Modelling the structural evolution, electronic structures and optical properties of Sc₆Se_n^0/- (n = 1–12) clusters

Abstract

The size-dependent structural evolution of scandium–selenium cluster remains poorly understood, particularly regarding the origin of growth transitions and the emergence of stable building blocks. Here, neutral and anionic Sc₆Se_n^0/- (n = 1–12) clusters were systematically investigated by global search techniques combined with B3LYP density functional theory calculations, with additional single-point validation at the B3LYP-D3(BJ) and DLPNO-CCSD(T) levels. The results reveal a clear two-stage growth behavior with n = 8 as the critical turning point. For n = 1–8, Se atoms sequentially occupy the eight electrostatic potential minima sites on the Sc₆ octahedral core, ultimately forming the highly symmetric Chevrel-phase Sc₆Se₈ cluster. This transition point is governed by both geometric and electronic factors. As a result, the clusters undergo structural reorganization for n = 9–12, giving rise to competing link-like and pentagonal-pyramidal motifs. Stability analyses based on average binding energy and second-order energy difference identify Sc₆Se₈ as the most distinguished cluster in the series. Simulated photoelectron, vibrational, and ultraviolet–visible spectra provide characteristic fingerprints for structural identification. In particular, Sc₆Se₈ exhibits pronounced aromaticity, strong visible-light absorption, and favorable excitonic features, highlighting its role as a magic super-atomic building block in the Sc–Se system.

The size-dependent structural evolution of scandium–selenium clusters remains poorly understood, particularly regarding the origin of growth transitions and the emergence of stable building blocks. Here, the authors combine global search techniques, density functional theory calculations and additional single-point validation to study neutral and anionic Sc₆Se_n^0/- (n = 1–12) clusters, reporting a two-stage growth behavior with n = 8 as the critical turning point, after which structural reorganization leads to competing link-like and pentagonal-pyramidal motifs.

Introduction

Metal selenides represent an important class of functional inorganic materials with unique structural, electronic, and optical properties, enabling broad applications in energy conversion, catalysis, microelectronics, and semiconductor technologies^1–3. Representative examples include high absorption coefficient and high efficiency CIGS (Cu(In,Ga)Se₂) solar cells⁴, high quantum yield (Zn,Cd)Se quantum dots^5,6, two-dimensional photo- and electrocatalytic (Mo,W)Se₂ materials^7,8, nano-structural NiSe₂ for supercapacitor electrode and superionic CoSe₂ conductor⁹, etc. Besides the above-mentioned applications, nanosized metal selenides possess attractive functionalization capability and improved biocompatibility, which are beneficial for constructing multifunctional platforms for bioimaging, biosensing, targeted drug delivery, and photothermal therapies. Representative examples include MoSe₂/Au@PEG for cancer photothermal therapies¹⁰, Rh₃Se₈ for bioimaging guidance¹¹, FeSe-based system for drug-delivery applications¹², etc. Driven by the growing needs of modern industry and society, the development of metal selenide nanomaterials has become a pressing priority across multiple scientific disciplines.

Pure selenium clusters possess distinctive structural motifs and electronic characteristics, which underpin their broad applicability in catalysis, energy-storage systems, and environmental remediation technologies^13,14. However, the presence of unsaturated Se–Se bonds and exposed lone-pair electrons renders selenium clusters intrinsically unstable, leading to structural degradation that compromises device durability. A feasible approach to improving stability and eliminating dangling bonds is to introduce transition metals into selenium clusters. For example, cadmium selenide clusters have attracted extensive attention due to their size-dependent electronic structures and tunable optical properties^15,16. In early 2006, Jose et al. integrated experimental characterization with ab initio density functional theory (DFT) calculation, revealing that the initial core was a (CdSe)₃ small cluster, and the presence of the ligand (HDA) assisted its growth to a larger (CdSe)_n (n ≥ 14) cluster¹⁷. Jager et al. employed a genetic algorithm with the DFT method to obtain the energy minimum Cd_xSe_y⁺ (x + y ≤ 26) structures. The results reveal strong composition-dependent trends, where the HOMO-LUMO and optical gaps can vary by more than 2 eV for a fixed size¹⁸. Xu et al. theoretically elucidate the structures and spectroscopic properties of small cadmium selenide clusters, where Cd₃Se₃, (Cd₃Se₃)₂, (Cd₃Se₃)₃, and Cd₄Se₄ represent the fundamental wurtzite and zinc blende structures, respectively¹⁹. Besides the above-mentioned, owing to the widespread use of CdSe in quantum dot technologies, a variety of theoretical investigations have been explored, such as (CdSe)_n (n = 1−16)²⁰, Cd₃₃Se₃₃²¹, and (CdSe)₁₆²², etc. Cui et al. present a systematic first-principles investigation of the size-dependent absorption, emission, and Stokes shifts of (ZnSe)_n (n = 1−13). The phenomenon of large Stokes shifts is attributed to the structural differences and electron delocalization on HOMO and LUMO levels²³. Nanavati et al. conducted a comparative study of (ZnSe)_n (n = 1−13) and surface passivation (ZnSe)_n (n = 1−13) by hydrogen atom. The results show surface passivation with partially charged H atoms removes dangling-bonds, restores local tetrahedral coordination, and significantly widens the HOMO–LUMO gaps²⁴. In addition to IIB group transition metal dopants, noble metals doping selenium clusters have also been studied^25,26. Li et al. employ the particle swarm optimization algorithm combined with the B3LYP functional to investigate the geometries, stabilities, and electronic structures of Cu_nSe (n = 1−8) clusters. The Cu_nSe clusters exhibit a clear dimensional evolution from one-dimension (n = 1) to two-dimension (n = 2) and three-dimension (n ≥ 3)²⁷. Guo et al. present a comprehensive DFT investigation of the geometries, relative stabilities, electronic structures, magnetic behaviors, and vibrational and electronic spectra of Cu_mSe_n (m + n = 5) clusters. The results show that stability is strongly correlated with the number of Cu-Se bonds and reaches a maximum for Cu₂Se₃²⁸. Zhang et al. present a comprehensive theoretical investigation of the geometric and spectroscopic properties of (CuSe)_n (n = 2−8). By TD-DFT calculation, such clusters have strong absorption in the 200–400 nm region and permissible excited-state transitions up to 10 eV, indicating that these clusters are promising UV-absorbing materials²⁹. Compared with the transition-metal doping strategy, rare-earth-element doping in selenium clusters has been far less explored and has mainly focused on diatomic systems, such as ScSe, YSe, PrSe, NdSe, SmSe, etc^30–32. The substantial potential of transition- and rare-earth–metal-doped selenium nanoclusters as advanced functional building blocks highlights the urgent need to develop new multifunctional materials³³.

