Structural, Vibrational, and Electronic Properties of Copper-Doped Silicon and Germanium Cation Clusters CuX _n ⁺ (X = Si or Ge, n = 6–16): A Density Functional Theory Study

Abstract

The incorporation of transitional elements into silicon or germanium-based semiconductor clusters not only notably improves their structural stability but also endows them with unprecedented multifunctionalities. In this work, the structural, vibrational, and electronic properties for copper-doped silicon and germanium cation clusters CuX _n ⁺ (X = Si or Ge, n = 6–16) are systematically investigated. The ground-state structures are identified using the PBE0 and mPW2PLYP method combined with a global search technique. The structure evolutions of CuSi _n ⁺ and CuGe _n ⁺ are both from adsorption to endohedral configurations. The transfer point for CuGe _n ⁺ is at n = 9 earlier than CuSi _n ⁺ at n = 12 due to the larger ionic radius of Ge compared to Si, which was further proven by the consistency between the simulated and the available experimental infrared spectra. Through comparative analysis of average binding energies and bond lengths, it is found that CuSi _n ⁺ exhibits higher stability than CuGe _n ⁺ of the same size. According to calculation results, the CuGe₁₀ ⁺ cluster has excellent stability, high structure symmetry, a proper HOMO–LUMO gap, and a wide absorption band in the visible light range, making it a potential candidate for semiconductor nanomaterials and photodetector applications.

1. Introduction

Silicon and germanium clusters have consistently attracted considerable interest from researchers due to their outstanding semiconductor properties, holding significant potential for applications in the field of microelectronics. − However, pure silicon and germanium clusters are inherently unstable due to the presence of dangling bonds in cluster surface, which can be overcome by doping with different elements to gain stabilities, interesting structures, and novel properties. − For example, doping with transition metals (TMs) has been shown to significantly improve cluster stability and bestow intriguing physical and chemical characteristics. − Numerous studies have reported the synthesis of transition-metal-doped silicon and germanium nanoclusters (e.g., Fe, Ru, Ti, Au, Cu) via laser vaporization. , The products, including CoSi _n ^– (n = 3–12), Au₂Si _n ^–/0 (n = 1–7), MnGe _n ^– (n = 3–14), FeGe _n ^–/0 (n = 3–12), and TiGe _n ^– (n = 7–12), have been extensively studied experimentally using photoelectron spectroscopy and quantum calculations. Ma et al. employed the generalized gradient approximation (GGA) functional to investigate the geometric configurations and magnetic properties of FeSi _n (n = 2–14) clusters. Their findings indicate that as the cluster size increased, the Fe atom moved from the Si clusters surface into the Si cage. Similarly, Wang et al. used the PW91 functional to systematically study the structures and magnetic properties of CoSi _n (n = 2–14) clusters. Their research shows that at n = 10, Co atoms are fully encapsulated within the Si cage, forming an endohedral structure, and that the clusters exhibit magnetic quenching at n = 7. Numerous literature reports indicate that a wide variety of transition-metal dopants can be encapsulated within silicon or germanium frameworks to yield thermodynamically stable endohedral cage structures. − Additionally, Nguyen et al. investigated the electronic structures of small-sized TiGe₂ ^–/0, VGe₃ ^–/0, and CrGe _n ^0/+ (n = 1–5) clusters using the multiconfigurational methods CASSCF/CASPT2 and CASSCF/NEVPT2. − Tran et al. employed similar multiconfigurational approaches to study the electronic structures and properties of small sized NbGe _n ^–/0/+ (n = 1–3) and VGe _n ^–/0 (n = 5–7) clusters. ,

Copper-doped silicon clusters, as typical semiconductors, also are widely researched. , Beck pioneered the study of the mass spectra of copper-doped silicon clusters using laser vaporization and supersonic expansion techniques. Duncan and colleagues investigated the photodissociation spectra of copper-doped silicon clusters and found that the dissociation of CuSi₇ ⁺ and CuSi₁₀ ⁺ clusters is primarily, indicating that copper atoms are on the surface rather than inside the silicon cage. Lievens and colleagues studied copper-doped silicon clusters through argon physical adsorption and found that the argon adsorption on CuSi _n ⁺ clusters significantly decreased at n = 12. , Recently, they measured the far-infrared vibrational spectra of MSi _n ⁺ (M = Cu, V) using argon-tagged infrared multiphoton dissociation (IR-MPD) techniques. Xu et al. systematically studied the structure and photoelectron spectra of CuSi _n ^– (n = 4–18) clusters using photoelectron spectroscopy combined with density functional theory. The results showed that the ground-state configuration of CuSi₁₂ ^– is a cage structure. Besides the experiment of copper-doped silicon clusters, there have been many theoretical studies on the structure and electronic properties of copper-doped silicon clusters. Early studies extensively investigated the geometric configurations, stability, and bonding characteristics of small CuSi _n (n = 1–6) clusters. − Recently, medium-sized CuSi _n (n = 8–16) clusters have also been systematically studied. − Despite extensive reports on the ground-state configurations of copper-doped silicon clusters, there are still controversies regarding the ground-state structure of CuSi₁₀ and the critical size for cage structures in CuSi _n clusters. For instance, recent theoretical studies suggest that the stable configuration of CuSi₁₀ is the D _5h endohedral structure and propose that n = 9 may be the minimum size for the silicon cage encapsulating a copper atom. In 2015, Lin et al. theoretically calculated that the stable configuration of neutral CuSi₁₀ is the D _4h endohedral structure, while the anion CuSi₁₀ ^– is the noncage structure.

Compared to copper-doped silicon clusters, there are far fewer research reports available on copper-doped germanium clusters currently. − Bandyopadhyay systematically studied the structure and electronic properties of CuGe _n (n = 1–20) and pointed out that CuGe₁₀ has excellent stability. In 2018, Rabilloud et al. used the PBE functional to systematically study the geometries and electronic structures of MGe _n (M = Cu, Au, Ag; n = 1–19) and concluded that the stable configurations of CuGe _n clusters are cage structures when n ≥ 10. Recently, our research group systematically studied the ground-state configurations and related electronic properties of neutral and anionic CuGe _n ^0/– (n = 4–13) using double-hybrid density functional methods. The study found that both neutral and anionic clusters exhibit cage structures at n = 9.

As previously mentioned, systematic quantum chemical studies on CuGe _n ⁺ are rare and most research on CuSi _n ⁺ clusters is experimentally based. Additionally, the structural and property similarities and differences between transition-metal-doped silicon and germanium clusters warrant further investigation. Herein, this manuscript systematically studies the ground-state configurations, evolution laws, vibrational properties, and related electronic properties of cationic CuX _n ⁺ (X = Si or Ge; n = 6–16) clusters using the double-hybrid density functional mPW2PLYP combined with global search techniques. This study aims to provide valuable insights for the research of other transition-metal-doped silicon and germanium clusters and to offer critical information for the development of new types of assembled nanomaterials.

