Effect of Vacancy, As, and Sb Dopants on the Gold-Capturing Ability of Cu2S during Gold Collection in Matte Processes

The technique of gold collection in matte can effectively improve the trapping efficiency of precious metals such as gold, silver, and platinum. However, the underlying mechanism of gold collection from high-temperature molten matte is complex and not well understood. In this work, the first-principle calculations were utilized to investigate the adsorption behavior of gold atoms on a Cu2S surface. The effects of vacancies and As and Sb doping on the gold-trapping ability of Cu2S were also explored, and the electronic properties of each adsorption system, including the charge density difference, density of states, and charge transfer, were systematically analyzed. The results show that the Cu-terminated Cu2S(111) surface has the lowest surface energy, and the Au atom is chemically adsorbed on the Cu2S(111) with an adsorption energy of −1.99 eV. The large adsorption strength is primarily ascribed to the strong hybridizations between Au-5d and Cu-3d orbitals. Additionally, the Cu vacancy can significantly weaken the adsorption strength of Cu2S(111) towards Au atoms, while the S vacancy can notably enhance it. Moreover, due to the formation of strong covalent As–Au/Sb–Au bonds, doping As and Sb into Cu2S(111) can enhance the gold-trapping capability of Cu2S, and the Sb doping exhibits superior effectiveness. Our studied results can provide theoretical guidance for improving the gold collection efficiency of Cu2S.


Introduction
The biological oxidation process [1,2] and fluidized roasting-cyanide leaching process are always employed to treat complex gold concentrates for the gold smelting industries [3,4].However, these two technologies, although relatively mature, exhibit poor adaptability to raw materials and are ineffective in processing complex concentrates [5].With the intensifying competition in the gold industry, there are more and more complex and difficult-to-process raw materials, such as As-containing, Sb-containing, or high-copper gold concentrates [6,7].Although these concentrates can be pre-treated by both the biological oxidation process and roasting process, the ideal technical indexes cannot be achieved.To address this issue, the technique of gold collection in matte is proposed and applied in gold smelting industries due to its significant advantages, such as large processing scale, low cost, and strong raw-material adaptability.This technique not only enhances the recovery rate of valuable metals, including gold, silver, and copper but also facilitates the comprehensive recovery of rare and precious metals [8,9].As is known, copper can serve as an effective collector of gold.By utilizing this property, the gold concentrates are effectively enriched from gangue and other base metals through the gold collection in the matte process.Subsequently, the individual metals can be separated to further improve the recovery rate of gold and other precious metals [10,11].
In recent years, extensive investigations have been conducted by scholars on the mechanism of gold collection from high-temperature molten matte [12][13][14][15][16][17].For instance, AVARMA et al. [15,16] proposed that the distribution ratio of precious metals, such as Au and Ag, in the iron olivine slag and copper matte was determined by the properties of copper matte.During the smelting process, the precious metal elements are enriched in the copper matte by substituting the Cu or Fe of matte in the form of sulfides, and a high capturing rate is observed in high-grade copper matte.However, some scholars have claimed [18] that the underlying mechanism of gold collection in matte lies in the similar crystal structure and lattice parameters between gold and copper in the molten state, resulting in the formation of solid solutions or intermetallic compounds.Nevertheless, it should be noted that both atomic radii and lattice constants of Cu and Au are significantly different [19,20].Moreover, the Cu 2 S in high-temperature molten matte exhibits a cubic structure, which is distinct from the face-centered cubic structure of gold, making it difficult for them to form solid solutions.Additionally, Guo et al. [11] argue that the multiphase distribution behavior of gold is determined by the smelting system and its thermodynamic properties, and the distribution of Au and Ag into molten matte leads to a reduction in the total Gibbs free energy of the system.In summary, the mechanism of Au captured in high-temperature smelting processes is complex, and there exists a lack of unanimity among scholars, highlighting the need for additional research in this area.
Previous experimental studies have revealed that high-temperature copper matte exhibits a good capturing ability towards gold, and the gold adsorption by copper matte should take place during the initial stage.Currently, the first-principle calculations based on the density functional theory (DFT) method can be employed to investigate the adsorption behaviors of metal atoms on solid surfaces at an atomic level [21][22][23][24].Therefore, this work used the DFT computations to explore the adsorption characteristics of gold atoms on the Cu 2 S(111) surface and analyzed the microscopic interactions between the gold atoms and Cu 2 S(111) by calculating the electronic properties of each adsorption system, including the density of states, charge density, and charge density difference.Furthermore, the influence of vacancy defects on the gold adsorption of Cu 2 S(111) was also investigated.Lastly, as the gold-containing raw materials often contain antimony and arsenic, which tend to enter the copper matte, it is essential to investigate the adsorption of gold atoms on the Cu 2 S(111) surface doped with As and Sb.In conclusion, this paper comprehensively explored the influence of vacancies and As/Sb doping on the adsorption strength of Cu 2 S towards Au atoms, aiming to reveal the microscopic mechanism of gold collection in matte processes.Our studied results can provide guidance for practitioners to improve the process of the gold-trapping capability of Cu 2 S.