Despite the substantial progress made for CdSe-, ZnSe-, and CuSe-based clusters, the size-dependent structural evolution and growth mechanism of scandium selenium clusters remain largely unexplored. Sc was selected in this study because, as an early transition metal with accessible valence orbitals and strong affinity toward selenium, it is expected to effectively stabilize selenium frameworks and significantly modulate their electronic structures. Existing studies on Sc–Se systems have mainly focused on diatomic species, and a systematic understanding of how Sc incorporation stabilizes selenium clusters, how the preferred structural motifs evolve with cluster size, and what drives the structural transition in the growth process is still lacking. In particular, it remains unclear whether a well-defined magic-size Sc–Se building block can emerge and how such a motif would influence the electronic and spectroscopic properties of the cluster series.

To address the above-mentioned gap, we systematically investigate neutral and anionic Sc₆Se_n^0/− (n = 1–12) clusters by combining global structural search with density functional theory calculations. The central question of this work is how scandium incorporation governs the size-dependent growth behavior of selenium clusters, especially why a distinct two-stage evolution occurs around n = 8. The results show that the growth pattern can indeed be divided into two regions: a pre-transition stage (n = 1–8), where Se atoms sequentially occupy the eight favorable adsorption sites on the Sc₆ octahedral core and ultimately form the Chevrel-phase Sc₆Se₈ cluster, and a post-transition stage (n = 9–12), where further Se addition induces structural reconstruction into competing link-like and pentagonal-pyramidal motifs. The change in motivation at n = 8 can be attributed to geometric growth and the complementary principle of electrostatic potential. On this basis, the relationships between structural evolution and relative stability, PES fingerprints, vibrational spectra, ultraviolet-visible spectrum, excitation behavior, aromaticity, and super-atomic character are further established. Particular attention is paid to Sc₆Se₈, whose outstanding performance across energetic, electronic, vibrational, and optical properties identifies it as a magic super-atomic cluster in the Sc–Se system.

Results and discussion

Evolution pattern and mechanism of Sc₆Se_n^0/− (n = 1−12)

Figure 1 shows the ground state structure and low-lying isomers of neutral Sc₆Se_n (n = 1−8) clusters calculated at the B3LYP level. The ground state structure of Sc₆Se_n (n = 1−8) calculated at B3LYP-D3(BJ) and DLPNO-CCSD(T) level are same as that at the B3LYP level. The structure and low-lying isomers of Sc₆Se_n (n = 1−8) at B3LYP-D3(BJ) are shown in Fig. S1, and each cluster energy of Sc₆Se_n^0/− (n = 1−12) at DLPNO-CCSD(T) level is collected in Table S2. Each neutral cluster is marked as Nx − y, where N, x, and y represent neutral, the number of Se atoms, and the energetic sequence from low to high. The spin multiplicities of the neutral Sc₆Se_n clusters are singlets, except for n = 5, which is a triplet, as seen in Supplementary Information, Table S1. Each cluster of electronic states is marked at figure. The growth of neutral Sc₆Se_n clusters (n = 1−8) is governed by a progressive face-capping process based on the Sc₆ octahedral framework. For the selenium-deficient clusters (n = 1−4), Se atoms are successively adsorbed on different faces of the Sc₆ octahedron, and the lowest-energy structures generally favor symmetric occupation of equivalent or opposite faces, indicating that dispersed face adsorption is energetically preferred at the early growth stage. As the Se content further increases (n = 5−6), the Se atoms successively capped on the vacant face of the Sc₆ octahedron and formed Se₂ subunits, reflecting Se–Se interactions in the cluster framework. For Sc₆Se₇, the low-lying structures can be regarded as defective derivatives of the Sc₆Se₈ Chevrel-phase cage. Upon reaching n = 8, the highly symmetric Sc₆Se₈ Chevrel-phase structure with O_h symmetry is formed, corresponding to the completion of face capping on the Sc₆ octahedral core and representing a particularly stable structural motif.

Fig. 1. Structures of Sc₆Se_n (n = 1–8) at B3LYP method.

The yellow and pink spheres represent Sc and Se atoms, respectively.

For anionic clusters, such an evolution mode also appears in anionic Sc₆Se_n⁻ (n = 1−8) cluster, whose structures are shown in Fig. S2. The ground state structures of Sc₆Se_n⁻ (n = 1−8) obtained by the B3LYP, B3LYP-D3(BJ), and DLPNO-CCSD(T) methods are consistent with Supplementary Information, Figs. S2, S3 and Table S2.

