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. 2026 Aug 6;11(32):48642–48651. doi: 10.1021/acsomega.6c06161

Carbon-Doping Modulation of Dual Aromaticity and Magnetic Responses in Fe–Boron Heterocluster Anions

Jun Ren †, Hui-Fang Li †,*, Jia-Ming Zhang ‡, Xing-Fu Chen ‡, Huai-Qian Wang †,‡,*
PMCID: PMC13491921  PMID: 42626472

Abstract

Heteroatom doping is an effective strategy to tune the structural stability and physicochemical properties of clusters. To address the out-of-plane distortion of transition metal atoms induced by the relatively large cavities of pure boron ligands, we performed a systematic theoretical study on the structural evolution and stabilization mechanisms of the FeC x B(8–x) – (x = 1–4) cluster series. By combining global minimum searches via ABCluster with density functional theory (DFT) calculations at the M06-2X/def2-TZVP level, we identified the global minimum structures and systematically investigated their structural features, bonding nature, and magnetic responses as a function of carbon doping. The results indicate that the introduction of carbon atoms effectively shrinks the ligand ring size and enhances the system’s geometric rigidity, eventually converging to a highly symmetric (C4V) bowl-shaped half-sandwich geometry for FeC4B4 –. Quantitative wave function analyses were performed using energy decomposition analysis (EDA-NOCV) and adaptive natural density partitioning (AdNDP). These analyses reveal that the high stability of FeC4B4 – arises from cooperative stabilization, involving carbon-doping-induced geometric optimization of the Fe–ring framework, substantial electrostatic attraction, and significant orbital interactions associated with bidirectional donation/back-donation between the Fe 3d orbitals and the alternating B–C hybrid ring. Both the π and δ electron systems satisfy the 4n+2 Hückel rule, endowing the cluster with distinct π+δ dual aromaticity. Furthermore, magnetic response analyses (NICS, ICSS, and GIMIC) consistently demonstrate that the pronounced diatropic current within the cluster does not originate from a single orbital but is synergistically driven by a globally delocalized electronic system involving the metal center. This work elucidates the microscopic mechanisms underlying the stabilization of 3D heteroatomic coordination frameworks via carbon doping, providing a robust theoretical basis for the rational design of novel nanomaterials with tunable electron delocalization and tailored magnetic responses.

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1. Introduction

Electron delocalization dominates the structural features and intrinsic properties of boron-based clusters. , Although pure boron clusters possess inherent multicenter delocalized bonding characteristics, their geometric stability is often compromised by high surface curvature and structural strain. − Introducing 3d transition metals via targeted doping is an effective strategy to enhance their stability. The d orbitals of transition metals can effectively overlap with the p orbitals of the boron framework. Such orbital interactions regulate bidirectional electron donation and back-donation, further enabling the formation of stable closed-shell electronic structures. This d-p orbital hybridization not only induces dual aromaticity and enhances overall electron delocalization but also rigidly anchors the metal center, providing an ideal structural platform for investigating the optical and magnetic properties of these clusters. Experimental and theoretical studies on transition-metal-doped boron clusters have demonstrated that metal encapsulation significantly improves framework rigidity and tunes the electronic structure. The hybridization between the transition metal’s d orbitals and the delocalized orbitals of the boron ring is the primary driving force behind this structural stability.

Among various transition metal dopants, Fe has garnered considerable attention in computational chemistry due to its unique 3d electronic configuration and remarkable catalytic activity. Pioneering work by Romanescu, Boldyrev, and coworkers revealed that Fe atoms can be stably embedded within boron rings to form classic “molecular wheels”, , while Saha, Sukumar, and colleagues established the stability of transition-metal-doped drum-like configurations. Concurrently, Popov’s group confirmed the viability of transition-metal-doped boron clusters through experimental techniques such as photoelectron spectroscopy. , Fundamental research by Liu et al. has shown that doping with 3d metals like Fe profoundly influences the system’s spin polarization and magnetic moment evolution. The distribution of unpaired electrons and the strength of d-p antibonding interactions directly dictate the spectral features and magnetic responses of these systems. − These significant findings establish the central role of Fe in modulating the properties of boron-based clusters, fueling the ongoing quest to design highly stable, magnetic cluster architectures. −

