Influences of coordination structures on the electronic properties of Zn ion and the adsorption of O-containing and S-containing molecules

Ligands in minerals have an important effect on the chemical properties of metal ions. The electronic properties of Zn ions formed by O and S ligands have been studied using density functional theory (DFT), and the interaction strength between O and S-containing molecules and Zn ions has been analyzed. The results show that the electronic properties of Zn ions may be influenced by the type of ligands, the number of ligands, and the distance between ligands and Zn ions. The adsorption capacity of zinc ions decreased with an the in increase ligand coordination number, but increased with an increase in the distance between the ligand and zinc ion. The adsorption of O- and S-containing molecules on sphalerite smithsonite and hemimorphite was then studied. It was indicated that O-containing molecules had a strong collecting ability for sphalerite, smithsonite and hemimorphite, but the adsorption capacity of S-containing molecules was weaker than that of O-containing molecules. The influence of water molecules on the adsorption behavior of O- and S-containing molecules was studied. The results of the calculations show that the relationship between H2O and O-containing sulfur-containing molecules is competitive adsorption on the surface of sphalerite smithsonite and hemimorphite. Adsorption of water molecules can reduce the adsorption energy of O-containing and S-containing molecules on mineral surfaces.


Introduction
Zinc is an important non-ferrous metal that primarily exists in nature in the forms of sphalerite, smithsonite, and hemimorphite.To extract and concentrate zinc resources, the flotation method is typically employed.Flotation is a physicochemical process that occurs at the surface of minerals [1] .The primary mechanism in the flotation process is the selective adsorption of flotation reagents on the mineral surface.The metal ions on the mineral surface act as active sites for the interaction with flotation reagents.Understanding the flotation process thoroughly and improving production parameters based on this understanding need extensive research into the mechanism of interaction between metal ions on the mineral surface and flotation reagents.To establish regularities, mineral processing experts have put up a variety of theoretical ideas.As early as the 1930s, the solubility product hypothesis was proposed in the literature [2] , which explained the interaction between collectors and metal ions on the mineral surface from a chemical reaction perspective.It suggested that the smaller the solubility product of the collector and metal ion, the easier the collector would interact with the mineral surface.In 1950, the molecular adsorption hypothesis was proposed in the literature [3] , which explained the relationship between different thiol collectors and the dissociation constant in sphalerite flotation [4] .In the mid-1950s [5][6] , the electrostatic interaction model was proposed in the literature, taking into account the relationship between the electrical properties of the mineral surface and the adsorption of reagents, where cationic collectors adsorb on negatively charged mineral surfaces, while anionic collectors adsorb on positively charged mineral surfaces.The literature also discovered the relationship between sulfide flotation and electrochemistry [7] , leading to the development of the sulfide flotation electrochemical theory, which has been a research hotspot for half a century.It explains the role of oxygen in flotation and the electron transfer mechanism between reagents and the mineral surface.The above theories can explain some flotation phenomena and contribute to the understanding of the flotation process.However, they still simplify the model of metal ions on the mineral surface into free ions in classical chemistry and fail to fully consider the limitations of mineral crystal chemistry and other properties.They do not provide a thorough understanding of the micro-mechanism of the interaction between flotation reagents and the mineral surface.The fundamental question of the existence state of metal ions on the mineral surface and their influence on the adsorption of flotation reagents has not been clearly understood, significantly limiting the understanding of mineral flotation mechanisms and the development of efficient reagents.In fact, the presence and properties of metal ions on the mineral surface are different significantly from their free ion states due to the influence of surrounding ions [8][9][10][11] .For example, both Sphalerite and smithsonite surfaces contain Zn ions, but their floatability is entirely different.This indicates that the coordinating atoms surrounding the metal ions in the mineral crystal structure have a significant constraining effect, resulting in differences in the floatability of different minerals.It can be seen that it is very important to study the effect of ligands on the chemical properties of metal ions in the crystal structure of minerals to understand the difference in the adsorption properties of flotation agents on different mineral surfaces.In recent years, the development of density functional theory in flotation has provided possibilities for exploring the influence of surface environment on the properties of metal ions.The literature has used density functional theory to study the effects of lattice defects and surface spatial structure on the properties of sulfide mineral surfaces and the adsorption of reagents [12][13][14][15][16][17][18] .Additionally, the hydrated environment on the mineral surface also has a significant impact on the adsorption of flotation reagents [19][20] .The aforementioned results all indicate that the interaction between metal ions on the mineral surface and reagent molecules is not only related to the properties of the metal ions themselves but also influenced by the surrounding environment.In order to study the difference in chemical properties of Zn ions on the surface of different kinds of zinc-containing minerals, the effect of ligand structure on the interaction between Zn ions and collectors was analyzed.In this study, first-principles calculations were employed to discuss the effects of factors such as the types of coordinating atoms, the number of ligands, and the distance between ligands on the technical charge and electrophilicity of zinc ions.The differences in the adsorption of different types of collectors on the mineral surface and the influence of water molecules on the adsorption of flotation reagents were investigated.The research results provide important references and insights for theoretical studies on mineral flotation and the design of reagent molecules.