From Fig. 2, each neutral cluster is marked as Nx-L, Nx-P, and Nx-C, where N, x represents neutral, number of Se atoms, and L, P, C represent different three motif types of link-like, pentagonal-pyramidal, and cage‑like, respectively. When n > 8, the growth behavior changes markedly. In contrast to n = 1−8, for n = 9−12, the energetic ordering of the lowest-lying isomers becomes method-dependent. For the B3LYP method, the evolution of the ground-state structures is found to predominantly follow a link-like (L-type) growth pattern. By comparison, the B3LYP-D3(BJ) and DLPNO-CCSD(T) results show good consistency, both revealing that the link-like and pentagonal-pyramidal motifs are closely competitive in energy and alternate as the ground-state structures along the growth sequence. These results are also shown at anionic Sc₆Se_n⁻ (n = 9−12) cluster seen in Supplementary Information Fig. S4 and Table S2.

Fig. 2. Structures of Sc₆Se_n (n = 9–12) at B3LYP and B3LYP-D3(BJ) methods.

The yellow and pink spheres represent Sc and Se atoms, respectively.

That is, the ground state predictions at the B3LYP-D3(BJ) and DLPNO-CCSD(T) levels show that the energetic ordering for n = 1−8 is fully consistent with the B3LYP results, confirming the robustness of the pre-transition growth regime. In contrast, for n = 9−12, the energetic ordering of the lowest-lying isomers becomes method-dependent. This behavior indicates that the post-transition region is characterized by several near-degenerate motifs on a relatively flat potential-energy surface, where small differences in the treatment of dispersion and electron correlation can alter the ordering of competing structures.

To gain a deeper understanding of the growth mechanism of Sc₆Se_n^0/− (n = 1−12), a schematic structural evolution diagram is presented in Fig. 3. In general, the growth can be divided into two stages, namely the pre-transition region (n = 1−8) and the post-transition region (n = 9−12), with n = 8 acting as the critical turning point. This two-stage behavior is jointly governed by geometric and electronic-structure effects.

Fig. 3.

Schematic diagram of structural growth.

From the geometric point of view, Fig. 4a, b show the van der Waals (vdW) surface area and vdW volume of Sc₆Se_n (n = 1−12). Both quantities increase gradually with increasing Se content, while a pronounced jump is observed from n = 8 to n = 9, indicating a clear structural transition. From the electronic-structure perspective, Fig. 4c, d displays the electrostatic potential (ESP) distribution of the Sc₆ octahedral core and its ESP range. Notably, the Sc₆ octahedron possesses eight ESP minima, each located above the center of one octahedral face. Se atoms act as electron acceptors during the formation of Sc₆Se_n clusters. They tend to gain electrons, so they preferentially adsorb at the electron-rich sites (ESP minima) on the Sc₆ octahedral core. As a result, the NPA charges in Table S3 show that Se atoms carry negative charges in the final clusters. In other words, the Sc₆ octahedral core provides only eight active adsorption sites for Se atoms. When n < 8, the Se atoms are sequentially accommodated at these eight face-centered active sites, leading to the gradual construction of the Sc₆Se₈ Chevrel-phase structure. However, once the Se number increases to n = 9, all favorable adsorption sites on the Sc₆ octahedral core have already been occupied. Further Se incorporation can no longer be accommodated on the intact octahedral framework without introducing unfavorable geometric crowding and electronic destabilization. As a consequence, the system is driven to undergo structural reorganization, giving rise to the link-like and pentagonal-pyramidal growth motifs observed in the post-transition region.

Fig. 4. Geometric and electrostatic potential characteristics of Sc₆Se_n (n =1−12) cluster.

a VdW surface area of Sc₆Se_n (n = 1−12). b Volume of Sc₆Se_n (n = 1−12). c ESP-mapped vdW surface of Sc₆, with local minima and maxima marked by red and green spheres, respectively. d Surface area within each ESP range on the vdW surface of Sc₆.

Photoelectron spectroscopy of Sc₆Se_n⁻ (n = 1−12)

Photoelectron spectroscopy (PES) is a powerful technique with high energy resolution and strong sensitivity to structural variations, making it particularly suitable for the characterization and identification of nanoclusters. Accordingly, the PES of Sc₆Se_n⁻ (n = 1−12) were simulated using the Outer Valence Green Function (OVGF) method, and the results are shown in Fig. 5. The PES plots set a Gaussian broadening value of 0.25 eV and select a curve of energy less than 5.6 eV. Each peak from energy low to high is denoted as X, A to E in alphabetical order. The vertical detachment energy (VDE) obtained from the ΔSCF and OVGF methods is summarized in Fig. 6a, b, respectively. For Sc₆Se_n⁻ (n = 1−7), the simulated OVGF PES exhibits a relatively dense distribution of ionization features in the low-energy region, with small separations between adjacent peaks. In contrast, for n > 8, the PES profiles become much more resolved, with well-separated and clearly distinguishable peaks. The VDE values obtained from ΔSCF at the B3LYP and B3LYP-D3(BJ) levels are the same. As shown in Fig. 6a, the VDE values of Sc₆Se_n⁻ (n = 1−8) obtained from the ΔSCF at B3LYP and OVGF methods exhibit a good linear correlation, with R² values of 0.95 and 0.92, respectively. This consistency indicates that the predicted VDEs are robust and may serve as useful fingerprints for identifying specific clusters in future experiments. For Sc₆Se₉⁻, the two competing motifs, namely the link-like (L) and pentagonal-pyramidal (P) structures, exhibit similar PES profiles; however, they can still be distinguished by their VDE values, with the P structure showing a larger VDE than the L structure. For Sc₆Se_n⁻ (n = 10−12), the L and P motifs can be readily distinguished by both the number of PES peaks and their VDE values, with the L structures exhibiting larger VDEs than the corresponding P structures. As shown in Fig. 6b, the VDE values predicted by the ΔSCF and OVGF methods display similar size-dependent trends for both the L and P motifs, further supporting their use in the structural identification of specific clusters.