2. Computational Method

The initial configurations of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) clusters were obtained using the Artificial Bee Colony Cluster (ABCluster) global search technique, − which has been widely used in many studies. − Typically, the ABCluster is an initial structures generator. The initio structures generated by ABCluster at least 400 isomers were optimized by the PBE0 method with basis sets using cc-pVDZ-PP for Si and Ge atoms and the small-core pseudopotential basis set ECP10MWB for Cu atoms. Additionally, configurations in other literature studies were reported, and substitution configurations of pure silicon clusters were calculated as a supplement. After the initial screening of isomers with relatively low energy, the PBE0 method combined with basis set cc-pVTZ wasused for second optimization. The optimization process did not restrict the symmetry of the configurations and considered the harmonic vibrations of each configuration to ensure that the optimized isomers are local minima on the potential energy surface. Based on this, further optimization was carried out using the high precision mPW2PLYP method combined with the cc-pVTZ basis set. The mPW2PLYP method is a double-hybrid density functional method that combines a fraction of exact Hartree–Fock exchange with second-order Mo̷ller–Plesset perturbation theory (MP2) like correlation correction to the density functional theory (DFT) calculation. This approach aims to improve the accuracy of the DFT calculations by incorporating higher-level electron correlation effects. Finally, the single-point energy of each optimized configuration was calculated by using the aug-cc-pVTZ basis set with dispersion functions under the mPW2PLYP method to ensure the accuracy of the ground-state configurations. All calculations were completed using the Gaussian 09 software package and all configurations are in the singlet electronic state.

The ab initio molecular dynamics (AIMD) of lowest energy structure of CuX _n ⁺ (X = Si or Ge, n = 6–16) were obtained using Orca software by the B97-c functional with def2-mTZVP for Cu Si and Ge atoms. The B97-c functional contains the Becke–Johnson damping scheme (D3BJ). ,

The DLPNO–CCSD­(T) method is performed by ORCA quantum chemistry code ,, to identify the reliable calculation. Due to the cation cluster system, the basis set for Cu, Si, and Ge are set as cc-pVTZ.

3. Results and Discussion

3.1. Low-Lying Configurations and Evolutions of CuX _n ⁺ (X = Si or Ge;n= 6–16) Clusters

In Figures and , the ground-state configurations of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16), as well as isomers with the most low-lying energy, are presented, along with the relative energies and point groups. In the figures, all the clusters are titled as “nS-x” or “nG-x”, where n means the number of Si or Ge atom, x stands for the order of cluster, “S” is for the CuSi _n ⁺ cluster, and “G” is for the CuGe _n ⁺ cluster.

1.

Ground-state structures and isomers of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–11) clusters calculated by the mPW2PLYP method. The red, cyan, and blue spheres represent Cu, Si, and Ge atoms, respectively.

2.

Ground-state structures and isomers of CuSi _n ⁺ and CuGe _n ⁺ (n = 12–16) clusters calculated by the mPW2PLYP method. The red, cyan, and blue spheres represent Cu, Si, and Ge atoms, respectively.

To prove the accuracy of the ground-state structures of CuX _n ⁺ (X = Si or Ge, n = 6–16), AIMD is performed, and the results are listed in Figures S1 and S2. All of the lowest energy structures as initial optimized structures are all considered. The coordinates of each lowest energy structure and isomers are listed in Table S1 (Supporting Information).

n = 6: For CuSi₆ ⁺ and CuGe₆ ⁺ clusters, their ground state configurations, 6S-0 and 6G-0, both have C _s symmetry and an ¹A’ electronic state. They are formed by adsorbing a Cu atom on the vertex of a tetragonal bipyramid Si₆ and Ge₆ but at the different sites: 6S-0 adsorbs at a vertex, while 6G-0 adsorbs on a face. It should be noted that the 6S-1 isomer of CuSi₆ ⁺, which was previously reported as the ground state configuration in the literature, has an energy 0.11 eV higher than 6S-0.

n = 7: The ground-state configurations of the CuSi₇ ⁺ and CuGe₇ ⁺ clusters can both be considered as the adsorption of a Cu atom on the pentagonal bipyramid of Si₇ or Ge₇ but at different adsorption sites. For CuSi₇ ⁺, ground-state configuration 7S-0 involves a Cu atom adsorbed on the edge of the central face of the pentagonal bipyramid Si₇, with C _2v symmetry. In contrast, for CuGe₇ ⁺, the lowest energy configuration 7G-0 involves a Cu atom adsorbed at a position closer to the side, with C _s symmetry.

n = 8: For the CuSi₈ ⁺ and CuGe₈ ⁺ clusters, their lowest energy configurations 8S-0 and 8G-0 are both structures with C _s symmetry, which can be considered as the adsorption of a Cu atom on pure Si₈ or Ge₈. For CuGe₈ ⁺, the semicage structure 8G-1 with C _2v symmetry is only 0.02 eV higher in energy than the lowest energy configuration 8G-0, indicating that they compete to be the ground-state configuration of CuGe₈ ⁺.

n = 9: For CuSi₉ ⁺, the lowest energy structure 9S-0 can be considered as a Cu atom adsorbed on the bicapped pentagonal bipyramid Si_9, belonging to the C ₁ point group. The structure 9S-1 is degenerate with 9S-0, having an energy difference of 0.03 eV. It can be viewed as a Cu atom replacing one Si atom in the bicapped pentagonal bipyramid and then adsorbing an additional Si atom on the surface, belonging to the C _s symmetry. Although the previously reported 9S-1 configuration is considered the ground state configuration of CuSi₉ ⁺, the literature also indicates that the 9S-0 configuration competes with 9S-1 to be the ground state configuration of CuSi₉ ⁺. For the CuGe₉ ⁺ cluster, the ground state configuration 9G-0 is the cage structure with the Cu atom located at the center of the Ge₉ cage composed of two triangles, quadrilaterals, and pentagons each, having C _2v symmetry. It is energetically lower than that of the exohedral isomers 9G-1 by 0.06 eV.

n = 10: The configuration 10S-0, with C ₁ symmetry, is the ground-state configuration of CuSi₁₀ ⁺, which can be considered as the adsorption of a Cu atom on the ground state configuration of the tetracapped trigonal prism Si₁₀. For the CuGe₁₀ ⁺ cluster, the ground-state configuration 10G-0 is a cage structure with a Cu atom at the center of the bicapped antiprismatic Ge₁₀ cage, possessing D _4d symmetry, and it is 0.50 eV lower in energy than the exohedral isomer 10G-1.

