A theoretical study on doping Pd-like superatoms into defective graphene quantum dots: an efficient strategy to design single superatom catalysts for the Suzuki reaction

Abstract

The rational design of non-precious metal catalysts as a replacement for Pd is of great importance for catalyzing various important chemical reactions. To realize this purpose, the palladium-like superatom NbN was doped into a defective graphene quantum dot (GQD) model with a double-vacancy site to design a novel single superatom catalyst, namely, NbN@GQD, based on density functional theory (DFT), and its catalytic activity for the Suzuki reaction was theoretically investigated. Our results reveal that this designed catalyst exhibits satisfactory activity with a small rate-limiting energy barrier of 25.7 kcal mol⁻¹, which is comparable to that (22.8 kcal mol⁻¹) of the commonly used Pd(PPh₃)₂ catalyst. In addition, the size and substituent effects of the GQD support on the catalytic activity of NbN@GQDs were systematically studied. It is found that increasing the GQD size slightly reduced the rate-limiting energy barrier to 24.1 kcal mol⁻¹ for the Suzuki reaction, whereas the introduction of electron-withdrawing groups at the edge of the GQD significantly enhanced it. Furthermore, progressively increasing the number of electron-withdrawing groups gradually improved the catalytic performance of NbN@GQD-(NO₂)_n with a low energy barrier of 19.3 kcal mol⁻¹. Thus, this study presents a rational strategy to design single superatom catalysts by doping noble metal-like superatoms into defective GQDs of different sizes or even a large-sized graphene.

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1. Introduction

The Suzuki reaction has revolutionized modern synthetic chemistry since its discovery in 1979, becoming one of the most powerful methods for constructing C–C bonds under mild conditions.^1–4 This transition metal-catalyzed reaction has found extensive applications in pharmaceutical synthesis,⁵ enabling the production of numerous drugs, including anticancer agents,⁶ antihypertensive medications,^7,8 and antibacterial compounds.⁹ The versatility of such a reaction stems from its excellent functional group tolerance, high yields, and ability to couple a wide range of aryl and heteroaryl substrates. Traditional catalytic systems employing Pd complexes with phosphine ligands have dominated industrial applications due to their remarkable efficiency and selectivity. However, these catalytic systems face significant challenges, including the high cost of palladium (current price ∼$200 000 per kg), potential metal contamination in the final products, and environmental concerns associated with heavy metal waste.^10,11 These limitations have spurred intensive research for developing alternative catalysts that can match or surpass the performance of conventional Pd catalysts while addressing their shortcomings.

The field of heterogeneous catalysis has witnessed remarkable progress with the development of single-atom catalysts (SACs),¹² where isolated metal atoms are anchored onto various supports, offering maximum atom utilization efficiency and unique electronic properties.¹³ More recently, the introduction of “superatoms”, a special kind of atomic clusters that mimic the electronic structures of individual atoms, has opened new possibilities for catalyst design.^14,15 These superatom clusters, typically composed of 2–20 atoms, exhibit tunable electronic structures through quantum confinement effects and can be precisely engineered to mimic the catalytic behavior of noble metals. When integrated into suitable supports, a new class of superatom-based catalysts, named single superatom catalysts (SSCs), can be prepared, as first proposed in 2023.^16–18 Such SSCs can combine the advantages of atomic dispersion and tailored electronic environments, potentially overcoming the limitations of conventional Pd catalysts. Both experimental and theoretical evidence confirm that the Pd-like superatom ZrO exhibits catalytic activity comparable to or even surpassing that of Pd in small molecule hydrocarbon activation,¹⁹ CO oxidation,¹⁶ N₂ reduction,¹⁷ and Suzuki coupling.²⁰ Whether the diatomic NbN molecule, which also shares analogous electronic properties to the Pd atom,²¹ could exhibit similar performance in catalysis remains an open question worthy of exploration.