Fig. 5.

Simulated PES of Sc₆Se_n⁻ (n = 1−12) by OVGF method.

Fig. 6. Vertical detachment energies of Sc₆Se_n⁻ anions show a linear trend for n = 1−8 and a volcano-shaped trend for n = 8−12.

a Linear relationship of VDE of Sc₆Se_n⁻ (n = 1−8). b Volcano plot of VDE of Sc₆Se_n⁻ (n = 8−12).

Relative stabilities of Sc₆Se_n^0/− (n = 1−12)

To evaluate the stability of Sc₆Se_n^0/− (n = 1–12) clusters, the average binding energy (ABE) and second-order energy difference (Δ²E) were employed as the primary descriptors. The ABE and Δ²E values are defined by Eqs. (1), (2), and (3).

$$ABE\left({\mathrm{Sc}}_6{\mathrm{Se}}_n\right)=\frac{6E\left(\mathrm{Sc}\right)+nE\left(\mathrm{Se}\right)-E\left({\mathrm{Sc}}_6{\mathrm{Se}}_n\right)}{n+6}$$ 1

$$ABE\left({\mathrm{Sc}}_6{\mathrm{Se}}_n^{-}\right)=\frac{6E\left(\mathrm{Sc}\right)+E\left(S{e}^{-}\right)+\left(n-1\right)E\left(\mathrm{Se}\right)-E\left({\mathrm{Sc}}_6{\mathrm{Se}}_n^{-}\right)}{n+6}$$ 2

$${\Delta }^{2}E\left(S{c}_{6}S{e}_n^{0/-}\right)=E\left(S{c}_{6}S{e}_{n+1}^{0/-}\right)+E\left(S{c}_{6}S{e}_{n-1}^{0/-}\right)-2E\left(S{c}_{6}S{e}_n^{0/-}\right)$$ 3

Specifically, ABE reflects the global stability of a cluster by measuring its average binding strength, whereas Δ²E characterizes the relative stability of a given size with respect to its neighboring clusters and is therefore particularly sensitive to size-specific stabilization or magic-size behavior. Since ABE usually varies smoothly with cluster size, it mainly provides information on the overall strengthening of the cluster framework, but does not by itself identify whether a particular size is exceptionally favored. In contrast, Δ²E is well suited to highlight local stability anomalies within the size series. Therefore, the combined use of ABE and Δ²E provides a more balanced assessment of cluster stability from both global and local perspectives.

As shown in Fig. 7a, b, the B3LYP level results reveal that the ABE and Δ²E provide complementary views of cluster stability. In Figs. 7a, for 1 ≤ n ≤ 8, the ABE values of both neutral and anionic clusters generally increase as the number of Se atoms grows, indicating that the progressive incorporation of Se atoms substantially stabilizes the Sc₆ framework. For Sc₆Se_n (n = 9−12), the ABE curve shows a slight decline and then levels off, suggesting that the major energetic stabilization has already been achieved upon formation of the Sc₆Se₈ framework. Due to the closed shell electronic structure of neutral clusters (except for Sc₆Se₅), the ABE of neutral clusters is consistently higher than that of their corresponding anionic counterparts, which can be proved by NPA analysis in Table S3 (Supplementary Information). The Δ²E curves in Fig. 7b exhibit three distinct peaks at n = 4, 6, and 8, indicating that such a cluster is more stable than its adjacent ones. Notably, the combined ABE and Δ²E results at the B3LYP level consistently identify Sc₆Se₈ as the most stable cluster with a magic-size feature in the series from both global and local perspectives. The same conclusion is further supported by the DLPNO-CCSD(T) level results shown in Fig. 7c, d. Although the ground state structures predicted by DLPNO-CCSD(T) level for n = 9–12 are not fully identical to those obtained at the B3LYP level, the overall ABE trend remains unchanged, and Sc₆Se₈ still exhibits the largest ABE value in the series. More importantly, the Δ²E curves in Fig. 7d again highlight Sc₆Se₈ as the most pronounced stability maximum in the size series.

Fig. 7. Stability trends of neutral and anionic Sc₆Se_n clusters are evaluated through average binding energies and second-order energy differences at two levels of theory.

a Average binding energies of Sc₆Se_n^0/− (n = 1–12) at the B3LYP level. b Second-order energy differences (Δ²E) at the B3LYP level. c ABEs at the DLPNO-CCSD(T) level. d Δ²E at the DLPNO-CCSD(T) level.

Therefore, the Sc₆Se₈ Chevrel-phase structure with O_h symmetry exhibits both the highest overall stability and the strongest relative stability with respect to its neighboring sizes, and can be identified as the magic cluster in the series.

Besides the above-mentioned, the energy gap (E_gap) as a type of important intrinsic physicochemical property, calculated by Eq. (4), is collected in Fig. S5.

$$\Delta E_{\mathrm{gap}}=\epsilon \left(\mathrm{lowest}\mathrm{unocc}\mathrm{among}\alpha ,\beta \right)-\epsilon \left(\mathrm{highest}\mathrm{occ}\mathrm{among}\alpha ,\beta \right)$$ 4

To further determine the effect of temperature, AIMD simulations were performed for each ground-state structure at 298.15 K for 2000 fs, and the results are presented in Figs. S6 and S7. It can be clearly seen that after 2000 fs, the structure is not decomposing; each minimum-energy structure obtained from the AIMD simulation corresponds to the selected structure, further indicating that the optimized structure at the B3LYP level is a local minimum on the potential energy surface.

