Figure 2a,b depict five optimized Cu₄Ag₁ trapezoidal bimetallic clusters and five optimized Cu₁Ag₄ trapezoidal bimetallic clusters using GGA/PBE. For both cases, the ground states of these clusters are two-dimensional trapezoidal configurations, consistent with previous studies [37]. For Cu₄Ag₁ clusters, the most stable bimetallic cluster is observed when the Ag atom is positioned at the bottom corners of the cluster (structures 1 and 5 in Figure 2a). This result implies that the bottom corner sites promote a more favorable electronic environment for the Ag atom, possibly owing to enhanced bonding interactions with the neighboring Cu atoms. The metastable state takes place when the Ag atom is located at the top corners of the cluster (structures 2 and 3 in Figure 2a), with an energy difference of approximately 0.07 eV compared to the most stable cluster. This metastable state indicates that the top corner positions are less favorable but still within a relatively low energy range, signifying potential flexibility in the structural variation of the clusters. The least stable structure is recognized when the Ag atom occupies the center of the cluster (structures 4 in Figure 2a), revealing an energy difference of 0.23 eV. Figure 2a also confirms that changing a Cu atom with an Ag atom at various sites within the cluster induces different degrees of deformation. This deformation is ascribed to changes in bond length, aligning with prior research [38]. Moreover, the calculated average bond length of Cu-Cu is 2.38 Å and of Cu-Ag is 2.51 Å, which is close to the bulk value of 2.53 Å [39].

For Cu₁Ag₄ clusters, the most favorable configuration for the bimetallic cluster is achieved when the Cu atom is situated at the center of the cluster, as observed in structure 1 of Figure 2b. This stability is consistent with previous studies [37,40,41]. The observed stability implies that the central sites provide a more favorable electrical environment for the Cu atom, possibly due to increased bonding interactions with the surrounding Ag atoms. A metastable condition occurs when the Cu atom is positioned at the upper corners of the cluster (structures 4 and 5 in Figure 2b), with an energy difference of about 0.07 eV compared to the most stable cluster. This indicates that although the top corner positions are not immensely favorable, they nevertheless fall within a low energy range, demonstrating a certain level of structural adaptability. The most unstable cluster is noted when the Cu atom is positioned in the cluster’s bottom corners (structures 2 and 3 in Figure 2b), inducing an energy difference of 0.21 eV. Moreover, Figure 2b reveals that replacing an Ag atom with a Cu atom at different sites of the cluster leads to different levels of distortion. The distortions observed are attributed to variations in the length of chemical bonds. In addition, the average bond lengths computed for Ag-Ag and Cu-Ag are 2.66 Å and 2.55 Å, respectively.

To clarify the charge transfer mechanism and electronic properties of the lowest-energy configuration of Cu₄Ag₁ and Cu₁Ag₄ clusters (see structures 1 in Figure 2a,b), we applied the Bader charge analysis technique, calculated the pDOS, and presented the CDD, as illustrated in Figure 3. Bader charge calculations demonstrate that for Cu₄Ag₁ cluster, the Ag atom gains ~0.18 e⁻ from the Cu atoms, while for Cu₁Ag₄ cluster, the Ag atoms gains ~0.22 e⁻ from the Cu atom, a phenomenon clearly proven in the CDD plot. The driving force behind this charge transfer is the difference in Pauling electronegativity between Ag (1.93) and Cu (1.90) [39]. Though the variation in electronegativity is relatively small, it is sufficient to induce an obvious electron transfer, revealing the sensitivity of these clusters to subtle electronic changes. The pDOS calculations further complement these analyses by illustrating the electronic states contributing to the bonding and stability of the cluster. For the Cu₄Ag₁ cluster, it is evidently observed that the states range between −3.3 eV and −0.8 eV and are dominated mainly by the d orbitals of Cu atoms, with the insignificant contribution of the d orbitals of the Ag atom at around −2.7 eV. The contribution of d orbitals of the Ag atom is more pronounced in the energy range between −4.8 eV and −3.35 eV, with a minor hybridization of the d orbitals of Cu atoms at nearly −3.9 eV.