Graphene quantum dots (GQDs), as a rising star in the family of carbon nanomaterials, have garnered intense interest since their discovery in 2008.^22–25 Their distinctive features, including tunable versatile surface chemistry and exceptional biocompatibility, enable broad applications in bioimaging,²⁶ drug delivery,²⁷ anticancer therapy,²⁸ treatment of chronic diseases,²⁹ catalysis,³⁰ and environmental remediation.³¹ Such carbon nanomaterials containing sp²-hybridized carbon atoms could serve as catalytic supports functioning as “electron sponges”³² or “electron buffers”,³³ which may modulate charge distribution on the supported active sites to enhance their catalytic performance. Thus, if they are employed as substrates of SSCs, GQD-based materials provide an ideal platform that synergizes the atomic dispersion of active sites with efficient electron-transfer pathways, potentially enabling unprecedented performance of SSCs for catalyzing chemical reactions that involve both oxidation and reduction processes, such as the Suzuki reaction.

Consequently, a GQD-supported SSC, namely, NbN@GQD, has been well-designed by embedding a diatomic NbN superatom into a selected defective GQD model with a double-vacancy site in this study. The catalytic activity of this designed SSC for the Suzuki reaction was first evaluated, which suggests its comparable performance to the commonly used Pd(PPh₃)₂.²⁰ To further improve the catalytic activity of this SSC, the size and substituent effects of GQD were also systematically studied. It is revealed that increasing the GQD size slightly improved its catalytic performance for the Suzuki reaction, whereas the edge functionalization with nitro groups results in a remarkable enhancement in catalytic performance. It is noted that the activity of NbN@GQD gradually increases along with the increasing number of nitro groups, and the fully substituted NbN@GQD-(NO₂)₁₆ exhibits even comparable performance to the SAC, i.e., Pd@GQD. Importantly, these designed catalysts exhibit spontaneous desorption of final products, avoiding the catalyst poisoning issue associated with the Pd@GQD catalyst. This work not only provides a new class of high-performance SSCs for the Suzuki reaction but also establishes a general strategy for improving the catalytic performance of such superatom-based catalysts through precise tuning of the electronic structures of substrates.

2. Computational details

All computations were performed using the Gaussian 16 software package³⁴ with the Perdew–Burke–Ernzerhof (PBE0) hybrid functional^35,36 in this work. The Def2-SVP basis set³⁷ was employed for Nb and Br atoms, while other elements were treated with the 6-31G(d) basis set for the geometric optimizations of NbN@GQD, Pd@GQD, and related structures. For the larger NbN@GQD-L, NbN@GQD-G (G = –NH₂ and –NO₂) and their related structures, structural optimizations were conducted at the 6-31G&Def2-SVP level, followed by single-point energy calculations at the 6-31G(d)&Def2-SVP level. The D3(BJ) correction³⁸ was incorporated for both single-point energy computations and natural bond orbital (NBO) analyses.³⁹ Solvent effects of a mixed water–ethanol (1 : 1) solvent^40,41 were considered via the solvation model based on density (SMD)⁴² during the study of the catalytic mechanism.

Visualization of electrostatic surface potentials (ESP),⁴³ interaction region indicator (IRI)⁴⁴ analysis, and natural population analysis (NPA) charge distributions were performed using Multiwfn^45,46 and VMD.⁴⁷ Electron density difference (EDD) maps and molecular orbital (MO) plots were generated by GaussView,⁴⁸ while molecular structures were plotted by Mercury.⁴⁹ The anisotropy of the induced current density (AICD)^50,51 analysis was assessed using the AICD-2.0 package, with results visualized via POV-Ray rendering.⁵² Additional computational details are provided in the SI.

3. Results and discussion

3.1 Design and characterization of NbN@GQD

The schematic diagram of the proposed design strategy to achieve SSCs is illustrated in Fig. 1a. As is well known, due to limitations of various preparation methods, the actually synthesized graphene usually has various defects. There are two carbon atoms that are missing in the graphene with double-vacancy defects. Thus, a diatomic NbN superatom can just be embedded into such a double-vacancy site to form a stable SSC. To verify this hypothesis, a GQD with one double-vacancy site (C₄₀H₁₆) was selected as a simple model of graphene, which has been doped by a NbN superatom to obtain a SSC, named NbN@GQD.