However, due to the relatively large coordination cavity and monotonous energy level distribution of pure boron rings, Fe atoms struggle to achieve optimal geometric and orbital matching, making them highly susceptible to out-of-plane distortion. , Therefore, heteroatom doping of the boron framework with carbonan element with higher electronegativity and a smaller covalent radiushas emerged as an effective strategy to tailor the delocalized electron network and the coordination environment. Recent studies indicate that binary boron–carbon rings exhibit excellent geometric and electronic tunability. − For instance, Cui et al. demonstrated that fine-tuning the B/C ratio can improve the geometric compatibility of large-radius atoms, activate d orbitals for bonding, and induce dual aromaticity, thereby facilitating the construction of high-coordination planar architecture. Similarly, Tan et al. found that transition metals can form multicoordinate structures within binary boron–carbon rings, releasing delocalized orbitals that generate strong magnetic ring currents. The introduction of carbon atoms not only physically constricts the coordination cavity but also fundamentally alters the electronic structure and electrostatic potential distribution of the ligand ring. Compared with previously reported boron–carbon clusters, the present work emphasizes not simply a new aromatic species, but a carbon-doping-driven route for regulating cavity size, ligand-field symmetry, and Fe–ring orbital matching in the FeC x B(8–x) – series. This evolution ultimately leads to a highly symmetric Fe-centered bowl-shaped half-sandwich framework with distinct π+δ dual aromaticity.

In this work, we aim to address the following three fundamental scientific questions: (1) How does progressive carbon doping in FeC x B(8–x) – clusters influence the structural evolution, geometric rigidity, and metal–ligand coordination environment? (2) What is the quantitative nature of the multichannel orbital interactions (σ, π, and δ) between Fe 3d orbitals and the B–C hybrid ring, and how do these interactions contribute to the overall stability and electronic delocalization? (3) How do the π and δ electron delocalization channels collectively determine the dual aromaticity and the global magnetic response of the Fe–B–C cluster system? Combining global minimum searches with DFT calculations, we systematically investigated the structural evolution, electronic properties, and magnetic responses of the series as a function of carbon dopant concentration, with a focus on dual aromaticity induced by carbon doping.

2. Methods

Within the framework of density functional theory (DFT), a three-step hierarchical structural screening strategy was employed to systematically search for the global minimum structures of anionic FeC x B(8–x) – (x = 1–4) clusters. First, unbiased global isomer exploration was performed via the ABCluster algorithm, , generating approximately 1200 initial candidate isomers for each stoichiometric composition. All these preliminary candidate configurations were initially optimized at the M06–2X/LANL2DZ − level with moderate precision using the Gaussian 09 program Subsequently, the 20 lowest-energy isomers were selected from the first step and further refined using the intermediate 6–311G­(d) basis set. Finally, according to a relative energy threshold of 3.0 eV, the top four energetically favorable isomers were selected and reoptimized at the high-precision all-electron def2-TZVP − basis set level to acquire accurate stable equilibrium configurations. Corresponding harmonic vibrational frequency calculations were performed at the same theoretical level to verify the structural stability of optimized clusters. For each composition, multiple spin multiplicities were explicitly considered, including singlet, doublet, triplet, and higher spin states where applicable. Geometry optimizations were carried out for all spin configurations, and the lowest-energy spin state for each isomer was identified based on total energy comparisons at the M06–2X/def2-TZVP level.

The M06–2X meta-GGA functional was adopted for all geometry optimizations and electronic structure analyses. It performs well in describing spin-state splitting and delocalized conjugated systems, and has been widely utilized to determine the energetic ordering of isomers in heteroatom-doped boron clusters. − To assess the methodological uncertainty associated with functional choice, we benchmarked the first four low-lying isomers of FeC4B4 – using ten density functionals at the def2-TZVP level (Table S1). All tested functionals consistently predict FeC4B4 –-I to be the global minimum, while the next three isomers remain 0.37–0.86, 0.62–1.33, and 0.93–1.91 eV higher in energy, respectively. Thus, although the detailed electronic structure of transition-metal-containing clusters may show some functional dependence, the structural assignment of FeC4B4 – as the global minimum is robust.

To unravel the chemical bonding nature and orbital interaction mechanism, adaptive natural density partitioning (AdNDP), − energy decomposition analysis (EDA) , as well as extended transition state-natural orbitals for chemical valence (ETS-NOCV) were adopted to analyze bonding characteristics. These methods were used to quantitatively characterize the orbital interactions between the Fe 3d orbitals and the [C4B4]− ring, with particular attention to the donation/back-donation channels and the respective σ-, π-, and δ-type contributions. Furthermore, the aromaticity and magnetic responses of the clusters were evaluated using nucleus-independent chemical shift (NICS), isochemical shielding surface (ICSS), and gauge-including magnetically induced current (GIMIC) calculations. − These magnetic analyses were used to probe the delocalization pattern and induced current response of the cluster. Because magnetic criteria in transition-metal-containing systems may be influenced by local magnetic anisotropy, the aromaticity assignment was made by combining magnetic descriptors with orbital-based bonding analyses. All wave function and electronic structure analyses were conducted using the Multiwfn 3.8 program, and the resulting spatial distributions were visualized with the VMD software.