Adsorption of Au Atom on Pristine Cu 2 S(111)
The Cu 2 S in high-temperature molten matte is a cubic structure with a space group of FM-3M, as shown in Figure 1a.Each unit cell contains four S atoms and eight Cu atoms.The calculated lattice constant in this work is 5.616 Å, which agrees well with previous computational and experimental values [25].Firstly, the most stable surface should be determined by comparing the surface energy (γ s ) of different terminated surfaces; the γ s can be calculated by [26,27] where E slab (N) is the total energy of the surface supercell, N is the number of atoms (or molecular formula) in the supercell, E bulk represents the energy of each atom (or molecular formula) in the bulk material, and A is the corresponding surface area.There are three highsymmetry low-index surfaces for the Cu 2 S, namely (100), (110) and (111).Among them, both Cu 2 S(100) and Cu 2 S(111) have two distinct terminations, namely Cu-termination and S-termination, as illustrated in Figure 1.While the Cu 2 S(110) only has one kind of surface, namely the Cu/S-end surface.The calculated surface energies of Cu-and Sterminated Cu 2 S(100) are 0.99 J/m 2 and 0.81 J/m 2 , respectively.And the surface energy of Cu 2 S(110) is 0.51 J/m 2 , while the surface energies of Cu-and S-terminated Cu 2 S(111) are 0.35 J/m 2 and 0.91 J/m 2 , respectively.Generally, the lower surface energy for a surface means its higher stability.Notably, the Cu-terminated Cu 2 S(111) exhibits the lowest surface energy, suggesting that it has the highest exposure probability during the high-temperature smelting process.Consequently, the subsequent study only focuses on the adsorption behavior of Au atoms on the Cu-terminated Cu 2 S(111) surface.
Molecules 2023, 28, x FOR PEER REVIEW 3 of 13 Cu2S(110) is 0.51 J/m 2 , while the surface energies of Cu-and S-terminated Cu2S(111) are 0.35 J/m 2 and 0.91 J/m 2 , respectively.Generally, the lower surface energy for a surface means its higher stability.Notably, the Cu-terminated Cu2S(111) exhibits the lowest surface energy, suggesting that it has the highest exposure probability during the high-temperature smelting process.Consequently, the subsequent study only focuses on the adsorption behavior of Au atoms on the Cu-terminated Cu2S(111) surface.Next, the 2 × 2 × 1 supercell of Cu2S(111) with 15 atomic layers is constructed to explore the adsorption behavior of the Au atom on the surface, as shown in Figure 2a.During the simulation process, the six-layer atoms at the bottom of the slab are fixed to mimic the bulk phase, while the remaining atoms and gold atoms are allowed to be relaxed.After full relaxation, the topmost Cu atoms and the second-layer S atoms are found to be located in the same plane (Figure 2b).It can be observed that there exist six possible adsorption sites for the Cu2S(111), namely the Cutop site, Stop site, BCu-S site, BS-S site, BCu-Cu site, and hollow site.For the adsorption process, the gold atoms are placed above the adsorption sites with a height of 2.5 Å, and then the initial structures are subjected to fully relaxed.The calculated adsorption energies of different systems are listed in Table 1.One can see that the adsorption energies of Au atoms on the Cu2S(111) range from −1.54 eV to −1.99 eV.The Au atom on the hollow site is moved on the top of BCu-Cu after full relaxation, and the adsorption energy (−1.99 eV) at the BCu-Cu site is higher than those of other adsorption sites.Therefore, the Au atom is preferentially adsorbed onto the BCu-Cu site.As shown in Figure 3, the distances between the Au atom and its two nearest copper atoms are 2.594 Å and 2.591 Å, respectively, both of which are smaller than the radii sum of Au and Cu atoms (rAu + rCu = 3.190 Å).Therefore, it can be inferred that the Au atom is chemically adsorbed onto the Cu2S(111) surface due to the large adsorption strength and small bond length.Next, the 2 × 2 × 1 supercell of Cu 2 S(111) with 15 atomic layers is constructed to explore the adsorption behavior of the Au atom on the surface, as shown in Figure 2a.During the simulation process, the six-layer atoms at the bottom of the slab are fixed to mimic the bulk phase, while the remaining atoms and gold atoms are allowed to be relaxed.After full relaxation, the topmost Cu atoms and the second-layer S atoms are found to be located in the same plane (Figure 2b).It can be observed that there exist six possible adsorption sites for the Cu 2 S(111), namely the Cutop site, Stop site, B Cu-S site, B S-S site, B Cu-Cu site, and hollow site.For the adsorption process, the gold atoms are placed above the adsorption sites with a height of 2.5 Å, and then the initial structures are subjected to fully relaxed.The calculated adsorption energies of different systems are listed in Table 1.One can see that the adsorption energies of Au atoms on the Cu 2 S(111) range from −1.54 eV to −1.99 eV.The Au atom on the hollow site is moved on the top of B Cu-Cu after full relaxation, and the adsorption energy (−1.99 eV) at the B Cu-Cu site is higher than those of other adsorption sites.Therefore, the Au atom is preferentially adsorbed onto the B Cu-Cu site.As shown in Figure 3, the distances between the Au atom and its two nearest copper atoms are 2.594 Å and 2.591 Å, respectively, both of which are smaller than the radii sum of Au and Cu atoms (r Au + r Cu = 3.190 Å).Therefore, it can be inferred that the Au atom is chemically adsorbed onto the Cu 2 S(111) surface due to the large adsorption strength and small bond length.In