For the Cu₁Ag₄ cluster, it is evident that the states within the energy range of −2 eV to −1.3 eV are mainly dominated by the d orbitals of Cu atoms, with a slight contribution from the d orbitals of the Ag atom at around −1.6 eV. In the energy range of −5.2 eV to −2.5 eV, the d orbitals of the Ag atom are more explicit, displaying minor hybridization with the d and s orbitals of the Cu atom near −3.8 eV and −2.7 eV, respectively. The incorporation of Cu into the Ag cluster leads to an improved occupation of the s orbitals of the Ag atoms, as clearly apparent by the overlapped state at −1 eV in Figure 2b. This occurrence likely implies that Cu doping facilitates the d-electrons transfer to the Ag atoms within the Cu₁Ag₄ cluster. This electron transfer was also found in the Ag₁₂Cu cluster [42].

For both clusters, doping an Ag atom in the Cu cluster and vice versa modifies the electronic structure, as evidenced by the changes in the DOS near the Fermi level (see Figure 3b). In particular, there is obvious hybridization between the d orbitals and sp orbitals near the Fermi level in the Cu atom and the p orbitals in the Ag atoms (see Figure 3a). Similarly, the Ag atoms display boosted overlap of their s orbitals with the sp hybridized orbitals of the Cu atom near the Fermi level (see Figure 3b). This leads to electron transfer from the Cu atom to the Ag atoms in both Cu₄Ag₁ and Cu₁Ag₄ clusters, resulting in a substantial splitting between the spin-up and spin-down DOS, which is consistent with previous reports [43]. This hybridization can improve the catalytic properties of the clusters by creating active sites with altered electronic environments, which are necessary for facilitating various chemical reactions.

Figure 4a,b illustrate ten optimized trapezoidal bimetallic clusters of Cu₃Ag₂ and Cu₂Ag₃, respectively, utilizing GGA/PBE methodology. In both systems, the clusters’ ground states reveal two-dimensional trapezoidal structures, corroborating the results of earlier research [37,40]. For Cu₃Ag₂ clusters, the most stable cluster is achieved when two Ag atoms are located at the bottom corners of the cluster (structures 1 in Figure 4a). This stability possibly arises from the bottom corner sites providing a more favorable electronic environment for the Ag atoms, potentially due to improved bonding interactions with the neighboring Cu atoms. A metastable state is noted for structures 3, 4, 5, 9, and 10 (see Figure 4a), with an energy difference of around 0.14 eV compared to the most stable cluster. The least stable structure arises for structures 2, 6, 7, and 8 (see Figure 4a), with an energy difference of 0.27 eV. Figure 4a further demonstrates that substituting of tow Cu atoms with Ag atoms at different sites within the cluster results in varying degrees of deformation, ascribed to alterations in bond lengths. Moreover, the calculated average bond lengths of the most stable cluster are 2.40 Å for Cu-Cu and 2.52 Å for Cu-Ag.

For Cu₂Ag₃ clusters, the most favorable arrangement is obtained when two Cu atoms are positioned within the center and top corners of the cluster, as depicted in structures 1 and 2 of Figure 4b. The observed stability implies that these sites offer a more favorable electronic environment for the Cu atom, likely due to enhanced bonding interactions with the surrounding Ag atoms. A metastable state is found for structures 4, 5, 6, 7, 8, 9, and 10 (see Figure 4b), with an energy difference of nearly 0.18 eV compared to the most stable cluster. This signifies that, while the bottom corner positions are less favorable, they remain within a low energy range, showing some degree of structural adaptability. The least stable cluster is observed when the Cu atoms are located at the bottom corners of the cluster (structure 3 in Figure 4b), resulting in an energy difference of about 0.32 eV. Moreover, Figure 4b shows that replacing Ag atoms with Cu atoms at various sites of the cluster induces different levels of distortion. These distortions are caused by changes in bond lengths. Furthermore, the computed average bond lengths for the lowest energy state are 2.62 Å, 2.42 Å, and 2.53 Å for Ag-Ag, Cu-Cu, and Cu-Ag, respectively.