3. Results and Discussion

3.1. Geometry Structures of FeC x B(8–x) – (X = 1–4)

To elucidate the structural evolution induced by progressive carbon doping, the geometric configurations of FeC x B(8–x) – clusters were systematically analyzed. Based on an unbiased global structure search and high-precision optimization, the global minimum (GM) structures (Figure ) and low-lying isomers (Figure S1 in the Supporting Information) of the FeC x B(8–x) – (x = 1–4) clusters at various spin multiplicities were obtained at the M06–2X/def2-TZVP level (Figure ). The Cartesian coordinates of the low-lying isomers are summarized in Table S2. The local minimum nature of these structures was verified by subsequent harmonic vibrational frequency calculations, confirming the absence of imaginary frequencies. A comparison of the structural evolution across different compositions reveals that as the number of carbon atoms increases, the geometric rigidity and coordination symmetry of the clusters change significantly.

1.

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Optimized global minimum (GM) structures of the FeC x B(8–x) – (x = 1–4) clusters at the M06–2X/def2-TZVP level. The point group symmetries and ground electronic states are given in parentheses. The B atoms are illustrated in pink, C in dark gray, and Fe in purple.

FeC1B7 – cluster, the GM structure (FeC1B7 – ‑ I) is a quasi-planar C2 V symmetric geometry with a closed-shell singlet ground state (1A1). However, its low-lying isomers (such as isomers II and III, located 0.27 and 0.45 eV higher in energy, respectively; see Figure S1) exhibit significant out-of-plane distortion, forming low-symmetry 3D structures. This indicates that introducing a single carbon atom is insufficient to completely overcome the structural strain caused by the large cavity size of the pure eight-membered boron ring, leaving a distinct geometric mismatch between the Fe atom and the ligand ring.

As the carbon doping ratio increases, the system gradually exhibits stronger structural regularity. For FeC2B6 –, the M06–2X/def2-TZVP results place isomer I only 0.01 eV above isomer II, already suggesting a method-sensitive energetic ordering for this composition. To further examine this point, additional CCSD­(T)/def2-TZVP calculations were carried out for the two lowest-lying structures, and the ordering was found to reverse, with FeC2B6 –-I lying 0.23 eV below FeC2B6 –-II. Therefore, the structural assignment for FeC2B6 – should be interpreted with appropriate caution. Rather than representing a uniquely defined intermediate, the x = 2 composition is better regarded as a method-sensitive region of the potential-energy surface. Importantly, this local uncertainty does not alter the broader structural trend across the FeC x B(8–x) – series, namely the carbon-doping-driven contraction of the ligand cavity and the progressive optimization of Fe–ring matching toward the highly symmetric FeC4B4 – framework.

At the carbon doping level x = 4, the global minimum of FeC4B4 – (FeC4B4 –-I, doublet 2A1) converges to a highly symmetric C4 V bowl-shaped half-sandwich structure. In this configuration, the central Fe atom is stably anchored above an alternating C–B ring. Unlike the 3D structural collapse frequently observed in the isomers of the x = 1 system, the four lowest-energy isomers of FeC4B4 – (Figure S1) all retain a well-defined half-sandwich framework. Even the higher-energy isomer FeC4B4 –-IV (+1.91 eV) exhibits only slight distortion. This confirms that introducing four carbon atoms, which possess smaller covalent radii, effectively shrinks the physical diameter of the ligand ring. This size reduction allows the ring’s geometric dimensions to match the spatial distribution of the Fe 3d orbitals, thereby significantly enhancing the rigidity of the 3D coordination framework.

This preference for nonadjacent carbon substitution reflects a general structural optimization principle in the FeC x B(8–x) – (x = 1–4) series. At intermediate doping levels, placing carbon atoms apart helps distribute the geometric and electronic perturbations more evenly over the ring, thereby avoiding excessive local contraction and maintaining a more delocalized ligand framework around the Fe center. In contrast, adjacent carbon substitution would concentrate the structural distortion within one sector of the ring and reduce the uniformity of the metal–ligand coordination environment. When x reaches 4, this effect becomes cooperative: the alternating B–C arrangement not only minimizes local strain but also generates a more regular ligand field and a more suitable cavity size for Fe coordination. As a result, the system no longer favors a locally distorted arrangement, but instead converges to the highly symmetric C 4 V bowl-shaped half-sandwich structure.

Thus, the stabilization of FeC4B4 – should be understood not only in electronic terms, but also as a consequence of improved geometric size matching: carbon substitution progressively contracts the ligand cavity and regularizes the coordination environment, thereby enabling more effective Fe–ring binding.