order to gain a deeper understanding of the interactions between the Au atom and Cu 2 S(111) surface, the charge density difference (CDD) and electron density distribution (EDD) of the most stable system are calculated, and the results are displayed in Figure 4. From Figure 4a,b, there are significant electron accumulation regions around the gold atom, while substantial electron depletion regions surround the two neighboring Cu atoms.This suggests that the partial electrons of Cu atoms are transferred to the Au atom, resulting in the formation of a strong Au-Cu metallic bond.Additionally, as depicted in Figure 4c, an abundance of electrons can be observed between the Au atom and its two neighboring Cu atoms, which indicates that these electrons are shared by them.This implies the Au-Cu metallic bond exhibits covalent characteristics, demonstrating that the strong interactions of Au and Cu atoms take place in the adsorption system.In order to gain a deeper understanding of the interactions between the Au atom and Cu2S(111) surface, the charge density difference (CDD) and electron density distribution (EDD) of the most stable system are calculated, and the results are displayed in Figure 4. From Figure 4a,b, there are significant electron accumulation regions around the gold atom, while substantial electron depletion regions surround the two neighboring Cu atoms.This suggests that the partial electrons of Cu atoms are transferred to the Au atom, resulting in the formation of a strong Au-Cu metallic bond.Additionally, as depicted in Figure 4c, an abundance of electrons can be observed between the Au atom and its two neighboring Cu atoms, which indicates that these electrons are shared by them.This implies the Au-Cu metallic bond exhibits covalent characteristics, demonstrating that the strong interactions of Au and Cu atoms take place in the adsorption system.In order to gain a deeper understanding of the interactions between the Au atom and Cu2S(111) surface, the charge density difference (CDD) and electron density distribution (EDD) of the most stable system are calculated, and the results are displayed in Figure 4. From Figure 4a,b, there are significant electron accumulation regions around the gold atom, while substantial electron depletion regions surround the two neighboring Cu atoms.This suggests that the partial electrons of Cu atoms are transferred to the Au atom, resulting in the formation of a strong Au-Cu metallic bond.Additionally, as depicted in Figure 4c, an abundance of electrons can be observed between the Au atom and its two neighboring Cu atoms, which indicates that these electrons are shared by them.This implies the Au-Cu metallic bond exhibits covalent characteristics, demonstrating that the strong interactions of Au and Cu atoms take place in the adsorption system.4a.One can see that there are strong interactions between the Au atom and Cu1 and Cu2 atoms, which is primarily attributed to the hybridizations between the Au-5d and Cu-3d orbitals.Specifically, the Au-5d orbital obviously overlaps with the Cu1-3d orbitals in the energy range of −3.94 eV to −0.38 eV, and two significant resonance peaks can be found at about −2.18 eV and −1.63 eV, resulting in the formation of strong Au-Cu metallic bonding.Furthermore, there is a relatively weak interaction between the Au-6s and Cu1-3d orbitals in the energy range of −1.90 eV to 0.40 eV, and a resonant peak appears at the Fermi level.In contrast, the orbital hybridization between the Au-5p and Au-sp remains minimal across the entire energy level, leading to their negligible interaction.Figure 5 gives the density of states of the most stable adsorbed Cu2S(111) with an Au atom, where Cu1 and Cu2 represent the two nearest-neighbor Cu atoms of the Au atom, as shown in Figure 4a.One can see that there are strong interactions between the Au atom and Cu1 and Cu2 atoms, which is primarily attributed to the hybridizations between the Au-5d and Cu-3d orbitals.Specifically, the Au-5d orbital obviously overlaps with the Cu1-3d orbitals in the energy range of −3.94 eV to −0.38 eV, and two significant resonance peaks can be found at about −2.18 eV and −1.63 eV, resulting in the formation of strong Au-Cu metallic bonding.Furthermore, there is a relatively weak interaction between the Au-6s and Cu1-3d orbitals in the energy range of −1.90 eV to 0.40 eV, and a resonant peak appears at the Fermi level.In contrast, the orbital hybridization between the Au-5p and Ausp remains minimal across the entire energy level, leading to their negligible interaction.Figure 5 gives the density of states of the most stable adsorbed Cu2S(111) with an Au atom, where Cu1 and Cu2 represent the two nearest-neighbor Cu atoms of the Au atom, as shown in Figure 4a.One can see that there are strong interactions between the Au atom and Cu1 and Cu2 atoms, which is primarily attributed to the hybridizations between the Au-5d and Cu-3d orbitals.Specifically, the Au-5d orbital obviously overlaps with the Cu1-3d orbitals in the energy range of −3.94 eV to −0.38 eV, and two significant resonance peaks can be found at about −2.18 eV and −1.63 eV, resulting in the formation of strong Au-Cu metallic bonding.Furthermore, there is a relatively weak interaction between the Au-6s and Cu1-3d orbitals in the energy range of −1.90 eV to 0.40 eV, and a resonant peak appears at the Fermi level.In contrast, the orbital hybridization between the Au-5p and Ausp remains minimal across the entire energy level, leading to their negligible interaction.