Fig. 1 (a) Schematic of the preparation and geometric structures of NbN@GQDs, where the Nb–N bond length (in Å), spin multiplicities (M) and symmetry are given. (b) IRI plot (isovalue = 1.000 a.u.) of sign(λ₂)ρ coloring of NbN@GQD with a scatter plot of IRI vs. sign(λ₂)ρ, where blue represents chemical bonding interactions, green represents vdW interactions, and red signifies the steric effect in the ring. (c) Time evolution of the potential energies and the corresponding structure at the highest energy position (red asterisk) of NbN@GQD during the ADMP MD simulation for 500 fs with a time step of 0.1 fs at 298 K. (d) EDD between the NbN subunit and graphene carrier (isovalue = 0.003 a.u.), where red and blue colors indicate regions of increasing and decreasing electron density, respectively. (e) NPA charge distribution (in eV) and (f) ESP plots of NbN@GQD, where the blue and yellow spheres represent the minima and maxima values of ESP (in kcal mol⁻¹, isovalue = 0.001 a.u.), respectively. (g) Frontier molecular orbital diagrams of NbN, pGQD, and NbN@GQD (isovalue = 0.020 a.u.).

After the structural optimization, the resulting NbN@GQD catalyst maintains the triplet spin state of the isolated NbN superatom. Besides, the planar geometric structure of the perfect GQD was also well preserved, though the NbN site protrudes slightly from the surface, exhibiting C_s symmetry. Notably, the raised Nb atom in this catalyst facilitates the adsorption and reaction of the substrates. A slight elongation of the Nb–N bond length (1.993 Å) is observed for NbN@GQD as compared to that of the isolated NbN superatom (1.645 Å). Even so, this bond length is still much shorter than the sum (2.35 Å) of the atomic radii of Nb and N,⁵³ indicative of the covalent interaction between the Nb and N atoms in this NbN@GQD catalyst. Besides, it can be clearly demonstrated by the IRI analysis that the interaction strength of the Nb–N bond is comparable to that of C–C bonds in the GQD support (see Fig. 1b). The calculated E_sol value of NbN@GQD is −93.2 kcal mol⁻¹ in the mixed water–ethanol (1 : 1) solvent, which suggests the good solubility of this nanostructure in such a mixed solution. Furthermore, the atom-centered density matrix propagation (ADMP) molecular dynamics (MD) simulations in the solvent environment reveal that the geometric configuration of NbN@GQD is well-preserved throughout the simulation time of 500 fs (see Fig. 1c). This MD simulation further confirms the high thermodynamic stability of NbN@GQD.

Fig. 1d presents the EDD plot between the NbN subunit and the GQD support with a double-vacancy site, which clearly shows the charge transfer from the NbN superatom to the GQD unit. As a result, the NbN subunit of NbN@GQD carries a positive charge of 0.574 |e| (see Fig. 1e), showing a local maximum of 97.0 kcal mol⁻¹ above the NbN unit in the ESP plot (see Fig. 1f). This strong interaction between NbN and GQD is quantified by a large E_int value of −296.65 kcal mol⁻¹, as listed in Table 1. These results provide a reasonable understanding of the structural stability of the designed catalyst. However, as shown in Fig. 1g, the E_g value (2.16 eV) of NbN@GQD is lower than those of 2.55 and 2.77 eV for the free NbN superatom and the corresponding perfect GQD without a double-vacancy (abbreviated as pGQD), respectively, because of the significantly lifted HOMO level. This indicates that NbN@GQD may possess superior catalytic activity to donate electrons, thereby initiating the oxidative addition step of the Suzuki reaction. This observation is further corroborated by the reduced VIE (5.31 eV) and VEA (0.91 eV) values of NbN@GQD as compared to the free NbN and the pGQD.

Table 1 The interaction energies (E_int, in kcal mol⁻¹) between NbN and GQD subunits in NbN@GQDs, and the solvation energies (E_sol, in kcal mol⁻¹), HOMO–LUMO gaps (E_g, in eV), vertical ionization energies (VIE, in eV), and vertical electron affinities (VEA, in eV) of NbN, pGQD, and NbN@GQD species

Species	E int	E sol	E g	VIE	VEA
NbN	—	−57.7	2.54	7.15	1.07
pGQD	—	−37.8	2.77	6.01	1.22
NbN@GQD	−295.65	−93.2	2.16	5.31	0.91