3.2. Electronic Structural Properties

To clarify the nature of Fe­[C4B4]− bonding interactions, EDA combined with ETS-NOCV was employed to quantify the multichannel σ/π/δ orbital coupling and associated charge transfer mechanisms. To further elucidate the interaction between the central Fe atom and the [C4B4]− fragment within the FeC4B4 – cluster, an EDA was performed at the M06–2X/def2-TZVP level of theory. As summarized in Table , the total interaction energy (ΔEint) between Fe and the [C4B4]− fragment is −87.74 kcal·mol–1, indicating a substantial stabilizing interaction. The attractive interaction primarily arises from the electrostatic contribution (ΔEels), which accounts for 48.33% of the total attraction, while the orbital interaction (ΔEorb) also provides a considerable contribution of 38.47%. This demonstrates that the binding between Fe and the [C4B4]− ring is not solely governed by electrostatic attraction (ionic character) via electron transfer, but also features considerable covalent character arising from the synergistic orbital coupling between the π* orbitals of the [C4B4]− ring and the 3d orbitals of the Fe atom.

1. Energy-Decomposition (EDA) and ETS-NOCV Analysis of the Interaction between Fe and [C4B4]− Ligands in FeC4B4–

Energy term Assignment Fe + [C4B4]−
ΔEint   –87.74  
ΔExrep   536.63  
ΔEc   –82.40 13.20%
ΔEels   –301.79 48.33%
ΔEorb   –240.18 38.47%
ΔEorb (ETS‑NOCV)   –1637.54  
ΔEorb (ETS‑NOCV‑α)   –874.69  
ΔEorb (ETS‑NOCV‑β)   –762.85  
ΔEorb (α‑1) Fe(d) ←[C4B4]− donation –301.51 18.41%
ΔEorb (α‑2) Fe(d) ←[C4B4]− δdonation –234.44 14.32%
ΔEorb (α‑3) Fe(d) ←[C4B4]− δdonation –196.40 11.99%
ΔEorb (α‑4) Fe(d) ←[C4B4]− π donation –96.79 5.91%
ΔEorb (α‑rest)   –45.55 2.78%
ΔEorb (β‑1) Fe(s) →[C4B4]− σ backdonation –164.75 10.06%
ΔEorb (β‑2) Fe(d) →[C4B4]− π backdonation –223.79 13.67%
ΔEorb (β‑3) Fe(d) →[C4B4]− π backdonation –204.58 12.49%
ΔEorb (β‑4) Fe(d) →[C4B4]− δbackdonation –116.98 7.14%
ΔEorb (β‑rest)   –52.75 3.22%
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Energy values are given in kcal/mol.

To further elucidate the nature of the orbital interactions between the Fe center and the [C4B4]− fragment in the FeC4B4 – cluster, the extended transition state–natural orbitals for chemical valence (ETS-NOCV) method was employed. This approach decomposes the total orbital interaction energy into independent pairwise charge transfer channels, enabling the simultaneous determination of the electron transfer direction, spatial distribution, and the associated energy contribution of each channel. As shown in Figure , a substantial bidirectional charge transfer exists between the Fe atom and the [C4B4]− fragment. Specifically, the α-spin channel corresponds to the ligand-to-metal donation from the [C4B4]− ring to the Fe atom, with an energy contribution (ΔEorb, α) of −874.69 kcal/mol. Conversely, the β-spin channel corresponds to the metal-to-ligand back-donation from the Fe atom to the [C4B4]− ring, with an energy contribution (ΔEorb, β) of −762.85 kcal/mol. These components account for 53.41% and 46.59% of the total ETS-NOCV orbital interaction energy, respectively. This indicates that the bonding between Fe and the [C4B4]− fragment is not a unidirectional electron transfer, but rather relies on the high-symmetry matching between the multicenter delocalized π* orbitals of the [C4B4]− ring and the 3d orbitals of the Fe atom. This reveals a typical donation/back-donation interaction pattern with cooperative σ-, π-, and δ-type orbital contributions, among which the δ-type π*–d coupling constitutes an important component of the Fe–ring interaction.

2.

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NOCV pairs and their corresponding NOCV orbitals of FeC4B4 – cluster.