To describe the charge transfer mechanism and the electronic properties of the lowest-energy structures of Cu₃Ag₂ and Cu₂Ag₃ clusters (see structures 1 in Figure 4a,b) we employed Bader charge analysis, calculated the pDOS, and illustrated the CDD, as presented in Figure 5. The Bader charge calculations indicate that in the Cu₃Ag₂ cluster, the Ag atoms gain approximately 0.30 e⁻ from the Cu atoms, whereas in the Cu₂Ag₃ cluster, the Ag atoms gain about 0.41 e⁻ from the Cu atoms. This phenomenon is clearly observed in the charge density difference plots seen in Figure 5a,b. The pDOS calculations offer further insights by identifying the electronic states that contribute to the bonding and stability of the clusters. In the Cu₃Ag₂ cluster, the energy range from −2.7 eV to −0.7 eV is predominantly influenced by the d orbitals of Cu atoms, with a modest contribution from the d states of the Ag atom around −2.1 eV. The Ag atom’s d orbitals are particularly prominent in the energy range from −4.8 eV to −3.1 eV, with a slight hybridization of the Cu atoms’ d orbitals.

In terms of the Cu₃Ag₂ cluster, the energy range from −2.5 eV to −0.8 eV is mainly dominated by the d orbitals of Cu atoms, with a small contribution from the d states of the Ag atom around −2.0 eV. The d states of the Ag atom become more prominent in the energy range from −5.0 eV to −2.5 eV, indicating modest hybridization with the d and s orbitals of the Cu atom around −4.0 eV and −2.7 eV, respectively. The incorporation of Cu into the Ag cluster results in a greater filling of the s orbitals of Ag atoms, as evidenced by the overlapping state at −1.1 eV in Figure 5b. This suggests that the addition of Cu facilitates the transfer of d-electrons to the Ag atoms in the Cu₂Ag₃ cluster. The electronic structure of both clusters is influenced by the doping of Ag and Cu atoms in the Cu cluster and vice versa. This effect is evident from the variations in the DOS near the Fermi level. Specifically, there is clear hybridization between the d states and sp levels near the Fermi level within the Cu atom, as well as the p orbitals within the Ag atoms (see Figure 5a). Similarly, the Ag atoms, which have neighboring atoms, demonstrate pronounced overlap of their s orbitals with the sp hybridized orbitals of the Cu atom around the Fermi level (see Figure 5b). This interaction causes the transfer of charge from the Cu atom to the Ag atoms in both Cu₄Ag₁ and Cu₁Ag₄ clusters, resulting in a significant separation between the spin-up and spin-down DOS. This observation is consistent with previous studies [43]. The hybridization can enhance the catalytic properties of the clusters by producing active sites with modified electronic environments, which are essential for facilitating several chemical reactions.