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To evaluate the affinity of NbN@GQD toward the substrates of the Suzuki reaction, phenyl bromide (PhBr) was introduced to approach the NbN unit from different orientations to construct multiple PhBr@NbN@GQD complexes. After optimization, the first three stable complexes, namely, isomers I–III, are presented in Fig. 2a. Fig. S1 shows the details of electron transfer between PhBr and NbN@GQD. The E_ads values of the three isomers decrease as the electron accumulation region (the isosurface with red color) gradually diminishes. It is evident that isomer I, which adopts a sandwich configuration, is the most stable one. In this configuration, the Nb atom of NbN@GQD forms a new Nb–C bond with each C atom of PhBr, resulting in a large adsorption energy of −53.2 kcal mol⁻¹. Consequently, the benzene ring undergoes substantial structural deformation, while the C–Br bond length (1.893 Å) hardly changes as compared to that of 1.892 Å for free PhBr. This is directly reflected in its EDD plot, where no change in electron distribution is observed for the C–Br bond in this isomer.

Fig. 2 (a) The optimized structures of PhBr@NbN@GQD complexes with relevant C–Br bond lengths (in Å) and E_ads values, where spin multiplicities are given in superscripts, the relative energies of isomers are shown as short blue lines, and the blue values are the NPA charges on the whole NbN@GQD units in the complexes. (b) Schematic of the possible mechanisms of the Suzuki reaction catalyzed by NbN@GQD, where Path I and Path II represent whether the B(OH)₃ is desorbed from the active center or not. (c) Gibbs free energy profiles of the Suzuki reaction catalyzed by NbN@GQDs with the corresponding geometric structures for Path I, where the spin multiplicity of each structure is indicated by the superscript and crucial bond lengths are given in Å. Gibbs free energy profiles of the rate-limiting step of the Suzuki reaction catalyzed by (d) NbN@GQD-1 and (e) NbN@GQD-2. (f) Correlation analysis plots of rate-limiting energy barriers vs. d-band centers for NbN@GQD, NbN@GQD-1, and NbN@GQD-2.

In addition, isomer II is formed when the benzene ring of PhBr adsorbs onto the Nb atom via its αC and βC atoms. In this isomer, the shorter spatial distance between the catalyst and the C–Br bond facilitates electron exchange between them, thereby promoting the C–Br bond activation (2.028 Å), as evidenced by the expanded region of increased electron density observed between the catalyst and the C–Br bond in Fig. S1. As for isomer III, PhBr is bound to the Nb site of NbN@GQD solely through the Br atom via a “point to point” mode, resulting in a complex with the E_ads value of −25.2 kcal mol⁻¹. Since the Br atom itself is in a negatively charged state, it tends to donate its lone pair to the catalyst in this adsorption mode, causing the NbN@GQD to carry a negative charge of −0.240 |e|. This substantial electron transfer also leads to a certain activation of the C–Br bond, whose length is elongated from 1.892 Å (for free PhBr) to 1.980 Å.

3.2 Suzuki reaction catalyzed by NbN@GQD

As mentioned above, NbN@GQD exhibits strong affinity toward the substrate (PhBr) of the Suzuki reaction. Therefore, the complete mechanism of the Suzuki reaction catalyzed by NbN@GQD was further studied to comprehensively evaluate the catalytic performance of NbN@GQD. As the B(OH)₃ near the active site significantly affects the energy barrier of reductive elimination,^20,54 two distinct pathways for this elementary step were compared, namely, Path I and Path II, which represent whether B(OH)₃ desorbs from the active site or not (see Fig. 2b). For comparison, the corresponding reaction profile for the Suzuki reaction catalyzed by the Pd-based SAC, namely, Pd@GQD, was also obtained and is given in Fig. S2.

Fig. 2c depicts the comprehensive details of the Suzuki reaction catalyzed by NbN@GQD. Initially, PhBr binds to the active site of the catalyst to generate IS1. Subsequently, IS1 absorbs 11.9 kcal mol⁻¹ of energy to adjust the position of PhBr. The αC and βC bind to the active site, reaching the transition state TS1 of oxidative addition. Following this activation, the C–Br bond is broken, and the C and Br atoms are connected to the Nb atom to form FS1. In an alkaline environment, the Ph–B(OH)₃⁻ anion, which is formed by combining the OH⁻ with Ph–B(OH)₂, replaces the Br⁻ anion in FS1, forming IS2. After crossing the transition state TS2 of this process (ΔG^‡ = 9.1 kcal mol⁻¹), the C–B bond undergoes activation and cleavage. Then, two distinct possible mechanisms for reductive elimination were considered. In Path I, B(OH)₃ desorbs from the reaction site after transmetalation, and two phenyl groups symmetrically bind to the Nb atom of NbN@GQD. These phenyl groups then approach each other, forming the final transition state TS3 (ΔG^‡ = 25.7 kcal mol⁻¹), ultimately leading to phenyl coupling and desorption. In contrast, as shown in Fig. S3, the B(OH)₃ remains near the reaction site throughout the reductive elimination process in Path II. This mechanism has an energy barrier of 29.2 kcal mol⁻¹, slightly higher than that of Path I, making it unfavorable for product formation.

