The optimized geometries of the GeSe_xTe_4−x (x = 0–4) tetrahedral units obtained in this work show strong consistency with structural parameters reported in previous experimental and theoretical studies, confirming the reliability of the present computational results. The calculated Ge-Se bond lengths range from 2.40 Å to 2.43 Å, while the Ge-Te bond lengths lie between 2.62 Å and 2.67 Å, which are showed in Table 1. These values are in close agreement with the reported averages of ~2.40 Å for Ge-Se and ~2.60 Å for Ge-Te bonds in amorphous Ge-Se and Ge-Te systems, respectively [15,16]. The slight overestimation observed here may be attributed to the use of hybrid functional and effective core potential basis sets, which tend to marginally elongate heavy-atom bonds due to relativistic and polarization effects. Meanwhile, the internal bond angles within the tetrahedra deviate slightly from the ideal 109.5°. The bond lengths and angles of the overall structure are within acceptable ranges. In addition, the isolated tetrahedral unit structure of the GeSe_xTe_4−x (x = 0, 1, 2, 3, 4) clusters are shown in Fig. 1.

The number and types of vibrational modes in the GeSe_xTe_4−x tetrahedral units can be further rationalized based on molecular symmetry and the general 3N − 6 rule [17,18], where N represents the number of atoms in a nonlinear molecule. For a tetrahedral cluster such as GeSe₄ (five atoms), this leads to 3 × 5 − 6 = 9 fundamental vibrational degrees of freedom. Group theoretical analysis within the T_d point group predicts that these nine modes transform as A₁ + E + 2F₂, all of which are Raman active, while only the F₂ modes are also infrared active. The A₁ mode corresponds to the symmetric stretching of the four Ge-Se (Ge-Te) bonds, whereas the triply degenerate F₂ modes involve asymmetric stretching and bending motions of the tetrahedron. As Te atoms are introduced, the molecular symmetry is progressively reduced (to C_3v, C_2v), leading to the splitting and mixing of degenerate F₂ modes. This symmetry lowering results in additional Raman-active components and a noticeable redistribution of vibrational intensities. All the Raman vibrational modes of GeSe_xTe_4−x clusters are shown in Table 2.

The calculated Raman-active vibrational frequencies of the GeSe₄ and GeTe₄ tetrahedral units exhibit excellent consistency with experimental observations reported for GeSe₂ and GeTe₂ glasses. For the GeSe₄ tetrahedron, the computed A₁ symmetric stretching mode (ν₁) appears at 194 cm⁻¹, which closely matches the experimentally observed Raman band centered around 201 cm⁻¹ attributed to the breathing vibration of corner-sharing GeSe_4/2 tetrahedra in Ge-Se glasses [19,20]. For the GeTe₄ tetrahedron, the computed A₁ mode appears at 123 cm⁻¹, which is in excellent agreement with the main Raman peak of GeTe₂ glasses observed between 127 cm⁻¹, corresponding to the symmetric stretching of Ge-Te bonds [21,22,23]. The consistency between the main vibrational frequencies of the GeSe₄ and GeTe₄ tetrahedral units and the corresponding literature values verifies the reliability of the calculations. On this basis, we further investigated the Raman vibrational frequencies of the GeSe_xTe_4−x mixed tetrahedra and their gradual evolution behavior.

The calculated Raman vibrational modes of the GeSe_xTe_4−x tetrahedra exhibit distinct frequency distributions with normalized intensity in Fig. 2, which reflect the local bonding environment around the Ge center. The symmetric stretching vibrations extracted from all GeSe_xTe_4−x mixed tetrahedra, as illustrated in Fig. 3, can be clearly categorized into two groups: (i) modes primarily associated with Ge-Se bonds and (ii) modes dominated by Ge-Te bonds. A systematic trend is observed in both categories, indicating that the vibrational frequency of the symmetric stretching mode strongly depends on the number of equivalent bonds of a given type within the tetrahedral unit. For the Ge-Se related symmetric stretching modes, the frequency gradually decreases as the number of Ge-Se bonds in the tetrahedron increases. Specifically, the mode involving a single Ge-Se bond (in GeSeTe₃) exhibits the highest frequency at 271 cm⁻¹, followed by 266 cm⁻¹ for two Ge-Se bonds (GeSe₂Te₂), 251 cm⁻¹ for three Ge-Se bonds (GeSe₃Te), and 194 cm⁻¹ for four Ge-Se bonds (GeSe₄). A similar frequency-decreasing trend is also observed for Ge-Te related symmetric stretching modes, which shift from 167 cm⁻¹ for a single Ge-Te bond (in GeSe₃Te) to 123 cm⁻¹ for four Ge-Te bonds (GeTe₄).

