₄H₂^2- is completely different from C₄H₄^2-. C₄H₄^2- is analogous to benzene and Al₄²⁻; six valence electrons participate in the ring current. Al₄H₄^2- also differs from C₄H₄²⁺. This must be understood in terms of the oxidation states of Al (+3) and C (+4). Figure 8 shows the formation of aromatic ring current in C₄H₄²⁺ cluster [1].

Due to thermal vibration, the positive charge on C4 attracts the π-electrons in double bond on C2-C3. After shifting to C4-C3, the C2 site becomes to electron deficient. This continuous cycling generates an aromatic ring current and a corresponding ring magnetic field. ¹H NMR shows that its ring magnetic field (δ = 11.2 ppm) is much stronger than that of the benzene ring (δ = 7.6 ppm). It appears that the electrostatic attraction between positive and negative charges is greater than the repulsive force between negative charges within the context of the ring current. Species such as the C₃H₃⁺ aromatic cluster also exhibits large chemical shift (δ=11.2 ppm). The C₄Ph₄²⁺ species is exactly the same as C₄H₄²⁺, with two π electrons moving along the periphery of the C-four-membered ring. The C-C distance in the C₄H₄²⁺ is about 1.45 Å, while C-C single bond length is 1.54 Å. The fact shows that the ring current shortened the bond length, as in benzene. Na₂Al₄H₄ derives its ring magnetism from the incoming electrons, and its bond distance is identical to its single bonds.

The examples mentioned above all involve anion and cation clusters. However, Figure 9 shows the first example of a neutral planar all-aluminum aromatic system.

The two horizontally positioned Al atoms each form three covalent bonds and has no unpaired active electron. The two vertically positioned Al atoms each form two covalent bonds and possess one unpaired electron. Two ellipsoidal lone pairs are located above and below the two vertically aligned Al atoms. They exert center-directed repulsive forces on the unpaired electrons on the Al atoms, forming two unpaired electrons with parallel spins orbiting above and below the plane. The resulting orbital magnetic field protects the molecular framework, rendering the system stable. The Al-Al distance is about 2.49 Å, slightly shorter than typical Al–Al single bonds. In essence, this aromaticity is identical to that of Ga₄²⁻; the difference is that the two unpaired electrons arise from internal reorganization rather than being donated by two K atoms. It can be said that the magnetism originates from enlarged π-orbits, distinct from the magnetic field found in a benzene ring by shifting the π-orbits in a double bond.

Facit:

Although they are all square-planar aromatic clusters, their ring currents and magnetic properties differ.

Type 1: six π-electrons, similar to benzene, C₄H₄^2-, Al₄^2-, B₄^2-, Ga₄^2-, Bi₄^2-, Au₄^2-, Ag₄^2-, Cu₄^2- and Hg₄^6-.

Type 2: two enlarged π-orbits from alkali counter ions, Al₄H₄^2-, B₄H₄^2-.

Type 3: real aromatic cluster, C₄H₄²⁺, C₄Ph₄²⁺.

Type 4: two enlarged π-orbits in neutral Al₄.

Electrons can be neither destroyed nor created. In theoretical analysis, the origin of all valence electrons must be identified.

References:

[1]      Wang, C. (2025). The Movement of Two Parallel Unpaired Electrons in Benzene and Aromatic Compounds. Adv Envi Man Rec, 8(3), 01-26.

[2]      Solà, M. (2017). Why Aromaticity Is a Suspicious Concept? Why? Front. Chem. 5(22), 1-4.

[3]      Solà, M. and Muñoz-Castro, A. (2025). Aromaticity of all metal cluster. Chem. Commun., 61(71), 14280-14291.

[4]        Li, X., Kuznetsov, A. E., Zhang, H.-F., Boldyrev A. I., Wang, L.-S. (2001). Observation of All-Metal Aromatic Molecules, Science, 291, 859-861.

[5]      Hoffmann, R. (2015). The Many Guises of Aromaticity. Is hype debasing a core chemical concept? Am. Sci. 103(1),18-22.

[6]      Ritter, S. K. (2015). Aromaticity By Any Other Name. C&EN Online Exclusive: Chemists discuss the merits of the unbridled use of the concept of aromaticity. American Scientist, 93(8).

[7]      Matsuo, T., and Sekiguchi, A. (2004). Cyclobutadiene dianion. Bull. Chem. Soc. Jpn., 77(2), 211-226.

[8]      Boldyrev, A. I. and Kuznetsov, A. E. (2002). On the Resonance Energy in New All-Metal Aromatic Molecules. Inorg. Chem., 41(3), 532–537.

[9]      Poater, J., Feixas, F., Bickelhaupt, F. M., Solà, M. (2011). All-metal aromatic clusters M₄²⁻ (M = B, Al, and Ga). Are π-electrons distortive or not?. Phys. Chem. Chem. Phys., 13(46): 20673–20681. 

[10]   Cisar, A. and Corbett, J. D. (1977). Polybismuth anions. Synthesis and crystal structure of a salt of the tetrabismuthide(^2-) ion, Bi₄^2- . A basis for the interpretation of the structure of some complex intermetallic phases. Inorg. Chem., 16, 2482–2487.

[11]    Wannere, C. S., Corminboeuf, C., Wang, X-F., Wodrich, M. D., King, R. B., Schleyer, P. R. (2005). Evidence for d Orbital Aromaticity in Square Planar Coinage Metal Clusters. J. Am. Chem. Soc., 127(15), 5701–5705.

[12]   Wang, C. (2025). New Understanding of Atomic Structure. Adv Envi Man Rec, 8(3), 01-18.

[13]   Ying-Chan Lin, Y.-C., et al. (2006). Experimental and Computational Studies of Alkali-Metal Coinage-Metal Clusters. J. Phys. Chem. A, 110, 4244-4250.

 [14]  Kuznetsov, A.E., Corbett, J.D., Wang, L.-S. and Boldyrev, A.I. (2001), Aromatic Mercury Clusters in Ancient Amalgams. Angew. Chem. Int. Ed., 40, 3369-3372.

[15]   Tkachuk, A. V. and Arthur Mar, A. (2006). Redetermination of Na₃Hg₂. Acta Cryst. E62, i129–i130.

[16]   Twamley, B., Power, P. P. (2000). Synthesis of the Square-Planar Gallium Species K₂[Ga₄(C₆H₃-2,6-Trip₂)₂] (Trip =C₆H₂-2,4,6-iPr₃): The Role of Aryl˗Alkali Metal Ion Interactions in the Structure of Gallium Clusters. Angew. Chem. Int. Ed. 39, 3500-3503.

[17]   Dhara, D., Endres, L., Souza, C., et al. (2025). A Neutral All-Aluminum Aromatic. ChemRxiv. https://doi.org/10.26434/chemrxiv-2025-hxz3v. Preprint.

[18]   Kuznetsov, A. E. and Boldyrev, A. I. (2002). Peculiar Transformation of a Nonaromatic Al₄Cl₄(NH₃)₄ into an Aromatic Na₂Al₄Cl₄(NH₃)₄. Inorg. Chem., 41(14), 3596–3598.