n = 11: For CuSi₁₁ ⁺, the semicage structure 11S-0 with C ₁ symmetry is the ground state configuration, which can be considered as the adsorption of a Cu atom and a Si atom on the pentagonal prism Si₁₀. For the CuGe₁₁ ⁺ cluster, the ground state configuration 11G-0 has C ₅ symmetry, also forming the endohedral structure where the Cu atom is located at the center of the pentagonal prism Ge₁₀ cage capped by a Ge atom.

n = 12: For CuSi₁₂ ⁺, ground-state configuration 12S-0 is a cage structure with C _s symmetry, where the Cu atom is located at the center of a distorted hexagonal prism Si₁₂. This matches perfectly with the previously experimentally predicted cage size. For CuGe₁₂ ⁺, the ground-state configuration 12G-0 is the cage structure with C _2v symmetry, which can be considered as adsorbing two Ge atoms on the ground state configuration of CuGe₁₀ ⁺. The icosahedral cage structure 12G-1 with D _5d symmetry is 0.32 eV higher in energy than that of 12G-0.

n = 13: The configuration 13S-0 with C ₁ symmetry is the ground-state structure of CuSi₁₃ ⁺, which can be considered as a Si atom adsorbed on the ground state configuration of CuSi₁₂ ⁺ and then distorted by the Jahn–Teller effect. The cage structure 13G-0 with C _3v symmetry and the ¹E electronic state is the lowest energy configuration for CuGe₁₃ ⁺, which is derived from the adsorption of a Ge atom on the icosahedral cage structure 12G-1. The isomer 13G-1, which is formed by the adsorption of a Ge atom on the ground-state configuration 12G-0 of CuGe₁₂ ⁺, is only 0.01 eV higher in energy than 13G-0, indicating that isomers 13G-0 and 13G-1 compete to be the ground-state configuration of CuGe₁₃ ⁺.

n = 14: The ground state structure of CuSi₁₄ ⁺ is the 14S-0 isomer, which has C _s symmetry and can be viewed as a Si atom adsorbed on the ground state structure of CuSi₁₃ ⁺. The ground state structure of CuGe₁₄ ⁺ is the 14G-0 isomer, which has C ₂ symmetry and can be regarded as a Ge atom adsorbed on the 13G-0 isomer of CuGe₁₃ ⁺.

n = 15: For CuSi₁₅ ⁺, the ground-state structure is the 15S-0 isomer with C _2v symmetry, which can be viewed as the Cu atom located at the center of the Si cage composed of the 12 quadrilateral faces, with an additional Si atom capping the structure. For CuGe₁₅ ⁺, the ground-state structure is the 15G-0 isomer with C _s symmetry, which can be considered as a Cu atom positioned at the center of a structure derived from the icosahedral cage after adsorbing three Ge atoms and undergoing distortion.

n = 16: For CuSi₁₆ ⁺, the isomers 16S-0 and 16S-1 compete for the ground-state structure with an energy difference of 0.04 eV. The lowest-energy isomer 16S-0, which has C _2v symmetry, features the Cu atom located at the center of the cage, composed of two hexagons, two pentagons, four quadrilaterals, and six triangles. The isomer 16S-1 with C ₁ symmetry has the Cu atom positioned at the center of the distorted fullerene-like structure. For the CuGe₁₆ ⁺ cluster, the ground-state structure is the 16G-0 isomer with C _2v symmetry, which is identical to the lowest-energy structure of CuSi₁₆ ⁺.

To ensure that the calculation is reliable, the DLPNO–CCSD­(T) calculation results are shown in Table S2 in the Supporting Information. Except for CuGe₉ ⁺, all the lowest structures are the same as the mPW2PLYP functional predicted. The relative energy of 9G-0 and 9G-1 of CuGe₉ ⁺ at the mPW2PLYP level is so close within 0.03 eV and separate at the DLPNO–CCSD­(T) method calculation and changed the ground state structure from 9G-0 to 9G-1. Due to no experimental compared to determine, there need to be carefully identified in future experiment.

From the above discussion on the ground-state structures, the growth patterns of both CuSi _n ⁺ and CuGe _n ⁺ clusters can be divided into growing from an adsorption configuration to the Cu atom embedded cage configuration, where the adsorption configuration involves the Cu atom adsorbed on pure Si _n ⁺ or Ge _n ⁺. For CuSi _n ⁺ clusters, an endohedral structure is formed at n = 12, while for CuGe _n ⁺ clusters, the cage-like structure appears at n = 9. The larger atomic radius of the Ge (0.53 Å) atom compared to the Si (0.4 Å) atom allows CuGe _n to form the endohedral structure earlier. After CuSi _n ⁺ forms the stable distorted hexagonal prism cage structure at n = 12, all configurations with n ≥ 13 can be viewed as resulting from the adsorption of the Si atoms onto the hexagonal prism. The CuGe _n ⁺ forms the stable bicapped antiprismatic cage structure with D _4d symmetry at n = 10. For subsequent sizes (n = 11, 12, 13), the clusters can be seen as arising from the adsorption of Ge atoms onto the bicapped antiprismatic cage. At n = 13, the regular icosahedral cage structure formed by adsorbing one Ge atom emerges as the ground state through a degenerate energy. For n = 14, 15, and 16, the clusters can be considered as resulting from the adsorption of Ge atoms onto the regular icosahedron.

It should be noted that the ground-state configuration of CuSi₆ ⁺ reported in this study, which was identified using our global search technology, was not previously documented in the previously literature. Furthermore, the findings regarding the formation of endohedral structures in CuSi _n ⁺ clusters at n = 12 align with conclusions from prior experimentally research.

3.2. The Infrared and Raman Spectra of CuX _n ⁺ (X = Si or Ge; n= 6–16) Clusters

Owing to the experimental inaccessibility of gas-phase cluster ground-state structures, infrared (IR) and Raman spectroscopic techniques constitute indispensable, complementary fingerprints for structural assignment. It is well-known that vibrational (IR/Raman) spectra reflect the intrinsic structure of the molecular system and contain rich information about its geometric configuration.

In this section, the IR and Raman spectra of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) under the PBE0 level with the aug-cc-pVTZ basis set are simulated, and their vibrational modes and corresponding frequencies are analyzed with the Multiwfn code. , For CuSi _n ⁺ (n = 6–11) with available experimental spectra, the simulated spectra were compared with the experimental ones. By comparison, the feasibility of the calculation scheme and the reliability of the predicted configuration are further verified.