In Figure , the deformation density plot of the α-1 NOCV channel shows that electron density primarily shifts from the [C4B4]− ring and accumulates at the Fe center. The corresponding NOCV orbitals exhibit overlap along the principal metal–ligand axis, confirming a donation process driven mainly by the Fe­(d) orbital accepting electron density from the ring. Contributing −301.51 kcal/mol, this represents the most dominant single bonding interaction. The deformation density plots for α-2 and α-3 both display characteristic four-lobed patterns around the metal center. Their corresponding orbitals exhibit effective symmetry matching between the Fe­(d) orbitals and the delocalized π* orbitals of the ring. This manifests as typical δ-type π*–d orbital coupling, demonstrating that the [C4B4]− ring provides substantial δ-donation to Fe via its multicenter π* orbitals, acting as a crucial pathway for fragment binding. The α-4 channel reflects the transfer of delocalized π electrons from the ring to the Fe­(d) orbitals (ΔE = −96.79 kcal/mol), suggesting that while π-donation from the [C4B4]− ring occurs, it is secondary to the π*-donation.

Correspondingly, the β-spin channels capture the metal-to-ligand back-donation. The deformation density of the β-1 channel illustrates electron flow from the Fe center to the [C4B4]− ring, originating primarily from axial coupling between the Fe(s) orbital and the ring’s acceptor orbitals, characteristic of Fe(s)→[C4B4]−σ back-donation. Meanwhile, the β-2 and β-3 channels exhibit back-donation from the Fe­(d) orbitals to the delocalized π orbitals of the ring. Their deformation density plots show distinct electron accumulation regions on both sides of the ring, and the associated orbital contours display typical overlap between the metal d orbitals and the ring’s π orbitals. This further highlights that π–d orbital coupling is a key component of the β-spin contribution to the binding between the Fe and [C4B4]− fragments.

The orbital interaction between the Fe center and the [C4B4]− ring is primarily a multichannel synergistic coupling comprising σ, π, and substantial δ components. The ligand-to-metal donation ([C4B4]− → Fe) slightly outweighs the metal-to-ligand back-donation (Fe→[C4B4]−), indicating that the [C4B4]− ring acts as both a strong electron donor and an effective electron acceptor. This establishes a pronounced bidirectional charge transfer between the two fragments. This observation aligns with the EDA results, which demonstrate that the interaction between Fe and the [C4B4]− ring is governed by both substantial electrostatic attractions and orbital interactions. Consequently, the bonding in the Fe-[C4B4]− system is not solely electrostatically driven; rather, it originates from a synergistic electrostatic and orbital stabilization mechanism featuring distinct covalent character.

The multichannel orbital interactions and the substantial π*-d, π-d orbital couplings revealed by the ETS-NOCV analysis indicate the presence of robust multicenter delocalized bonding within the FeC4B4 – cluster. To further elucidate this bonding behavior and determine whether this global delocalization is a general feature of the carbon-doped series or unique to this specific composition, the Adaptive Natural Density Partitioning (AdNDP) method was employed across the FeC x B(8–x) – (x = 1–4) clusters.

As illustrated in Figure , the highly symmetric FeC4B4 – cluster exhibits an optimal delocalized network. In addition to the eight localized 2c–2e C–B σ bonds, the [C4B4]− ring features three completely delocalized 8c–2e π bonds. These bonds contribute a total of six π electrons, satisfying the Hückel 4n+2 (n = 1) rule and confirming that the ring exhibits typical π-aromatic character. Similarly, for the global FeC4B4 – cluster, three 9c–2e π bonds delocalized over the entire metal–ligand framework can be identified. Furthermore, a highly symmetric 9c–2e δ bond is observed, encompassing two δ electrons. This electron count formally satisfies the Hückel 4n+2 (n = 0) rule for δ-aromaticity. Consistent with the pronounced δ-donation and δ-back-donation components identified in the ETS-NOCV analysis, this δ orbital arises from the precise symmetry matching between the Fe 3d orbitals and the delocalized π* orbitals of the ring, resulting in continuous electron delocalization across the entire cluster. Consequently, the FeC4B4 – cluster demonstrates pronounced π+δ dual aromaticity, illustrating that its global electronic delocalization is governed by the synergistic participation of multiple orbital channels.

3.

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AdNDP localized bonds of FeC4B4 –.

Crucially, this robust π+δ dual aromaticity is strictly unique to the perfectly structurally matched FeC4B4 – configuration. As shown in the AdNDP analyses for the lower-doped clusters (x = 1–3, Figure S6), the geometric mismatch and lower structural symmetry inherent in these species disrupt optimal global orbital overlap. Instead of forming highly symmetric, continuous 9c-2e π and δ bonds across the entire framework, their delocalized electron networks are largely fragmented into localized lower-center bonds (e.g., 4c–2e, 5c–2e, and 6c–2e π/σ bonds). It is only at the precise stoichiometry of x = 4 that the physical dimensions of the alternating B–C ring perfectly match the spatial distribution of the Fe 3d orbitals. This optimal geometric compatibility drives the formation of the globally delocalized network, demonstrating that the pronounced dual aromaticity is a unique signature of the FeC4B4 – cluster rather than a general consequence of arbitrary carbon doping.