Bimetallic clusters have gathered substantial interest due to their remarkable catalytic activity and reduced susceptibility to CO₂ poisoning [44]. The primary aim of this research is to understand the reactivity of CO₂ gas molecules on CumAgn bimetallic clusters. Therefore, we explore the influence of compositional changes on the reactivity of CO₂ molecules across bimetallic clusters of Cu_mAg_n. Before adsorbing the CO₂ molecule onto the Cu_mAg_n bimetallic clusters, we optimized the isolated CO₂ molecule using GGA/DFT (see Figure A1 in Appendix A). The calculated bond length (d_C=O = 1.172 Å for CO₂) and bond angle (θ_OCO = 179.96° for CO₂) are in agreement with the findings of previous studies [45,46]. The initial phase of the catalytic conversion of CO₂ involves the adsorption mechanism, where the molecule can either undergo physisorption or chemisorption onto the catalyst [26,45,47]. In the chemisorbed state, CO₂ displays elongated C-O bonds and a decreased O-C-O bond angle, shifting from a linear to a bent configuration. This transformation implies that CO₂ activation occurs due to electron transfer from the metal catalyst to the CO₂ molecule’s π molecular orbitals [7,48]. Conversely, in the physisorbed state, CO₂ retains its gas-phase characteristics, with an O-C-O bond angle of 180° and a C-O bond length of 1.18 Å. To provide a more systematic investigation, we carried out additional calculations on the Ag₅ and Cu₅ mono-clusters interacting with CO₂, as shown in Figure A2. The relative energies of optimized Cu₅@CO₂ structures (Figure A2b) illustrate that structure 1 is the most stable, with an adsorption energy (0.70 eV) comparable to that of the Cu₄Ag₁@CO₂ cluster. In contrast, the Ag₅@CO₂ configurations (Figure A2a) display a slightly different stability trend, with Structure 1 also being the most favorable but exhibiting different adsorption characteristics compared to Cu₅@CO₂. The pDOS and CDD plots for Ag₅@CO₂ and Cu₅@CO₂ are presented in Figure A2c,d, respectively. The pDOS for Ag₅@CO₂ signifies a less pronounced interaction between the Ag d-orbitals and CO₂ at lower energy states (~−4.5 eV), while the Cu₅@CO₂ cluster reveals remarkable hybridization between the Cu d-orbitals and the CO₂ orbitals in the range between −1 and −5 eV. This difference in electronic structure agrees with the CDD plots, where Cu₅@CO₂ exhibits more charge density transfer to the CO₂ molecule than Ag₅@CO₂, similar to the trend observed in Cu₄Ag₁@CO₂. Comparing these results with the Cu₄Ag₁@CO₂ cluster, we observe that Cu₅@CO₂ possesses a higher charge transfer capacity, which could suggest enhanced CO₂ activation. However, the mixed composition in Cu₄Ag₁@CO₂ favors both stability and effective electron transfer, giving an ideal balance for CO₂ activation. This systematic comparison emphasizes the role of Cu and Ag content in impacting the adsorption behavior and electronic attribution, aiding to enhance the design principles for efficient CO₂ reduction catalysts.

Considering the most stable configuration of the Cu₄Ag₁ bimetallic cluster, i.e., structure 1 in Figure 2a, we placed the CO₂ molecule at different sites of the cluster as displayed in Figure 6a, and we found that structure 1 is the most stable configuration compared to the metastable state, specifically, structure 2, with an energy difference of roughly 0.5 eV. In structure 1, the CO₂ is highly adsorbed on the bimetallic cluster with an adsorption energy of 0.95 eV, implying a chemisorption process. Our result showed that the systems responsible for CO₂ activation consistently illustrate effective adsorption and significant charge transfer of around 0.6 e¯ from the Cu₄Ag₁ to the CO₂ molecule. This process leads to the transformation of the CO₂ molecule from a linear to a bent structure (θ_OCO = 135.5° for CO₂), along with an elongation of the C-O bonds (d_O-C-O = 1.29, 1.24 Å), which is in good agreement with a previously published study on bimetallic CuNi nanoparticles [45]. The CO₂ molecule favorably binds to the top sites of the Cu4Ag1 bimetallic cluster, forming bonds with two Cu atoms (d_O-Cu = 1.95 Å and d_C-Cu = 1.96 Å). The adsorption of CO₂ on Cu₄Ag₁ bimetallic clusters results in modifications in the geometric structures of the clusters, with an observed Cu−Cu average bond length of approximately 2.41 Å. The outcomes indicate that bonding the CO₂ to two Cu atoms in Cu₄Ag₁ bimetallic clusters can enhance their surface activity.