Effect of the Vacancy on the Au Adsorption of Cu 2 S(111)
During the high-temperature melting process, some atoms can acquire enough energy to break free from the surrounding atoms and create vacancies on the Cu 2 S(111) surface.These vacancies have a significant impact on the redistribution of charge density and subsequently affect the adsorption of gold atoms.Therefore, it is necessary to investigate the effect of vacancies on the adsorption of Au atoms on the Cu 2 S(111).As displayed in Figure 6a-c Conversely, the S vacancy can dramatically enhance the adsorption strength.Therefore, it can be inferred that the S vacancies on the Cu2S(111) surface can enhance the gold-capturing efficiency of Cu2S. Figure 7 shows the CDD plots of Au@Cu2S(111)-Cuvac and Au@Cu2S(111)-Svac systems.In the Cu vacancy system, the Au atom gains about 0.013 e, as proved by the red region around it.In contrast, the three neighboring S atoms all experience a charge loss of 0.069 e.This indicates the partial electrons of S atoms are transferred to the Au atom, leading to the formation of a weak Au-S covalent bond.In the S vacancy system (Figure 7b), the abundant electron accumulation regions can be observed around the Au and Cu atoms, while the electron depletion regions are accumulated around the S atoms.This suggests that some electrons of S atoms are also transferred to the Au and Cu atoms, with the Au atom gaining about 0.131 e.Thus, the charge transfer number of Au in the Au@Cu2S(111)-Svac system is significantly greater than that in the Au@Cu2S(111)-Cuvac system, which leads to the stronger interaction between Au atom and Cu2S(111)-Svac.
The charge density distributions of the two adsorption systems are displayed in Figure 8.In the Au@Cu2S(111)-Cuvac system (Figure 8a), the Au atom shares some charges with the first-layer S atoms, resulting in the formation of a strong Au-S covalent bond.However, the Au atom only shares a small number of electrons with the Cu atoms in the Figure 7 shows the CDD plots of Au@Cu 2 S(111)-Cuvac and Au@Cu 2 S(111)-Svac systems.In the Cu vacancy system, the Au atom gains about 0.013 e, as proved by the red region around it.In contrast, the three neighboring S atoms all experience a charge loss of 0.069 e.This indicates the partial electrons of S atoms are transferred to the Au atom, leading to the formation of a weak Au-S covalent bond.In the S vacancy system (Figure 7b), the abundant electron accumulation regions can be observed around the Au and Cu atoms, while the electron depletion regions are accumulated around the S atoms.This suggests that some electrons of S atoms are also transferred to the Au and Cu atoms, with the Au atom gaining about 0.131 e.Thus, the charge transfer number of Au in the Au@Cu 2 S(111)-Svac system is significantly greater than that in the Au@Cu 2 S(111)-Cuvac system, which leads to the stronger interaction between Au atom and Cu 2 S(111)-Svac.
The charge density distributions of the two adsorption systems are displayed in Figure 8.In the Au@Cu 2 S(111)-Cuvac system (Figure 8a), the Au atom shares some charges with the first-layer S atoms, resulting in the formation of a strong Au-S covalent bond.However, the Au atom only shares a small number of electrons with the Cu atoms in the subsurface, leading to the formation of weak Au-Cu metallic bonds.In contrast, in the Au@Cu 2 S(111)-Svac system (Figure 8b), the adsorbed Au atom shares a large amount of electrons with the first-layer Cu atoms and shares massive electrons with the second-layer Cu atoms, which results in the formation of two strong Au-Cu metallic bonds.This explains why the Cu 2 S(111)-Svac exhibits the stronger adsorption strength towards the Au atom.
The density of states (DOSs) of Au@Cu 2 S(111)-Cuvac and Au@Cu 2 S(111)-Svac systems were also calculated and shown in Figure 9. From Figure 9a, the obvious orbital hybridizations between Au-d and S-p can be found in the energy range of −7.50 to 0.00 eV, and there is a slight orbital overlap between Au-s and S-p within the range of 0.00 to 1.35 eV.In addition, the weak orbital hybridizations between Au-d and Cu-d can be found in the energy ranging from −7.50 to 0.00 eV.However, none of these hybridizations results in prominent resonance peaks.Thus, the Cu 2 S(111)-Cuvac exhibits the weak adsorption strength of the Au atom.For the Au@Cu 2 S(111)-Svac system, as shown in Figure 9b, there is an obvious overlap between the Au-d orbital and d orbital of the first layer Cu atom in the energy range of −7.50 eV to −0.50 eV, and two distinct resonance peaks can be observed at approximately −4.80 eV and −2.70 eV, which results in the formation of strong Au-Cu metallic bonds.Furthermore, the significant hybridizations between the Au-d orbital and d orbital of the second layer Cu atom can also be found within the energy range −7.50 eV to 0.00 eV, leading to the formation of a strong Au-Cu metallic bond.Therefore, the Cu 2 S(111)-Svac exhibits strong adsorption capacity for Au atom.
Molecules 2023, 28, x FOR PEER REVIEW 7 of 13 subsurface, leading to the formation of weak Au-Cu metallic bonds.In contrast, in the Au@Cu2S(111)-Svac system (Figure 8b), the adsorbed Au atom shares a large amount of electrons with the first-layer Cu atoms and shares massive electrons with the second-layer Cu atoms, which results in the formation of two strong Au-Cu metallic bonds.This explains why the Cu2S(111)-Svac exhibits the stronger adsorption strength towards the Au atom.Molecules 2023, 28, x FOR PEER REVIEW 7 of 13 subsurface, leading to the formation of weak Au-Cu metallic bonds.In contrast, in the Au@Cu2S(111)-Svac system (Figure 8b), the adsorbed Au atom shares a large amount of electrons with the first-layer Cu atoms and shares massive electrons with the second-layer atoms, which results in the formation of two strong Au-Cu metallic bonds.This explains why the Cu2S(111)-Svac exhibits the stronger adsorption strength towards the Au atom.   is an obvious overlap between the orbital and d orbital of the first layer Cu atom in the energy range of −7.50 eV to −0.50 eV, and two distinct resonance peaks can be observed at approximately −4.80 eV and −2.70 eV, which results in the formation of strong Au-Cu metallic bonds.Furthermore, the significant hybridizations between the Au-d orbital and d orbital of the second layer Cu atom can also be found within the energy range of −7.50 eV to 0.00 eV, leading to the formation of a strong Au-Cu metallic bond.Therefore, the Cu2S(111)-Svac exhibits strong adsorption capacity for Au atom.