In contrast, the high stability of previously reported pure boron analogues (FeB8 –and FeB9 –) originates from π+σ dual aromaticity, whereas our FeC4B4 –structure triggers a distinctly different π+δ dual aromatic mechanism through perfect geometric matching.

To further cross-verify these bonding characteristics in real space, the interaction region indicator (IRI), localized orbital locator (LOL), and topological parameters at the bond critical points (BCPs) from the quantum theory of atoms in molecules (QTAIM) were systematically evaluated, and the corresponding results are provided in the Supporting Information (Figures S3–S5 and Tables S3–S6). These analyses serve as complementary real-space evidence for the proposed stabilization mechanism: the IRI and LOL distributions support the presence of spatially continuous and partially delocalized Fe–ring interactions, whereas the QTAIM topological descriptors further substantiate the existence of effective bonding interactions within the Fe–B–C framework. In this way, the SI results help connect the orbital-interaction picture obtained from EDA/ETS-NOCV and AdNDP with a real-space description of the bonding network. They do not by themselves define aromaticity, but they support the delocalized bonding framework that underlies the subsequent π+δ aromaticity assignment.

3.3. Aromaticity of FeC4B4 –

To elucidate the origin of dual (π + δ) aromaticity and the magnetic response behavior of the FeC4B4 – cluster, the NICSZZ and ICSSZZ, and gauge-including magnetically induced current (GIMIC) analyses were performed. As shown in Figure , distinct blue regions with negative values are observed both at 0.5 Å below the ring plane (a) and in the space between the ring plane and the Fe atom (b), indicating a substantial magnetic shielding effect in the central region of the ring. The NICSZZ contour map was evaluated at 0.5 Å below the least-squares C4B4 ring plane, rather than at the conventional 1.0 Å position, because the C4B4 ring in FeC4B4 – is slightly nonplanar and the Fe center is located only about 1.10 Å above the ring plane. Thus, a 0.5 Å plane on the side opposite to Fe provides a more suitable probe of the ring-centered shielding region in this nonplanar half-sandwich system. This magnetic shielding primarily arises from the three 8c–2e delocalized π bonds in the [C4B4]− ring that satisfy the Hückel 4n+2 rule, confirming the π-aromaticity of the system. In addition, the extra 8c–2e π* orbitals, together with the 8*2c–2e sigma orbitals, contribute to the blue ring-shaped demasking region in Figure d.

4.

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NICSZZ and ICSSZZ analyses of the FeC4B4 – cluster. (a) NICSZZ contour map calculated at 0.5 Å below the ring plane; (b) NICSZZ contour map in the plane between the [C4B4]− ring and the Fe atom; (c) NICSZZ contour map in the xz plane; (d) 3D isosurface of ICSSZZ (isovalue = ±5.00 ppm); (e) ICSSZZ contour map in the plane between the [C4B4]− ring and the Fe atom; (f) ICSSZZ contour map in the xz plane. Blue and red regions represent shielding (negative values) and deshielding (positive values), respectively. All distances are given in Bohr.

Notably, in Figure c, the negative NICSZZ region is not confined to the interior of the [C4B4]− ring but extends toward the Fe atom. This indicates that electron delocalization is not limited to the ligand ring but encompasses the metal center, reflecting a global delocalization characteristic. This magnetic shielding region exhibits a continuous distribution perpendicular to the ring plane and maintains a high intensity near the Fe atom. This suggests that the coordination of Fe does not disrupt the inherent cyclic electron delocalization of the ring; rather, it enhances axial electron delocalization via orbital coupling. The electron density distributions of the three 8c–2e delocalized π bonds and the single 9c–2e δ bond in FeC4B4 – encompass the entire metal–ligand framework. This aligns with the pronounced π and δ orbital couplings observed in the ETS-NOCV analysis. The axially extended magnetic shielding regions in the NICSZZ and ICSSZZ plots can be attributed to the contributions of the π and δ delocalization channels. This indicates that the involvement of the Fe 3d orbitals not only reinforces the π delocalization system but also introduces additional delocalization pathways.

We note, however, that in a transition-metal-containing cluster such axially extended shielding may partly reflect local magnetic anisotropy around the Fe center. Therefore, the assignment of δ aromaticity should not be based on NICS/ICSS alone, but on its consistency with the AdNDP and ETS-NOCV results. The ICSSZZ analysis (Figure d–f) is consistent with the NICSZZ results. Its 3D isosurfaces reveal a continuous negative shielding region spanning the Fe atom and the­[C4B4]− ring, further demonstrating the presence of a global diatropic current within the system. The FeC4B4 – cluster represents a multichannel delocalized system dominated by π-aromaticity, supplemented by δ-electron delocalization facilitated by the metal. Although the δ-electron count formally satisfies the Hückel rule and exhibits delocalization characteristics at both the orbital and magnetic response levels. Although the δ channel is more spatially localized than the ligand-centered π system, it makes a substantial contribution to the Fe–ring interaction and is an indispensable component of the global delocalization in FeC4B4 –.