Infrared and Raman spectra of Sc₆Se_n^0/− (n = 1−12)

Infrared and Raman spectra provide key structural characteristics and bond vibrations of clusters. The main difference between an IR-active mode and a Raman-active mode lies in the corresponding selection rule: IR intensity is associated with a change in dipole moment during vibration, whereas Raman intensity is governed by a change in polarizability. Consequently, the dominant peaks in the two spectra of the same cluster are not necessarily identical. In general, vibrational modes dominated by directional Se–Sc bond stretching or bending tend to generate stronger IR intensity, whereas symmetric breathing or collective framework deformations more effectively enhance Raman intensity. The theoretical IR and Raman spectra of neutral Sc₆Se_n (n = 1–12) are shown in Figs. 8 and 9. The anionic clusters show spectral features and dominant vibrations similar to neutral counterparts seen in Supplementary Information, Fig. S8.

Fig. 8. IR and Raman spectra of Sc₆Se_n (n = 1–8).

The blue arrows indicate vibrational displacement direction.

Fig. 9. IR and Raman spectra of Sc₆Se_n (n = 9–12).

The blue arrows indicate vibrational displacement direction.

As shown in Fig. 8, for Sc₆Se_n (n = 1−8), the strongest Raman peaks are mainly characterized by breathing modes centered on the Sc₆ octahedron core, involving concerted inward and outward radial displacements. These motions of the Sc₆-centered skeleton produce pronounced Raman responses. In contrast, the strongest IR peaks are mainly associated with directional Se–Sc stretching, stretching-coupled wagging, asymmetric stretching, scissoring, or bending vibrations, which induce larger dipole-moment changes during vibration. Therefore, for n = 1–8, the dominant Raman peaks mainly reflect breathing-type motions of the Sc₆ core framework, whereas the dominant IR peaks are governed primarily by localized directional bond vibrations.

As shown in Fig. 9, the IR spectra of Sc₆Se_n (n = 9−12) exhibit two internally consistent patterns according to structural type. For the link-like structures, the strongest IR peaks at 347, 337, 333, and 323 cm⁻¹ are dominated by direction-selective Se–Sc stretching-dominated framework deformations. For the pentagonal-pyramidal structures, the strongest IR peaks at 356, 351, 346, and 329 cm^-1 display the same character.

Overall, the IR and Raman spectra of Sc₆Se_n (n = 1–12) provide useful vibrational fingerprints for structural identification. For n = 1–8, the dominant spectral features in the 236–272 cm⁻¹ region are characterized by breathing motions of the Sc₆ centered framework, which are characteristic of octahedral–core–based structures. In contrast, for n = 9–12, the dominant spectral features shift to the 323–356 cm⁻¹ region, where the strongest peaks of both link-like and pentagonal-pyramidal isomers are dominated by Se–Sc stretching dominated framework deformations, indicating the formation of reconstructed Se–rich motifs. Therefore, the evolution of the characteristic IR and Raman peaks directly reflects the structural transition from Sc₆ core-based clusters to reconstructed Se–rich frameworks.

To further elucidate the vibrational characteristics of the Sc doped Se clusters, Sc₆Se₈ is selected as a representative structure. The potential energy distribution (PED) analysis is performed using the VEDA program developed by Jamróz^34,35. The IR and Raman-active vibrational modes of Sc₆Se₈ are shown in Fig. 10, and the corresponding calculated frequencies ν_calc, IR intensities I_IR, Raman activities A_R, symmetry, PED contributions, and Vibration modes are summarized in Table 1. The most intense IR-active mode at 310.40 cm⁻¹ is a triply degenerate T_1u vibration, which corresponds to opposite stretching vibrations between the central Sc₄ ring and the Se₄ ring on both sides along the X, Y, and Z directions, respectively. The PED analysis shows that the internal coordinates s9, s12, and s10 contribute mainly about 14%, 10%, and 11%, respectively. In contrast, the most intense Raman-active mode at 236.23 cm⁻¹ is an A_1g vibration, mainly presenting a breathing vibration of the Sc₆ octahedron. Its PED is dominated by the internal coordinate s30, with a contribution of about 13%. These two dominant modes provide a representative example of the different vibrational origins of the strongest IR and Raman responses: the former is dominated by directional stretching motions, whereas the latter is associated with a highly symmetric breathing mode. The mode at 204.49 cm⁻¹ is another triply degenerate IR-active T_1u vibration, corresponding to the coupled stretching vibration of the two Sc atoms and opposite torsional vibration of the two Se₄ ring along the X, Y, and Z directions. Its major PED contributions come from s26 (13%), s10 (10%), and s2 (10%). The 188.06 cm⁻¹ mode is dominated by a breathing vibration of the Se₈ unit. The IR-active mode at 140.70 cm⁻¹ is also a triply degenerate T_1u vibration mixing with the bending vibration of Sc₆ octahedron and opposite rocking vibration of Se₈ along the X, Y, and Z directions, with major PED contributions coming from s25 (12%), s22 (17%), and s16 (10%). The Raman-active modes at 131.05 cm⁻¹ and 111.15 cm⁻¹ both are triply degenerate T_2g vibrations. The former involves torsional and stretching vibrations of the Se₈ unit, whereas the latter involves bending and rocking vibrations of the Se₈ unit together with rocking vibrations of the Sc₄ unit. The 122.81 cm⁻¹ mode is a doubly degenerate E_g vibration involving bending, torsional, and breathing vibration along the Z and Y directions, with major PED contributions coming from s19 (15%) and s27 (10%).