Effect of As and Sb Dopant on the Au Adsorption of Cu2S
Currently, the presence of complex and challenging gold-containing raw materials has become increasingly prevalent, resulting in the inevitable ingress of As and Sb into copper matte.Therefore, it is necessary to study the adsorption of Au atom on the Cu2S(111) with As and Sb doping.As illustrated in Figure 10, the As and Sb atoms have the potential to be incorporated into Cu-site or S-site of Cu2S(111).To determine their preferred substitution sites, the binding energy (Ebin) of different doping systems is determined by [28,29] In this equation, E As/Sb-Cu2S111 is the total energy of As/Sb-doped Cu2S(111), E Cu2S111-vac is the total energy of Cu2S(111) with a Cu or S vacancy, and the E As/Sb is the energy of a single As/Sb atom in its bulk phase.It should be noted that a system with a lower binding energy tends to be more stable.Herein, the binding energies of various doped systems were calculated and displayed in Figure 10c.One can see that the binding energies at the S-site are significantly lower than those at the Cu-site for both As-and Sb-

Effect of As and Sb Dopant on the Au Adsorption of Cu 2 S
Currently, the presence of complex and challenging gold-containing raw materials has become increasingly prevalent, resulting in the inevitable ingress of As and Sb into copper matte.Therefore, it is necessary to study the adsorption of Au atom on the Cu 2 S(111) with As and Sb doping.As illustrated in Figure 10, the As and Sb atoms have the potential to be incorporated into Cu-site or S-site of Cu 2 S(111).To determine their preferred substitution sites, the binding energy (E bin ) of different doping systems is determined by [28,29] In this equation, E As/Sb−Cu2S111 is the total energy of As/Sb-doped Cu 2 S(111), E Cu2S111−vac is the total energy of Cu 2 S(111) with a Cu or S vacancy, and the E As/Sb is the energy of a single As/Sb atom in its bulk phase.It should be noted that a system with a lower binding energy tends to be more stable.Herein, the binding energies of various doped systems were calculated and displayed in Figure 10c.One can see that the binding energies at the S-site are significantly lower than those at the Cu-site for both As-and Sb-doped systems.Therefore, the doping of As/Sb at the S-site exhibits superior stability, and its stability is larger than that of clean Cu 2 S(111) due to the smaller binding energy.Consequently, the subsequent investigations only focus on the Cu 2 S(111) with As/Sb doped at the S-site.
For the As/Sb-doped Cu 2 S(111), there exist five possible adsorption sites, including the Astop site, Cutop site, B Cu-As site, B As-S site, and hollow site, as shown in Figure 10b.By performing geometric optimization and comparing the E ads of different adsorption systems, the two most stable adsorption structures are obtained (Figure 11).The atomic structures of As-and Sb-doped Cu 2 S(111) undergo significant deformation after Au adsorption, and the Au atom is preferentially adsorbed on the B Cu-As or B Cu-Sb site.Furthermore, the adsorption energies of Au atoms on As-and Sb-doped Cu 2 S(111) are −2.11eV and −2.28 eV, respectively, both of which are higher than the that of Au atoms on pure Cu 2 S(111).Therefore, we can infer that both As and Sb doping can enhance the gold-capturing ability of Cu 2 S, with Sb doping having a more pronounced effect.Additionally, there are abundant yellow regions between As/Sb and Au atoms, as plotted in Figure 11b,d, illustrating that the substantial electrons are shared by them, and the As-Cu or Sb-Au covalent bond is formed.Moreover, the adsorbed Au atoms in the two systems also share some electrons with the two Cu atoms in the second layer, implying that the Au-Cu metallic bonds are formed.the As/Sb-doped Cu 2 S(111) exhibits strong adsorption capabilities for gold atoms.
Molecules 2023, 28, x FOR PEER REVIEW 9 of 13 doped systems.Therefore, the doping of As/Sb at the S-site exhibits superior stability, and its stability is larger than that of clean Cu2S(111) due to the smaller binding energy.Consequently, the subsequent investigations only focus on the Cu2S(111) with As/Sb doped at the S-site.For the As/Sb-doped Cu2S(111), there exist five possible adsorption sites, including the Astop site, Cutop site, BCu-As site, BAs-S site, and hollow site, as shown in Figure 10b.By performing geometric optimization and comparing the Eads of different adsorption systems, the two most stable adsorption structures are obtained (Figure 11).The atomic structures of As-and Sb-doped Cu2S(111) undergo significant deformation after Au adsorption, and the Au atom is preferentially adsorbed on the BCu-As or BCu-Sb site.Furthermore, the adsorption energies of Au atoms on As-and Sb-doped Cu2S(111) are −2.11eV and −2.28 eV, respectively, both of which are higher than the that of Au atoms on pure Cu2S(111).Therefore, we can infer that both As and Sb doping can enhance the gold-capturing ability of Cu2S, with Sb doping having a more pronounced effect.Additionally, there are abundant yellow regions between As/Sb and Au atoms, as plotted in Figure 11b,d, illustrating that the substantial electrons are shared by them, and the As-Cu or Sb-Au covalent bond is formed.Moreover, the adsorbed Au atoms in the two systems also share some electrons with the two Cu atoms in the second layer, implying that the Au-Cu metallic bonds are formed.Therefore, the As/Sb-doped Cu2S(111) exhibits strong adsorption capabilities for gold atoms.From Figure 12a, the Au-d orbital undergoes significant hybridization with As-p orbital in the energy range of −7.50 eV to 2.50 eV and exhibits a weak interaction with s, d orbitals of As atom.Moreover, a prominent resonance peak is observed at about −3.60 eV.And there is a strong orbital overlap between Au-d and Cu-d in the energy range of −7.50 eV to 0.00 eV.Further, the abundant charges are accumulated between the Au and As atoms, as depicted by the CDD of Figure 12c.Specifically, the Au atom gains approximately 0.098 e, while the As atom loses about 0.109 e, resulting in the formation of a strong As-Au covalent bond.Meanwhile, an amount of charge is present between the Au and two Cu atoms in the second layer, demonstrating that the Au-Cu metallic bond is formed.
When the Au atom is adsorbed on the Sb-doped Cu 2 S(111) (Figure 12b), the Au-d orbital strongly interacts with the Sb-p orbital in the energy range of −7.50 eV to 2.50 eV, and a small resonant peak can be at around −9.30 eV for the Au-s and Sb-s orbitals, resulting in the strong interactions between Au and Sb atoms.Moreover, a significant orbital overlap exists between the Au-d and Cu-d orbitals, ranging from −7.50 eV to 0.00 eV.As shown in Figure 12d, the Au atom gains approximately 0.147 e, while the Sb atom loses about 0.121 e.The larger charge transfer number between Au and Sb atoms indicates the Au-Sb covalent bond has a larger strength in comparison with the Au-As covalent bond.Similarly, the Au-Cu metallic bond is also formed between the Au and two Cu atoms in the second layer.Thus, the adsorption strength of the Au atom on Sb-doped Cu 2 S(111) is greater than that on As-doped Cu 2 S(111).In summary, the initial stage of gold-capturing by copper matte is an adsorption process [11], and a higher adsorption energy of gold on the Cu2S surface means a higher goldcapturing efficiency.Based on the above discussion, the clean Cu2S(111) possesses a superior ability to capture gold due to its large adsorption energy.And the S vacancy on the Cu2S(111) enhances the gold-trapping capability, while the Cu vacancy reduces the goldcapturing efficacy.Therefore, the practitioners should focus on controlling the actual operation technique to increase the number of S vacancies.Additionally, doping As/Sb into the S site of Cu2S(111) significantly improves the gold-trapping capability of Cu2S, which implies that the presence of arsenic and antimony compounds in the raw materials is beneficial to the gold collection in the matte process.These results can provide practical guidance for practitioners to improve the process of the gold-trapping efficacy of Cu2S and also pave the way for the comprehensive utilization of arsenic and antimony-containing gold concentrates.