Figure presents the simulated IR and Raman spectra of CuSi _n ⁺ (n = 6–16). Imaginary frequencies are not found in any of the results, indicating that all structures are in the stable configuration. For the CuSi₆ ⁺ cluster, the infrared spectrum shows two distinct peaks at 441.09 (A’ mode) and 535.5 (A’ mode) cm^–1, which align well with the experimental values observed at 445 and 530–540 cm^–1. The peak at 441.09 cm^–1 corresponds to the stretching vibration of the Si–Si bond, while the peak at 535.5 cm^–1 is attributed to the overall breathing vibration involving the Cu–Si bond. The Raman spectrum has two distinct peaks at 358.35 (A’ mode) and 432.49 (A’ mode) cm^–1, both corresponding to the breathing vibrations between Si–Si bonds. The IR spectra of the ground-state configuration, previously reported in the literature and corresponding to the isomer 6S-1 in this paper, are also compared (see Supporting Information, Figure S3). The comparison shows that the spectrum of 6S-0 matches the experimental spectrum better. In the IR spectrum of the CuSi₇ ⁺ cluster, three main peaks are visible at 344.04 (B² mode), 406.93 (A¹ mode), and 424.27 (B² mode) cm^–1, all corresponding to breathing vibrations between Si–Si bonds. These peak positions align well with the experimental peaks at 340 cm^–1 and between 380 and 420 cm^–1. In the simulated Raman spectrum, two distinct peaks at 316.39 (A¹ mode) and 424.236 (A¹ mode) cm^–1 are observed, both corresponding to stretching vibration modes of the Si–Si bonds. For the CuSi₈ ⁺ cluster, the simulated IR spectrum nicely reproduces the experimental bands centered at 281, 353, 405, and 460 cm^–1 (calculated: 286.03 cm^–1, A’; 350.9 cm^–1, A’; 407.39 cm^–1, A″; and 448.38 cm^–1, A’). These breathing vibrations are localized Si–Si stretches. The most dominant Raman vibration wave of CuSi₈ ⁺ cluster residing at 420.22 cm^–1 (A’ mode) correpsonds to stretching vibration of the Si–Si bonds. For the IR spectrum of the CuSi₉ ⁺ cluster, 9S-0 exhibits one band centered at 464.7 cm^–1 (A mode), and one less intense peak at 456.77 cm^–1 (A’ mode), which is matched the 458 cm^–1 of experimental spectrum. The IR spectrum of 9S-1, with only 0.03 eV less stable than 9S-0, also matches well with the experiment, especially for the experiment at 437 cm^–1 (simulated: 431.71 cm^–1, A). For both isomers, the highest frequency band originates from a stretching of the Si–Si moiety. In the Raman spectrum of the CuSi₉ ⁺ cluster, the lowest-energy isomer 9S-0 shows two distinct peaks at 297.45 and 382.05 cm^–1, both corresponding to breathing vibration modes of the Si–Si bonds. The isomer 9S-1 also exhibits two peaks at 319.50 and 405.57 cm^–1, resulting from the same vibrational modes. By comparison with experimental spectra, it can be inferred that isomers 9S-0 and 9S-1 are in competition for the ground-state structure of CuSi₉ ⁺. For the CuSi₁₀ ⁺ clusters, the highest-energy band of the ground state structure 10S-0 is centered at 436.79 cm^–1 (A mode) and one less intense peak is centered at 409.29 cm^–1 (A mode), which matches the intense bands around 430 cm^–1 of the experimental spectrum. As mentioned in the literature providing experimental values, for larger clusters with poor overall symmetry, the experimental IR-MPD spectrum is not as distinct as that of smaller clusters. The experimental infrared spectrum of the CuSi₁₀ ⁺ cluster has many indistinct peaks. However, we consider that the experimental spectrum is reasonably well reproduced by the ground-state configuration 10S-0. Each of the normal modes represents a combined Si–Si stretching vibration, where the Cu atom is hardly involved in the vibrations. The Raman spectrum of isomer 10S-0 also has many peaks. Three distinct peaks at 332.39 (A mode), 344.65 (A mode), and 363.73 (A mode) cm^–1 correspond to breathing vibration modes of the Si–Si bonds. The infrared spectrum of the CuSi₁₁ ⁺ cluster, like that of CuSi₁₀ ⁺, has many indistinct small peaks. However, there are obvious high peaks between 420 and 500 cm^–1, which match well with the peak at 460.85 cm^–1 (A mode) in the calculated spectrum of stable structure 11S-0. The Raman spectrum of isomer 11S-0 also has many peaks. However, there is a distinct peak at 342.22 cm^–1, which corresponds to the breathing vibrational mode of Si–Si bonds. These peaks are mainly due to the breathing vibrations of Si–Si bonds.

3.

IR and Raman spectra of CuSi _n ⁺ (n = 6–11) clusters. The upmost panel shows the experiment IR spectra. Reprinted in part with permission from Journal of the American Chemical Society 2010, 132 (44), 15589–15602. Copyright 2010, American Chemical Society.

Seen in Figure , for the CuSi₁₂ ⁺ cluster, the infrared spectrum of the 12S-0 configuration has its highest peak at 441.38 cm^–1 (A’ mode), resulting from the stretching vibrations between Si and Si atoms in the silicon cage. Two secondary peaks at 228.99 (A’ mode) and 264.42 cm^–1 (A″ mode) are due to the combination of breathing vibrations of the central Cu atom and the distorted hexagonal prism cage. The Raman spectrum shows two high peaks at 281 (A’ mode) and 383.31 cm^–1 (A’ mode), corresponding to cooperative breathing vibrations and cage stretching vibrations, respectively. Some small peaks for 12S-0 exist between 100 and 200 cm^–1. The infrared and Raman spectra of the 12S-0 configuration within the 100–500 cm^–1 range are provided in Supporting Information Figure S4. For CuSi₁₃ ⁺, the IR peaks at 373.75, 389.65, and 502.63 cm^–1 correspond to framework breathing. The Raman peaks show the Cu–Si framework stretching. For CuSi₁₄ ⁺, the IR and Raman spectra show peaks from Cu–Si framework coupling vibrations. For CuSi₁₅ ⁺, the strongest vibration peaks in the IR and Raman spectra correspond to Si–Si stretching and silicon cage breathing, with the central Cu atom remaining stationary. For CuSi₁₆ ⁺, the IR spectrum shows three distinct peaks at 342.14, 363.34, and 499.05 cm^–1, corresponding to breathing vibrations of the Si₁₆ cage structure and coupled stretching vibrations of the Si–Si bonds. The Raman spectrum also shows prominent peaks at 302.51 and 290.56 cm^–1, attributed to the breathing vibrations of the Si₁₆ cage framework.