Computational models
Density functional theory (DFT) was used to investigate Zn oxide and sulfide minerals.The CASTEP module was utilized for electronic and structural calculations, while the DMol3 module was employed for adsorption simulations.In order to investigate the effects of the types of coordination atoms, the number of ligands and the distance between ligands and metal ions on the chemical properties of metal ions, the effects of different factors on the chemical properties of metal ions were investigated.Mineral models of MeO and MeS were constructed by coordinating O and S ligands to simulate oxide and sulfide minerals, respectively.Then the adsorption of collector molecules containing O and S on these minerals was simulated.In the CASTEP calculations, ultrasoft pseudopotentials were employed to evaluate the interaction between valence electrons and ions.The self-consistent field convergence accuracy was set to 2.0×10 −6 eV/atom, and the displacement between two atoms was constrained to be less than 2.0×10 −3 Å. Convergence thresholds for maximum energy change, force, and stress during geometry optimization were set to 2×10 −5 eV/atom, 0.05 eV/Å, and 0.1 GPa, respectively.For the DMol3 calculations, convergence thresholds for energy change, maximum force, maximum displacement, maximum step size, and self-consistent field were set to 1.0×10 −5 Ha, 2.0×10 −3 Ha•Å −1 , 5.0×10 −3 Å, 0.3 Å, and 1.0×10 −6 eV/atom, respectively.We utilized the DNP atomic orbital basis set, including all electrons in the calculation.The GGA-PBE exchange-correlation function was employed for both CASTEP and DMol3 calculations.The electrophilicity of a metal ion represents the strength of its interaction with negatively charged groups.Based on the electrophilicity of metal ions, the action of ligands can be discussed.The electrophilicity of metal ions can be characterized using the Fukui index.A larger value of ƒ+ (M) indicates that the metal ion is more prone to attack by ligands, indicating higher electrophilicity.Table 2 presents the calculated electrophilic indices of Zn at different coordination numbers using first-principles theoretical calculations.The electrophilicity at coordination number 0 represents the electrophilicity of the free ion.From Table 2, it can be observed that as the coordination number increases, the electrophilicity of the Zn ion decreases, and the influence of ligand O on the electrophilicity of the metal ion is weaker compared to ligand S. Furthermore, Table 3 demonstrates that with an increase in the coordination distance, the electrophilicity of the Zn ion gradually increases, and again, the influence of the ligand O on the electrophilicity of the metal ion is weaker compared to the ligand S.