Figure 6b shows the adsorption of CO₂ on bimetallic Cu₁Ag₄ clusters. In this case, the CO₂ molecule exhibits a preference for the “top” site, yet no bonds form between CO₂ and silver atoms. Considering the most stable configuration of the Cu₁Ag₄ bimetallic cluster as depicted in structure 1 in Figure 2b, we positioned the CO₂ molecule at various sites on the cluster, as demonstrated in Figure 6b. Our estimates revealed that structure 1 remains the most stable structure, in contrast to the metastable state, structure 2, with an energy difference of nearly 0.13 eV. In structure 1, although the CO₂ molecule exhibits high adsorption on the bimetallic cluster with an adsorption energy of 0.87 eV, the bond angles (θ_OCO = 179.67° for CO₂) and bond lengths of CO₂ (d_O=C=O = 1.18, 1.19 Å) closely resemble those found in isolated CO₂. This could be explained by slight charge transfer to the CO₂ molecule, which is nearly 0.03 e¯. The calculated average bond length of Ag-Ag was observed to be approximately 2.63 Å, which is in good agreement with the study of Ag₅@CO₂ [49]. It can be concluded that although the adsorption energies of CO₂ are comparable for both systems, the degree of electron transfer to CO₂ varies substantially, which distinguishes the process of CO₂ activation. Further comparison of both systems’ geometric structural parameters is illustrated in Table 1.

To elucidate the factors affecting the chemisorption of CO₂ on the Cu₄Ag₁ bimetallic cluster, we performed calculations to determine the pDOS as demonstrated in Figure 7a. As illustrated in Figure 7a and supported by reference [50], Cu₄Ag₁@CO₂ exhibits delocalized orbitals around the Fermi level, which is clearly evident by the hybridization of sp orbitals of Cu and O. This overlap can facilitate substantial electron transfer from these clusters to CO₂, which in turn stabilizes the chemisorbed state. In contrast, the overlap orbitals of Cu₁Ag₄ with O (p) orbitals of the CO₂ molecule are characterized by considerably lower energy levels from the Fermi level, which can be observed at −4.7 eV in Figure 7b. Furthermore, our investigation into the electron excitation of Cu₄Ag₁ clusters shows that the energy level of the lowest unoccupied molecular orbital (LUMO) in CO₂ closely matches the excitation energies of p electrons in Cu₄Ag₁ clusters (see states at 3.2 eV in Figure 7a). This alignment enables the transfer of excited hot electrons from the LUMO of Cu₄Ag₁ clusters to the LUMO of CO₂ owing to the strong coupling between their orbitals. The resultant electron-transfer state possesses a chemisorption state, which drastically reduces the energy barriers for breaking the C-O bond and forming CO [51]. While in the Cu₁Ag₄ system, we observed no hybridized LUMO states of the CO₂ molecule with the Cu₁Ag₄ cluster, implying a stable state of the CO₂ molecule. In addition, the excess charge observed near the O atom signifies its predominant role in the adsorption of the CO₂ molecule rather than the C atom [46]. Charge density maps, as shown in Figure 7a, corroborate our results regarding the electron transfer from the clusters to the CO₂ molecule.

Upon analyzing the most stable configuration of the Cu₃Ag₂ bimetallic cluster, structure 1 in Figure 4a, we explored the positioning of the CO₂ molecule at various sites on the cluster, as shown in Figure 8a. Our calculation indicates that structure 1 represents the most stable cluster, with an energy difference of about 0.40 eV compared to the less stable structure 5. Structure 1 shows strong CO₂ adsorption on the bimetallic cluster, with an adsorption energy of 0.81 eV, indicative of a chemisorption mechanism. Our results further demonstrate that systems involved in CO₂ activation typically reveal strong adsorption and moderate electron transfer, approximately 0.14 e⁻, from the Cu₃Ag₂ bimetallic cluster to the CO₂ molecule. This interaction induces a transformation in the CO₂ molecule from a linear to a bent geometry (θ_OCO = 137.65° for CO₂) and elongates the C-O bonds (d_O=C=O = 1.27, 1.26 Å). The CO₂ molecule selectively binds to the sites on the Cu₄Ag₁ bimetallic cluster with the highest adsorption, forming chemical bonds with two Cu atoms (d_O-Cu = 2.10 Å and d_C-Cu = 2.07 Å). The adsorption of CO₂ on the Cu₃Ag₂ cluster results in geometric alterations, with an average bond length of approximately 2.44 Å between Cu atoms. These results imply that the surface activity of Cu₃Ag₂ bimetallic clusters can be enhanced by the bonding of CO₂ to two Cu atoms.