It is evident that the reductive elimination with an energy barrier of 25.7 kcal mol⁻¹ can be considered the rate-limiting step, which is comparable to that of 22.8 kcal mol⁻¹ for Pd(PPh₃)₂.²⁰ This suggests that the designed NbN@GQD exhibits promising performance for the Suzuki reaction. Additionally, as shown in Fig. 2d and e and S4, two contrast catalysts with separated Nb and N atoms, namely, NbN@GQD-1 (Nb and N separated by one C atom) and NbN@GQD-2 (Nb and N separated by two C atoms), were employed to evaluate the distance effects^55,56 and verify whether the high activity of NbN@GQD is dependent on the NbN unit functioning as an integral superatom. Comparative results reveal that the rate-limiting barriers of the Suzuki reaction catalyzed by the three catalysts increase progressively with the elongation of the Nb–N distance, i.e., NbN@GQD (25.7 kcal mol⁻¹) < NbN@GQD-1 (31.4 kcal mol⁻¹) < NbN@GQD-2 (35.8 kcal mol⁻¹). This variation in energy barriers can be attributed to the changes in the d-band center positions. As illustrated in Fig. 2f, the d-band centers of the three catalysts exhibit a strong linear correlation with their respective rate-limiting barriers. The lowest d-band center of NbN@GQD leads to the smallest energy barrier for catalyzing this C–C coupling process. Furthermore, to investigate the influence of the Nb coordination number on catalytic performance, two NbN@GQD structures with different nitrogen atom coordination environments, namely, two N atoms coordinated NbN₂ (NbN@GQD-3) and three N atoms coordinated NbN₃ (NbN@GQD-4), were also systematically examined. As shown in Fig. S5, the calculated energy barriers for the reductive elimination step of the Suzuki reaction catalyzed by NbN@GQD-3 and NbN@GQD-4 were 27.3 and 26.8 kcal mol⁻¹, respectively (see Fig. S5a), which are both higher than that of 25.7 kcal mol⁻¹ for NbN@GQD. These results clearly indicate that doping the integral NbN superatom into GQD is the best choice, revealing the high catalytic activity of such SSCs.

Despite the favorable catalytic performance of NbN@GQD for the Suzuki reaction, its activity is still slightly lower than that of the corresponding Pd@GQD, with a rate-limiting barrier of 19.2 kcal mol⁻¹ (see Fig. S2). To further improve the catalytic performance of NbN@GQD, a larger GQD model (C₁₂₈H₂₈) was also adopted to support the NbN superatom, yielding a SSC denoted as NbN@GQD-L to examine whether size effects could enhance the catalytic activity of such SSCs (see Fig. S6). The results demonstrate that NbN@GQD-L improves the catalytic performance for both transmetalation and reductive elimination steps, and reduces the rate-limiting barrier from 25.7 to 24.1 kcal mol⁻¹. This indicates that enlarging the support size may be a good approach to enhance the activity of such SSCs.

3.3 Suzuki reaction catalyzed by NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)_n (n = 4, 8, and 16)

Considering that the peripheral benzene rings surrounding the NbN unit in NbN@GQD are all conjugated, introducing electron-withdrawing and electron-donating groups at the edge of the GQD support should be an effective strategy to modulate the charge distribution of active sites, thereby promoting the electron exchange between the substrates and the catalyst to meet diverse reaction requirements. As a result, four electron-donating amino (–NH₂) groups and electron-withdrawing nitro (–NO₂) groups were introduced to replace the four hydrogen atoms at the two ends of NbN@GQD along the NbN axial direction, yielding two distinct SSCs, i.e., NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)₄, as shown in Fig. 3a. After geometric optimization, the Nb–N bonds in both catalysts are shortened from 1.993 Å to 1.986 Å (see Fig. 3b). The EDD plots in Fig. 3c reveal that the electron density at the edge of the support increases after the introduction of amino groups, whereas it decreases upon the introduction of nitro groups. Thus, the electron-donating and electron-withdrawing groups effectively regulate the charge distribution on NbN subunits, ultimately endowing NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)₄ with the charges of 0.552 |e| and 0.618 |e| on the NbN subunits, respectively (see Fig. S7a). Even so, the AICD analysis in Fig. S7b demonstrates that these two catalysts still retain the strong electron delocalization characteristics of GQD after ligand substitution.