Calculation Method and Details
All calculations in this work were performed using the DMol 3 package [30] within the Materials Studio 2019 software.The Perdew-Burke-Ernzerh (PBE) functional of generalized gradient approximation (GGA) was chosen as the exchange-correlation functional [31].The DFT semicore pseudopotential (DSSP) method [32] was used to treat the interactions between core electrons and nucleus.The double numerical polarization (DNP) basis set [32] and a cutoff radius of 5.2 Å were adopted during the simulation process.For geometry optimization, the energy convergence tolerance, the maximum force, and the maximum displacement were set to 1.0 × 10 −5 Ha, 2.0 × 10 −3 Ha/Å and 5 × 10 −3 Å, respectively.The self-consistent field (SCF) tolerance for convergence was set to 1.0 × 10 −5 Ha.For the bulk Cu2S, the k-point meshes of 10 × 10 × 10 sampled in the Brillouin zone [33] were used.For the slab models, the k-points meshes of 5 × 5 × 1 and 10 × 10 × 1 were used for the geometry optimization and electronic property calculations, respectively.To account for the periodicity of the adsorption system, a vacuum layer of 15 Å was applied in the z-direction to eliminate the interactions between periodic structures.
The adsorption energy (Eads) can be used to evaluate the interaction strength between Au atom and Cu2S surface, which can be obtained by the following equation [24,34]: In summary, the initial stage of gold-capturing by copper matte is an adsorption process [11], and a higher adsorption energy of gold on the Cu 2 S surface means a higher gold-capturing efficiency.Based on the above discussion, the clean Cu 2 S(111) possesses a superior ability to capture gold due to its large adsorption energy.And the S vacancy on the Cu 2 S(111) enhances the gold-trapping capability, while the Cu vacancy reduces the gold-capturing efficacy.Therefore, the practitioners should focus on controlling the actual operation technique to increase the number of S vacancies.Additionally, doping As/Sb into the S site of Cu 2 S(111) significantly improves the gold-trapping capability of Cu 2 S, which implies that the presence of arsenic and antimony compounds in the raw materials is beneficial to the gold collection in the matte process.These results can provide practical guidance for practitioners to improve the process of the gold-trapping efficacy of Cu 2 S and also pave the way for the comprehensive utilization of arsenic and antimony-containing gold concentrates.