Fig. 10.

Vibrational modes of Sc₆Se₈, the blue arrows indicate vibrational displacement direction.

Table 1.

The ν_calc (cm⁻¹), I_IR (km/mol), A_R (Åamu⁻¹), Symm, PED (%), and vibration modes of Sc₆Se₈ clusters

νcalc	IIR	AR	Symm	PED	Vibration modes
310.40	119.66	0	T1u	s9 (14); s12(10); s10(11)	STRE
236.23	0	107.14	A1g	s30(-13)	OUT
204.49	56.52	0	T1u	s26(-13); s10(10); s2(-10)	TORS + STRE
188.06	0	16.43	T2g	/	/
140.70	8.63	0	T1u	s25(-12); s22(17); s16(-10)	BEND + OUT
131.05	0	7.63	T2g	s3(10); s1(-10); s6(-11)	STRE + TORS
122.81	0	7.05	Eg	s19(15); s27(10)	BEND + OUT + TORS
111.15	0	6.48	T2g	s24(-10); s15(18); s31(-12)	BEND + OUT

Notably, because the Sc₆Se₈ cluster belongs to the O_h symmetry, vibrational motions along symmetry-equivalent directions become energetically equivalent, giving rise to triply degenerate T_1u and T_2g modes and doubly degenerate E_g modes. In this sense, the rich set of degenerate vibrations arises from the high symmetry of the Chevrel-phase framework.

Super-atomic character of the Sc₆Se₈ nanocluster

To elucidate the intrinsic electronic origin of the magic stability of the Sc₆Se₈ cluster, NPA, Adaptive Natural Density Partitioning (AdNDP)³⁶, and molecular orbital (MO) analysis were carried out, as shown in Table S3 and Fig. 11a, b.

Fig. 11. Electronic structure and bonding pattern of the Sc₆Se₈ cluster revealed by molecular orbital and AdNDP analyses.

a Molecular orbital. b Adaptive Natural Density Partitioning (AdNDP) analysis.

As shown in Table S3, the NPA results indicate that the Se 4s electrons are largely localized. Correspondingly, from Fig. 11b, the AdNDP analysis identifies eight Se-centered one-center two-electron (1c–2e) lone pairs with occupation numbers of about 1.79 |e|, indicating that 16 electrons are localized as nonbonding electron pairs on the Se atoms. The remaining 50 electrons, mainly derived from the Se 4p² and Sc 3d¹4s² valence orbitals, can be assigned to twenty-four 2c–2e bonds and one 6c–2e delocalized bond. So, as shown in Fig. 11b, the closed-shell configuration satisfies the super-atomic rule of 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁶2D¹⁰. Therefore, Sc₆Se₈ can be regarded as a magic cluster with enhanced stability.

Ultraviolet‒visible spectrum of the Sc₆Se₈ nanoclusters

Because of the outstanding stabilities of Sc₆Se₈ observed, the further optical properties are explored. The ultraviolet‒visible (UV‒vis) spectrum of Sc₆Se₈ is calculated by time-dependent density functional theory (TD-DFT)³⁷ at B3LYP with the BS-3 basis set level. The 120 excited states are considered to cover the full UV‒vis region. The simulated UV–vis spectrum is shown in Fig. 12a with a Gaussian broadening of 0.25 eV, where S denotes the singlet state. As illustrated in Fig. 12a, four distinct absorption peaks can be clearly identified. The strongest peak at 621 nm corresponds to the transition of the ground state S₀ to S₄ (99.9%). To further understand the transition feature, the natural transition orbital (NTO) analysis³⁸ is performed and shown in Fig. 12b. The transition of S₀ → S₄ originates primarily from the NTO pair transfer of NTO199 → NTO200 (91.8%), where NTO199 and NTO200 correspond to the highest occupied natural transition orbital (HONTO) and the lowest unoccupied natural transition orbital (LUNTO), respectively. The absorption peak at 503 nm primarily originates from the transitions of S₀ → S₁₅, contributing 99.9%. It can be composed of two pairs of NTO transition of NTO199 → NTO200 (48.7%) and NTO198 → NTO201 (48.7%). The second strongest peak appears at 444 nm and is mainly contributed by the S₀ → S₂₉ (81.9%) and S₀ → S₄₁ (18.0%). The former is dominated by the NTO transitions NTO199 → NTO200 (43.3%) and NTO198 → NTO201 (43.3%), while the latter is primarily associated with the NTO199 → NTO200 (84.4%). The absorption peak at 338 nm primarily originates from the transitions of S₀ → S₁₁₂ with a contribution of 99.9%, which corresponds to four pairs of NTO transitions, including NTO199 → NTO200 (25.1%), NTO198 → NTO201 (25.1%), NTO197 → NTO202 (10.2%), and NTO196 → NTO 203(9.5%).

Fig. 12. The optical absorption of Sc₆Se₈ is characterized by its simulated UV–vis spectrum and the dominant natural transition orbitals.

a Simulated UV‒vis spectrum of Sc₆Se₈. b Natural transition orbitals (NTOs) for the main excitation contribution.

It can be observed that the ultraviolet-visible (UV–vis) spectrum of the Sc₆Se₈ cluster covers the range from 300 to 800 nm. Moreover, the visible-light region contributes 98.7% of the total absorption, suggesting that the cluster possesses a strong visible-light response and is highly promising for applications in solar energy conversion and optoelectronic devices.