Adsorption of O-and S-containing collectors on Zn ions
For the present study, the S-containing collector(ethylxanthate (CH3CH2-OCSSH)) and the Ocontaining collector(fatty acid (CH3CH2-COOH)) are chosen as the adsorbent representatives.Tables 4 and 5 show the adsorption energies of S-and O-containing collector molecules.
This demonstrates that O-and S-containing collectors have different binding energies with Zn ions under different coordination environments.In each coordination environment, the binding energy between fatty acids and Zn ions is greater than that between xanthate and Zn ions, indicating a stronger binding ability between fatty acids and Zn ions.Table 4 shows that as the number of ligands increases, the binding energy between O-and S-containing collectors and Zn ions decreases.This indicates that both O and S ligands reduce the electrophilic ability of Zn ions, thereby lowering the binding energy between Zn ions and O-and S-containing collectors.Moreover, as shown in Table 4, the binding energy between O-and S-containing collectors and Zn ions increases with an increase in the relative distance between ligands.This suggests that both O and S ligands, when their relative distance from Zn ions gradually increases, have a diminishing effect on Zn ions, thereby enhancing the binding energy between Zn ions and O-and S-containing collectors.
To investigate the difference in binding energy between O-and S-containing collectors and Zn ions, the adsorption configurations of Zn and O-and S-containing collectors were studied.The value of overlap population between carbon-oxygen has been computed via integration of bonding state to Fermi level.COOP analysis reveals that the COOP value for the C-O bond before adsorption is 0.47, which decreases to 0.43 after adsorption.This suggests that there is no significant feedback effect from Zn ions on the fatty acid, as the molecular orbitals exhibit minor changes.In contrast, the C-S bond lengths in xanthate are 1.705Å and 1.695Å, and upon adsorption of Zn ions, they increase to 1.762Å and 1.763Å, indicating a noticeable change in the molecular structure of xanthate upon adsorption.The COOP value for the C-S bond before adsorption is 0.44, which decreases to 0.36 after adsorption, indicating the presence of a feedback π -bonding interaction between Zn ions and xanthate, which can reduce the strength of the C-S bond.From this result, it can be seen that the adsorption energy of water is more than the adsorption energy of S molecules on the surface of the three zinc-containing minerals and that the adsorption energy of O molecules is greater than the adsorption energy of water molecules.It is evident that the interaction between mineral surface activity sites and collector is affected by the coordination structure of mineral surface activity sites

Conclusions
In this study, the effect of O ligands and S ligands on the electronic properties of Zn ions was investigated using density functional theory.The calculated results show that Zn ions coordinated with O have more positive charges than Zn ions coordinated with S. In addition, an analysis of the Fukui index indicates that Zn ions coordinated with O are more likely to exhibit stronger electron absorption characteristics.The increase in the number of ligands or the distance between the ligands and the central ion could enhance the electron absorption characteristics of Zn ions.This indicates that the properties of ligands significantly affect the adsorption capacity of zinc ions.The S-containing collector (ethyl xanthate, CH3CH2-OCSSH) and the O-containing collector (fatty acid, CH3CH2-COOH) were selected to conduct adsorption simulations in order to investigate the influence of ligands on the adsorption characteristics of zinc ions.The results revealed that S-containing molecules can form π backbonding with zinc ions, whereas the O-containing molecules cannot.With an increase in the coordination number of ligands, the adsorption capacity of zinc ions decreases.However, with an increase in the distance between the ligands and zinc ions, the adsorption capacity of zinc ions increases.
The adsorption of O-and S-containing molecules on sphalerite, smithsonite, and hemimorphite was investigated.The findings showed that the adsorption capability of molecules containing sulfur (S) was slightly weaker than that of molecules containing oxygen (O) towards sphalerite, smithsonite, and hemimorphite.
Additionally, the investigation explores how water molecules affect the adsorption of molecules containing O and S. The results of simulations showed that H2O and molecules containing O-or Scompete for adsorption on the surfaces of sphalerite, smithsonite, and hemimorphite.The adsorption energy for both molecules containing O and molecules containing S on the mineral surfaces decreased in the presence of water molecules.

Figure 1 .
Figure 1.Models of Zn oxide minerals formed by coordinated O.

Figure 2 .
Figure 2. Models of Zn sulfide minerals formed by coordinated S.

Figure 3 .
Figure 3. Models of O-and S-containing collectors.