Calculation Method and Details
All calculations in this work were performed using the DMol 3 package [30] within the Materials Studio 2019 software.The Perdew-Burke-Ernzerh (PBE) functional of generalized gradient approximation (GGA) was chosen as the exchange-correlation functional [31].The DFT semicore pseudopotential (DSSP) method [32] was used to treat the interactions between core electrons and nucleus.The double numerical polarization (DNP) basis set [32] and a cutoff radius of 5.2 Å were adopted during the simulation process.For geometry optimization, the energy convergence tolerance, the maximum force, and the maximum displacement were set to 1.0 × 10 −5 Ha, 2.0 × 10 −3 Ha/Å and 5 × 10 −3 Å, respectively.The self-consistent field (SCF) tolerance for convergence was set to 1.0 × 10 −5 Ha.For the bulk Cu 2 S, the k-point meshes of 10 × 10 × 10 sampled in the Brillouin zone [33] were used.For the slab models, the k-points meshes of 5 × 5 × 1 and 10 × 10 × 1 were used for the geometry optimization and electronic property calculations, respectively.To account for the periodicity of the adsorption system, a vacuum layer of 15 was applied in the z-direction to eliminate the interactions between periodic structures.
The adsorption energy (E ads ) can be used to evaluate the interaction strength between Au atom and Cu 2 S surface, which can be obtained by the following equation [24,34]: where E Cu 2 S/Au is the total energy of Au atom adsorbed on Cu 2 S surface, E Cu 2 S and E Au are the energies of clean Cu 2 S surface and a single Au atom, respectively.

Conclusions
In this work, the DFT method was employed to investigate the adsorption behavior of the Au atom on the Cu 2 S surface, and the effects of Cu/S vacancy and As/Sb doping on the Au adsorption of Cu 2 S were also explored, which aims to reveal the micro-mechanism of gold collection in matte.The main conclusions are as follows:

Figure 2 .
Figure 2. (a) Atomic structure of Cu-terminated Cu2S(111) and (b) its six possible adsorption sites.The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 3 .
Figure 3. Side view (a) and top view (b) of the most stable structure of Au atom adsorbed on the Cu-terminated Cu2S(111).The orange, yellow and pink balls represent the Cu, S and Au atoms, respectively.

Figure 2 .
Figure 2. (a) Atomic structure of Cu-terminated Cu 2 S(111) and (b) its six possible adsorption sites.The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 2 .
Figure 2. (a) Atomic structure of Cu-terminated Cu2S(111) and (b) its six possible adsorption sites.The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 3 .
Figure 3. Side view (a) and top view (b) of the most stable structure of Au atom adsorbed on the Cu-terminated Cu2S(111).The orange, yellow and pink balls represent the Cu, S and Au atoms, respectively.

Figure 3 .
Figure 3. Side view (a) and top view (b) of the most stable structure of Au atom adsorbed on the Cu-terminated Cu 2 S(111).The orange, yellow and pink balls represent the Cu, S and Au atoms, respectively.

Figure 5
Figure5gives the density of states of the most stable adsorbed Cu 2 S(111) with an Au atom, where Cu1 and Cu2 represent the two nearest-neighbor Cu atoms of the Au atom, as shown in Figure4a.One can see that there are strong interactions between the Au atom and Cu1 and Cu2 atoms, which is primarily attributed to the hybridizations between the Au-5d and Cu-3d orbitals.Specifically, the Au-5d orbital obviously overlaps with the Cu1-3d orbitals in the energy range of −3.94 eV to −0.38 eV, and two significant resonance peaks can be found at about −2.18 eV and −1.63 eV, resulting in the formation of strong Au-Cu metallic bonding.Furthermore, there is a relatively weak interaction between the Au-6s and Cu1-3d orbitals in the energy range of −1.90 eV to 0.40 eV, and a resonant peak appears at the Fermi level.In contrast, the orbital hybridization between the Au-5p and Au-sp remains minimal across the entire energy level, leading to their negligible interaction.

Figure 4 .
Figure 4. (a) Side view and (b) top view of charge density difference (CDD), and (c) electron density distribution (EDD, e/Å 3 ) for the most adsorbed Cu2S(111) with an Au atom.The red and green regions in (a,b) represent the electron gains and losses, and the isovalue of CDD is ±0.005 e/Å 3 .The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 5 .
Figure 5. Density of states (DOSs) of the most stable adsorption system for the Au atom on Cuterminated Cu2S(111), the Fermi level is set to zero.

Figure 4 .
Figure 4. (a) Side view and (b) top view of charge density difference (CDD), and (c) electron density distribution (EDD, e/Å 3 ) for the most adsorbed Cu 2 S(111) with an Au atom.The red and green regions in (a,b) represent the electron gains and losses, and the isovalue of CDD is ±0.005 e/Å 3 .The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 4 .
Figure 4. (a) Side view and (b) top view of charge density difference (CDD), and (c) electron density distribution (EDD, e/Å 3 ) for the most adsorbed Cu2S(111) with an Au atom.The red and green regions in (a,b) represent the electron gains and losses, and the isovalue of CDD is ±0.005 e/Å 3 .The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 5 .
Figure 5. Density of states (DOSs) of the most stable adsorption system for the Au atom on Cuterminated Cu2S(111), the Fermi level is set to zero.