To further provide a quantitative comparison with representative anionic boron-based clusters, local NMR shielding tensor calculations were performed for B9 –, CoB8 –, RhB8 –, and FeC4B4 – at the M06–2X/def2-TZVP level. Because FeC4B4 – adopts a nonplanar bowl-shaped half-sandwich structure, the conventional ring-center NICS point is not directly applicable. Therefore, the ghost atom was consistently placed at the center of the triangular plane formed by the central atom and two adjacent peripheral atoms for all systems. As shown in Table , B9 – and CoB8 – exhibit negative NICS zz values of −67.87 and −49.26 ppm, respectively, while RhB8 – shows a much weaker NICS zz value of −6.83 ppm. FeC4B4 – also displays a negative NICS zz value of −28.39 ppm, indicating a local shielding contribution in the selected triangular region. More importantly, FeC4B4 – possesses a remarkably large shielding anisotropy of 5627.77 ppm, far exceeding those of B9 –, CoB8 –, and RhB8 –. This result indicates that carbon doping does not simply lead to a more negative single NICS zz value, but induces a highly anisotropic local magnetic response, which is consistent with the strong Fe 3d–ligand π/δ orbital coupling revealed by the EDA and ETS-NOCV analyses.

2. Local NICS Tensor Comparison for Representative Anionic Boron-Based Clusters Calculated at the M06-2X/def2-TZVP Level.

System σiso/ppm σ zz /ppm NICSiso/ppm NICS zz /ppm Anisotropy/ppm
B9 – 35.86 67.87 –35.86 –67.87 48.01
CoB8 – 59.34 49.26 –59.34 –49.26 183.38
RhB8 – –29.19 6.83 +29.19 –6.83 77.79
FeC4B4 – 571.22 28.39 –571.22 –28.39 5627.77
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a

The structures of the reference species B9 – [refs ], CoB8 – [refs ], and RhB8 – [refs ] were adopted and recalculated at the M06–2X/def2-TZVP level to ensure data consistency.

To further elucidate the specific contributions of occupied orbitals to the magnetic response in the FeC4B4 – cluster, its gauge-including magnetically induced current was evaluated. Figure presents the primary molecular orbitals responsible for the GIMIC and their corresponding current density maps (magnetic field along the positive Z-axis). As illustrated, the total diatropic current of the FeC4B4 – cluster originates from the synergistic contributions of multiple occupied orbitals. Similarly, the pronounced global diatropic ring currents are also systematically observed across the other doped configurations from x = 1 to 3, visually confirming that the global electron delocalization is an intrinsic feature of this cluster series (Figure S8). This indicates that aromatic current response is not exclusive to FeC4B4 –, but represents a common electronic feature of the FeC x B8–x – series. What distinguishes FeC4B4 – is that carbon doping drives the cluster to the most symmetric and rigid Fe-centered framework, in which the Fe–ring geometric matching and the cooperative π/δ delocalization are most clearly manifested. To further quantify the magnetic response, bond current strengths were evaluated by integrating the induced current density through bond-centered cross sections. The detailed cross-sectional current maps and numerical values are provided in Figure S7. The results confirm that the diatropic current is not confined to the ligand periphery, but also involves the Fe-connected bonding framework. The frontier orbitals primarily reflect the delocalized interactions between the Fe atom and the [C4B4]− ring, constituting the main source of the diatropic current in the inner region of the system. Specifically, the metal–ligand delocalized orbitals, dominated by π and δ components, collectively generate a pronounced paratropic current on the inner side. This aligns with the significant π and δ donation/back-donation features identified by the ETS-NOCV analysis, indicating that the Fe 3d orbitals play a critical role in establishing the global delocalized current pathways.

5.

5

Open in a new tab

Magnetic induced currents in the FeC4B4 – cluster. (a) Total current generated by all occupied molecular orbitals. (b) Paratropic current contributed by the [C4B4]− π* and C–B σ bonding orbitals. (c) Diatropic current contributed by the frontier Fe ring delocalized orbitals. (d) Diatropic current contributed by the [C4B4]− π orbitals and lower-level occupied molecular orbitals.