Figure 8b shows the adsorption process of CO₂ on bimetallic Cu₂Ag₃ clusters. In this scenario, after examining the most stable arrangement of the Cu₂Ag₃ bimetallic cluster, which is referred to as structure 1 in Figure 4b, we considered the placement of the CO₂ molecule at several locations on the cluster, as shown in Figure 8b. The result indicates that structure 1 is the most stable configuration, showing an energy difference of roughly 0.13 eV when compared to the less stable structure 4. Structure 1 exhibits a high adsorption for CO₂, as evidenced by its strong adsorption with an energy of 0.81 eV, implying a chemisorption process. Our result also reveals that systems responsible for CO₂ activation generally demonstrate substantial adsorption and a high level of electron transfer, around 0.53 e⁻, from the Cu₂Ag₃ bimetallic cluster to the CO₂ molecule. This interaction causes the CO₂ molecule to transition from a straight shape to a curved one (θ_OCO = 140.36° for CO₂) and lengthens the C-O bonds (d_O=C=O = 1.24, 1.26 Å). The CO₂ molecule exhibits a strong preference for binding to the top site on the Cu₂Ag₃ bimetallic cluster, making chemical bonds with one Cu atom and one Ag atom (with bond distances of d_O-Cu = 2.10 Å, d_O-Ag = 2.45 Å, and d_C-Cu = 2.03 Å). The results indicate that the surface reactivity of Cu₂Ag₃ bimetallic clusters can be improved through the bonding of CO₂ to the top site of the cluster. Table 2 presents a detailed comparison of the geometric structural parameters of both systems.

To elucidate the factors influencing the chemisorption of CO₂ on the Cu₃Ag₂ bimetallic cluster, we performed calculations to determine pDOS, as shown in Figure 9a. Figure 9a indicates that Cu₃Ag₂@CO₂ exhibits delocalized states near the Fermi level, evidenced by the hybridization of Ag (s), Cu (d), and O (p), and C (p) orbitals. This overlapping orbital facilitates charge transfer from the cluster to CO₂, thereby stabilizing the chemisorbed state. Similarly, the orbitals of the Cu₂Ag₃ cluster overlap with the CO₂ orbitals, namely Cu (p), Cu (d), O (p), and C (p), as observed at Fermi energy in Figure 9b. This hybridization allows charge transfer from the cluster to CO₂. Additionally, our analysis of electron excitation in Cu₃Ag₂ clusters shows that the energy level of the LUMO in CO₂ closely matches the excitation energies of p electrons in Cu₃Ag₂ clusters (see states at 3.2 eV in Figure 9a). The alignment between the LUMO of Cu₄Ag₁ clusters and the LUMO of CO₂ facilitates effective transmission of excited hot electrons due to strong orbital coupling. This charge-transfer state adopts a chemisorption structure, effectively lowering the energy barriers for C-O bond dissociation and CO formation. Similarly, in the Cu₁Ag₄ system, the energy level of the LUMO in CO₂ aligns closely with the excitation energies of the p electrons of Cu and s electrons of Ag, particularly at the states around 3.5 eV, as illustrated in Figure 9b. This alignment between the LUMO of Cu₄Ag₁ clusters and the LUMO of CO₂ enables the efficient transfer of excited hot electrons, supported by a strong orbital interaction. Furthermore, the presence of excess charge near the O atom suggests its predominant role in CO₂ adsorption, as opposed to the C atom. The CDD maps presented in Figure 9a,b corroborate our results regarding electron transfer from the clusters to the CO₂ molecule.