To further estimate the potential of Sc₆Se₈ as ideal self-assembly semiconductor materials, the crystal structure is constructed, as shown in Fig. 13a. The UV‒vis spectrum of the solid phase was calculated by TD-DFT at the PBE level. The visible-light region contributes more than 90% of the total absorption, further proved it as assembly building block can be promising used for optoelectronic semiconductor materials.

Fig. 13. The crystal structure and corresponding simulated optical absorption of Sc₆Se₈ are shown.

a Crystal structure of Sc₆Se₈. b Simulated UV‒vis spectrum of Sc₆Se₈.

Excitation behavior analysis of the Sc₆Se₈ nanocluster

To gain deeper insights into the excitation behavior of Sc₆Se₈, the hole-electron analysis and inter-fragment charge transfer (IFCT) developed by Lu et al.³⁹ is performed. Figure 14 shows the hole (blue) and electron (gray) iso-surfaces in several key excitations. The fragments 1 and 2 are assigned to the Sc₆ octahedron and the Se₈ cube. For S₀ → S₄ (621 nm), the charge transfer is from Se₈ to Sc₆ with 0.10 a.u. electron. The hot mapping reveals it belongs to local excitation (LE) with an intrinsic local excitation percentage of 67.4%. For S₀ → S₁₅ (503 nm), the excitation behavior expresses clearly charge transfer (CT) excitation. From iso-surfaces and hot mapping, the charge transfer from Se₈ to Sc₆ with 0.68 a.u. electron. The peak at 444 nm mainly originated from two transitions of S₀ → S₂₉ and S₀ → S₄₁. For S₀ → S₂₉, similar to S₀ → S₁₅, the obvious CT excitation is observed, which is 0.59 a.u. electron from Se₈ to Sc₆. The hot mapping also reveals that charge transfer from fragment 2 blue to fragment 1 red. For S₀ → S₄₁, it describes the dominant LE with 62.32% of intrinsic local excitation and 37.68% of intrinsic charge transfer. For S₀ → S₁₁₂ (338 nm), as shown in hot mapping, it exhibits an obvious direction from Se₈ to Sc₆, corresponding to CT excitation.

Fig. 14. The hole-electron iso-surfaces and hot mapping of S₀ to S₄, S₁₅, S₂₉, S₄₁, S₁₁₂.

The blue and gray regions represent the hole and electron regions.

To quantitatively characterize the excitation behavior of Sc₆Se₈, several indicators are collected in Table 2. The index D(Å) is defined as the distance between the center of mass of the holes and electrons. For Sc₆Se_8, D(Å) equals zero, indicating that the center of mass of holes and electrons overlaps in the center cage of Sc₆Se₈. The indicators S_r, t(Å), and H(Å) are employed to evaluate the degree of hole-electron separation. For S₀ → S₁₅, S₀ → S₂₉, and S₀ → S₁₁₂, their S_r values are smaller than those of S₀ → S₄ and S₀ → S₄₁, indicating the difference between CT excitation and LE. All t(Å) values are negative, indicating that the charge transfer is not unidirectional. The H(Å) reflects the average distribution of electrons and holes. The transitions of CT excitation type exhibit larger H(Å) values. The hole delocalization index (HDI) is smaller than the electron delocalization index (EDI) for each transition, indicating that the electrons are more delocalized than the holes. The exciton binding energy reflects the stability of the exciton. All transitions show larger exciton binding energy values (E_coul > 3 eV), which is beneficial for optoelectronic and photonic device applications.

Table 2.

The D, S_r, H, t, coulomb attraction energy, HDI, and EDI indices of excitation state of 621, 503, 444, and 338 nm of Sc₆Se₈ nanocluster

Cluster	Transition	D(Å)	Sr	t(Å)	H(Å)	Ecoul	HDI	EDI
621 nm	S0 → S4	0	0.66	−1.40	2.82	4.38	5.15	8.28
503 nm	S0 → S15	0	0.38	−1.64	3.24	4.13	3.66	6.51
444 nm	S0 → S29	0	0.55	−1.87	3.13	4.21	3.36	5.60
444 nm	S0 → S41	0	0.61	−1.74	2.98	4.03	4.77	5.86
338 nm	S0 → S112	0	0.59	−1.85	3.21	3.44	2.68	4.52

Aromaticity of the Sc₆Se₈ nanocluster

As optoelectronic building block materials, stability is crucial for maintaining reliable optical responses and long-term device performance. The stability can be effectively evaluated using iso-chemical shielding surfaces (ICSS)⁴⁰. In three-dimensional space, each point is assigned an ICSS value, which is defined as the negative of the nucleus-independent chemical shift (NICS)⁴¹. The ICSS is calculated by the gauge-independent atomic orbital (GIAO)⁴² method at the B3LYP level. As shown in Fig. 15a, the red iso-surface (0.05 ppm) corresponds to magnetic shielding regions, and the blue iso-surface (−0.05 ppm) corresponds to de-shielding regions. Due to the O_h symmetry of the cluster, the shielding and de-shielding regions show a distinct symmetric distribution. Figure 15b shows the ICSS value along the line from the cage center to the outer region. The maximum ICSS value reaches 5.15 ppm at the cage center, indicating a significant magnetic shielding effect in the inner-cage region. As the distance increases, the shielding value gradually decreases. At 0.53 Å out of the center, the ICSS value changes from positive to negative, meaning the critical position from the magnetic shielding region to the de-shielding region. When the distance increases to 1.2 Å, the ICSS value reaches the minimum of -5.96 ppm, corresponding to the strongest magnetic de-shielding effect. Figure 15c shows the color-filled ICSS cross-section. Warm and cool colors correspond to regions with higher and lower magnetic shielding, respectively. The color-filled cross-section agrees with ICSS iso-surfaces, and the cage center exhibits pronounced magnetic shielding. Overall, Sc₆Se₈ displays aromatic character, which contributes to the enhanced stability of the whole cluster.