4.

IR and Raman spectra of CuSi _n ⁺ (n = 12–16) clusters.

The IR and Raman spectra of CuGe _n ⁺ (n = 6–16) clusters are shown in Figure . For CuGe₆ ⁺, three main peaks are observed in the IR spectrum and four in the Raman spectrum. The highest IR peak at 246.57 cm^–1 is due to rocking bending vibrations of Ge₆ with the Cu atom fixed. Other peaks correspond to Ge–Ge bond stretching and coupled Cu–Ge stretching vibrations. In the Raman spectrum, the highest peak at 228.84 cm^–1 arises from the overall rocking bending vibrations of the cluster. For CuGe₇ ⁺, two prominent peaks are seen in both the IR and Raman spectra, corresponding to rocking bending vibrations of Ge₇ and bending vibrations of CuGe₇. For CuGe₈ ⁺, the spectra of isomers 8G-0 and 8G-1 are provided due to the degenerate energy. In the IR spectrum of 8G-0, peaks at 221.82 and 254.9 cm^–1 correspond to stretching vibrations of the Ge–Ge bonds and the Cu–Ge bond. In the Raman spectrum, peaks at 207.38 and 243.55 cm^–1 arise from the breathing vibrations of CuGe₈ and stretching vibrations of one Cu–Ge bond. In the IR and Raman spectra of the half-cage isomer 8G-1, three and one distinct peaks appear, respectively. In the IR spectrum, the three peaks correspond to bending vibrations of the Cu atom in different directions. The single peak in the Raman spectrum at 231.37 cm^–1 is due to the breathing vibrations. In the IR spectra of CuGe _n ⁺ cage clusters for n = 9, 10, and 11, prominent peaks appear due to bending vibrations of the central Cu atom within the germanium cage. For n = 9, the two peaks at 293.54 and 299.31 cm^–1 correspond to B² and A¹ modes. For n = 10, two peaks at 290.86 and 314.72 cm^–1 are also in the B² and A¹ modes. For n = 11, three peaks at 241.04, 284.94, and 296.23 cm^–1 are all A’ modes. In their Raman spectra, breathing vibration peaks appear at 215.95, 212.89, and 204.99 cm^–1. For CuGe₁₂ ⁺, three distinct peaks are found in the IR spectrum and one in the Raman spectrum. In the IR spectrum, the peaks at 270.67 and 222.14 cm^–1 correspond to bending vibrations of the Cu atom within the Ge cage. The peak at 296.73 cm^–1 corresponds to stretching vibrations of two adsorbed Ge atoms and their connecting bond on the Ge₁₀. Consistent with previous cage structures, the Raman peak of 12G-0 at 207.43 cm^–1 is attributed to breathing vibrations. For CuGe₁₃ ⁺, the IR and Raman spectra of two energy-degenerate configurations are presented. In the IR spectrum of 13G-0, the strongest peak at 223.26 cm^–1 corresponds to bending vibrations of the Cu atom within the germanium cage. Two higher peaks at 241.71 and 200.72 cm^–1 are attributed to stretching vibrations of the Ge atom adsorbed on the icosahedron and its connecting bond and bending vibrations of the Cu atom in different directions within the germanium cage. In the IR spectrum of 13G-1, the strongest peak at 252.12 cm^–1 is due to the stretching vibrations of one Ge atom adsorbed on the Ge₁₀ cage and its connecting bond. Both 13G-0 and 13G-1 exhibit prominent Raman peaks from breathing vibrations at 186.06 and 188.08 cm^–1, respectively. Additionally, in the Raman spectrum of 13G-1, one significant peak at 254.44 cm^–1 corresponds to stretching vibrations of two Ge atoms adsorbed on the Ge₁₀ cage and their respective connecting bonds. For CuGe₁₄ ⁺, the IR spectrum shows peaks from bending vibrations of the Cu atom within the Ge cage and breathing vibrations of the Ge₁₂. In the Raman spectrum, peaks at 196.56 and 171.74 cm^–1 correspond to rocking bending and breathing vibrations of the Ge₁₂. For CuGe₁₅ ⁺ and CuGe₁₆ ⁺, the strongest peaks in the IR spectra are due to breathing vibrations of the Ge cage. The Raman spectra also show prominent peaks from breathing vibrations.

5.

IR and Raman spectra of CuGe _n ⁺ (n = 6–16) clusters.

As is known from the above description, the IR and Raman activity shows different spectra for these compounds and reflects the influence of geometrical changes. The breathing and stretching vibrations of Si–Si or Ge–Ge bonds, as well as the involvement of the Cu atom in different modes, are key factors in determining the spectral characteristics. For CuSi _n ⁺ clusters, the IR spectra are dominated by breathing modes of Si–Si bonds, while Raman spectra show both breathing and stretching modes. For the cage structure, the participation of the central Cu atom varies, with bending or stretching vibrations appearing in certain clusters. Similarly, for CuGe _n ⁺ clusters, the spectra are influenced by the breathing and stretching of Ge–Ge bonds, with the involvement of the Cu atom leading to distinct peaks.

The highest infrared peak wavenumbers for CuSi _n ⁺ (n = 6–16) are in the range of 373.75–499.50 cm^–1, while the Raman peaks are between 281 and 432.49 cm^–1. For CuGe _n ⁺ (n = 6–16), infrared peaks are in the 221.82–299.31 cm^–1 range, and Raman peaks are between 1174.67 and 234.82 cm^–1. Compared with CuSi _n ⁺, CuGe _n ⁺ shows reduced wavenumbers and increased wavelengths. These patterns indicate that the most stable compounds with these components might have potential applications in sensing devices, especially in the infrared range.

To summarize the above discussion, these distinctive far-infrared signatures not only enable rapid structural identification of Cu-doped Si or Ge clusters but also establish a quantitative spectral library for the rational design of next-generation infrared sensors and optoelectronic nanomaterials.

3.3. Relative Stabilities, Average Bond Length, and HOMO–LUMO Gap of CuX _n ⁺ (X = Si or Ge; n= 6–16) Clusters

To explore the stability and semiconductor properties of the clusters, the average binding energy (ABE), second-order energy difference (Δ² E), average bond length (ABL), and HOMO–LUMO gap (E _gap) of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) are calculated and presented in Figures and and Table . The calculation formulas for ABE and second-order energy difference are as following:

$$ABE(\mathrm{Cu}{X_n}^{+})=[nE(X)+E({\mathrm{Cu}}^{+})-E(\mathrm{Cu}{X_n}^{+})]/(n+1)$$ 1

$${\Delta }^{2}E(\mathrm{Cu}{X_n}^{+})=E(\mathrm{Cu}{{X_{n-}}_1}^{+})+E(\mathrm{Cu}{{X_{n+}}_1}^{+})-2E(\mathrm{Cu}{X_n}^{+})$$ 2

6.