Fig. 3 (a) Schematic for modifying NbN@GQDs via introducing electron-donating amino (–NH₂) groups and electron-withdrawing nitro (–NO₂) groups. (b) Most stable structures of NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)₄. (c) EDD plots between the substituents and NbN@GQD of NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)₄. (isovalue = 0.001 a.u.), where red and blue colors indicate regions of increasing and decreasing electron density, respectively. Gibbs free energy profiles of the Suzuki reaction catalyzed by (d) NbN@GQD-(NH₂)₄ and (e) NbN@GQD-(NO₂)₄ with the corresponding geometric structures for Path I, where the spin multiplicity of each structure is indicated by the superscript and crucial bond lengths are given in Å.

Fig. 3d and e present the detailed mechanisms of Suzuki reaction catalyzed by NbN@GQD-(NH₂)₄ and NbN@GQD-(NO₂)₄, respectively. For both catalysts, the reaction preferentially proceeds following Path I with a lower energy barrier in either case of the reductive elimination pathway. Specifically, for NbN@GQD-(NH₂)₄, the oxidative addition step exhibits an extremely low energy barrier of 4.1 kcal mol⁻¹, and the energy required to reach the TS2 of the transmetalation step is also relatively low. However, the energy barrier for the reductive elimination step rises to 26.7 kcal mol⁻¹, making it the rate-determining step of the reaction. In contrast, for NbN@GQD-(NO₂)₄, the energy barrier for oxidative addition slightly increases to 12.0 kcal mol⁻¹, while the barriers for the other two steps decrease to 8.0 and 23.1 kcal mol⁻¹, respectively. This can be understood by the fact that the introduction of an amino group results in reduced VIE (4.85 eV) and VEA (0.69 eV) values for NbN@GQD-(NH₂)₄ (see Table S5), indicating its stronger electron-donating ability. During the activation of PhBr, the abundant electrons provided by the amino groups facilitate the cleavage of the C–Br bond, making this step thermodynamically favorable. However, during phenyl coupling, the reduced electron-accepting capability of NbN@GQD-(NH₂)₄, combined with its higher electron density, makes it difficult to accept electrons from the biphenyl product, thereby hindering reductive elimination. Conversely, NbN@GQD-(NO₂)₄ exhibits increased VIE (6.19 eV) and VEA (2.18 eV) values. The significantly enhanced VEA suggests strong electron-accepting ability, which promotes reductive elimination. Thus, the electron-withdrawing effect of nitro groups can enhance the catalytic performance of NbN@GQD, providing an effective strategy to improve the performance of this NbN-based catalyst via modifying the edge of GQD with electron-withdrawing groups.