Fig. 15. The magnetic shielding environment of the Sc₆Se₈ cage is characterized by ICSS iso-surfaces, line profiles, and cross-section maps.

a ICSS iso-surfaces of Sc₆Se₈. b ICSS value along a line from the cage center to the outer region. c Color-filled cross-section of the ICSS.

Conclusion

In summary, the structural evolution, stability, and spectroscopic properties of neutral and anionic Sc₆Se_n^0/− (n = 1–12) were systematically investigated by a global search technique combined with density functional theory calculation. The results reveal a distinct two-stage growth pattern with n = 8 as the critical turning point. For n = 1–8, Se atoms sequentially occupy the eight EPS minima sites on the Sc₆ octahedral core, leading to the formation of the highly symmetric Chevrel-phase Sc₆Se₈ cluster. For n = 9–12, further Se incorporation induces structural reorganization into competing link-like and pentagonal-pyramidal motifs. This transition originates from the combined effects of geometric site saturation and electronic-structure reorganization. Method comparison further confirms that the energetic ordering is robust for n = 1–8, whereas the post-transition region is associated with a relatively flat potential-energy surface.

The stability analyses based on average binding energy and second-order energy difference consistently identify Sc₆Se₈ as the most distinguished cluster in the series. Spectroscopic simulations, including PES, IR, Raman, and UV–vis results, further establish clear structure-dependent signatures that are useful for distinguishing different cluster motifs. The outstanding aromatic, strong visible-light absorption, super-atomic and excitonic properties of Sc₆Se₈ further indicate that this cluster is not only a stability maximum, but also a suitable building block for next-generation semiconductor optoelectronic materials.

Methods

All computations were carried out using the Gaussian 09 quantum chemistry package⁴³. The initial structures were generated by ABCluster software^44–46. Each anionic and neutral Sc₆Se_n^0/− (n = 1–12) with 400 initial isomers were optimized by B3LYP functional^47,48 with BS-1 (Sc for LANL2DZ⁴⁹ and Se for ECP28MWB⁵⁰). Second, the low-lying isomers within 0.8 eV were further optimized at the B3LYP level using the BS-II (Sc and Se for def2-TZVP⁵¹). Frequency calculations were performed to confirm that the optimized structures correspond to true local minima. Finally, single point energies were calculated at the B3LYP level using the BS-III (Sc and Se for def2-TZVPPD^51,52). Visualization of results was performed using Multiwfn^53,54 and VMD software⁵⁵.

o investigate the method effect of Sc₆Se_n^0/− (n = 1–12), each ground state structure was calculated with a single point energy at the BS-III basis set by B3LYP-D3(BJ)^47,48,56,57, and DLPNO-CCSD(T)^58–60 in ORCA⁶¹. The Natural Population Analysis (NPA) was performed by the NBO 7⁶² software.

The solid phase of Sc₆Se₈ was visualized by VESTA⁶³, and its ultraviolet-visible spectrum was simulated by CP2K^64,65 quantum chemistry software using the PBE functional⁶⁶, with basis set DZVP-MOLOPT-SR-GTH-q11^67,68 for Sc and DZVP-MOLOPT-SR-GTH-q6^67,68 for Se.

The PES spectra were simulated using the Outer Valence Green’s Function (OVGF)^69,70 method with the aug-cc-pVDZ basis set for Sc^71,72 and Se⁷³, respectively.

The Ab Initio Molecular Dynamics (AIMD) of each cluster was performed by the B97-c functional⁷⁴ using the ORCA software. Such a method contains the def2-mTZVP basis set and Becke−Johnson damping scheme (D3-BJ).

Author contributions

Liyuan Hou: Writing—original draft. Jucai Yang: Visualization, Supervision. Chenliang Hao: Formal analysis. Xueyan Dong: Writing—review & editing, Supervision. Caixia Dong: Data curation, Conceptualization. Zhaofeng Yang: Writing—review & editing, Supervision, Funding acquisition.

Peer review

Peer review information

Communications Chemistry thanks Peter L Rodríguez-Kessler and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Funding

Zhaofeng Yang discloses support for the research of this work from the National Natural Science Foundation of China [grant number 22563006], the Inner Mongolia Autonomous Region High-Level Talent Introduction and Research Support Project [grant number DC2400002178], the Doctoral Initiation Fund Project of Inner Mongolia University of Technology [grant number BS2024059], the Central Guidance for Local Scientific and Technological Development Funding Projects [grant number 2024ZY0134], the Special Programs for Research in First-Class Disciplines [grant number YLXKZX-NGD-016], and the Key Laboratory of Environmental Pollution Control and Remediation at Universities of the Inner Mongolia Autonomous Region. Xueyan Dong discloses support for the research of this work from the Inner Mongolia Natural Science Foundation [grant number 2022MS02001], the Doctoral Initiation Fund Project of Inner Mongolia University of Technology [grant number DC2300001273]. Jucai Yang discloses support for the research of this work from the Talent Revitalizing Inner Mongolia Project [grant number 2025TEL09]. All other authors declare no relevant funding.

Data availability

All data needed to evaluate the conclusions in this study are provided in the manuscript, Supplementary Information, and Supplementary Data files. All the data used for plotting and structure coordinates are provided in the Supplementary Data (xlsx).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42004-026-02068-6.