(a) ABE and (b) Δ² E of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) clusters (in eV).

7.

E _gap of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) clusters.

1. ABE (in eV) and ABL (in Å) of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) Clusters.

		ABL				ABL
Isomer	ABE	Si–Si	Cu–Si	Isomer	ABE	Ge–Ge	Cu–Ge
CuSi6 +	3.24	2.42	2.24	CuGe6 +	3.01	2.58	2.46
CuSi7 +	3.37	2.47	2.33	CuGe7 +	3.12	2.61	2.49
CuSi8 +	3.31	2.47	2.45	CuGe8 +	3.08	2.65	2.51
CuSi9 +	3.39	2.42	2.38	CuGe9 +	3.12	2.62	2.46
CuSi10 +	3.49	2.46	2.45	CuGe10 +	3.28	2.68	2.47
CuSi11 +	3.45	2.41	2.48	CuGe11 +	3.25	2.60	2.51
CuSi12 +	3.47	2.41	2.58	CuGe12 +	3.24	2.64	2.54
CuSi13 +	3.48	2.42	2.51	CuGe13 +	3.25	2.63	2.67
CuSi14 +	3.54	2.41	2.47	CuGe14 +	3.28	2.62	2.71
CuSi15 +	3.56	2.47	2.58	CuGe15 +	3.31	2.68	2.55
CuSi16 +	3.59	2.43	2.61	CuGe16 +	3.33	2.59	2.74

In the equations where X = Si or Ge.

As shown in Figure a, the ABE trends of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) are similar, both increasing as the cluster size grows. From Figure and Table , the ABE of CuSi _n ⁺ is higher than the ABE of CuGe _n ⁺ across all sizes, indicating better stability for CuSi _n ⁺ compared to CuGe _n ⁺. Table shows that the average Si–Si bond length in CuSi _n ⁺ (2.42–2.47 Å) is smaller than the Ge–Ge bond length in CuGe _n ⁺ (2.58–2.68 Å), which explains the better stability of CuSi _n ⁺ and aligns with the ionic radii of Si (0.4 Å) and Ge (0.53 Å). The higher peaks of ABE at n = 7 and 10 can been seen, indicated that CuSi₇ ⁺, CuSi₁₀ ⁺, CuGe₇ ⁺, and CuGe₁₀ ⁺ have good stability. As shown in the second order energy difference diagram in Figure b, CuSi₁₀ ⁺ and CuGe₁₀ ⁺ are more stable than their neighboring clusters.

These results highlight the critical role of atomic size and bond strength in determining cluster stability, with CuSi _n ⁺ exhibiting good stability due to shorter covalent bonds and stronger Si–Si interactions compared to those of Ge–Ge.

To assess whether the enhanced stabilities of CuSi₇ ⁺, CuSi₁₀ ⁺, CuGe₇ ⁺, and CuGe₁₀ ⁺ originate from interactions between the Cu 3d manifold and the valence orbitals of Si or Ge, the electronic state of these clusters were examined. Mulliken population analyses were performed to quantify the percentage contributions of d _z ², d _xy , d _yz , d _xz , and d _x ² _–y ² within all occupied orbitals; the resulting values are reported in Table . Each d-orbital exhibits a population exceeding 50%, indicating that the Cu 3d electrons are actively engaged in cluster bonding.

2. Cu 3d-State Contributions in the CuSi₇, CuSi₁₀, CuGe₇, and CuGe₁₀ Clusters Obtained from Mulliken Population Analysis .

	Cu d-state contribution (%)
cluster	d z 2	d xz	d yz	D x 2- y 2	d xy
CuSi7 +	98.92	98.49	98.58	97.26	98.15
CuSi10 +	93.86	97.38	96.61	93.45	94.50
CuGe7 +	97.23	97.28	96.53	96.98	97.06
CuGe10 +	95.51	94.36	94.36	99.27	95.48

^aAll the values are given in percentage.

The HOMO–LUMO gap is a good reflector for the semiconductor properties of clusters. Owing to the overestimation of energy gap by the mPW2PLYP functional, additional E _gap values were computed with the PBE0 functional to compare. Figure presents the E _gap of CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) calculated under the mPW2PLYP and PBE0 methods that structures are both based on the optimized at the mPW2PLYP level. It can be observed from Figure that the E _gap curves of CuSi _n ⁺ and CuGe _n ⁺ clusters show similar trends in both methods with the positions of maximum and minimum gaps consistent between the two calculation methods. As shown in Figure , the E _gap values of CuSi _n ⁺ are higher than that of CuGe _n ⁺ in most sizes except for n = 12, 13, and 14. For the E _gap of CuSi _n ⁺, the maximum E _gap is 3.61 eV (5.31 eV at the mPW2PLYP level) for CuSi₇ ⁺, and the minimum is 1.73 eV (3.06 eV at the mPW2PLYP level) for CuSi₁₂ ⁺. For the E _gap of CuGe _n ⁺, CuGe₆ ⁺ has the maximum E _gap of 3.31 eV (4.98 eV at the mPW2PLYP level), and CuGe₁₅ ⁺ has the minimum of 2.36 eV (3.71 eV at the mPW2PLYP level). Among the E _gap of the caged cluster of CuGe _n ⁺ (n = 9–16), CuGe₁₆ ⁺ and CuGe₁₀ ⁺ have the highest and second-highest E _gap values of 3.07 eV (4.50 eV at mPW2PLYP level) and 2.78 eV (4.11 eV at mPW2PLYP level), respectively, and both values are consistent with typical semiconductor properties. It can be revealed that CuGe₁₀ ⁺ has a proper semiconductor energy gap. The exceptional stability and E _gap of CuGe₁₀ ⁺, combined with its high symmetry and distinct electronic configuration, position it as a promising candidate for the design of tunable semiconductor nanomaterials.

Collectively, among the clusters examined, CuSi₁₀ ⁺ and CuGe₁₀ ⁺ exhibit superior thermodynamic stability, with CuGe₁₀ ⁺ additionally demonstrating exceptional semiconducting characteristics. Consequently, CuGe₁₀ ⁺ not only bridges the gap between molecular clusters and functional nanoscale semiconductors but also provides a structurally well-defined platform for the rational engineering of next-generation optoelectronic and sensing devices.