Could the catalytic performance of NbN@GQD for the Suzuki reaction be further enhanced by increasing the number of nitro groups? To address this, NbN@GQD-(NO₂)₈ with eight nitro substituents was optimized and is shown in Fig. 4a, where the Nb–N bond length remained at 1.986 Å. Additionally, considering the successful synthesis of edge-perchlorinated pyrrole-fused analogue of warped nanographene (azaWNG) and perfluorinated warped nanographenes (PFWNG),^57,58 NbN@GQD-(NO₂)₁₆ with sixteen nitro groups was also optimized and is presented in Fig. 4a. The ADMP MD simulation was performed in mixed solvent environments to rigorously evaluate the stability of NbN@GQD-(NO₂)₁₆. The result in Fig. S8 demonstrates that the geometric configuration of NbN@GQD-(NO₂)₁₆ was well preserved throughout the simulation trajectory for 200 fs, which provides additional confirmation of its high thermodynamic stability. In NbN@GQD-(NO₂)₁₆, the Nb–N bond length is increased to 2.052 Å, and the whole structure undergoes significant distortion, adopting a saddle-shaped geometry (see Fig. S9a), which is consistent with the reported PFWNG.⁵⁷ As illustrated in Fig. S9b, despite the substantial structural deformation of NbN@GQD-(NO₂)₁₆, its π-conjugated structure remained intact, exhibiting strong electron delocalization characteristics that effectively disperse the electron density of NbN subunits, which also exhibits striking similarities with the reported PFWNG.⁵⁷ This is corroborated in Fig. 4b, where significant electron transfer from NbN@GQD to the peripheral nitro groups is observed, especially in a region of pronounced decrease in electron density that appears on the Nb atom in NbN@GQD-(NO₂)₁₆. Consequently, the NbN subunits of NbN@GQD-(NO₂)₈ and NbN@GQD-(NO₂)₁₆ exhibit NPA charges of 0.651 |e| and 0.688 |e|, respectively (see Fig. S9c). Thus, the NPA charges on the NbN subunits follow the trend of NbN@GQD-(NH₂)₄ (0.552 |e|) < NbN@GQD (0.574 |e|) < NbN@GQD-(NO₂)₄ (0.618 |e|) < NbN@GQD-(NO₂)₈ (0.651 |e|) < NbN@GQD-(NO₂)₁₆ (0.688 |e|) (see Fig. 4c). This suggests that NbN@GQD with more electron-withdrawing substituents may exhibit superior catalytic performance for the Suzuki reaction.

Fig. 4 (a) Most stable structures and (b) EDD plots between the substituents and NbN@GQDs of NbN@GQD-(NO₂)₈ and NbN@GQD-(NO₂)₁₆ (isovalue = 0.001 a.u.), where red and blue colors indicate regions of increasing and decreasing electron density, respectively. (c) NPA charges on the NbN subunits of all the studied catalysts. Gibbs free energy profiles of the Suzuki reaction catalyzed by (d) NbN@GQD-(NO₂)₈ and (e) NbN@GQD-(NO₂)₁₆ with the corresponding geometric structures, where the spin multiplicity of each structure is indicated by the superscript and crucial bond lengths are given in Å. (f) Correlation analysis of rate-limiting energy barriers vs. d-band centers for all the studied NbN-based catalysts. (g) Rate-limiting energy barriers of the Suzuki reaction catalyzed by all the studied catalysts.

Fig. 4d and e exhibit the complete reaction mechanisms of the Suzuki reaction catalyzed by NbN@GQD-(NO₂)₈ and NbN@GQD-(NO₂)₁₆, respectively. Upon the introduction of more nitro groups, the oxidative addition steps exhibit negligible change in energy barriers, while the reductive elimination processes show gradually reduced energy barriers due to the enlarged VIE and VEA values. Notably, NbN@GQD-(NO₂)₁₆ demonstrated an exceptionally high VEA value of 4.47 eV, reducing its reductive elimination barrier to 13.6 kcal mol⁻¹. As a result, reductive elimination no longer serves as the rate-limiting step, while the transmetalation steps turn out to be the rate-determining steps with energy barriers of 22.3 and 19.3 kcal mol⁻¹ for NbN@GQD-(NO₂)₈ and NbN@GQD-(NO₂)₁₆, respectively.

Additionally, it is interesting to find that the rate-limiting barriers of these studied catalysts show a strong linear correlation with their low d-band center values (see Fig. 4f). Fig. 4g summarizes the rate-limiting barriers for all the studied catalysts. Comparative analysis confirms that the substitution of nitro groups gradually enhances the catalytic performance of NbN@GQD for the Suzuki reaction, which even surpasses the classical Pd(PPh₃)₂ catalyst with a rate-limiting barrier of 22.8 kcal mol⁻¹. Moreover, the NbN@GQD-(NO₂)₁₆ achieves comparable performance to that of Pd@GQD (19.2 kcal mol⁻¹).