In addition to the isolated tetrahedral units, edge-sharing tetrahedral (EST) structures in the Ge-Se-Te system were also investigated. Owing to the different proportions of Se and Te atoms, a variety of mixed edge-sharing configurations can be formed. To ensure a systematic and comparable analysis, this study adopted a symmetric substitution approach. Specifically, substitutions were introduced in pairs at equivalent atomic sites within the symmetric edge-sharing tetrahedral framework, thereby maintaining the overall structural symmetry and allowing a clear observation of compositional evolution. Following this substitution scheme, nine distinct symmetric configurations were constructed, as illustrated in Fig. 4. The optimized structural parameters, including Ge-Ch (Ch = Se, Te) bond lengths and inter-tetrahedral bond angles, are summarized in Table 3.

Fig. 5 presents the normalized-intensity vibrational-mode frequencies of the edge-sharing clusters. Given the complexity and the large number of vibrational modes in edge-sharing tetrahedral (EST) structures, the present study focuses on the breathing vibration of the four-membered rings as the primary subject of analysis, which considered as the most intense Raman active mode of the edge-sharing Ge₂Ch₆ (Ch = Se, Te) structure arises from the in-phase symmetric stretching (breathing) vibration ν(A₁) of the two GeCh₄ tetrahedra. Table 4 collects the computed symmetric breathing frequencies ν(A₁) of the four-membered rings formed in edge-sharing clusters. Three distinct ring types occur in the dataset: (i) Ge-Se-Ge-Se, (ii) Ge-Se-Ge-Te, and (iii) Ge-Te-Ge-Te. For each ring type the calculations were performed for a series of clusters in which Se atoms occupying the ring-corner (top-corner) positions are progressively replaced by Te.

The results show two clear and mutually consistent trends in Fig. 6. First, comparing the three ring chemistries at equivalent degrees of substitution demonstrates that the ring breathing frequency systematically decreases as the average chalcogen changes from Se, mixed Se/Te to Te. The pure Ge-Se-Ge-Se rings give the vibrational mode frequencies from 213, 205 to 198 cm⁻¹ for 0, 1 and 2 Te substitutions at the specified corner sites, respectively, the mixed Ge-Se-Ge-Te rings occupy an frequency shift from 182, 176 to 170 cm⁻¹, and the pure Ge-Te-Ge-Te rings present the frequencies decreasing from 166, 157 to 142 cm⁻¹, which can be seen that the ring breathing frequency decrease with the increasing of Te substitutions at the specified corner sites. Second, within each ring class ((i) Ge-Se-Ge-Se, (ii) Ge-Se-Ge-Te, and (iii) Ge-Te-Ge-Te.) the breathing frequency decreases monotonically as the number of Te atoms in the ring local environment increases. the breathing frequency is highest for Ge-Se-Ge-Se rings, the middle for Ge-Se-Ge-Te rings and lowest for Ge-Te-Ge-Te rings.

For the ethane-like “Ch₃Ge-GeCh₃” structural motifs with a central Ge-Ge bond and six terminal Ch atoms (Ch = Se or Te).in the Ge-Se-Te system, the analysis primarily focused on the stretching vibration modesand their dependence on the Se/Te ratio at the terminal sites. To ensure structural symmetry and to systematically reveal the compositional evolution, a symmetric even-substitution scheme was adopted, in which two equivalent terminal atoms were simultaneously replaced in each step. This approach yielded four representative configurations, as illustrated in Fig. 7, and the optimized bond lengths and bond angles for these structures are summarized in Table 5.

Fig. 8 shows the frequencies of vibrational modes in ethane-like Ge₂Se_2xTe_6−2x (x = 0, 1, 2, 3) clusters with intensity normalization. From all the vibrational modes of the above structure, the main two vibrational modes in terms of intensity are selected based on their D₃d symmetry classification using point-group analysis, as shown in Table 6. The strongest feature arises from the A_1g breathing mode, in which all six Ge-Ch (Ch = Se or Te) bonds extend and contract in unison while the two GeCh₃ fragments remain collinear; this in-phase motion produces the largest change in molecular polarizability and therefore dominates the spectrum. The second-stronging contribution is the E_g antisymmetric stretch, where the two GeCh₃ units oscillate out of phase: as one Ge-Ch bond lengthens, its counterpart across the Ge–Ge axis shortens. According to literature [24], the ethane-like Se₃Ge-GeSe₃ structural unit is characterized by the peak at 175 cm⁻¹, which is well matched with the calculated vibration frequency of Se₃Ge-GeSe₃ cluster attributed to ν(A_1g) mode (173 cm⁻¹)—in Table 6. The close agreement between the calculated results and the literature data validates the scientific rationality of the computational approach.

A comparative analysis of the main stretching modes with ν(A_1g) and ν(E_g) in Fig. 9 revealed a clear and consistent trend: the stretching vibration frequency decreases progressively with increasing Te content in the terminal positions. These results further demonstrate that the substitution of Se by Te significantly alters the local bonding environment and vibrational response of ethane-like clusters in chalcogenide glass networks.