3.4. Adiabatic Ionization Potential and NPA of CuX _n ⁺ (X = Si or Ge; n= 6–16) Clusters

The adiabatic ionization potential (AIP) is an important physical property for studying the structure, bonding, and electronic properties of clusters, calculated and discussed in this section. The AIP is the energy difference between the ground-state configuration of the monovalent cation cluster and the lowest energy configuration of the corresponding neutral cluster. The AIP of CuSi _n and CuGe _n (n = 6–16) clusters are listed in Table . It can be deduced from Table that (i) the AIP of CuSi _n ranges from 5.58 to 6.57 eV, with the peak at n = 9 and bottom at n = 7, and the AIP of CuGe _n is between 5.07 and 6.66 eV, with the maximum at n = 9 and the minimum at n = 16. (ii) The small differences in AIP between CuSi _n and CuGe _n can be attributed to the losing electron in a similar site of the Cu atom, as indicated by the natural population analysis (see below).

3. The AIP (in eV) of CuSi _n and CuGe _n (n= 6–16) Clusters.

cluster	AIP	cluster	AIP
CuSi6 +	6.50	CuGe6 +	6.43
CuSi7 +	5.58	CuGe7 +	5.70
CuSi8 +	6.53	CuGe8 +	6.36
CuSi9 +	6.57	CuGe9 +	6.66
CuSi10 +	6.02	CuGe10 +	6.25
CuSi11 +	6.30	CuGe11 +	5.99
CuSi12 +	6.29	CuGe12 +	6.37
CuSi13 +	6.09	CuGe13 +	5.92
CuSi14 +	6.19	CuGe14 +	5.62
CuSi15 +	5.78	CuGe15 +	5.70
CuSi16 +	5.62	CuGe16 +	5.07

Natural population analysis (NPA) of the most stable structure for CuSi _n ⁺ and CuGe _n ⁺ (n = 6–16) clusters are carried out at the mPW2PLYP level with aug-cc-pVTZ basis set for Cu, Si, and Ge atoms. The valence configurations of natural population analysis and charge of the Cu atom are shown in Table . From Table , it can be revealed that the valence electron configurations of Cu atoms for CuSi _n ⁺ clusters are 4s ^0.34–0.723d ^9.71–9.874p ^0.01–2.37 and for CuGe _n ⁺ clusters are 4s ^0.44–0.833d ^9.74–9.834p ^0.22–2.93. The charge analysis indicates that Cu atoms act as electron donors before cage formation and switch to electron acceptor afterward. For cationic clusters, the lost electron is mainly contributed by the Cu atom.

4. NPA and Charge of a Cu Atom (in a.u.) for CuSi _n ⁺ and CuGe _n ⁺ (n= 6–16) Clusters.

species	charge	electron configuration	species	charge	electron configuration
CuSi6 +	0.71	[core]4s 0.363d 9.874p 0.01	CuGe6 +	0.45	[core]4s 0.443d 9.834p 0.22
CuSi7 +	0.65	[core]4s 0.343d 9.854p 0.11	CuGe7 +	0.42	[core]4s 0.453d 9.834p 0.23
CuSi8 +	0.33	[core]4s 0.493d 9.794p 0.32	CuGe8 +	0.27	[core]4s 0.503d 9.804p 0.35
CuSi9 +	0.49	[core]4s 0.393d 9.814p 0.24	CuGe9 +	–2.50	[core]4s 0.833d 9.744p 2.77
CuSi10 +	0.37	[core]4s 0.433d 9.814p 0.33	CuGe10 +	–2.72	[core]4s 0.803d 9.764p 2.93
CuSi11 +	–0.27	[core]4s 0.583d 9.754p 0.83	CuGe11 +	–2.49	[core]4s 0.783d 9.774p 2.75
CuSi12 +	–1.55	[core]4s 0.683d 9.714p 2.05	CuGe12 +	–2.29	[core]4s 0.773d 9.774p 2.58
CuSi13 +	–1.79	[core]4s 0.733d 9.724p 2.23	CuGe13 +	–1.87	[core]4s 0.723d 9.734p 2.30
CuSi14 +	–1.92	[core]4s 0.723d 9.724p 2.37	CuGe14 +	–1.68	[core]4s 0.713d 9.774p 2.05
CuSi15 +	–1.40	[core]4s 0.653d 9.774p 1.80	CuGe15 +	–2.03	[core]4s 0.723d 9.774p 2.40
CuSi16 +	–1.28	[core]4s 0.683d 9.754p 1.70	CuGe16 +	–1.13	[core]4s 0.653d 9.774p 1.56

In summary, the AIP and NPA results collectively indicate that Cu atoms play a significant role in the electronic properties of both CuSi _n ⁺ and CuGe _n ⁺ clusters. The relatively higher AIP values for CuSi _n ⁺ clusters suggest greater stability compared to CuGe _n ⁺ clusters. The transition of Cu atoms from electron donors to acceptors upon cage formation highlights the dynamic role of Cu in these systems. These findings provide valuable insights into the electronic structure and stability of transition metal-doped silicon and germanium clusters, which are crucial for their potential applications in nanoscale electronic and optoelectronic devices.

3.5. Molecular Orbital Analyses and Optical Absorption Spectrum of CuGe₁₀ ⁺

The CuGe₁₀ ⁺ cluster not only has good stability but also has the proper energy gap. Moreover, its D _4d symmetric structure and closed shell electronic configuration make it a promising building block for new nanostructured materials. Therefore, to reveal further insights of orbitals and electronic information on the CuGe₁₀ ⁺ cluster, the molecular orbitals (MOs) and density of states (DOS) are simulated and analyzed, shown in Figures and , respectively. CuSi₁₀ ⁺ also exhibits good stability and semiconductor properties but has a less symmetric structure, and its molecular orbitals of HOMO and LUMO, density of states, and UV–vis spectrum are provided in the Figures S5, S6, and S7 (Supporting Information). The CuGe₁₀ ⁺ cluster, with 50 valence electrons, can be described by the superatom model as [1S²1P⁶1D⁹2D⁹1F²2S²1F¹¹2P⁶]. Figures and show that the 1S jellium model shell featuring a σ bond is mainly formed by the 4s-orbitals of Cu and Ge atoms. The 1P is characterized with π bonds between the 4s-orbitals of the Ge atoms and the 4p-orbitals of the Cu atom. The 1D primarily comes from the 4s-orbitals of the Ge atoms and the 3d-orbitals of the Cu atom. The 2D is constructed from the interaction between the 3d-orbitals of the Cu atom and the 4s-orbitals of the Ge atoms. The 2S is a σ bond mainly composed of the 3s-orbitals of the Cu atom and the 4p-orbitals of the Ge atoms. The 1F, which is σ + π bonds from the 4s- and 4p-orbitals of the Ge atoms, is distributed across six degenerate orbitals (HOMO–3 to HOMO–8) and one degenerate orbital (HOMO–10). The σ bond of 2P molecular orbitals is found between the 4p-orbitals of the Cu atom and 4s4p orbitals of peripheral Ge atoms. All of the above orbitals contribute to the thermal stability of the whole CuGe₁₀ ⁺ cluster. The LUMO is an σ bond contributed by the 4s-orbitals of peripheral Ge atoms. This results in a proper HOMO–LUMO gap, facilitating electron transfer and making it suitable for photoelectric device. The complex hybridization of Cu and Ge orbitals together with its high symmetry and closed-shell configuration renders CuGe₁₀ ⁺ a structurally stable and electronically tunable system, making it highly suitable for the development of nanoscale devices.