Figure 5 .
Figure 5. Density of states (DOSs) of the most stable adsorption system for the Au atom on Cuterminated Cu 2 S(111), the Fermi level is set to zero.
, there are two types of vacancy defects on the Cu 2 S(111) surface, namely Cu vacancy and S vacancy.Based on this, the adsorption energies of Au atoms on the Cu 2 S(111) surface with Cu vacancy (Cu 2 S(111)-Cuvac) and S vacancy (Cu 2 S(111)-Svac) are calculated, and the most stable adsorption structures are depicted in Figure 6d-g.The adsorption energies of Au atoms on Cu 2 S(111)-Cuvac and Cu 2 S(111)-Svac are −0.91 eV and −3.04 eV, respectively.Compared with the Au@Cu 2 S(111) system (E ads = −1.99eV), the presence of Cu vacancy can significantly weaken the adsorption of Au atom on Cu 2 S(111).Conversely, the S vacancy can dramatically enhance the adsorption strength.Therefore, it can be inferred that the S vacancies on the Cu 2 S(111) surface can enhance the gold-capturing efficiency of Cu 2 S. calculated, and the most stable adsorption structures are depicted in Figure 6d-g.The adsorption energies of Au atoms on Cu2S(111)-Cuvac and Cu2S(111)-Svac are −0.91 eV and −3.04 eV, respectively.Compared with the Au@Cu2S(111) system (Eads = −1.99eV), the presence of Cu vacancy can significantly weaken the adsorption of Au atom on Cu2S(111).

Figure 12
Figure12displays the DOSs and CDD of the most stable Au@As/Sb-doped Cu2S(111) From Figure12a, the Au-d orbital undergoes significant hybridization with As-p orbital in the energy range of −7.50 eV to 2.50 eV and exhibits a weak interaction with s, d orbitals of As atom.Moreover, a prominent resonance peak is observed at about −3.60 eV.And there is a strong orbital overlap between Au-d and Cu-d in the energy range of −7.50 eV to 0.00 eV.Further, the abundant charges are accumulated between the Au and As atoms as depicted by the CDD of Figure12c.Specifically, the Au atom gains approximately 0.098 e, while the As atom loses about 0.109 e, resulting in the formation of a strong As-Au covalent bond.Meanwhile, an amount of charge is present between the Au and two Cu atoms in the second layer, demonstrating that the Au-Cu metallic bond is formed.When the Au atom is adsorbed on the Sb-doped Cu2S(111) (Figure12b), the Au-d orbital strongly interacts with the Sb-p orbital in the energy range of −7.50 eV to 2.50 eV and a small resonant peak can be observed at around −9.30 eV for the Au-s and Sb-s orbitals, resulting in the strong interactions between Au and Sb atoms.Moreover, a significant orbital overlap exists between the Au-d and Cu-d orbitals, ranging from −7.50 eV to 0.00 eV.As shown in Figure12d, the Au atom gains approximately 0.147 e, while the Sb atom loses about 0.121 e.The larger charge transfer number between Au and Sb atoms indicates

Figure 11 .
Figure 11.The lowest-energy structures of Au adsorbed on As/Sb-doped Cu 2 S(111) (a,c) and their corresponding charge density distributions (b,d).The orange and yellow balls represent the Cu and S atoms, respectively.

Figure 12
Figure12displays the DOSs and CDD of the most stable Au@As/Sb-doped Cu 2 S(111).From Figure12a, the Au-d orbital undergoes significant hybridization with As-p orbital in the energy range of −7.50 eV to 2.50 eV and exhibits a weak interaction with s, d orbitals of As atom.Moreover, a prominent resonance peak is observed at about −3.60 eV.And there is a strong orbital overlap between Au-d and Cu-d in the energy range of −7.50 eV to 0.00 eV.Further, the abundant charges are accumulated between the Au and As atoms, as depicted by the CDD of Figure12c.Specifically, the Au atom gains approximately 0.098 e, while the As atom loses about 0.109 e, resulting in the formation of a strong As-Au covalent bond.Meanwhile, an amount of charge is present between the Au and two Cu atoms in the second layer, demonstrating that the Au-Cu metallic bond is formed.When the Au atom is adsorbed on the Sb-doped Cu 2 S(111) (Figure12b), the Au-d orbital strongly interacts with the Sb-p orbital in the energy range of −7.50 eV to 2.50 eV,

Molecules 2023 , 13 Figure 12 .
Figure 12.Density of states (a,b) and charge density difference (c,d) of Au adsorbed on As/Sb-doped Cu2S(111), the Cu atoms in (a,b) are labeled by the dashed circles in (c,d).

Figure 12 .
Figure 12.Density of states (a,b) and charge density difference (c,d) of Au adsorbed on As/Sb-doped Cu 2 S(111), the Cu atoms in (a,b) are labeled by the dashed circles in (c,d).

Table 1 .
Adsorption energies of Au atom on the Cu 2 S(111) with different adsorption sites.

Table 1 .
Adsorption energies of Au atom on the Cu2S(111) with different adsorption sites.

Table 1 .
Adsorption energies of Au atom on the Cu2S(111) with different adsorption sites.