To delve into the intrinsic mechanism of how substituent effects modulate the catalytic performance of NbN@GQD, the analysis of frontier molecular orbital (FMO) interactions⁵⁹ in these studied SSCs has been carried out and shown in Fig. 5. Fig. 5a and b present the MOs and density of states (DOS) of the five studied NbN-based SSCs. It is noted that the HOMO and LUMO energy levels of the five catalysts gradually shift downward, leading to a progressive reduction in their ability to donate electrons as the substituents surrounding the GQD support of these catalysts changed from amino ligands to ligand-free, then to the gradually increased nitro ligands. As a result, the VIE and VEA values of these catalysts also gradually increase with the enhancement of the inductive effect (see Fig. 5c), indicating a continuous improvement in their electron-accepting capability. Fig. 5d and S10 demonstrate that the catalysts always exhibit a tendency to withdraw electrons from the reactants in key reaction steps such as transmetalation and reductive elimination. Consequently, as the number of electron-withdrawing groups of NbN@GQD-(NO₂)_n (n = 4, 8, and 16) catalysts increases, the catalytic performance is significantly enhanced. These results demonstrate that the rational introduction of electron-withdrawing substituents can effectively improve the catalytic performance of such SSCs.

Fig. 5 (a) Molecular orbitals (MOs) and (b) density of states (DOS) diagrams of studied catalysts. The occupied and unoccupied energy levels are respectively represented by the blue and red lines in a. In b, the solid and dashed black lines denote the positions of the HOMO and LUMO levels for the α and β orbitals of each cluster, respectively. (c) Evolution of the VIE and VEA values of the studied catalysts. (d) NPA charges on the catalysts during reductive elimination in the mixed solution.

In addition, to comprehensively evaluate the practical utility of these proposed SSCs, the crucial aryl coupling step of losartan synthesis (a widely prescribed antihypertensive drug) catalyzed by NbN@GQD and NbN@GQD-(NO₂)₁₆ was simulated and shown in Fig. S11. It can be observed that the energy barriers of this considered step catalyzed by NbN@GQD and NbN@GQD-(NO₂)₁₆ are 23.3 and 14.7 kcal mol⁻¹, respectively, which suggests their potential in catalyzing the synthesis of real drugs in pharmaceutical manufacturing.

4. Conclusions

A novel GQD-supported single superatom catalyst (NbN@GQD) for the famous Suzuki reaction was designed and investigated in this DFT study. Results show that NbN@GQD has a moderate catalytic activity with a rate-limiting energy barrier of 25.7 kcal mol⁻¹ for this reaction, and modifying the GQD edge with electron-withdrawing nitro groups significantly enhances its catalytic performance. Further studies confirm that increasing the number of nitro groups leads to a progressive improvement in catalytic activity, and the fully substituted NbN@GQD-(NO₂)₁₆ catalyst achieves a comparable performance to that of the Pd@GQD catalyst. These findings not only provide an efficient way to achieve promising alternatives to traditional Pd-based SACs for C–C coupling reactions based on the superatom concept, but also offer a general strategy for enhancing catalytic performance through the rational modulation of the electronic structure of such SSCs. Additionally, since diverse coupling reactions share analogous fundamental steps, these proposed SSCs are also anticipated to demonstrate satisfactory efficacy in catalyzing other C–C or C–N coupling reactions. However, additional experimental and theoretical validation is required to substantiate this assumption.

Author contributions

Zhi-Chao Zhang: writing – data curation and formal analysis. Zi-Xin Ling: data curation and formal analysis. Shu-Ying Huang: validation and writing – review and editing. Wei-Ming Sun: conceptualization, supervision, methodology, software, funding acquisition, and writing – review and editing.

Conflicts of interest

There are no conflicts to declare. The data supporting this article have been included as part of the SI. Supplementary information: computational details; method and basis’ set test for the isomer I and energy barrier; VIE, VEA, LUMO, HOMO, and E_g values of ligated-NbN@GQD; Gibbs free energy profiles of Suzuki reaction catalyzed by Pd@GQD, NbN@GQD-L, NbN@GQD-3 and NbN@GQD-4; VDW, NPA, AICD and ADMP MD simulation plots of studied catalysts; structures of reductive elimination of Suzuki reaction catalyzed by studied catalysts; charges of NPA charges on catalysts during the transmetalation catalyzed by studied catalysts; cartesian coordinates of crucial structures. See DOI: https://doi.org/10.1039/d5nr02730f.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22373016) and Fujian Provincial Natural Science Foundation of China (2021J01682). Numerical computations were performed on the Hefei Advanced Computing Center and the National Supercomputing Center in Shenzhen.

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