8.

Molecular orbital maps for the CuGe₁₀ ⁺ cluster.

9.

DOS for the CuGe₁₀ ⁺ cluster.

To further understand the chemical bonding characteristics of the close shell CuGe₁₀ ⁺ cluster, the adaptive natural density partitioning (AdNDP) method is carried out. The bond pattern of CuGe₁₀ ⁺ can be described as nc-2e where n is the number of centers and two-electron bonds. The number of n picks from 1 to the maximum number of atoms in the cluster. From Figure , the 50 valence electrons of D _4d -symmetric CuGe₁₀ ⁺ are classified into four categories: lone pairs, 2c-2e, 4c-2e, and 11c-2e bonds. Eight peripheral Ge atoms each bear a lone pair, whereas the two axial Ge atoms form eight localized 2c-2e Ge–Ge σ bonds with the peripheral Ge atoms, each containing 1.81 electrons. The central Cu atom forms eight localized σ + π bonds with three adjacent Cu atoms on the periphery, with each bond containing 1.99 electrons. Finally, one delocalized 11c-2e σ bonds connect the central Cu atom to the outer Ge₁₀ cage, thereby stabilizing the fully encapsulated CuGe₁₀ ⁺ cluster.

10.

AdNDP analysis of the CuGe₁₀ ⁺ cluster.

With the good and excellent photoelectric properties for CuGe₁₀ ⁺, its UV–vis spectrum is studied. The 120 excited states are simulated to fully cover the UV–vis scope, using PBE0 time-dependent density functional theory with the aug-cc-pVTZ basis set for Ge and Cu atoms. The full width at half-maximum (fwhm) value is 0.3 eV, as shown in Figure . The near-ultraviolet region of the figure shows three distinct peaks, while the visible region has two relatively broad ones. The first peak is located at 229 nm, which can be divided into transition of S₀→S₁₀₀, S₀→S₈₇, S₀→S₁₁₂, and S₀→S₉₆ with contributions of 20.51%, 20.19%, 17.73%, and 13.21%, respectively. The second absorption peak at 246 nm mainly comes from S₀→S₈₇ (42.54%), S₀→S₇₆ (11.59%), S₀→S₆₃ (9.81%), and S₀→S₉₆ (9.79%). The last absorption band in the near-ultraviolet region is between 272 and 315 nm, with the strongest peak at 292 nm from S₀→S₄₃ (59.6%), S₀→S₆₃ (16.97%), and S₀→S₅₅ (14.72%). The absorption band between 361 and 506 nm has the strongest peak at 405 nm, contributed by S₀→S₂₁ (72.74%) and S₀→S₁₅ (26.35%). The peak at 607 nm comes from the S₀→S₅ transitions (98.5%). The broad absorption range of the CuGe₁₀ ⁺ cluster in the near-ultraviolet region indicates its potential as a material of choice for ultrasensitive near-ultraviolet photodetectors. The multipeak absorption profile of CuGe₁₀ ⁺, extending across both ultraviolet and visible regions, highlights its potential for use in broadband optoelectronic sensors and photovoltaic systems where efficient light harvesting across multiple wavelengths is crucial.

11.

UV–vis spectrum of the CuGe₁₀ ⁺ cluster.

4. Conclusions

In this study, the structural, vibrational, and electronic properties of copper-doped silicon and germanium cation clusters (CuX _n ⁺ where X = Si or Ge and n = 6–16) are systematically investigated by using PEB0 and mPW2PLYP and global optimization techniques. The findings reveal that the structural evolution of both CuSi _n ⁺ and CuGe _n ⁺ progresses from adsorption configurations to endohedral structures. Notably, CuSi _n ⁺ forms cage structures at n = 12, whereas CuGe _n ⁺ adopts endohedral configurations earlier at n = 9. This difference is attributed to the larger ionic radius of Ge (0.53Å) compared to Si (0.4 Å). The vibrational properties, analyzed through simulated IR and Raman spectra, align well with the experimental data of IR, validating the accuracy of our theoretical approach. Through average binding energy analysis, it is found that the stability of CuSi _n ⁺ is better than CuGe _n ⁺. Electronic property analyses, including HOMO–LUMO gaps, adiabatic ionization potentials, and natural population analysis, demonstrate that copper atoms transform electron donors to acceptors as cluster evolution. The CuGe₁₀ ⁺ cluster stands out due to its exceptional stability, high structure symmetry, a typical semiconductor HOMO–LUMO gap, and broad optical absorption in the near-ultraviolet range, suggesting its potential as a building block for semiconductor nanomaterials and photoelectric devices.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c05549.

• Figure S1: AIMD of the CuSi _n ⁺ (n = 6–16) cluster; Figure S2: AIMD of the CuGe _n ⁺ (n = 6–16) cluster; Figure S3: IR of the CuSi₆ ⁺ cluster; Figure S4: IR of the CuSi₁₂ ⁺ cluster; Figure S5: molecular orbital maps of the HOMO and LUMO for the CuSi₁₀ ⁺ cluster; Figure S6: DOS for the CuSi₁₀ ⁺ cluster; Figure S7: UV–vis spectrum of the CuSi₁₀ ⁺ cluster; Table S1: coordinates of CuX _n ⁺ (X = Si or Ge, n = 6–16); Table S2: relative energy (in Hartree) of CuX _n ⁺ (X = Si or Ge, n = 6–16), calculated by the DLPNO–CCSD­(T) method with the cc-pVTZ basis set (PDF)

This work was supported by the National Natural Science Foundation of China (Grant No. 21863007), the Fundamental Research Funds for the Inner Mongolia Autonomous Region (NZJK202212), and the Key Laboratory of Environmental Pollution Control and Remediation at Universities of Inner Mongolia Autonomous Region.

The authors declare no competing financial interest.