Figure 4 .
Figure 4.The adsorption models of O-and S-containing collectors with Zn ions.Figures 3 and 4 depict the molecular configurations of the fatty acid and xanthate, which are O-and Scontaining collectors, respectively, as well as the binding models of O-and S-containing collectors with Zn ions.From the figures, it can be observed that the C-O bond lengths in the fatty acid are 1.265 Å and 1.266 Å, and after adsorption onto Zn ions, the C-O bond lengths become 1.286 Å and 1.292 Å, indicating a negligible change in the molecular structure of the fatty acid upon adsorption.The positive and negative values of COOP are bonding and anti-bonding states, respectively.The value of overlap population between carbon-oxygen has been computed via integration of bonding state to Fermi level.COOP analysis reveals that the COOP value for the C-O bond before adsorption is 0.47, which decreases to 0.43 after adsorption.This suggests that there is no significant feedback effect from Zn ions on the fatty acid, as the molecular orbitals exhibit minor changes.In contrast, the C-S bond lengths in xanthate are 1.705Å and 1.695Å, and upon adsorption of Zn ions, they increase to 1.762Å and 1.763Å, indicating a noticeable change in the molecular structure of xanthate upon adsorption.The COOP value for the C-S bond before adsorption is 0.44, which decreases to 0.36 after adsorption, indicating the presence of a feedback π -bonding interaction between Zn ions and xanthate, which can reduce the strength of the C-S bond.

Figures
Figures 5, 6, and 7 illustrate the adsorption configurations of O-and S-containing collector and water on the surfaces of sphalerite, smithsonite, and hemimorphite, respectively.The calculated adsorption energies of O-and S-containing collectors and water on the surfaces are as follows: -405.992kJ/mol, -313.61kJ/mol, and -324.02kJ/mol for sphalerite; -386.46 kJ/mol, -298.67 kJ/mol and -344.65 kJ/mol for smithsonite; and -352.43 kJ/mol, -299.71kJ/mol and -311.89kJ/mol for hemimorphite.From this result, it can be seen that the adsorption energy of water is more than the adsorption energy of S molecules on the surface of the three zinc-containing minerals and that the adsorption energy of O molecules is greater than the adsorption energy of water molecules.It is evident that the interaction

Figure 5 .
Figure 5.The adsorption configurations of O-and S-containing collectors and water on the surface of sphalerite.

Figure 6 .
Figure 6.The adsorption configurations of O-and S-containing collectors and water on the surface of smithsonite.

Figure 7 .
Figure 7.The adsorption configurations of O-and S-containing collectors and water on the surface of hemimorphite.

Figure 8 .
Figure 8. Competitive adsorption model of O-and S-containing collectors on sphalerite.

Figure 9 .
Figure 9. Competitive adsorption model of O-and S-containing collectors on smithsonite.

Figure 10 .
Figure 10.Competitive adsorption model of O-and S-containing collectors on hemimorphite.Water-competitive adsorption models on the surfaces of sphalerite, smithsonite, and hemimorphite are shown in Figures8, 9, and 10.It is known that the adsorption energies of O-and S-containing collectors on the surfaces of sphalerite and smithsonite, respectively, can be -360.99kJ/moland -262.02kJ/mol and -341.27kJ/mol and -280.26kJ/mol,respectively, in the presence of water molecules.The adsorption energies of an O-and S-containing collector on hemimorphite's surface are -328.43kJ/mol and -251.87 kJ/mol, respectively.As can be shown, water molecules can make O and S molecules less likely to adhere to the surfaces of three zinc minerals.

Table 1 .
Parameters in Different Coordination Models of Zinc Ions.

Table 2 .
Electrophilicity of Zn Ion under Different Constraint Conditions.

Table 3 .
Electrophilicity of Zn Ion at Different Constraint Distances.

Table 4 .
Electrophilicity of Zn Ion at Different Constraint Distances.

Table 5 .
Adsorption energy of O-and S-containing collectors in the model at different constraint distances，kJ/mol.