In addition to these metal–ligand delocalized orbitals, the π orbitals of the [C4B4]− ring and certain lower-lying occupied orbitals mainly contribute to the diatropic current on the outer periphery of the ring. This is consistent with the 8c–2e multicenter delocalized π bonds revealed by AdNDP, suggesting that these orbitals predominantly represent a ligand-centered delocalized electron system. Conversely, the HOMO π* of the [C4B4]− ring and the highly localized orbitals originating from the C–B framework σ bonds are the primary sources of the paratropic current. However, the contribution from these localized orbitals is secondary; their intensity is significantly weaker than the global diatropic ring current driven by the Fe–[C4B4]− delocalized π/δ orbitals, thus serving merely to modulate the local current distribution.

Taken together, the NICS, ICSS, GIMIC, and ETS-NOCV results indicate that the π and δ channels in FeC4B4 – play complementary rather than simply hierarchical roles. Energetically, the δ-related ETS-NOCV channels (α-2, α-3, and β-4) account for 33% of the total orbital interaction, which is comparable to the π-related channels (α-4, β-2, and β-3, 32%), showing that δ coupling is not negligible in stabilizing the Fe–ring interaction. However, the two channels differ in spatial manifestation and magnetic response. The π system is more broadly delocalized over the­[C4B4]− ring and mainly governs the ligand-centered peripheral diatropic response, whereas the δ channel is more concentrated in the Fe-involving axial region and mainly reinforces the inner current pathway and the magnetic shielding that extends from the ring toward the Fe center. Therefore, FeC4B4 – is best described as a π+δ doubly aromatic system with a π-dominant ligand-centered framework and a substantial metal-assisted δ contribution to global delocalization.

4. Conclusions

The ground-state structures and low-lying isomers of the FeC x B(8–x) – (x = 1–4) cluster series were systematically identified and characterized. The results reveal that ultimately converges to a highly stable, C4 V-symmetric bowl-shaped half-sandwich ground-state geometry. EDA and ETS-NOCV indicate that the high stability of this system arises not only from dominant electrostatic interactions but also from substantial orbital interactions and bidirectional charge transfer between the 3d orbitals of the central Fe atom and the [C4B4]− ring. Notably, the δ-type π*–d coupling between the π* orbitals of the [C4B4]− ring and the Fe 3d orbitals constitutes an important part of the orbital stabilization of the Fe–ring framework. However, the overall rigidity and stability of the cluster are more appropriately understood as arising from the combined effects of carbon-doping-induced geometric optimization, substantial electrostatic attraction, and multichannel Fe–ring orbital interactions. Furthermore, NICS, ICSS, and GIMIC analyses indicate that the significant paratropic current in the system is driven by the π and δ delocalized orbitals formed between the Fe and B–C hybrid rings, giving it significant aromaticity in the ring plane. These findings offer valuable theoretical insights into the stabilizing mechanisms of Fe-doped B–C hybrid ring clusters and provide a robust theoretical foundation for designing novel boron-based functional nanomaterials with controllable electron delocalization and customized magnetic responses. More broadly, the present results suggest a general design strategy for transition-metal-doped boron–carbon clusters. The electronic structure and aromaticity can be effectively regulated by tuning the heteroatom composition, which adjusts the size and symmetry of the coordination ring to achieve optimal spatial and energetic matching between the metal 3d orbitals and the delocalized ligand orbitals. Such orbital matching enables controllable multichannel interactions, thereby allowing systematic modulation of electron delocalization and magnetic response behavior. This strategy may provide a useful guideline for the rational design of boron-based functional nanomaterials beyond the specific FeC4B4 – system.

Supplementary Material

ao6c06161_si_001.pdf (1.5MB, pdf)

Acknowledgments

The Natural Science Foundation of Fujian Province of China (Grant Nos. 2025J01181 and 2023J01141) and the Natural Science Foundation of Xiamen (Grant No. 3502Z202373051).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c06161.

  • Benchmark results of different density functionals for FeC x B(8–x) – (x = 1–4) clusters at the def2-TZVP level (Table S1); Cartesian coordinate information on the four lowest-energy isomers of FeC x B(8–x) – (x = 1–4) clusters (Table S2); topological parameters at the bond critical points based on AIM analysis (Tables S3–S6); structures of the top four low-lying isomers (Figure S1); spin density distribution isosurfaces (Figure S2); interaction region indicator (IRI) isosurfaces (Figure S3); localized orbital locator (LOL) isosurfaces (Figure S4); molecular graphs based on AIM analysis (Figure S5); AdNDP localized bonding patterns for the low-doped FeC x B(8–x) – (x = 1–3) clusters (Figure S6); bond-current-strength analysis of the FeC4B4 – cluster (Figure S7); gauge-including magnetically induced current (GIMIC) maps (Figure S8) (PDF)

The authors declare no competing financial interest.

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